TSTP Solution File: SWW297+1 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW297+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:25:53 EDT 2023
% Result : Theorem 44.90s 43.91s
% Output : Proof 44.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW297+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : nanocop.sh %s %d
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu May 18 22:21:54 EDT 2023
% 0.12/0.34 % CPUTime :
% 44.90/43.91
% 44.90/43.91 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 44.90/43.91 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.90/43.91 %-----------------------------------------------------
% 44.90/43.91 ncf(matrix, plain, [(52794 ^ _2081197) ^ [] : [-(c_Natural_Oevaln(v_com, 52789 ^ [], v_n, 52792 ^ []))], (52796 ^ _2081197) ^ [] : [v_fun2(52788 ^ [], 52792 ^ [])], (52779 ^ _2081197) ^ [_2081214, _2081216] : [v_fun1(_2081216, _2081214), 52782 ^ _2081197 : [(52783 ^ _2081197) ^ [_2081279] : [c_Natural_Oevaln(v_com, _2081214, hAPP(c_Nat_OSuc, v_n), _2081279), -(v_fun2(_2081216, _2081279))]]], (52791 ^ _2081197) ^ [] : [-(v_fun1(52788 ^ [], 52789 ^ []))], !, (52435 ^ _775212) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (14843 ^ _775212) ^ [_1023970, _1023972] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1023970), _1023972) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1023972 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1023970 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26694 ^ _775212) ^ [_1244287] : [-(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)), _1244287)))], (43513 ^ _775212) ^ [_1625484, _1625486, _1625488] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625484, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1625484, tc_HOL_Obool), tc_HOL_Obool)), _1625486), _1625488)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1625484, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625484, tc_HOL_Obool), _1625486)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625484, tc_HOL_Obool), _1625488)))], (37296 ^ _775212) ^ [_1469259, _1469261, _1469263, _1469265, _1469267, _1469269, _1469271] : [c_Typedef_Otype__definition(_1469259, _1469261, _1469263, _1469265, _1469267), hBOOL(hAPP(hAPP(c_member(_1469261), _1469269), _1469267)), hBOOL(hAPP(hAPP(c_member(_1469261), _1469271), _1469267)), 37307 ^ _775212 : [(37314 ^ _775212) ^ [] : [_1469269 = _1469271, -(hAPP(_1469265, _1469269) = hAPP(_1469265, _1469271))], (37308 ^ _775212) ^ [] : [hAPP(_1469265, _1469269) = hAPP(_1469265, _1469271), -(_1469269 = _1469271)]]], (26121 ^ _775212) ^ [_1232864, _1232866, _1232868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1232864, 26122 ^ [_1232864, _1232866, _1232868])), hAPP(_1232866, 26122 ^ [_1232864, _1232866, _1232868]))), -(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), _1232866), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1232868))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1232864), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1232868))) = 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)), _1232866)), _1232864)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1232868)))], (52223 ^ _775212) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (40056 ^ _775212) ^ [_1543035, _1543037, _1543039, _1543041] : [hBOOL(hAPP(c_Predicate_ODomainP(_1543035, _1543037, _1543039), _1543041)), -(hBOOL(hAPP(hAPP(_1543039, _1543041), 40059 ^ [_1543035, _1543037, _1543039, _1543041])))], (10347 ^ _775212) ^ [_943641, _943643, _943645, _943647] : [class_Rings_Oordered__ring(_943641), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943641), _943643), _943645)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943641), _943647), c_Groups_Ozero__class_Ozero(_943641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943641), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943641), _943645), _943647)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943641), _943643), _943647))))], (8009 ^ _775212) ^ [_903846, _903848] : [class_Rings_Ocomm__semiring__1(_903846), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903846), _903848), c_Groups_Ozero__class_Ozero(_903846)) = c_Groups_Ozero__class_Ozero(_903846))], (19031 ^ _775212) ^ [_1099262, _1099264, _1099266, _1099268] : [class_Rings_Odivision__ring(_1099262), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099262), _1099264), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099262), _1099266), _1099268)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099262), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099262), _1099264), _1099266)), _1099268))], (29572 ^ _775212) ^ [_1301907, _1301909, _1301911] : [_1301907 = c_Orderings_Obot__class_Obot(tc_fun(_1301909, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_1301909), _1301911), _1301907))], (17149 ^ _775212) ^ [_1067123] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1067123)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067123)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1067123))], (2392 ^ _775212) ^ [_810112, _810114, _810116, _810118, _810120, _810122] : [-(c_Product__Type_Ointernal__split(_810122, _810118, _810114) = c_Product__Type_Ointernal__split(_810120, _810116, _810112)), _810122 = _810120, _810118 = _810116, _810114 = _810112], (29397 ^ _775212) ^ [_1298279] : [-(hAPP(c_Int_Onat, _1298279) = 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, _1298279)), 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)))))))], (39289 ^ _775212) ^ [_1519785, _1519787, _1519789] : [class_Lattices_Odistrib__lattice(_1519785), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519785), _1519787)), -(_1519787 = c_Orderings_Obot__class_Obot(tc_fun(_1519785, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1519785), _1519789), c_Big__Operators_Olattice__class_OSup__fin(_1519785, _1519787)) = c_Big__Operators_Olattice__class_OSup__fin(_1519785, hAPP(c_Set_OCollect(_1519785), hAPP(hAPP(c_COMBB(tc_fun(_1519785, tc_HOL_Obool), tc_HOL_Obool, _1519785), c_HOL_OEx(_1519785)), hAPP(hAPP(c_COMBC(_1519785, tc_fun(_1519785, tc_HOL_Obool), tc_fun(_1519785, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519785, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1519785, tc_HOL_Obool), tc_fun(_1519785, tc_HOL_Obool)), _1519785), c_COMBS(_1519785, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519785, tc_HOL_Obool), tc_fun(_1519785, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1519785), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519785), c_fconj)), hAPP(hAPP(c_COMBC(_1519785, tc_fun(_1519785, _1519785), tc_fun(_1519785, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519785, tc_HOL_Obool), tc_fun(tc_fun(_1519785, _1519785), tc_fun(_1519785, tc_HOL_Obool)), _1519785), c_COMBB(_1519785, tc_HOL_Obool, _1519785)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1519785), _1519789))))), hAPP(hAPP(c_COMBC(_1519785, tc_fun(_1519785, tc_HOL_Obool), tc_HOL_Obool), c_member(_1519785)), _1519787))))))], (10201 ^ _775212) ^ [_940969, _940971, _940973] : [class_Rings_Olinordered__ring__strict(_940969), 10204 ^ _775212 : [(10219 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940969), _940971), _940973)), c_Groups_Ozero__class_Ozero(_940969)))), 10220 ^ _775212 : [(10227 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940969), _940971), c_Groups_Ozero__class_Ozero(_940969))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940969), c_Groups_Ozero__class_Ozero(_940969)), _940973))], (10221 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940969), c_Groups_Ozero__class_Ozero(_940969)), _940971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940969), _940973), c_Groups_Ozero__class_Ozero(_940969)))]]], (10205 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940969), _940971), _940973)), c_Groups_Ozero__class_Ozero(_940969))), 10210 ^ _775212 : [(10213 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940969), _940973), c_Groups_Ozero__class_Ozero(_940969))))], (10211 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940969), c_Groups_Ozero__class_Ozero(_940969)), _940971)))]], 10214 ^ _775212 : [(10217 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940969), c_Groups_Ozero__class_Ozero(_940969)), _940973)))], (10215 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940969), _940971), c_Groups_Ozero__class_Ozero(_940969))))]]]]], (21503 ^ _775212) ^ [_1143361, _1143363] : [-(_1143361 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1143363, _1143361), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1143363), _1143361)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1143363, _1143361)))))], (2246 ^ _775212) ^ [_807917, _807919, _807921, _807923] : [-(c_Divides_Odivmod__int(_807923, _807919) = c_Divides_Odivmod__int(_807921, _807917)), _807923 = _807921, _807919 = _807917], (6617 ^ _775212) ^ [_880191, _880193, _880195, _880197] : [class_Groups_Oordered__cancel__ab__semigroup__add(_880191), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880191), _880193), _880195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880191), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880191), _880197), _880193)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880191), _880197), _880195))))], (50985 ^ _775212) ^ [_1798163, _1798165, _1798167, _1798169, _1798171, _1798173] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1798163, _1798165, _1798167, _1798169, c_Lazy__Sequence_Olazy__sequence_OInsert(_1798165, _1798171, _1798173)) = hAPP(hAPP(_1798169, _1798171), _1798173))], (29630 ^ _775212) ^ [_1302950, _1302952, _1302954, _1302956] : [hBOOL(hAPP(hAPP(c_member(_1302950), _1302952), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1302950, tc_HOL_Obool)), _1302954), _1302956))), hBOOL(hAPP(hAPP(c_member(_1302950), _1302952), _1302956))], (4964 ^ _775212) ^ [_850886, _850888] : [_850888 = _850886, -(c_List_Omember(_850888) = c_List_Omember(_850886))], (26533 ^ _775212) ^ [_1241571, _1241573] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1241571), _1241573)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1241573), _1241571)))], (43480 ^ _775212) ^ [_1624648, _1624650, _1624652] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624648, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1624648, tc_HOL_Obool), _1624650)), _1624652) = c_Orderings_Obot__class_Obot(tc_fun(_1624648, tc_HOL_Obool)), 43483 ^ _775212 : [(43484 ^ _775212) ^ [_1624783] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1624648, tc_HOL_Obool)), _1624783), _1624650)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624648, tc_HOL_Obool)), _1624783), _1624652) = c_Orderings_Obot__class_Obot(tc_fun(_1624648, tc_HOL_Obool)))]]], (12464 ^ _775212) ^ [_980266, _980268, _980270, _980272] : [class_Divides_Osemiring__div(_980266), -(c_Divides_Odiv__class_Omod(_980266, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980266), _980268), c_Divides_Odiv__class_Omod(_980266, _980270, _980272)), _980272) = c_Divides_Odiv__class_Omod(_980266, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980266), _980268), _980270), _980272))], (18053 ^ _775212) ^ [_1081563, _1081565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1081563), 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)))), _1081565)), 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)))), _1081563)) = 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), _1081565), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1081563))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9056 ^ _775212) ^ [_921965, _921967, _921969] : [class_Orderings_Olinorder(_921965), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921965), _921967), _921969))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921965), _921969), _921967)))], (42750 ^ _775212) ^ [_1607342, _1607344] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607342, _1607342)), hAPP(hAPP(c_Product__Type_OPair(_1607342, _1607342), _1607344), _1607344)), c_Relation_OId(_1607342))))], (17787 ^ _775212) ^ [_1077236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1077236)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1077236), c_Int_OMin)))], (22160 ^ _775212) ^ [_1155831] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1155831)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155831)), 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))))], (46909 ^ _775212) ^ [_1710431, _1710433] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1710431), hAPP(c_List_Oset(tc_Nat_Onat), _1710433))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1710431), 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)), _1710433))))], (49267 ^ _775212) ^ [_1761045, _1761047] : [-(_1761045 = c_List_Olist_ONil(_1761047)), -(hAPP(c_List_Ohd(_1761047), hAPP(c_List_Orev(_1761047), _1761045)) = c_List_Olast(_1761047, _1761045))], (19055 ^ _775212) ^ [_1099836, _1099838, _1099840] : [class_Rings_Odivision__ring(_1099836), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1099836), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099836), _1099838), _1099840)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099836), hAPP(c_Groups_Ouminus__class_Ouminus(_1099836), _1099838)), _1099840))], (22234 ^ _775212) ^ [_1157518, _1157520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157518)), hAPP(c_Nat_OSuc, _1157520))), -(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(_1157518))), 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)), _1157520)))))], (43529 ^ _775212) ^ [_1625833] : [class_Complete__Lattice_Ocomplete__lattice(_1625833), -(c_Complete__Lattice_OSup__class_OSup(_1625833, c_Orderings_Obot__class_Obot(tc_fun(_1625833, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1625833))], (23218 ^ _775212) ^ [_1177456, _1177458, _1177460, _1177462, _1177464, _1177466] : [-(hAPP(c_Product__Type_Oapfst(_1177456, _1177458, _1177460, _1177462), hAPP(hAPP(c_Product__Type_OPair(_1177456, _1177460), _1177464), _1177466)) = hAPP(hAPP(c_Product__Type_OPair(_1177458, _1177460), hAPP(_1177462, _1177464)), _1177466))], (16505 ^ _775212) ^ [_1056044, _1056046] : [class_Groups_Oabs__if(_1056044), 16508 ^ _775212 : [(16515 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056044), _1056046), c_Groups_Ozero__class_Ozero(_1056044)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1056044), _1056046) = _1056046)], (16509 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056044), _1056046), c_Groups_Ozero__class_Ozero(_1056044))), -(hAPP(c_Groups_Oabs__class_Oabs(_1056044), _1056046) = hAPP(c_Groups_Ouminus__class_Ouminus(_1056044), _1056046))]]], (50931 ^ _775212) ^ [_1796995, _1796997, _1796999] : [-(_1796995 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1796997), c_List_Oreplicate(_1796997, _1796995, _1796999)) = hAPP(hAPP(c_Set_Oinsert(_1796997), _1796999), c_Orderings_Obot__class_Obot(tc_fun(_1796997, tc_HOL_Obool))))], (23114 ^ _775212) ^ [_1175303, _1175305, _1175307, _1175309] : [class_Orderings_Olinorder(_1175303), 23117 ^ _775212 : [(23118 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175303), _1175305), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1175303), _1175307), _1175309))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175303), _1175305), _1175307))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175303), _1175305), _1175309)))], (23128 ^ _775212) ^ [] : [23129 ^ _775212 : [(23132 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175303), _1175305), _1175309))], (23130 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175303), _1175305), _1175307))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175303), _1175305), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1175303), _1175307), _1175309))))]]], (38774 ^ _775212) ^ [_1504145] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1504145), c_Int_OInteg)), -(_1504145 = hAPP(c_Int_ORep__Integ, 38777 ^ [_1504145]))], (48705 ^ _775212) ^ [_1749996] : [class_Orderings_Olinorder(_1749996), -(c_List_Olinorder__class_Osorted(_1749996, c_List_Olist_ONil(_1749996)))], (13418 ^ _775212) ^ [_997804] : [-(_997804 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _997804), _997804) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35103 ^ _775212) ^ [_1421474, _1421476, _1421478, _1421480] : [class_Orderings_Oorder(_1421474), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421474, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1421474, _1421476), _1421478)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1421474, _1421478), _1421480)) = c_Orderings_Obot__class_Obot(tc_fun(_1421474, tc_HOL_Obool)))], (23022 ^ _775212) ^ [_1173746, _1173748, _1173750, _1173752] : [class_Orderings_Olinorder(_1173746), 23025 ^ _775212 : [(23034 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173746), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173746), _1173748), _1173750)), _1173752))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173746), _1173748), _1173752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173746), _1173750), _1173752))], (23026 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173746), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173746), _1173748), _1173750)), _1173752)), 23029 ^ _775212 : [(23032 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173746), _1173750), _1173752)))], (23030 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173746), _1173748), _1173752)))]]]]], (4080 ^ _775212) ^ [_837130, _837132] : [_837132 = _837130, -(c_Power_Opower__class_Opower(_837132) = c_Power_Opower__class_Opower(_837130))], (29046 ^ _775212) ^ [_1291149, _1291151, _1291153] : [class_Orderings_Oorder(_1291149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291149), _1291151), _1291153)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1291149, _1291153, _1291151) = c_Orderings_Obot__class_Obot(tc_fun(_1291149, tc_HOL_Obool)))], (34271 ^ _775212) ^ [_1403090, _1403092, _1403094, _1403096, _1403098] : [hAPP(c_Relation_OImage(_1403090, _1403090, _1403092), hAPP(hAPP(c_Set_Oinsert(_1403090), _1403094), c_Orderings_Obot__class_Obot(tc_fun(_1403090, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1403090, _1403090, _1403092), hAPP(hAPP(c_Set_Oinsert(_1403090), _1403096), c_Orderings_Obot__class_Obot(tc_fun(_1403090, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1403090, _1403098, _1403092), hBOOL(hAPP(hAPP(c_member(_1403090), _1403096), _1403098)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1403090, _1403090)), hAPP(hAPP(c_Product__Type_OPair(_1403090, _1403090), _1403094), _1403096)), _1403092)))], (33549 ^ _775212) ^ [_1386283, _1386285, _1386287] : [class_Lattices_Olattice(_1386283), hAPP(_1386285, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1386283), 33554 ^ [_1386283, _1386285, _1386287]), 33555 ^ [_1386283, _1386285, _1386287])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1386283), hAPP(_1386285, 33554 ^ [_1386283, _1386285, _1386287])), hAPP(_1386285, 33555 ^ [_1386283, _1386285, _1386287])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386283), _1386287)), -(_1386287 = c_Orderings_Obot__class_Obot(tc_fun(_1386283, tc_HOL_Obool))), -(hAPP(_1386285, c_Big__Operators_Olattice__class_OSup__fin(_1386283, _1386287)) = c_Big__Operators_Olattice__class_OSup__fin(_1386283, hAPP(c_Set_Oimage(_1386283, _1386283, _1386285), _1386287)))], (39217 ^ _775212) ^ [_1516745] : [-(c_Wellfounded_Ofinite__psubset(_1516745) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1516745, tc_HOL_Obool), tc_fun(_1516745, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1516745, tc_HOL_Obool), tc_fun(_1516745, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1516745, tc_HOL_Obool), tc_fun(tc_fun(_1516745, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1516745, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1516745, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1516745, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1516745, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1516745, tc_HOL_Obool)), c_COMBS(tc_fun(_1516745, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1516745, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1516745, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1516745, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1516745, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1516745, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1516745)))))], (22940 ^ _775212) ^ [_1172297, _1172299, _1172301, _1172303, _1172305] : [class_Orderings_Olinorder(_1172297), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172297), _1172299), _1172301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172297), _1172303), _1172305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172297), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1172297), _1172299), _1172303)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1172297), _1172301), _1172305))))], (34071 ^ _775212) ^ [_1398232, _1398234, _1398236, _1398238] : [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), _1398232), _1398234)), 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), _1398236), _1398238)), 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), _1398232), _1398238)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398236), _1398234))))], (44571 ^ _775212) ^ [_1654064, _1654066, _1654068, _1654070] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654064), tc_List_Olist(_1654064))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654064), tc_List_Olist(_1654064)), _1654066), _1654068)), c_List_Olistrel(_1654064, _1654070)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654064)), _1654066) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654064)), _1654068), 44577 ^ _775212 : [(44580 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1654064, _1654064)), hAPP(hAPP(c_Product__Type_OPair(_1654064, _1654064), hAPP(hAPP(c_List_Onth(_1654064), _1654066), 44576 ^ [_1654064, _1654066, _1654068, _1654070])), hAPP(hAPP(c_List_Onth(_1654064), _1654068), 44576 ^ [_1654064, _1654066, _1654068, _1654070]))), _1654070))], (44578 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44576 ^ [_1654064, _1654066, _1654068, _1654070]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654064)), _1654066))))]]], (3892 ^ _775212) ^ [_834272, _834274] : [_834274 = _834272, -(c_Groups_Otimes__class_Otimes(_834274) = c_Groups_Otimes__class_Otimes(_834272))], (45222 ^ _775212) ^ [_1670590, _1670592] : [-(hAPP(hAPP(c_List_Ozip(_1670590, _1670590), _1670592), _1670592) = hAPP(hAPP(c_List_Omap(_1670590, tc_prod(_1670590, _1670590)), hAPP(hAPP(c_COMBS(_1670590, _1670590, tc_prod(_1670590, _1670590)), c_Product__Type_OPair(_1670590, _1670590)), c_COMBI(_1670590))), _1670592))], (36651 ^ _775212) ^ [_1455667, _1455669, _1455671, _1455673] : [c_Fun_Oinj__on(_1455667, _1455669, _1455671, _1455673), -(hAPP(c_Finite__Set_Ocard(_1455669), hAPP(c_Set_Oimage(_1455667, _1455669, _1455671), _1455673)) = hAPP(c_Finite__Set_Ocard(_1455667), _1455673))], (12342 ^ _775212) ^ [_978272, _978274] : [class_Rings_Olinordered__idom(_978272), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978272), _978274), c_Groups_Ozero__class_Ozero(_978272))), -(c_Groups_Osgn__class_Osgn(_978272, _978274) = hAPP(c_Groups_Ouminus__class_Ouminus(_978272), c_Groups_Oone__class_Oone(_978272)))], (1894 ^ _775212) ^ [_801743, _801745] : [-(class_Rings_Odvd(_801743)), _801745 = _801743, class_Rings_Odvd(_801745)], (39884 ^ _775212) ^ [_1538545, _1538547] : [-(hAPP(c_Relation_ODomain(_1538545, _1538547), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1538545, _1538547), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1538545, tc_HOL_Obool)))], (14509 ^ _775212) ^ [_1017630, _1017632] : [class_Groups_Omonoid__mult(_1017630), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1017630), _1017632), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1017632)], (48418 ^ _775212) ^ [_1744763, _1744765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1744763), _1744765)), -(c_List_Oupt(_1744763, hAPP(c_Nat_OSuc, _1744765)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1744763, _1744765)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1744765), c_List_Olist_ONil(tc_Nat_Onat))))], (38820 ^ _775212) ^ [_1504946] : [class_Lattices_Osemilattice__sup(_1504946), -(c_Finite__Set_Ofun__left__comm__idem(_1504946, _1504946, c_Lattices_Osemilattice__sup__class_Osup(_1504946)))], (20789 ^ _775212) ^ [_1130616, _1130618, _1130620, _1130622] : [class_Fields_Olinordered__field__inverse__zero(_1130616), class_Int_Onumber(_1130616), 20796 ^ _775212 : [(20797 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130616), _1130618), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620))), _1130622)), 20800 ^ _775212 : [(20807 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), c_Groups_Ozero__class_Ozero(_1130616)), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620)))), 20810 ^ _775212 : [(20817 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620)), c_Groups_Ozero__class_Ozero(_1130616)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), c_Groups_Ozero__class_Ozero(_1130616)), _1130622)))], (20811 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620)), c_Groups_Ozero__class_Ozero(_1130616))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130616), _1130622), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620))), _1130618)))]]], (20801 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), c_Groups_Ozero__class_Ozero(_1130616)), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), _1130618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130616), _1130622), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620)))))]]], (20823 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130616), _1130618), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620))), _1130622))), 20826 ^ _775212 : [(20829 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), _1130618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130616), _1130622), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620))))], (20827 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), c_Groups_Ozero__class_Ozero(_1130616)), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620))))]], 20830 ^ _775212 : [(20833 ^ _775212) ^ [] : [20834 ^ _775212 : [(20837 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130616), _1130622), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620))), _1130618))], (20835 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620)), c_Groups_Ozero__class_Ozero(_1130616))))]], 20838 ^ _775212 : [(20841 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), c_Groups_Ozero__class_Ozero(_1130616)), _1130622))], (20839 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620)), c_Groups_Ozero__class_Ozero(_1130616)))]]], (20831 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130616), c_Groups_Ozero__class_Ozero(_1130616)), hAPP(c_Int_Onumber__class_Onumber__of(_1130616), _1130620)))]]]]], (40190 ^ _775212) ^ [_1546363, _1546365, _1546367] : [-(c_Relation_Orefl__on(_1546363, _1546365, _1546367)), 40194 ^ _775212 : [(40197 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1546363, _1546363, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1546363, tc_fun(_1546363, tc_HOL_Obool), tc_fun(_1546363, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1546363, tc_HOL_Obool), tc_fun(_1546363, tc_HOL_Obool)), _1546363), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1546363)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546363), c_fconj), hAPP(hAPP(c_COMBC(_1546363, tc_fun(_1546363, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546363)), _1546365)))), hAPP(hAPP(c_COMBC(_1546363, tc_fun(_1546363, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546363)), _1546365))), 40193 ^ [_1546363, _1546365, _1546367]))], (40195 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546363, _1546363)), 40193 ^ [_1546363, _1546365, _1546367]), _1546367)))]], 40199 ^ _775212 : [(40202 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546363, _1546363)), hAPP(hAPP(c_Product__Type_OPair(_1546363, _1546363), 40198 ^ [_1546363, _1546365, _1546367]), 40198 ^ [_1546363, _1546365, _1546367])), _1546367))], (40200 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1546363), 40198 ^ [_1546363, _1546365, _1546367]), _1546365)))]]], (23094 ^ _775212) ^ [_1174945, _1174947, _1174949, _1174951] : [class_Orderings_Olinorder(_1174945), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174945), _1174947), _1174949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174945), _1174947), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174945), _1174951), _1174949))))], (2060 ^ _775212) ^ [_804946, _804948, _804950, _804952] : [-(c_SMT_Oz3div(_804952, _804948) = c_SMT_Oz3div(_804950, _804946)), _804952 = _804950, _804948 = _804946], (39719 ^ _775212) ^ [_1535403, _1535405, _1535407, _1535409] : [c_Wellfounded_Owf(_1535403, _1535405), c_Wellfounded_Owf(_1535407, _1535409), -(c_Wellfounded_Owf(tc_prod(_1535403, _1535407), c_Wellfounded_Olex__prod(_1535403, _1535407, _1535405, _1535409)))], (34110 ^ _775212) ^ [_1399468, _1399470] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399468), c_Orderings_Obot__class_Obot(tc_fun(_1399468, tc_HOL_Obool))), _1399470) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399468, tc_HOL_Obool), tc_HOL_Obool)))], (4322 ^ _775212) ^ [_840923, _840925, _840927, _840929] : [-(c_List_Olist__update(_840929, _840925) = c_List_Olist__update(_840927, _840923)), _840929 = _840927, _840925 = _840923], (25553 ^ _775212) ^ [_1220505, _1220507, _1220509] : [class_Orderings_Olinorder(_1220505), 25556 ^ _775212 : [(25563 ^ _775212) ^ [] : [_1220507 = _1220509, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1220505), _1220507) = hAPP(c_SetInterval_Oord__class_OlessThan(_1220505), _1220509))], (25557 ^ _775212) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1220505), _1220507) = hAPP(c_SetInterval_Oord__class_OlessThan(_1220505), _1220509), -(_1220507 = _1220509)]]], (45919 ^ _775212) ^ [_1687638, _1687640, _1687642, _1687644, _1687646] : [-(hAPP(hAPP(c_List_Olist__update(_1687638, hAPP(hAPP(c_List_Olist__update(_1687638, _1687640), _1687642), _1687644)), _1687642), _1687646) = hAPP(hAPP(c_List_Olist__update(_1687638, _1687640), _1687642), _1687646))], (21919 ^ _775212) ^ [_1151208] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1151208)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1151208)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9083 ^ _775212) ^ [_922429, _922431] : [class_Groups_Oone(_922429), 9086 ^ _775212 : [(9093 ^ _775212) ^ [] : [_922431 = c_Groups_Oone__class_Oone(_922429), -(c_Groups_Oone__class_Oone(_922429) = _922431)], (9087 ^ _775212) ^ [] : [c_Groups_Oone__class_Oone(_922429) = _922431, -(_922431 = c_Groups_Oone__class_Oone(_922429))]]], (45120 ^ _775212) ^ [_1668493, _1668495, _1668497, _1668499] : [_1668499 = c_List_Olist_ONil(_1668495), -(c_List_Olist_ONil(_1668493) = hAPP(hAPP(c_List_Omap(_1668495, _1668493), _1668497), _1668499))], (44208 ^ _775212) ^ [_1642704, _1642706, _1642708] : [-(c_List_Oset__Cons(_1642704, _1642706, _1642708) = hAPP(c_Set_OCollect(tc_List_Olist(_1642704)), hAPP(hAPP(c_COMBB(tc_fun(_1642704, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1642704)), c_HOL_OEx(_1642704)), hAPP(hAPP(c_COMBB(tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool)), tc_fun(_1642704, tc_HOL_Obool), tc_List_Olist(_1642704)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool), tc_HOL_Obool, _1642704), c_HOL_OEx(tc_List_Olist(_1642704)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1642704), tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool)), tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1642704, tc_fun(tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool), tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool))), tc_fun(tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool)), tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool))), tc_List_Olist(_1642704)), c_COMBS(_1642704, tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool), tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1642704, tc_fun(tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool), tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool))), tc_List_Olist(_1642704)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1642704), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool), tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool)), _1642704), c_COMBS(tc_List_Olist(_1642704), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool)), tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1642704)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool), tc_fun(tc_List_Olist(_1642704), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1642704), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1642704)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1642704), tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_List_Olist(_1642704))), tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1642704), tc_List_Olist(_1642704)), tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool)), tc_fun(tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_List_Olist(_1642704))), tc_fun(_1642704, tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool))), tc_List_Olist(_1642704)), c_COMBB(tc_fun(tc_List_Olist(_1642704), tc_List_Olist(_1642704)), tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool), _1642704)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1642704), tc_List_Olist(_1642704)), tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool)), tc_List_Olist(_1642704)), c_COMBB(tc_List_Olist(_1642704), tc_HOL_Obool, tc_List_Olist(_1642704))), c_fequal))), c_List_Olist_OCons(_1642704)))))), hAPP(hAPP(c_COMBC(_1642704, tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool), tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool), tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool)), _1642704), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1642704))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1642704), c_fconj), hAPP(hAPP(c_COMBC(_1642704, tc_fun(_1642704, tc_HOL_Obool), tc_HOL_Obool), c_member(_1642704)), _1642706)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1642704), tc_fun(tc_List_Olist(_1642704), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1642704))), _1642708)))))))], (37567 ^ _775212) ^ [_1475700, _1475702, _1475704, _1475706, _1475708] : [class_Groups_Ocomm__monoid__add(_1475700), class_Groups_Ocomm__monoid__mult(_1475700), _1475702 = _1475704, c_Nat__Transfer_Onat__set(_1475704), 37585 ^ _775212 : [(37588 ^ _775212) ^ [] : [hAPP(_1475706, 37584 ^ [_1475700, _1475702, _1475704, _1475706, _1475708]) = hAPP(_1475708, 37584 ^ [_1475700, _1475702, _1475704, _1475706, _1475708])], (37586 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37584 ^ [_1475700, _1475702, _1475704, _1475706, _1475708])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1475700), _1475706), _1475702) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1475700), _1475708), _1475704))], (8435 ^ _775212) ^ [_911649, _911651, _911653] : [class_Rings_Olinordered__ring__strict(_911649), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911649), _911651), c_Groups_Ozero__class_Ozero(_911649))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911649), _911653), c_Groups_Ozero__class_Ozero(_911649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911649), c_Groups_Ozero__class_Ozero(_911649)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911649), _911651), _911653))))], (48378 ^ _775212) ^ [_1743518, _1743520, _1743522, _1743524] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743518)), _1743520))), c_List_Ofoldr(tc_List_Olist(_1743522), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1743522)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1743522))), _1743524, 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(_1743518)), _1743520)), c_List_Ofoldr(tc_List_Olist(_1743522), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1743522)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1743522), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1743522)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1743522)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1743522), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1743522)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1743522), tc_List_Olist(_1743522), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1743522)))), _1743524), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (33569 ^ _775212) ^ [_1386686] : [-(c_Wellfounded_Omeasure(_1386686) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1386686), c_Wellfounded_Oless__than))], (34943 ^ _775212) ^ [_1417178, _1417180, _1417182, _1417184] : [class_Lattices_Osemilattice__inf(_1417178), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417178), _1417180), _1417182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417178), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1417178), _1417184), _1417180)), _1417182)))], (14923 ^ _775212) ^ [_1025237, _1025239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025239), _1025237)), -(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), _1025237), _1025239))))], (40728 ^ _775212) ^ [_1558708, _1558710, _1558712, _1558714, _1558716, _1558718, _1558720, _1558722] : [c_Finite__Set_Ofolding(_1558708, _1558710, _1558712, _1558714), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558708), _1558716)), -(hAPP(c_Fun_Ocomp(_1558710, _1558710, _1558718, hAPP(_1558712, _1558720)), hAPP(c_Fun_Ocomp(_1558710, _1558710, _1558718, hAPP(_1558714, _1558716)), _1558722)) = hAPP(c_Fun_Ocomp(_1558710, _1558710, _1558718, hAPP(_1558714, _1558716)), hAPP(c_Fun_Ocomp(_1558710, _1558710, _1558718, hAPP(_1558712, _1558720)), _1558722)))], (5797 ^ _775212) ^ [_866662, _866664, _866666, _866668] : [-(c_Com_Ocom_OWhile(_866662, _866664) = c_Com_Ocom_OWhile(_866666, _866668)), _866662 = _866666, _866664 = _866668], (45856 ^ _775212) ^ [_1686105, _1686107, _1686109, _1686111, _1686113] : [-(hAPP(hAPP(c_List_Omap(_1686105, _1686107), _1686109), hAPP(hAPP(c_List_Oappend(_1686105), _1686111), _1686113)) = hAPP(hAPP(c_List_Oappend(_1686107), hAPP(hAPP(c_List_Omap(_1686105, _1686107), _1686109), _1686111)), hAPP(hAPP(c_List_Omap(_1686105, _1686107), _1686109), _1686113)))], (31835 ^ _775212) ^ [_1351028, _1351030, _1351032] : [class_Orderings_Olinorder(_1351028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1351028, tc_HOL_Obool)), _1351030), _1351032)), -(_1351030 = c_Orderings_Obot__class_Obot(tc_fun(_1351028, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351028), _1351032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351028), c_Big__Operators_Olinorder__class_OMin(_1351028, _1351032)), c_Big__Operators_Olinorder__class_OMin(_1351028, _1351030))))], (46222 ^ _775212) ^ [_1695564, _1695566, _1695568, _1695570, _1695572] : [hAPP(hAPP(c_List_Odrop(_1695564), _1695566), _1695568) = hAPP(hAPP(c_List_Olist_OCons(_1695564), _1695570), _1695572), -(hAPP(hAPP(c_List_Onth(_1695564), _1695568), _1695566) = _1695570)], (6334 ^ _775212) ^ [_875310, _875312] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_875310, _875312)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_875312)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43136 ^ _775212) ^ [_1616943] : [-(c_Nat_Ofunpow(_1616943) = c_Nat_Ocompow(_1616943, _1616943))], (44899 ^ _775212) ^ [_1662354, _1662356, _1662358] : [c_Fun_Oinj__on(_1662354, _1662356, _1662358, c_Orderings_Otop__class_Otop(tc_fun(_1662354, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1662354), tc_List_Olist(_1662356), hAPP(c_List_Omap(_1662354, _1662356), _1662358), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1662354), tc_HOL_Obool))))], (30514 ^ _775212) ^ [_1324819, _1324821, _1324823, _1324825] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1324819, tc_HOL_Obool)), _1324821), hAPP(hAPP(c_Set_Oinsert(_1324819), _1324823), _1324825)))), 30517 ^ _775212 : [(30520 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1324819, tc_HOL_Obool)), _1324821), _1324825))], (30518 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1324819), _1324823), _1324825)))]], 30521 ^ _775212 : [(30524 ^ _775212) ^ [] : [30525 ^ _775212 : [(30528 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1324819, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324819, tc_HOL_Obool)), _1324821), hAPP(hAPP(c_Set_Oinsert(_1324819), _1324823), c_Orderings_Obot__class_Obot(tc_fun(_1324819, tc_HOL_Obool))))), _1324825))], (30526 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1324819), _1324823), _1324821)))]], 30529 ^ _775212 : [(30532 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1324819, tc_HOL_Obool)), _1324821), _1324825))], (30530 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324819), _1324823), _1324821))]]], (30522 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324819), _1324823), _1324825))]]], (50122 ^ _775212) ^ [_1779755, _1779757, _1779759, _1779761, _1779763] : [class_Orderings_Olinorder(_1779755), 50128 ^ _775212 : [(50131 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1779755), hAPP(_1779761, _1779763)), hAPP(_1779761, 50127 ^ [_1779755, _1779757, _1779759, _1779761, _1779763])))], (50129 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779757), 50127 ^ [_1779755, _1779757, _1779759, _1779761, _1779763]), hAPP(c_List_Oset(_1779757), _1779759))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1779757, _1779755, _1779761), _1779763), _1779759) = hAPP(hAPP(c_List_Olist_OCons(_1779757), _1779763), _1779759))], (15137 ^ _775212) ^ [_1029485, _1029487, _1029489, _1029491, _1029493, _1029495] : [class_Rings_Oordered__ring(_1029485), 15140 ^ _775212 : [(15147 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029485), _1029487), _1029493)), _1029489)), _1029491)), _1029495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029485), _1029487), _1029489)), _1029491)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029485), _1029493), _1029489)), _1029495))))], (15141 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029485), _1029487), _1029489)), _1029491)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029485), _1029493), _1029489)), _1029495))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029485), _1029487), _1029493)), _1029489)), _1029491)), _1029495)))]]], (40098 ^ _775212) ^ [_1543764, _1543766, _1543768, _1543770] : [40100 ^ _775212 : [(40103 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1543766, hAPP(_1543768, 40099 ^ [_1543764, _1543766, _1543768, _1543770]))), hAPP(_1543766, 40099 ^ [_1543764, _1543766, _1543768, _1543770])))], (40101 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1543764, 40099 ^ [_1543764, _1543766, _1543768, _1543770])))]], -(c_Wellfounded_Owf(_1543770, hAPP(c_Set_OCollect(tc_prod(_1543770, _1543770)), hAPP(c_Product__Type_Oprod_Oprod__case(_1543770, _1543770, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1543770, tc_HOL_Obool), tc_fun(_1543770, tc_HOL_Obool), _1543770), hAPP(c_COMBS(_1543770, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543770), c_fconj), _1543764))), hAPP(hAPP(c_COMBC(_1543770, tc_fun(_1543770, _1543770), tc_fun(_1543770, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543770, tc_HOL_Obool), tc_fun(tc_fun(_1543770, _1543770), tc_fun(_1543770, tc_HOL_Obool)), _1543770), c_COMBB(_1543770, tc_HOL_Obool, _1543770)), c_fequal)), _1543768))))))], (5647 ^ _775212) ^ [_864182, _864184, _864186, _864188, _864190] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_864182, _864184), _864186, _864188, _864190), 5651 ^ _775212 : [(5654 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_864184, 5650 ^ [_864182, _864184, _864186, _864188, _864190], _864188, _864190))], (5652 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_864182, _864186, _864188, 5650 ^ [_864182, _864184, _864186, _864188, _864190]))]]], (25547 ^ _775212) ^ [_1220232, _1220234, _1220236, _1220238, _1220240, _1220242] : [class_Groups_Ocomm__monoid__add(_1220232), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1220234, _1220232), hAPP(hAPP(c_COMBC(_1220234, tc_fun(_1220236, tc_HOL_Obool), _1220232), hAPP(hAPP(c_COMBB(tc_fun(_1220236, _1220232), tc_fun(tc_fun(_1220236, tc_HOL_Obool), _1220232), _1220234), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1220236, _1220232)), _1220238)), _1220240)), _1220242) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1220236, _1220232), hAPP(hAPP(c_COMBC(_1220236, tc_fun(_1220234, tc_HOL_Obool), _1220232), hAPP(hAPP(c_COMBB(tc_fun(_1220234, _1220232), tc_fun(tc_fun(_1220234, tc_HOL_Obool), _1220232), _1220236), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1220234, _1220232)), hAPP(c_COMBC(_1220234, _1220236, _1220232), _1220238))), _1220242)), _1220240))], (15987 ^ _775212) ^ [_1045964] : [class_Groups_Oordered__ab__group__add__abs(_1045964), -(hAPP(c_Groups_Oabs__class_Oabs(_1045964), c_Groups_Ozero__class_Ozero(_1045964)) = c_Groups_Ozero__class_Ozero(_1045964))], (8115 ^ _775212) ^ [_905998, _906000, _906002] : [class_Rings_Oring__1(_905998), -(hAPP(c_Int_Oring__1__class_Oof__int(_905998), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _906000), _906002)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905998), hAPP(c_Int_Oring__1__class_Oof__int(_905998), _906000)), hAPP(c_Int_Oring__1__class_Oof__int(_905998), _906002)))], (38741 ^ _775212) ^ [_1503449, _1503451, _1503453, _1503455, _1503457] : [c_Finite__Set_Ofolding__one__idem(_1503449, _1503451, _1503453), hAPP(_1503455, hAPP(hAPP(_1503451, 38746 ^ [_1503449, _1503451, _1503453, _1503455, _1503457]), 38747 ^ [_1503449, _1503451, _1503453, _1503455, _1503457])) = hAPP(hAPP(_1503451, hAPP(_1503455, 38746 ^ [_1503449, _1503451, _1503453, _1503455, _1503457])), hAPP(_1503455, 38747 ^ [_1503449, _1503451, _1503453, _1503455, _1503457])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503449), _1503457)), -(_1503457 = c_Orderings_Obot__class_Obot(tc_fun(_1503449, tc_HOL_Obool))), -(hAPP(_1503455, hAPP(_1503453, _1503457)) = hAPP(_1503453, hAPP(c_Set_Oimage(_1503449, _1503449, _1503455), _1503457)))], (17731 ^ _775212) ^ [_1076325] : [_1076325 = c_Int_OMin, -(c_Int_OBit1(_1076325) = c_Int_OMin)], (8225 ^ _775212) ^ [_907856, _907858, _907860] : [class_Groups_Ogroup__add(_907856), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907856), _907858), _907860) = c_Groups_Ozero__class_Ozero(_907856), -(hAPP(c_Groups_Ouminus__class_Ouminus(_907856), _907858) = _907860)], (39833 ^ _775212) ^ [_1537390, _1537392, _1537394] : [c_Wellfounded_Owf(_1537390, _1537392), c_Wellfounded_Owf(_1537390, _1537394), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1537390, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1537390, _1537390), _1537392)), hAPP(c_Relation_ORange(_1537390, _1537390), _1537394)) = c_Orderings_Obot__class_Obot(tc_fun(_1537390, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1537390, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1537390, _1537390), tc_HOL_Obool)), _1537392), _1537394)))], (49518 ^ _775212) ^ [_1766478, _1766480, _1766482] : [class_Orderings_Olinorder(_1766478), c_List_Olinorder__class_Osorted(_1766478, _1766480), -(c_List_Olinorder__class_Osorted(_1766478, c_List_OdropWhile(_1766478, _1766482, _1766480)))], (29770 ^ _775212) ^ [_1305696, _1305698, _1305700] : [hBOOL(hAPP(hAPP(c_member(_1305696), _1305698), hAPP(c_fequal, _1305700))), -(_1305698 = _1305700)], (46891 ^ _775212) ^ [_1709954, _1709956, _1709958] : [class_Orderings_Olinorder(_1709954), -(c_Big__Operators_Olattice_OSup__fin(_1709954, c_Orderings_Oord__class_Omax(_1709954), hAPP(c_List_Oset(_1709954), hAPP(hAPP(c_List_Olist_OCons(_1709954), _1709956), _1709958))) = hAPP(c_List_Ofoldl(_1709954, _1709954, c_Orderings_Oord__class_Omax(_1709954), _1709956), _1709958))], (29280 ^ _775212) ^ [_1295731, _1295733] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1295731), _1295733))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1295731), hAPP(c_Nat_OSuc, _1295733)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (43362 ^ _775212) ^ [_1621684, _1621686] : [class_Complete__Lattice_Ocomplete__lattice(_1621684), -(c_Complete__Lattice_OInf__class_OInf(_1621684, _1621686) = c_Complete__Lattice_OSup__class_OSup(_1621684, hAPP(c_Set_OCollect(_1621684), hAPP(hAPP(c_COMBB(tc_fun(_1621684, tc_HOL_Obool), tc_HOL_Obool, _1621684), c_HOL_OAll(_1621684)), hAPP(hAPP(c_COMBB(tc_fun(_1621684, tc_HOL_Obool), tc_fun(_1621684, tc_HOL_Obool), _1621684), hAPP(c_COMBS(_1621684, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1621684), c_fimplies), hAPP(hAPP(c_COMBC(_1621684, tc_fun(_1621684, tc_HOL_Obool), tc_HOL_Obool), c_member(_1621684)), _1621686)))), c_Orderings_Oord__class_Oless__eq(_1621684))))))], (11694 ^ _775212) ^ [_967215] : [_967215 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967215), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2444 ^ _775212) ^ [_810924, _810926] : [_810926 = _810924, -(c_Nitpick_Ofrac(_810926) = c_Nitpick_Ofrac(_810924))], (6583 ^ _775212) ^ [_879530, _879532, _879534, _879536] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_879530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879530), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879530), _879532), _879534)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879530), _879532), _879536))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879530), _879534), _879536)))], (6312 ^ _775212) ^ [_874852, _874854] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874852), hAPP(c_Nat_OSuc, _874854)))), 6313 ^ _775212 : [(6316 ^ _775212) ^ [_874940] : [_874852 = hAPP(c_Nat_OSuc, _874940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874940), _874854))], (6314 ^ _775212) ^ [] : [_874852 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (12817 ^ _775212) ^ [_986649, _986651] : [class_Rings_Olinordered__idom(_986649), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986649), c_Groups_Ozero__class_Ozero(_986649)), _986651)), -(c_Groups_Osgn__class_Osgn(_986649, _986651) = c_Groups_Oone__class_Oone(_986649))], (9679 ^ _775212) ^ [_931672, _931674, _931676, _931678] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_931672), 9682 ^ _775212 : [(9689 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931672), _931676), _931678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931672), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931672), _931674), _931676)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931672), _931674), _931678))))], (9683 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931672), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931672), _931674), _931676)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931672), _931674), _931678))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931672), _931676), _931678)))]]], (33489 ^ _775212) ^ [_1384458, _1384460, _1384462, _1384464] : [c_FunDef_Oreduction__pair(_1384458, _1384460), -(c_FunDef_Oreduction__pair(_1384462, hAPP(hAPP(c_FunDef_Orp__inv__image(_1384458, _1384462), _1384460), _1384464)))], (27970 ^ _775212) ^ [_1270724] : [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)), _1270724))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1270724)))], (49434 ^ _775212) ^ [_1764577, _1764579, _1764581] : [hBOOL(hAPP(c_List_Odistinct(_1764577), _1764579)), -(hBOOL(hAPP(c_List_Odistinct(_1764577), c_List_OtakeWhile(_1764577, _1764581, _1764579))))], (52625 ^ _775212) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (7597 ^ _775212) ^ [_896591, _896593] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896591), _896593) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896593), _896591))], (20845 ^ _775212) ^ [_1131739, _1131741] : [20846 ^ _775212 : [(20849 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131741), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20847 ^ _775212) ^ [] : [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), _1131739), _1131741)))]], -(c_Divides_OnegDivAlg(_1131739, _1131741) = 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), _1131739), _1131741)))], (5160 ^ _775212) ^ [_853936, _853938, _853940, _853942] : [-(c_List_Olexord(_853942, _853938) = c_List_Olexord(_853940, _853936)), _853942 = _853940, _853938 = _853936], (29058 ^ _775212) ^ [_1291345, _1291347, _1291349, _1291351] : [_1291345 = c_Orderings_Obot__class_Obot(tc_fun(_1291347, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1291347, _1291349, hAPP(c_COMBK(_1291349, _1291347), _1291351)), _1291345) = c_Orderings_Obot__class_Obot(tc_fun(_1291349, tc_HOL_Obool)))], (50084 ^ _775212) ^ [_1778964, _1778966] : [class_Orderings_Olinorder(_1778964), hBOOL(hAPP(c_Finite__Set_Ofinite(_1778964), _1778966)), 50092 ^ _775212 : [(50095 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1778964, 50091 ^ [_1778964, _1778966]))], (50097 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1778964), 50091 ^ [_1778964, _1778966])))], (50099 ^ _775212) ^ [_1779290] : [-(_1779290 = 50091 ^ [_1778964, _1778966]), hAPP(c_List_Oset(_1778964), _1779290) = _1778966, c_List_Olinorder__class_Osorted(_1778964, _1779290), hBOOL(hAPP(c_List_Odistinct(_1778964), _1779290))], (50093 ^ _775212) ^ [] : [-(hAPP(c_List_Oset(_1778964), 50091 ^ [_1778964, _1778966]) = _1778966)]]], (14009 ^ _775212) ^ [_1008199, _1008201] : [-(_1008199 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14012 ^ _775212 : [(14019 ^ _775212) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1008201, _1008199) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1008201), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1008199)) = 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), _1008201), _1008199))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (14013 ^ _775212) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1008201, _1008199) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1008201), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1008199)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1008201), _1008199)))]]], (13358 ^ _775212) ^ [_996849] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _996849, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29758 ^ _775212) ^ [_1305402, _1305404, _1305406] : [hAPP(hAPP(c_COMBC(_1305402, tc_fun(_1305402, tc_HOL_Obool), tc_HOL_Obool), c_member(_1305402)), _1305404) = hAPP(hAPP(c_COMBC(_1305402, tc_fun(_1305402, tc_HOL_Obool), tc_HOL_Obool), c_member(_1305402)), _1305406), -(_1305404 = _1305406)], (16035 ^ _775212) ^ [_1046910, _1046912, _1046914] : [class_Rings_Olinordered__idom(_1046910), -(hAPP(c_Groups_Oabs__class_Oabs(_1046910), hAPP(hAPP(c_Power_Opower__class_Opower(_1046910), _1046912), _1046914)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1046910), hAPP(c_Groups_Oabs__class_Oabs(_1046910), _1046912)), _1046914))], (18203 ^ _775212) ^ [_1084290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084290), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1084290)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31293 ^ _775212) ^ [_1341475, _1341477, _1341479, _1341481, _1341483, _1341485] : [hBOOL(hAPP(hAPP(c_member(_1341475), _1341477), c_SetInterval_Oord_OgreaterThanAtMost(_1341475, _1341479, _1341481, _1341483, _1341485))), 31296 ^ _775212 : [(31299 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1341479, _1341477), _1341485)))], (31297 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1341481, _1341483), _1341477)))]]], (37697 ^ _775212) ^ [_1478831, _1478833, _1478835, _1478837, _1478839, _1478841, _1478843] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1478831, _1478833, _1478835, _1478837, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1478831, tc_HOL_Obool)), _1478839), hAPP(hAPP(c_Set_Oinsert(_1478831), _1478841), c_Orderings_Obot__class_Obot(tc_fun(_1478831, tc_HOL_Obool))))), _1478843)), hBOOL(hAPP(hAPP(c_member(_1478831), _1478841), _1478839)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1478831, _1478833, _1478835, _1478837, _1478839), hAPP(hAPP(_1478835, _1478841), _1478843))))], (52593 ^ _775212) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (18293 ^ _775212) ^ [_1085859, _1085861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1085859)), c_Int_OBit0(_1085861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085859), _1085861)))], (25657 ^ _775212) ^ [_1223196, _1223198, _1223200] : [class_Orderings_Olinorder(_1223196), 25660 ^ _775212 : [(25667 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1223196), _1223198), _1223200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1223196, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1223196), _1223198)), hAPP(c_SetInterval_Oord__class_OlessThan(_1223196), _1223200))))], (25661 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1223196, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1223196), _1223198)), hAPP(c_SetInterval_Oord__class_OlessThan(_1223196), _1223200))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1223196), _1223198), _1223200)))]]], (48550 ^ _775212) ^ [_1747051] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1747051) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1747051)))], (27672 ^ _775212) ^ [_1263638, _1263640] : [class_Groups_Oordered__ab__group__add(_1263638), -(hAPP(c_Set_Oimage(_1263638, _1263638, c_Groups_Ouminus__class_Ouminus(_1263638)), hAPP(c_SetInterval_Oord__class_OatLeast(_1263638), _1263640)) = hAPP(c_SetInterval_Oord__class_OatMost(_1263638), hAPP(c_Groups_Ouminus__class_Ouminus(_1263638), _1263640)))], (18753 ^ _775212) ^ [_1093830, _1093832, _1093834] : [class_Rings_Olinordered__idom(_1093830), 18756 ^ _775212 : [(18765 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093830), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093830), hAPP(hAPP(c_Power_Opower__class_Opower(_1093830), _1093832), 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(_1093830), _1093834), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1093830)))), _1093832 = c_Groups_Ozero__class_Ozero(_1093830), _1093834 = c_Groups_Ozero__class_Ozero(_1093830)], (18757 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093830), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093830), hAPP(hAPP(c_Power_Opower__class_Opower(_1093830), _1093832), 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(_1093830), _1093834), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1093830))), 18760 ^ _775212 : [(18763 ^ _775212) ^ [] : [-(_1093834 = c_Groups_Ozero__class_Ozero(_1093830))], (18761 ^ _775212) ^ [] : [-(_1093832 = c_Groups_Ozero__class_Ozero(_1093830))]]]]], (23970 ^ _775212) ^ [_1191787, _1191789] : [class_Rings_Ocomm__semiring__1(_1191787), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1191787), c_Groups_Ozero__class_Ozero(_1191787)), _1191789)), -(_1191789 = c_Groups_Ozero__class_Ozero(_1191787))], (11985 ^ _775212) ^ [_972119] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _972119) = _972119)], (47398 ^ _775212) ^ [_1720605, _1720607, _1720609, _1720611] : [hBOOL(hAPP(c_List_Olistsp(_1720605, _1720607), hAPP(hAPP(c_List_Olist_OCons(_1720605), _1720609), _1720611))), 47401 ^ _775212 : [(47404 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1720605, _1720607), _1720611)))], (47402 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1720607, _1720609)))]]], (28976 ^ _775212) ^ [_1290013, _1290015, _1290017] : [class_Orderings_Oorder(_1290013), _1290015 = _1290017, -(c_SetInterval_Oord__class_OatLeastAtMost(_1290013, _1290015, _1290017) = hAPP(hAPP(c_Set_Oinsert(_1290013), _1290015), c_Orderings_Obot__class_Obot(tc_fun(_1290013, tc_HOL_Obool))))], (45504 ^ _775212) ^ [_1678607, _1678609] : [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), _1678607), _1678609))), 45507 ^ _775212 : [(45514 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1678607), _1678609))), -(c_List_Oupto(_1678607, _1678609) = c_List_Olist_ONil(tc_Int_Oint))], (45508 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1678607), _1678609)), -(c_List_Oupto(_1678607, _1678609) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1678607), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1678607), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1678609)))]]], (24078 ^ _775212) ^ [_1193538, _1193540] : [_1193538 = _1193540, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193538), _1193540)))], (21697 ^ _775212) ^ [_1146937, _1146939, _1146941, _1146943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146937, tc_HOL_Obool)), _1146939), _1146941)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146937, tc_HOL_Obool)), _1146941), _1146943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146937, tc_HOL_Obool)), _1146939), _1146943)))], (52039 ^ _775212) ^ [_1820712, _1820714] : [c_Equiv__Relations_Opart__equivp(_1820712, _1820714), 52043 ^ _775212 : [(52048 ^ _775212) ^ [] : [-(c_Predicate_Otransp(_1820712, _1820714))], (52046 ^ _775212) ^ [] : [-(c_Predicate_Osymp(_1820712, _1820714))], (52044 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1820714, 52042 ^ [_1820712, _1820714]), 52042 ^ [_1820712, _1820714])))]]], (52627 ^ _775212) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (28896 ^ _775212) ^ [_1288631, _1288633, _1288635] : [-(hAPP(hAPP(c_Set_Oinsert(_1288631), _1288633), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288631, tc_HOL_Obool)), _1288635), hAPP(hAPP(c_Set_Oinsert(_1288631), _1288633), c_Orderings_Obot__class_Obot(tc_fun(_1288631, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_1288631), _1288633), _1288635))], (8860 ^ _775212) ^ [_918884, _918886, _918888] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918884), _918886)), _918888) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918884), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918886), _918888)))], (26549 ^ _775212) ^ [_1241926, _1241928] : [-(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)), _1241926)), 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), _1241928), _1241926))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1241926), _1241928))], (10713 ^ _775212) ^ [_950244] : [10715 ^ _775212 : [(10718 ^ _775212) ^ [] : [hBOOL(hAPP(_950244, 10714 ^ [_950244]))], (10716 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10714 ^ [_950244])))]], 10719 ^ _775212 : [(10720 ^ _775212) ^ [_950371] : [-(hBOOL(hAPP(_950244, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _950371))))]]], (14929 ^ _775212) ^ [_1025342, _1025344] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025342), _1025344)), hAPP(c_Nat_OSuc, _1025342))))], (21211 ^ _775212) ^ [_1138468, _1138470] : [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), _1138468), _1138470))), 21214 ^ _775212 : [(21223 ^ _775212) ^ [] : [-(c_Divides_OnegDivAlg(_1138468, _1138470) = hAPP(c_Divides_Oadjust(_1138470), c_Divides_OnegDivAlg(_1138468, 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)))), _1138470)))), -(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), _1138468), _1138470)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1138470), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21215 ^ _775212) ^ [] : [21216 ^ _775212 : [(21219 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1138470), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21217 ^ _775212) ^ [] : [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), _1138468), _1138470)))]], -(c_Divides_OnegDivAlg(_1138468, _1138470) = 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), _1138468), _1138470)))]]], (28734 ^ _775212) ^ [_1285690, _1285692, _1285694, _1285696] : [class_Complete__Lattice_Ocomplete__lattice(_1285690), -(_1285692 = c_Orderings_Obot__class_Obot(tc_fun(_1285694, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1285694, _1285690), _1285692), hAPP(c_COMBK(_1285690, _1285694), _1285696)) = _1285696)], (17351 ^ _775212) ^ [_1070045] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1070045), 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), _1070045)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1070045)))], (30478 ^ _775212) ^ [_1324113, _1324115, _1324117] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1324113), _1324115)), -(hBOOL(hAPP(hAPP(c_member(_1324113), _1324117), _1324115))), -(hAPP(c_Finite__Set_Ocard(_1324113), hAPP(hAPP(c_Set_Oinsert(_1324113), _1324117), _1324115)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1324113), _1324115)))], (37405 ^ _775212) ^ [_1471618, _1471620, _1471622, _1471624, _1471626] : [hBOOL(hAPP(hAPP(c_member(_1471618), _1471620), hAPP(c_Set_Ovimage(_1471618, _1471622, _1471624), _1471626))), -(hBOOL(hAPP(hAPP(c_member(_1471622), hAPP(_1471624, _1471620)), _1471626)))], (45790 ^ _775212) ^ [_1684825, _1684827, _1684829] : [-(hAPP(hAPP(c_List_Oappend(_1684825), _1684827), _1684829) = c_List_Olist_ONil(_1684825)), _1684827 = c_List_Olist_ONil(_1684825), _1684829 = c_List_Olist_ONil(_1684825)], (6170 ^ _775212) ^ [_872719, _872721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872719), hAPP(c_Nat_OSuc, _872721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872719), _872721))), -(_872719 = _872721)], (4472 ^ _775212) ^ [_843222, _843224, _843226, _843228, _843230, _843232, _843234, _843236] : [-(c_List_Omaps(_843236, _843232, _843228, _843224) = c_List_Omaps(_843234, _843230, _843226, _843222)), _843236 = _843234, _843232 = _843230, _843228 = _843226, _843224 = _843222], (40071 ^ _775212) ^ [_1543286, _1543288] : [c_Wellfounded_Owf(_1543286, _1543288), -(c_Wellfounded_Owf(tc_List_Olist(_1543286), c_List_Olex(_1543286, _1543288)))], (29084 ^ _775212) ^ [_1291900, _1291902, _1291904, _1291906, _1291908] : [_1291900 = c_Orderings_Obot__class_Obot(tc_fun(_1291902, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1291904), _1291906), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291902, tc_fun(_1291904, tc_HOL_Obool)), _1291900), _1291908)) = hAPP(hAPP(c_Set_Oinsert(_1291904), _1291906), c_Orderings_Obot__class_Obot(tc_fun(_1291904, tc_HOL_Obool))))], (19013 ^ _775212) ^ [_1098905, _1098907] : [class_Rings_Odivision__ring__inverse__zero(_1098905), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1098905), _1098907), c_Groups_Ozero__class_Ozero(_1098905)) = c_Groups_Ozero__class_Ozero(_1098905))], (16615 ^ _775212) ^ [_1058157, _1058159, _1058161, _1058163, _1058165] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1058157, _1058159), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1058161), _1058163))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1058159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1058165)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1058157, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058159), _1058165)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1058161), _1058165)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058159), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1058161, _1058165))), _1058163)))))], (50983 ^ _775212) ^ [_1798130] : [-(c_Lazy__Sequence_Oyieldn(_1798130) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1798130), _1798130, c_Lazy__Sequence_Oyield(_1798130)))], (43783 ^ _775212) ^ [_1632139, _1632141, _1632143, _1632145] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632139, _1632139)), hAPP(hAPP(c_Product__Type_OPair(_1632139, _1632139), _1632141), _1632143)), c_Transitive__Closure_Otrancl(_1632139, _1632145))), 43787 ^ _775212 : [(43790 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632139, _1632139)), hAPP(hAPP(c_Product__Type_OPair(_1632139, _1632139), 43786 ^ [_1632139, _1632141, _1632143, _1632145]), _1632143)), c_Transitive__Closure_Ortrancl(_1632139, _1632145))))], (43788 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632139, _1632139)), hAPP(hAPP(c_Product__Type_OPair(_1632139, _1632139), _1632141), 43786 ^ [_1632139, _1632141, _1632143, _1632145])), _1632145)))]]], (45720 ^ _775212) ^ [_1683446, _1683448, _1683450, _1683452, _1683454] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1683446), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683448)), _1683450)))), -(hAPP(hAPP(c_List_Olist__update(_1683448, hAPP(hAPP(c_List_Oappend(_1683448), _1683450), _1683452)), _1683446), _1683454) = hAPP(hAPP(c_List_Oappend(_1683448), _1683450), hAPP(hAPP(c_List_Olist__update(_1683448, _1683452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1683446), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683448)), _1683450))), _1683454)))], (8836 ^ _775212) ^ [_918495, _918497] : [-(_918495 = hAPP(c_Int_Onat, _918497)), 8839 ^ _775212 : [(8842 ^ _775212) ^ [] : [_918497 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918495)], (8840 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _918497)))]], 8843 ^ _775212 : [(8846 ^ _775212) ^ [] : [_918495 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8844 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _918497))]]], (52421 ^ _775212) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (35385 ^ _775212) ^ [_1427894, _1427896, _1427898] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1427894), _1427896)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427894), _1427898)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1427894), _1427896)), hAPP(c_Finite__Set_Ocard(_1427894), _1427898)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1427894), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427894, tc_HOL_Obool)), _1427896), _1427898))), hAPP(c_Finite__Set_Ocard(_1427894), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427894, tc_HOL_Obool)), _1427896), _1427898))))], (39190 ^ _775212) ^ [_1515949, _1515951, _1515953, _1515955] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515949), hAPP(c_Set_OCollect(_1515949), _1515951))), 39193 ^ _775212 : [(39194 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515953), hAPP(c_Set_OCollect(_1515953), hAPP(hAPP(c_COMBB(tc_fun(_1515949, tc_HOL_Obool), tc_HOL_Obool, _1515953), c_HOL_OEx(_1515949)), hAPP(hAPP(c_COMBB(tc_fun(_1515949, tc_HOL_Obool), tc_fun(_1515949, tc_HOL_Obool), _1515953), hAPP(c_COMBS(_1515949, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515949), c_fconj), _1515951))), _1515955))))), 39197 ^ _775212 : [(39198 ^ _775212) ^ [_1516232] : [hBOOL(hAPP(_1515951, _1516232)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1515953), hAPP(c_Set_OCollect(_1515953), hAPP(hAPP(c_COMBC(_1515953, _1515949, tc_HOL_Obool), _1515955), _1516232)))))]]], (39204 ^ _775212) ^ [] : [39206 ^ _775212 : [(39209 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515953), hAPP(c_Set_OCollect(_1515953), hAPP(hAPP(c_COMBC(_1515953, _1515949, tc_HOL_Obool), _1515955), 39205 ^ [_1515949, _1515951, _1515953, _1515955]))))], (39207 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1515951, 39205 ^ [_1515949, _1515951, _1515953, _1515955])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1515953), hAPP(c_Set_OCollect(_1515953), hAPP(hAPP(c_COMBB(tc_fun(_1515949, tc_HOL_Obool), tc_HOL_Obool, _1515953), c_HOL_OEx(_1515949)), hAPP(hAPP(c_COMBB(tc_fun(_1515949, tc_HOL_Obool), tc_fun(_1515949, tc_HOL_Obool), _1515953), hAPP(c_COMBS(_1515949, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515949), c_fconj), _1515951))), _1515955))))))]]], (20373 ^ _775212) ^ [_1122678, _1122680, _1122682, _1122684] : [class_Fields_Olinordered__field__inverse__zero(_1122678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122678), _1122680), _1122682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122678), _1122684), c_Groups_Ozero__class_Ozero(_1122678))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122678), c_Groups_Ozero__class_Ozero(_1122678)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122678), _1122680), _1122682))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122678), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122678), _1122684), _1122680)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122678), _1122684), _1122682))))], (49406 ^ _775212) ^ [_1764017, _1764019, _1764021, _1764023, _1764025] : [-(hAPP(hAPP(c_List_Ozip(_1764017, _1764019), _1764021), c_List_OtakeWhile(_1764019, _1764023, _1764025)) = c_List_OtakeWhile(tc_prod(_1764017, _1764019), hAPP(c_Fun_Ocomp(_1764019, tc_HOL_Obool, tc_prod(_1764017, _1764019), _1764023), c_Product__Type_Osnd(_1764017, _1764019)), hAPP(hAPP(c_List_Ozip(_1764017, _1764019), _1764021), _1764025)))], (45907 ^ _775212) ^ [_1687414, _1687416, _1687418, _1687420] : [hAPP(hAPP(c_List_Oappend(_1687414), _1687416), _1687418) = hAPP(hAPP(c_List_Oappend(_1687414), _1687420), _1687418), -(_1687416 = _1687420)], (20477 ^ _775212) ^ [_1124696, _1124698, _1124700, _1124702] : [class_Fields_Olinordered__field(_1124696), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124696), c_Groups_Ozero__class_Ozero(_1124696)), _1124698)), 20484 ^ _775212 : [(20491 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124696), _1124700), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124696), _1124702), _1124698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124696), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124696), _1124700), _1124698)), _1124702)))], (20485 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124696), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124696), _1124700), _1124698)), _1124702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124696), _1124700), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124696), _1124702), _1124698))))]]], (45250 ^ _775212) ^ [_1671595, _1671597, _1671599, _1671601, _1671603, _1671605] : [-(hAPP(hAPP(c_List_Ozip(_1671595, _1671597), hAPP(hAPP(c_List_Omap(_1671599, _1671595), _1671601), _1671603)), _1671605) = hAPP(hAPP(c_List_Omap(tc_prod(_1671599, _1671597), tc_prod(_1671595, _1671597)), hAPP(c_Product__Type_Oprod_Oprod__case(_1671599, _1671597, tc_prod(_1671595, _1671597)), hAPP(hAPP(c_COMBB(_1671595, tc_fun(_1671597, tc_prod(_1671595, _1671597)), _1671599), c_Product__Type_OPair(_1671595, _1671597)), _1671601))), hAPP(hAPP(c_List_Ozip(_1671599, _1671597), _1671603), _1671605)))], (51187 ^ _775212) ^ [_1802837, _1802839, _1802841] : [c_List_Oall__interval__int(_1802837, _1802839, _1802841), -(c_List_Olist__all(tc_Int_Oint, _1802837, c_List_Oupto(_1802839, _1802841)))], (43402 ^ _775212) ^ [_1623007, _1623009, _1623011, _1623013] : [-(hAPP(c_Set_Oimage(_1623007, _1623009, _1623011), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623007, tc_HOL_Obool), _1623013)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1623007, tc_HOL_Obool), tc_fun(_1623009, tc_HOL_Obool)), _1623013), c_Set_Oimage(_1623007, _1623009, _1623011)))], (34829 ^ _775212) ^ [_1414780, _1414782, _1414784] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414780, tc_HOL_Obool)), _1414782), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414780, tc_HOL_Obool)), _1414782), _1414784)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414780, tc_HOL_Obool)), _1414782), _1414784))], (41726 ^ _775212) ^ [_1580175] : [class_Groups_Oab__semigroup__mult(_1580175), -(c_Finite__Set_Ofun__left__comm(_1580175, _1580175, c_Groups_Otimes__class_Otimes(_1580175)))], (25482 ^ _775212) ^ [_1218731, _1218733] : [class_Orderings_Oorder(_1218731), 25489 ^ _775212 : [(25494 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218731), hAPP(_1218733, 25487 ^ [_1218731, _1218733])), hAPP(_1218733, 25488 ^ [_1218731, _1218733])))], (25492 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 25488 ^ [_1218731, _1218733]), 25487 ^ [_1218731, _1218733]))], (25490 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 25487 ^ [_1218731, _1218733]), 25488 ^ [_1218731, _1218733])))]], -(c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1218731, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1218733))], (23384 ^ _775212) ^ [_1180601, _1180603, _1180605] : [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), _1180601), _1180603))), -(hBOOL(hAPP(hAPP(_1180605, _1180601), _1180603))), 23391 ^ _775212 : [(23394 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23390 ^ [_1180601, _1180603, _1180605]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1180605, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23389 ^ [_1180601, _1180603, _1180605])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23390 ^ [_1180601, _1180603, _1180605]))))], (23400 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1180605, 23389 ^ [_1180601, _1180603, _1180605]), 23390 ^ [_1180601, _1180603, _1180605]))], (23392 ^ _775212) ^ [] : [-(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), 23389 ^ [_1180601, _1180603, _1180605]), 23390 ^ [_1180601, _1180603, _1180605]))))]]], (48274 ^ _775212) ^ [_1740301, _1740303, _1740305, _1740307] : [-(hAPP(c_List_Ofilter(_1740301, _1740303), hAPP(hAPP(c_List_Oappend(_1740301), _1740305), _1740307)) = hAPP(hAPP(c_List_Oappend(_1740301), hAPP(c_List_Ofilter(_1740301, _1740303), _1740305)), hAPP(c_List_Ofilter(_1740301, _1740303), _1740307)))], (752 ^ _775212) ^ [_786730, _786732, _786734, _786736] : [-(c_Wellfounded_Owf(_786734, _786730)), c_Wellfounded_Owf(_786736, _786732), _786736 = _786734, _786732 = _786730], (34983 ^ _775212) ^ [_1418529, _1418531, _1418533, _1418535, _1418537] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418529, tc_fun(_1418531, tc_HOL_Obool)), _1418533), hAPP(hAPP(c_COMBB(tc_fun(_1418531, tc_HOL_Obool), tc_fun(_1418531, tc_HOL_Obool), _1418529), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418531, tc_HOL_Obool)), _1418535)), _1418537)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418531, tc_HOL_Obool)), _1418535), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418529, tc_fun(_1418531, tc_HOL_Obool)), _1418533), _1418537)))], (17725 ^ _775212) ^ [_1076250] : [c_Int_OBit1(_1076250) = c_Int_OMin, -(_1076250 = c_Int_OMin)], (1474 ^ _775212) ^ [_796493, _796495] : [-(class_Finite__Set_Ofinite(_796493)), _796495 = _796493, class_Finite__Set_Ofinite(_796495)], (52441 ^ _775212) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (36982 ^ _775212) ^ [_1462716, _1462718, _1462720, _1462722, _1462724] : [c_Fun_Oinj__on(_1462716, _1462718, _1462720, _1462722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462718, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1462716, _1462718, _1462720), _1462722)), _1462724)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462718), _1462724)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1462716), _1462722)), hAPP(c_Finite__Set_Ocard(_1462718), _1462724))))], (30256 ^ _775212) ^ [_1317333, _1317335, _1317337, _1317339, _1317341, _1317343] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1317333, tc_fun(_1317335, tc_fun(_1317337, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1317333, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1317335, _1317337), tc_HOL_Obool), tc_fun(_1317335, tc_fun(_1317337, tc_HOL_Obool)), _1317333), hAPP(c_COMBC(_1317335, tc_fun(tc_prod(_1317335, _1317337), tc_HOL_Obool), tc_fun(_1317337, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317337, tc_fun(tc_fun(tc_prod(_1317335, _1317337), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1317335, _1317337), tc_HOL_Obool), tc_fun(_1317337, tc_HOL_Obool)), _1317335), c_COMBC(_1317337, tc_fun(tc_prod(_1317335, _1317337), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317337, tc_prod(_1317335, _1317337)), tc_fun(_1317337, tc_fun(tc_fun(tc_prod(_1317335, _1317337), tc_HOL_Obool), tc_HOL_Obool)), _1317335), hAPP(c_COMBB(tc_prod(_1317335, _1317337), tc_fun(tc_fun(tc_prod(_1317335, _1317337), tc_HOL_Obool), tc_HOL_Obool), _1317337), c_member(tc_prod(_1317335, _1317337)))), c_Product__Type_OPair(_1317335, _1317337))))), _1317339)), _1317341), _1317343)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1317335, _1317337)), hAPP(hAPP(c_Product__Type_OPair(_1317335, _1317337), _1317341), _1317343)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1317333, tc_fun(tc_prod(_1317335, _1317337), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1317333, tc_HOL_Obool))), _1317339))))], (48238 ^ _775212) ^ [_1739696, _1739698, _1739700, _1739702] : [-(hBOOL(hAPP(_1739696, _1739698))), -(c_List_Oremove1(_1739700, _1739698, hAPP(c_List_Ofilter(_1739700, _1739696), _1739702)) = hAPP(c_List_Ofilter(_1739700, _1739696), _1739702))], (21637 ^ _775212) ^ [_1145716, _1145718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145718), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1145716), _1145718) = 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), _1145716), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1145718)))))], (22314 ^ _775212) ^ [_1159523, _1159525, _1159527] : [class_Int_Onumber__ring(_1159523), 22317 ^ _775212 : [(22324 ^ _775212) ^ [] : [-(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), _1159525)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1159523), hAPP(c_Int_Onumber__class_Onumber__of(_1159523), _1159527)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1159525))) = c_Groups_Oone__class_Oone(_1159523))], (22318 ^ _775212) ^ [] : [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), _1159525))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1159523), hAPP(c_Int_Onumber__class_Onumber__of(_1159523), _1159527)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1159525))) = hAPP(hAPP(c_HOL_OLet(_1159523, _1159523), hAPP(hAPP(c_Power_Opower__class_Opower(_1159523), hAPP(c_Int_Onumber__class_Onumber__of(_1159523), _1159527)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159525))), hAPP(hAPP(c_COMBS(_1159523, _1159523, _1159523), hAPP(hAPP(c_COMBB(_1159523, tc_fun(_1159523, _1159523), _1159523), c_Groups_Otimes__class_Otimes(_1159523)), hAPP(c_Groups_Otimes__class_Otimes(_1159523), hAPP(c_Int_Onumber__class_Onumber__of(_1159523), _1159527)))), c_COMBI(_1159523))))]]], (27183 ^ _775212) ^ [_1254127, _1254129, _1254131] : [class_Lattices_Osemilattice__sup(_1254127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254127), _1254129), _1254131)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254127), _1254131), _1254129) = _1254131)], (38993 ^ _775212) ^ [_1508807, _1508809, _1508811, _1508813] : [-(hBOOL(hAPP(hAPP(c_member(_1508807), _1508809), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1508807, tc_HOL_Obool)), _1508811), hAPP(c_Set_OCollect(_1508807), _1508813))))), hBOOL(hAPP(hAPP(c_member(_1508807), _1508809), _1508811)), hBOOL(hAPP(_1508813, _1508809))], (17337 ^ _775212) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (11834 ^ _775212) ^ [_969376, _969378] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969376), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969376), _969378))))], (3012 ^ _775212) ^ [_820278, _820280, _820282, _820284, _820286, _820288] : [-(c_SetInterval_Oord_OlessThan(_820288, _820284, _820280) = c_SetInterval_Oord_OlessThan(_820286, _820282, _820278)), _820288 = _820286, _820284 = _820282, _820280 = _820278], (5358 ^ _775212) ^ [_856961, _856963] : [_856963 = _856961, -(c_Set_OCollect(_856963) = c_Set_OCollect(_856961))], (38468 ^ _775212) ^ [_1498293, _1498295, _1498297] : [class_Orderings_Olinorder(_1498293), hBOOL(hAPP(c_Finite__Set_Ofinite(_1498293), _1498295)), hBOOL(hAPP(hAPP(c_member(_1498293), _1498297), _1498295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498293), hAPP(c_Finite__Set_Ofold1(_1498293, c_Orderings_Oord__class_Omin(_1498293)), _1498295)), _1498297)))], (46200 ^ _775212) ^ [_1695091, _1695093, _1695095, _1695097] : [-(hAPP(hAPP(c_List_Odrop(_1695091), _1695093), hAPP(hAPP(c_List_Otake(_1695091), _1695095), _1695097)) = hAPP(hAPP(c_List_Otake(_1695091), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1695095), _1695093)), hAPP(hAPP(c_List_Odrop(_1695091), _1695093), _1695097)))], (12428 ^ _775212) ^ [_979548, _979550] : [class_Divides_Osemiring__div(_979548), -(c_Divides_Odiv__class_Omod(_979548, _979550, _979550) = c_Groups_Ozero__class_Ozero(_979548))], (36751 ^ _775212) ^ [_1457645, _1457647, _1457649] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1457645), _1457647)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1457645, tc_HOL_Obool)), _1457647), hAPP(c_Set_Oimage(_1457645, _1457645, _1457649), _1457647))), -(c_Fun_Oinj__on(_1457645, _1457645, _1457649, _1457647))], (7387 ^ _775212) ^ [_892570, _892572] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _892570)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _892572)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892570), _892572)))], (18381 ^ _775212) ^ [_1087325] : [-(c_Int_Osucc(c_Int_OBit1(_1087325)) = c_Int_OBit0(c_Int_Osucc(_1087325)))], (13497 ^ _775212) ^ [_999102, _999104, _999106, _999108] : [class_Divides_Osemiring__div(_999102), -(_999104 = c_Groups_Ozero__class_Ozero(_999102)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_999102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999102), _999104), _999106)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999102), _999104), _999108)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_999102), _999106), _999108))], (37992 ^ _775212) ^ [_1486949, _1486951, _1486953, _1486955, _1486957, _1486959] : [hBOOL(hAPP(hAPP(c_member(_1486949), _1486951), _1486953)), 37995 ^ _775212 : [(38002 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1486955, tc_HOL_Obool)), _1486957), _1486959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1486955, _1486949), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1486955, _1486949), _1486957), hAPP(c_COMBK(tc_fun(_1486949, tc_HOL_Obool), _1486955), _1486953))), hAPP(hAPP(c_Product__Type_OSigma(_1486955, _1486949), _1486959), hAPP(c_COMBK(tc_fun(_1486949, tc_HOL_Obool), _1486955), _1486953)))))], (37996 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1486955, _1486949), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1486955, _1486949), _1486957), hAPP(c_COMBK(tc_fun(_1486949, tc_HOL_Obool), _1486955), _1486953))), hAPP(hAPP(c_Product__Type_OSigma(_1486955, _1486949), _1486959), hAPP(c_COMBK(tc_fun(_1486949, tc_HOL_Obool), _1486955), _1486953)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1486955, tc_HOL_Obool)), _1486957), _1486959)))]]], (3428 ^ _775212) ^ [_826920, _826922, _826924, _826926, _826928, _826930, _826932, _826934] : [-(c_New__Random__Sequence_Oneg__map(_826934, _826930, _826926, _826922) = c_New__Random__Sequence_Oneg__map(_826932, _826928, _826924, _826920)), _826934 = _826932, _826930 = _826928, _826926 = _826924, _826922 = _826920], (24806 ^ _775212) ^ [_1206155, _1206157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206155)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1206155), _1206157)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206157), _1206155))], (45698 ^ _775212) ^ [_1682937, _1682939, _1682941, _1682943, _1682945, _1682947, _1682949] : [-(hAPP(hAPP(c_List_Ozip(_1682937, _1682939), hAPP(hAPP(c_List_Olist__update(_1682937, _1682941), _1682943), _1682945)), hAPP(hAPP(c_List_Olist__update(_1682939, _1682947), _1682943), _1682949)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1682937, _1682939), hAPP(hAPP(c_List_Ozip(_1682937, _1682939), _1682941), _1682947)), _1682943), hAPP(hAPP(c_Product__Type_OPair(_1682937, _1682939), _1682945), _1682949)))], (1504 ^ _775212) ^ [_796868, _796870] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_796868)), _796870 = _796868, class_Groups_Oordered__ab__semigroup__add__imp__le(_796870)], (16357 ^ _775212) ^ [_1052915, _1052917, _1052919] : [class_Int_Onumber__ring(_1052915), class_Rings_Olinordered__idom(_1052915), 16364 ^ _775212 : [(16371 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052917), _1052919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052915), hAPP(c_Int_Onumber__class_Onumber__of(_1052915), _1052917)), hAPP(c_Int_Onumber__class_Onumber__of(_1052915), _1052919))))], (16365 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052915), hAPP(c_Int_Onumber__class_Onumber__of(_1052915), _1052917)), hAPP(c_Int_Onumber__class_Onumber__of(_1052915), _1052919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052917), _1052919)))]]], (15725 ^ _775212) ^ [_1041238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1041238)), -(_1041238 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041238), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (45172 ^ _775212) ^ [_1669601, _1669603] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669601)), _1669603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1669603 = c_List_Olist_ONil(_1669601))], (45220 ^ _775212) ^ [_1670501, _1670503, _1670505, _1670507] : [-(hAPP(hAPP(c_List_Otake(_1670501), _1670503), hAPP(hAPP(c_List_Olist_OCons(_1670501), _1670505), _1670507)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1670501), c_List_Olist_ONil(_1670501), hAPP(hAPP(c_COMBB(tc_List_Olist(_1670501), tc_List_Olist(_1670501), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1670501), _1670505)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1670501), tc_List_Olist(_1670501)), c_List_Otake(_1670501)), _1670507)), _1670503))], (39973 ^ _775212) ^ [_1540509, _1540511] : [c_FunDef_Oreduction__pair(_1540509, _1540511), 39976 ^ _775212 : [(39979 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1540509, _1540509), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1540509, _1540509, _1540509), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1540509, _1540509), tc_HOL_Obool), tc_fun(tc_prod(_1540509, _1540509), tc_HOL_Obool)), _1540511)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1540509, _1540509), tc_HOL_Obool), tc_fun(tc_prod(_1540509, _1540509), tc_HOL_Obool)), _1540511))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1540509, _1540509), tc_HOL_Obool), tc_fun(tc_prod(_1540509, _1540509), tc_HOL_Obool)), _1540511))))], (39977 ^ _775212) ^ [] : [-(c_Wellfounded_Owf(_1540509, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1540509, _1540509), tc_HOL_Obool), tc_fun(tc_prod(_1540509, _1540509), tc_HOL_Obool)), _1540511)))]]], (25713 ^ _775212) ^ [_1224733, _1224735, _1224737, _1224739, _1224741] : [class_Groups_Ocomm__monoid__add(_1224733), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1224735), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1224737), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1224733), _1224739), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1224735, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1224737), _1224741))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224733), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1224733), _1224739), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1224735, _1224737))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1224733), _1224739), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1224737), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1224737), _1224741)))))], (52243 ^ _775212) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (41512 ^ _775212) ^ [_1575581, _1575583, _1575585] : [class_Lattices_Olattice(_1575581), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575581), _1575583)), -(hBOOL(hAPP(hAPP(c_member(_1575581), _1575585), _1575583))), -(c_Big__Operators_Olattice__class_OSup__fin(_1575581, hAPP(hAPP(c_Set_Oinsert(_1575581), _1575585), _1575583)) = hAPP(hAPP(c_Finite__Set_Ofold(_1575581, _1575581, c_Lattices_Osemilattice__sup__class_Osup(_1575581)), _1575585), _1575583))], (16777 ^ _775212) ^ [_1061277, _1061279, _1061281] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1061277, _1061279), _1061281)), -(c_Divides_Odivmod__nat(_1061277, _1061279) = _1061281)], (33421 ^ _775212) ^ [_1382413] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1382413)), -(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))), _1382413)), c_FunDef_Omax__weak)))], (38202 ^ _775212) ^ [_1492714, _1492716, _1492718, _1492720, _1492722, _1492724, _1492726, _1492728, _1492730] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492714, _1492716)), hAPP(hAPP(c_Product__Type_OPair(_1492714, _1492716), _1492718), _1492720)), _1492722)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492724, _1492726)), hAPP(hAPP(c_Product__Type_OPair(_1492724, _1492726), hAPP(_1492728, _1492718)), hAPP(_1492730, _1492720))), hAPP(c_Set_Oimage(tc_prod(_1492714, _1492716), tc_prod(_1492724, _1492726), c_Product__Type_Omap__pair(_1492714, _1492724, _1492716, _1492726, _1492728, _1492730)), _1492722))))], (47887 ^ _775212) ^ [_1731428, _1731430, _1731432] : [hBOOL(hAPP(c_List_Odistinct(_1731428), _1731430)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1731428)), c_Enum_On__lists(_1731428, _1731432, _1731430))))], (47959 ^ _775212) ^ [_1733028, _1733030] : [hBOOL(hAPP(c_List_Odistinct(_1733028), _1733030)), -(c_List_Oremdups(_1733028, _1733030) = _1733030)], (33396 ^ _775212) ^ [_1381868, _1381870, _1381872, _1381874] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1381868), _1381870)), 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)), _1381872), _1381868)), 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)), _1381874), _1381870)), 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)), _1381872), _1381874)), _1381870)), c_FunDef_Omax__weak)))], (16799 ^ _775212) ^ [_1061695, _1061697] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1061695) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1061697), 16802 ^ _775212 : [(16805 ^ _775212) ^ [] : [-(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), _1061697))))], (16803 ^ _775212) ^ [] : [-(_1061695 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1061697)))]]], (52681 ^ _775212) ^ [_1828266, _1828268, _1828270, _1828272, _1828274, _1828276] : [-(hAPP(hAPP(hAPP(c_COMBC(_1828266, _1828268, _1828270), _1828272), _1828274), _1828276) = hAPP(hAPP(_1828272, _1828276), _1828274))], (45826 ^ _775212) ^ [_1685469, _1685471, _1685473] : [c_List_Olist_ONil(_1685469) = hAPP(hAPP(c_List_Oappend(_1685469), _1685471), _1685473), 45829 ^ _775212 : [(45832 ^ _775212) ^ [] : [-(_1685473 = c_List_Olist_ONil(_1685469))], (45830 ^ _775212) ^ [] : [-(_1685471 = c_List_Olist_ONil(_1685469))]]], (12650 ^ _775212) ^ [_983875, _983877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _983875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _983877, _983875)), _983875)))], (46754 ^ _775212) ^ [_1707145, _1707147, _1707149, _1707151] : [-(hAPP(c_List_Orotate(_1707145, _1707147), hAPP(c_List_Orotate(_1707145, _1707149), _1707151)) = hAPP(c_List_Orotate(_1707145, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1707147), _1707149)), _1707151))], (7691 ^ _775212) ^ [_898518, _898520, _898522, _898524, _898526] : [class_Rings_Ocomm__semiring__1(_898518), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898518), _898520), _898522)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898518), _898524), _898526)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898518), _898520), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898518), _898522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898518), _898524), _898526))))], (40596 ^ _775212) ^ [_1555528, _1555530, _1555532] : [-(c_Hilbert__Choice_OEps(tc_prod(_1555528, _1555530), _1555532) = c_Hilbert__Choice_OEps(tc_prod(_1555528, _1555530), hAPP(c_Product__Type_Oprod_Oprod__case(_1555528, _1555530, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1555530, tc_prod(_1555528, _1555530)), tc_fun(_1555530, tc_HOL_Obool), _1555528), hAPP(c_COMBB(tc_prod(_1555528, _1555530), tc_HOL_Obool, _1555530), _1555532)), c_Product__Type_OPair(_1555528, _1555530)))))], (46480 ^ _775212) ^ [_1701395, _1701397, _1701399] : [hBOOL(hAPP(c_List_Odistinct(_1701395), _1701397)), -(hBOOL(hAPP(c_List_Odistinct(_1701395), c_List_Osublist(_1701395, _1701397, _1701399))))], (12087 ^ _775212) ^ [_973844] : [-(hAPP(c_Nat_OSuc, _973844) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _973844))], (44857 ^ _775212) ^ [_1661456, _1661458, _1661460, _1661462, _1661464] : [hAPP(hAPP(c_List_Omap(_1661456, _1661458), _1661460), _1661462) = hAPP(hAPP(c_List_Omap(_1661456, _1661458), _1661460), _1661464), c_Fun_Oinj__on(_1661456, _1661458, _1661460, c_Orderings_Otop__class_Otop(tc_fun(_1661456, tc_HOL_Obool))), -(_1661462 = _1661464)], (22416 ^ _775212) ^ [_1161892, _1161894, _1161896, _1161898, _1161900, _1161902, _1161904, _1161906] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1161892, _1161894, _1161896), _1161898), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1161900, _1161902, tc_prod(_1161892, _1161894)), _1161904), _1161906)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1161900, _1161902, _1161896), hAPP(hAPP(c_COMBB(tc_fun(_1161902, tc_prod(_1161892, _1161894)), tc_fun(_1161902, _1161896), _1161900), hAPP(c_COMBB(tc_prod(_1161892, _1161894), _1161896, _1161902), hAPP(c_Product__Type_Oprod_Oprod__case(_1161892, _1161894, _1161896), _1161898))), _1161904)), _1161906))], (15599 ^ _775212) ^ [_1038946, _1038948, _1038950, _1038952] : [class_Rings_Olinordered__semidom(_1038946), hAPP(hAPP(c_Power_Opower__class_Opower(_1038946), _1038948), _1038950) = hAPP(hAPP(c_Power_Opower__class_Opower(_1038946), _1038952), _1038950), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038946), c_Groups_Ozero__class_Ozero(_1038946)), _1038948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038946), c_Groups_Ozero__class_Ozero(_1038946)), _1038952)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1038950)), -(_1038948 = _1038952)], (24000 ^ _775212) ^ [_1192273, _1192275] : [_1192273 = _1192275, 24003 ^ _775212 : [(24006 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192275), _1192273)))], (24004 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192273), _1192275)))]]], (14503 ^ _775212) ^ [_1017539, _1017541] : [class_Rings_Ocomm__semiring__1(_1017539), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1017539), _1017541), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1017541)], (46774 ^ _775212) ^ [_1707563, _1707565, _1707567] : [_1707567 = c_List_Olist_ONil(_1707563), -(hAPP(c_List_Orotate(_1707563, _1707565), _1707567) = c_List_Olist_ONil(_1707563))], (3620 ^ _775212) ^ [_829906, _829908, _829910, _829912] : [-(c_Relation_ORange(_829912, _829908) = c_Relation_ORange(_829910, _829906)), _829912 = _829910, _829908 = _829906], (42511 ^ _775212) ^ [_1600237, _1600239, _1600241] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600237, tc_fun(_1600239, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1600237, tc_HOL_Obool))), _1600241) = c_Orderings_Otop__class_Otop(tc_fun(_1600239, tc_HOL_Obool)))], (50019 ^ _775212) ^ [_1777646, _1777648, _1777650, _1777652, _1777654, _1777656] : [-(c_New__Random__Sequence_Opos__union(_1777646, _1777648, _1777650, _1777652, _1777654, _1777656) = c_New__DSequence_Opos__union(_1777646, hAPP(hAPP(hAPP(_1777648, _1777652), _1777654), _1777656), hAPP(hAPP(hAPP(_1777650, _1777652), _1777654), _1777656)))], (15305 ^ _775212) ^ [_1033002, _1033004, _1033006, _1033008] : [class_Rings_Olinordered__semidom(_1033002), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033002), c_Groups_Oone__class_Oone(_1033002)), _1033004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033002), hAPP(hAPP(c_Power_Opower__class_Opower(_1033002), _1033004), _1033006)), hAPP(hAPP(c_Power_Opower__class_Opower(_1033002), _1033004), _1033008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033006), _1033008)))], (24174 ^ _775212) ^ [_1195014, _1195016, _1195018] : [_1195014 = _1195016, 24185 ^ _775212 : [(24188 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195018), _1195014))], (24186 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195014), _1195018)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195016), _1195018)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195018), _1195016)))], (39554 ^ _775212) ^ [_1529403, _1529405, _1529407, _1529409, _1529411, _1529413, _1529415, _1529417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529403, _1529405), tc_HOL_Obool)), _1529407), hAPP(hAPP(c_Product__Type_OSigma(_1529403, _1529405), _1529409), hAPP(c_COMBK(tc_fun(_1529405, tc_HOL_Obool), _1529403), _1529411)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529405, _1529413), tc_HOL_Obool)), _1529415), hAPP(hAPP(c_Product__Type_OSigma(_1529405, _1529413), _1529411), hAPP(c_COMBK(tc_fun(_1529413, tc_HOL_Obool), _1529405), _1529417)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529403, _1529413), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1529403, _1529405, _1529413), _1529407), _1529415)), hAPP(hAPP(c_Product__Type_OSigma(_1529403, _1529413), _1529409), hAPP(c_COMBK(tc_fun(_1529413, tc_HOL_Obool), _1529403), _1529417)))))], (10673 ^ _775212) ^ [_949500, _949502] : [-(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), _949500), _949502)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _949500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _949502))], (41802 ^ _775212) ^ [_1581595, _1581597, _1581599, _1581601, _1581603, _1581605, _1581607] : [c_Finite__Set_Ofun__left__comm(_1581595, _1581597, _1581599), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1581595, _1581597, _1581599, _1581601, _1581603), _1581605)), hBOOL(hAPP(hAPP(c_member(_1581595), _1581607), _1581603)), 41814 ^ _775212 : [(41817 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1581595, _1581597, _1581599, _1581601, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1581595, tc_HOL_Obool)), _1581603), hAPP(hAPP(c_Set_Oinsert(_1581595), _1581607), c_Orderings_Obot__class_Obot(tc_fun(_1581595, tc_HOL_Obool))))), 41813 ^ [_1581595, _1581597, _1581599, _1581601, _1581603, _1581605, _1581607])))], (41815 ^ _775212) ^ [] : [-(_1581605 = hAPP(hAPP(_1581599, _1581607), 41813 ^ [_1581595, _1581597, _1581599, _1581601, _1581603, _1581605, _1581607]))]]], (22782 ^ _775212) ^ [_1169011, _1169013, _1169015, _1169017, _1169019] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1169011, _1169013, _1169015), _1169017), _1169019) = hAPP(hAPP(_1169017, hAPP(c_Product__Type_Ofst(_1169011, _1169013), _1169019)), hAPP(c_Product__Type_Osnd(_1169011, _1169013), _1169019)))], (22732 ^ _775212) ^ [_1167804, _1167806, _1167808, _1167810] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1167804, _1167806, _1167808), hAPP(hAPP(c_COMBB(tc_fun(_1167806, tc_prod(_1167804, _1167806)), tc_fun(_1167806, _1167808), _1167804), hAPP(c_COMBB(tc_prod(_1167804, _1167806), _1167808, _1167806), _1167810)), c_Product__Type_OPair(_1167804, _1167806))) = _1167810)], (2474 ^ _775212) ^ [_811379, _811381, _811383, _811385, _811387, _811389] : [-(c_Nitpick_Oplus__frac(_811389, _811385, _811381) = c_Nitpick_Oplus__frac(_811387, _811383, _811379)), _811389 = _811387, _811385 = _811383, _811381 = _811379], (32491 ^ _775212) ^ [_1363809, _1363811, _1363813] : [class_Orderings_Olinorder(_1363809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363809), _1363811)), -(hBOOL(hAPP(hAPP(c_member(_1363809), _1363813), _1363811))), -(_1363811 = c_Orderings_Obot__class_Obot(tc_fun(_1363809, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1363809, c_Orderings_Oord__class_Omax(_1363809), hAPP(hAPP(c_Set_Oinsert(_1363809), _1363813), _1363811)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363809), _1363813), c_Big__Operators_Olattice_OSup__fin(_1363809, c_Orderings_Oord__class_Omax(_1363809), _1363811)))], (12187 ^ _775212) ^ [_975622, _975624, _975626] : [12188 ^ _775212 : [(12191 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975624), _975626))], (12189 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _975622)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975622), _975624)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975622), _975626))))], (48143 ^ _775212) ^ [_1736645, _1736647, _1736649] : [48145 ^ _775212 : [(48148 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1736645), tc_List_Olist(_1736645), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1736645), tc_fun(tc_List_Olist(_1736645), tc_Nat_Onat), tc_fun(tc_List_Olist(_1736645), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1736645), tc_Nat_Onat), tc_fun(tc_List_Olist(_1736645), tc_HOL_Obool)), tc_List_Olist(_1736645)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1736645))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1736645)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1736645))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1736645)))), 48144 ^ [_1736645, _1736647, _1736649]))], (48146 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1736645), tc_List_Olist(_1736645))), 48144 ^ [_1736645, _1736647, _1736649]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1736645), tc_List_Olist(_1736645))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1736645), tc_List_Olist(_1736645)), _1736647), _1736649)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1736645))), _1736647) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1736645))), _1736649), 48153 ^ _775212 : [(48160 ^ _775212) ^ [] : [_1736647 = _1736649, -(c_List_Oconcat(_1736645, _1736647) = c_List_Oconcat(_1736645, _1736649))], (48154 ^ _775212) ^ [] : [c_List_Oconcat(_1736645, _1736647) = c_List_Oconcat(_1736645, _1736649), -(_1736647 = _1736649)]]], (26001 ^ _775212) ^ [_1230518, _1230520, _1230522, _1230524] : [class_Groups_Ocomm__monoid__add(_1230518), 26004 ^ _775212 : [(26011 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1230520)), _1230522))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1230518), _1230524), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1230522, hAPP(c_Nat_OSuc, _1230520))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230518), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1230518), _1230524), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1230522, _1230520))), hAPP(_1230524, hAPP(c_Nat_OSuc, _1230520))))], (26005 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1230520)), _1230522)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1230518), _1230524), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1230522, hAPP(c_Nat_OSuc, _1230520))) = c_Groups_Ozero__class_Ozero(_1230518))]]], (17861 ^ _775212) ^ [_1078471, _1078473] : [class_Int_Onumber__ring(_1078471), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078471), hAPP(c_Int_Onumber__class_Onumber__of(_1078471), c_Int_OBit1(c_Int_OPls))), _1078473) = _1078473)], (52235 ^ _775212) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (39215 ^ _775212) ^ [_1516717] : [-(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)))), _1516717))))], (45194 ^ _775212) ^ [_1670047, _1670049] : [-(c_List_Osublist(_1670047, c_List_Olist_ONil(_1670047), _1670049) = c_List_Olist_ONil(_1670047))], (12446 ^ _775212) ^ [_979853, _979855, _979857, _979859] : [class_Divides_Osemiring__div(_979853), -(c_Divides_Odiv__class_Omod(_979853, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979853), _979855), _979857), _979859) = c_Divides_Odiv__class_Omod(_979853, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979853), _979855), c_Divides_Odiv__class_Omod(_979853, _979857, _979859)), _979859))], (25827 ^ _775212) ^ [_1226812, _1226814, _1226816, _1226818, _1226820] : [class_Orderings_Olinorder(_1226812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1226812, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1226812, _1226814), _1226816)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1226812, _1226818), _1226820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226812), _1226816), _1226814))), 25838 ^ _775212 : [(25841 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226812), _1226816), _1226820)))], (25839 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226812), _1226818), _1226814)))]]], (42079 ^ _775212) ^ [_1588392, _1588394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1588392), _1588394)), -(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), _1588392), _1588394)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (17695 ^ _775212) ^ [_1075776, _1075778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1075776)), c_Int_OBit1(_1075778))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075776), _1075778)))], (30833 ^ _775212) ^ [_1332007, _1332009] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1332007), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1332009)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332007), _1332009)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332009), _1332007)))], (27491 ^ _775212) ^ [_1260099, _1260101, _1260103, _1260105] : [class_Orderings_Olinorder(_1260099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260099), _1260101), _1260103)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260099), _1260103), _1260105)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260099, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1260099, _1260101, _1260103)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1260099, _1260103), _1260105)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1260099, _1260101, _1260105))], (7677 ^ _775212) ^ [_898181, _898183, _898185, _898187] : [class_Rings_Ocomm__semiring__1(_898181), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898181), _898183), _898185)), _898187) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898181), _898183), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898181), _898185), _898187)))], (17781 ^ _775212) ^ [_1077135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1077135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1077135))))], (52255 ^ _775212) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (32673 ^ _775212) ^ [_1367351, _1367353, _1367355] : [class_Orderings_Olinorder(_1367351), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367351), _1367353)), -(_1367353 = c_Orderings_Obot__class_Obot(tc_fun(_1367351, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367351), _1367355)), -(_1367355 = c_Orderings_Obot__class_Obot(tc_fun(_1367351, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1367351, c_Orderings_Oord__class_Omin(_1367351), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1367351, tc_HOL_Obool)), _1367353), _1367355)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367351), c_Big__Operators_Olattice_OInf__fin(_1367351, c_Orderings_Oord__class_Omin(_1367351), _1367353)), c_Big__Operators_Olattice_OInf__fin(_1367351, c_Orderings_Oord__class_Omin(_1367351), _1367355)))], (1324 ^ _775212) ^ [_794618, _794620] : [-(class_Rings_Oidom(_794618)), _794620 = _794618, class_Rings_Oidom(_794620)], (4970 ^ _775212) ^ [_850971, _850973, _850975, _850977] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850977, _850973) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850975, _850971)), _850977 = _850975, _850973 = _850971], (7865 ^ _775212) ^ [_901468, _901470] : [class_Groups_Ogroup__add(_901468), 7868 ^ _775212 : [(7875 ^ _775212) ^ [] : [c_Groups_Ozero__class_Ozero(_901468) = _901470, -(c_Groups_Ozero__class_Ozero(_901468) = hAPP(c_Groups_Ouminus__class_Ouminus(_901468), _901470))], (7869 ^ _775212) ^ [] : [c_Groups_Ozero__class_Ozero(_901468) = hAPP(c_Groups_Ouminus__class_Ouminus(_901468), _901470), -(c_Groups_Ozero__class_Ozero(_901468) = _901470)]]], (6130 ^ _775212) ^ [_872189] : [-(_872189 = 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)), _872189)))], (8213 ^ _775212) ^ [_907646, _907648] : [class_Groups_Ogroup__add(_907646), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907646), hAPP(c_Groups_Ouminus__class_Ouminus(_907646), _907648)), _907648) = c_Groups_Ozero__class_Ozero(_907646))], (5591 ^ _775212) ^ [_863229, _863231, _863233, _863235] : [c_Natural_Oevaln(_863229, _863231, _863233, _863235), -(c_Natural_Oevaln(_863229, _863231, hAPP(c_Nat_OSuc, _863233), _863235))], (47446 ^ _775212) ^ [_1721582, _1721584, _1721586, _1721588, _1721590, _1721592] : [class_Orderings_Olinorder(_1721582), -(hAPP(_1721584, _1721586) = hAPP(_1721584, _1721588)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1721590, _1721582, _1721584), _1721588), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1721590, _1721582, _1721584), _1721586), _1721592)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1721590, _1721582, _1721584), _1721586), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1721590, _1721582, _1721584), _1721588), _1721592)))], (5390 ^ _775212) ^ [_857437, _857439, _857441, _857443, _857445, _857447, _857449, _857451] : [-(c_Fun_Ocomp(_857451, _857447, _857443, _857439) = c_Fun_Ocomp(_857449, _857445, _857441, _857437)), _857451 = _857449, _857447 = _857445, _857443 = _857441, _857439 = _857437], (4626 ^ _775212) ^ [_845741, _845743, _845745, _845747] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_845747, _845743) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_845745, _845741)), _845747 = _845745, _845743 = _845741], (45377 ^ _775212) ^ [_1674897, _1674899, _1674901, _1674903] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1674897) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1674899), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1674897)), hAPP(hAPP(c_List_Olist_OCons(_1674899), _1674901), _1674903)) = hAPP(hAPP(c_List_Olist_OCons(_1674899), _1674901), hAPP(hAPP(c_List_Otake(_1674899), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1674897)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1674903)))], (17295 ^ _775212) ^ [_1069239] : [class_Int_Onumber__ring(_1069239), -(hAPP(c_Int_Onumber__class_Onumber__of(_1069239), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1069239))], (50977 ^ _775212) ^ [_1797779, _1797781] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1797779)), _1797781) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1797779, tc_Lazy__Sequence_Olazy__sequence(_1797779)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1797779, tc_Lazy__Sequence_Olazy__sequence(_1797779), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1797779), tc_Nat_Onat), _1797779), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1797779), 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(_1797779)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1797779)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1797779), _1797781)))], (27045 ^ _775212) ^ [_1251343, _1251345, _1251347] : [class_Lattices_Osemilattice__sup(_1251343), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251343), _1251345), _1251347) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251343), _1251347), _1251345))], (41608 ^ _775212) ^ [_1577258, _1577260] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1577258, _1577258)), _1577260)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1577258, _1577258)), c_Transitive__Closure_Otrancl(_1577258, _1577260))))], (49241 ^ _775212) ^ [_1760456, _1760458] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760456)), hAPP(c_List_Orev(_1760456), _1760458)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760456)), _1760458))], (7633 ^ _775212) ^ [_897316, _897318] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _897316), _897318) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _897318), _897316))], (7393 ^ _775212) ^ [_892756, _892758, _892760, _892762, _892764] : [c_Com_Ocom_OLocal(_892756, _892758, _892760) = c_Com_Ocom_OWhile(_892762, _892764)], (44100 ^ _775212) ^ [_1639567, _1639569, _1639571] : [c_FunDef_Ois__measure(_1639567, _1639569), -(c_FunDef_Ois__measure(tc_prod(_1639567, _1639571), hAPP(hAPP(c_COMBB(_1639567, tc_Nat_Onat, tc_prod(_1639567, _1639571)), _1639569), c_Product__Type_Ofst(_1639567, _1639571))))], (42812 ^ _775212) ^ [_1608829] : [-(c_Transitive__Closure_Ortrancl(_1608829, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1608829, _1608829), tc_HOL_Obool))) = c_Relation_OId(_1608829))], (28744 ^ _775212) ^ [_1285845, _1285847, _1285849, _1285851] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1285845, tc_fun(_1285847, tc_HOL_Obool)), _1285849), _1285851) = c_Orderings_Obot__class_Obot(tc_fun(_1285847, tc_HOL_Obool)), 28747 ^ _775212 : [(28748 ^ _775212) ^ [_1285961] : [hBOOL(hAPP(hAPP(c_member(_1285845), _1285961), _1285849)), -(hAPP(_1285851, _1285961) = c_Orderings_Obot__class_Obot(tc_fun(_1285847, tc_HOL_Obool)))]]], (32139 ^ _775212) ^ [_1356254, _1356256] : [class_Orderings_Olinorder(_1356254), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356254), _1356256)), -(_1356256 = c_Orderings_Obot__class_Obot(tc_fun(_1356254, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1356254), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356254), 32152 ^ [_1356254, _1356256]), 32153 ^ [_1356254, _1356256])), hAPP(hAPP(c_Set_Oinsert(_1356254), 32152 ^ [_1356254, _1356256]), hAPP(hAPP(c_Set_Oinsert(_1356254), 32153 ^ [_1356254, _1356256]), c_Orderings_Obot__class_Obot(tc_fun(_1356254, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1356254), c_Big__Operators_Olinorder__class_OMax(_1356254, _1356256)), _1356256)))], (33487 ^ _775212) ^ [_1384376, _1384378, _1384380] : [-(c_Wellfounded_Omlex__prod(_1384376, _1384378, _1384380) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1384376), _1384376), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1384376, c_Wellfounded_Oless__than, _1384380)), hAPP(hAPP(c_COMBS(_1384376, _1384376, tc_prod(tc_Nat_Onat, _1384376)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1384376, tc_prod(tc_Nat_Onat, _1384376)), _1384376), c_Product__Type_OPair(tc_Nat_Onat, _1384376)), _1384378)), c_COMBI(_1384376))))], (18239 ^ _775212) ^ [_1084899, _1084901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084899), _1084901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1084899)), c_Int_OBit1(_1084901))))], (19595 ^ _775212) ^ [_1108952, _1108954] : [class_Rings_Odivision__ring__inverse__zero(_1108952), 19598 ^ _775212 : [(19605 ^ _775212) ^ [] : [-(_1108954 = c_Groups_Ozero__class_Ozero(_1108952)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108952), _1108954), _1108954) = c_Groups_Oone__class_Oone(_1108952))], (19599 ^ _775212) ^ [] : [_1108954 = c_Groups_Ozero__class_Ozero(_1108952), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108952), _1108954), _1108954) = c_Groups_Ozero__class_Ozero(_1108952))]]], (50893 ^ _775212) ^ [_1795640, _1795642, _1795644, _1795646] : [-(hAPP(hAPP(c_List_Oappend(_1795640), c_List_Oreplicate(_1795640, _1795642, _1795644)), hAPP(hAPP(c_List_Olist_OCons(_1795640), _1795644), _1795646)) = hAPP(hAPP(c_List_Olist_OCons(_1795640), _1795644), hAPP(hAPP(c_List_Oappend(_1795640), c_List_Oreplicate(_1795640, _1795642, _1795644)), _1795646)))], (2922 ^ _775212) ^ [_818835, _818837, _818839, _818841, _818843, _818845, _818847, _818849] : [-(c_New__DSequence_Opos__bind(_818849, _818845, _818841, _818837) = c_New__DSequence_Opos__bind(_818847, _818843, _818839, _818835)), _818849 = _818847, _818845 = _818843, _818841 = _818839, _818837 = _818835], (29593 ^ _775212) ^ [_1302250, _1302252] : [-(hBOOL(hAPP(hAPP(c_member(_1302250), 29594 ^ [_1302250, _1302252]), _1302252))), -(_1302252 = c_Orderings_Obot__class_Obot(tc_fun(_1302250, tc_HOL_Obool)))], (49760 ^ _775212) ^ [_1771463, _1771465] : [-(hAPP(c_List_OremoveAll(_1771463, _1771465), c_List_Olist_ONil(_1771463)) = c_List_Olist_ONil(_1771463))], (31140 ^ _775212) ^ [_1338167, _1338169, _1338171, _1338173] : [-(c_Nitpick_Ofold__graph_H(_1338167, _1338169, _1338171, _1338173, c_Orderings_Obot__class_Obot(tc_fun(_1338167, tc_HOL_Obool)), _1338173))], (28830 ^ _775212) ^ [_1287579, _1287581, _1287583] : [class_Groups_Ocomm__monoid__add(_1287579), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1287581, _1287579), _1287583), c_Orderings_Obot__class_Obot(tc_fun(_1287581, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1287579))], (5112 ^ _775212) ^ [_853180, _853182, _853184, _853186, _853188, _853190] : [-(c_Relation_OImage(_853190, _853186, _853182) = c_Relation_OImage(_853188, _853184, _853180)), _853190 = _853188, _853186 = _853184, _853182 = _853180], (35045 ^ _775212) ^ [_1420011, _1420013, _1420015, _1420017] : [-(hBOOL(hAPP(hAPP(c_member(_1420011), _1420013), _1420015))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420011, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1420011), _1420013), _1420017)), _1420015) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420011, tc_HOL_Obool)), _1420017), _1420015))], (14323 ^ _775212) ^ [_1014130, _1014132, _1014134] : [class_Groups_Omonoid__mult(_1014130), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014130), hAPP(hAPP(c_Power_Opower__class_Opower(_1014130), _1014132), _1014134)), _1014132) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014130), _1014132), hAPP(hAPP(c_Power_Opower__class_Opower(_1014130), _1014132), _1014134)))], (27081 ^ _775212) ^ [_1252113, _1252115, _1252117, _1252119] : [class_Lattices_Osemilattice__sup(_1252113), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252113), _1252115), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252113), _1252117), _1252119)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252113), _1252117), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252113), _1252115), _1252119)))], (4178 ^ _775212) ^ [_838647, _838649, _838651, _838653, _838655, _838657] : [-(c_List_Osublist(_838657, _838653, _838649) = c_List_Osublist(_838655, _838651, _838647)), _838657 = _838655, _838653 = _838651, _838649 = _838647], (39587 ^ _775212) ^ [_1530331, _1530333, _1530335, _1530337, _1530339] : [-(hAPP(c_Relation_ORange(_1530331, _1530333), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1530331, _1530333)), hAPP(hAPP(c_Product__Type_OPair(_1530331, _1530333), _1530335), _1530337)), _1530339)) = hAPP(hAPP(c_Set_Oinsert(_1530333), _1530337), hAPP(c_Relation_ORange(_1530331, _1530333), _1530339)))], (18281 ^ _775212) ^ [_1085636, _1085638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1085636)), c_Int_OBit0(_1085638))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085636), _1085638)))], (28229 ^ _775212) ^ [_1275753, _1275755, _1275757] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1275753), _1275755)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1275753), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1275753, tc_HOL_Obool)), _1275755), _1275757))))], (5468 ^ _775212) ^ [_858664, _858666] : [_858666 = _858664, -(tc_List_Olist(_858666) = tc_List_Olist(_858664))], (19061 ^ _775212) ^ [_1099965, _1099967, _1099969] : [class_Fields_Ofield__inverse__zero(_1099965), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099965), hAPP(c_Groups_Ouminus__class_Ouminus(_1099965), _1099967)), hAPP(c_Groups_Ouminus__class_Ouminus(_1099965), _1099969)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099965), _1099967), _1099969))], (16935 ^ _775212) ^ [_1063738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1063738)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1063738))], (21533 ^ _775212) ^ [_1143881, _1143883, _1143885, _1143887] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1143881, _1143883), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1143885), _1143887))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1143881), _1143883), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1143887), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1143885)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1143885)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1143887), 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), _1143883), _1143887))))))], (5901 ^ _775212) ^ [_868677, _868679, _868681, _868683, _868685, _868687] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_868677, _868679, _868681), _868683, _868685, _868687), 5906 ^ _775212 : [(5909 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_868679, _868683, _868685, _868687))], (5907 ^ _775212) ^ [] : [-(hBOOL(hAPP(_868677, _868683)))]], 5910 ^ _775212 : [(5913 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_868681, _868683, _868685, _868687))], (5911 ^ _775212) ^ [] : [hBOOL(hAPP(_868677, _868683))]]], (1234 ^ _775212) ^ [_793493, _793495] : [-(class_Groups_Ogroup__add(_793493)), _793495 = _793493, class_Groups_Ogroup__add(_793495)], (50556 ^ _775212) ^ [_1789064, _1789066, _1789068, _1789070] : [-(c_List_Olist__all(_1789064, _1789066, hAPP(hAPP(c_List_Olist_OCons(_1789064), _1789068), _1789070))), hBOOL(hAPP(_1789066, _1789068)), c_List_Olist__all(_1789064, _1789066, _1789070)], (48103 ^ _775212) ^ [_1735833, _1735835, _1735837, _1735839] : [class_Orderings_Olinorder(_1735833), -(hAPP(c_List_Oset(_1735835), c_List_Olinorder__class_Osort__key(_1735835, _1735833, _1735837, _1735839)) = hAPP(c_List_Oset(_1735835), _1735839))], (17121 ^ _775212) ^ [_1066563, _1066565, _1066567] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066563))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066565)), _1066567)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066565)), _1066567))], (40330 ^ _775212) ^ [_1549406, _1549408, _1549410, _1549412] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1549406), _1549408)), 40336 ^ _775212 : [(40339 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1549410), hAPP(_1549412, 40335 ^ [_1549406, _1549408, _1549410, _1549412])))], (40337 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1549406), 40335 ^ [_1549406, _1549408, _1549410, _1549412]), _1549408)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1549410), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1549406, tc_fun(_1549410, tc_HOL_Obool)), _1549408), _1549412))))], (5690 ^ _775212) ^ [_864912, _864914, _864916, _864918, _864920] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_864912, _864914), _864916, _864918, _864920), 5694 ^ _775212 : [(5697 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_864914, 5693 ^ [_864912, _864914, _864916, _864918, _864920], _864918, _864920))], (5695 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_864912, _864916, _864918, 5693 ^ [_864912, _864914, _864916, _864918, _864920]))]]], (40758 ^ _775212) ^ [_1559315, _1559317, _1559319, _1559321, _1559323, _1559325] : [c_Finite__Set_Ofolding(_1559315, _1559317, _1559319, _1559321), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559315), _1559323)), -(hBOOL(hAPP(hAPP(c_member(_1559315), _1559325), _1559323))), -(hAPP(_1559321, hAPP(hAPP(c_Set_Oinsert(_1559315), _1559325), _1559323)) = hAPP(c_Fun_Ocomp(_1559317, _1559317, _1559317, hAPP(_1559321, _1559323)), hAPP(_1559319, _1559325)))], (11330 ^ _775212) ^ [_961232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _961232)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _961232)) = _961232)], (23756 ^ _775212) ^ [_1188121, _1188123] : [hAPP(c_Code__Numeral_Onat__of, _1188121) = hAPP(c_Code__Numeral_Onat__of, _1188123), -(_1188121 = _1188123)], (22722 ^ _775212) ^ [_1167556] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1167556), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1404 ^ _775212) ^ [_795618, _795620] : [-(class_Lattices_Odistrib__lattice(_795618)), _795620 = _795618, class_Lattices_Odistrib__lattice(_795620)], (3572 ^ _775212) ^ [_829196, _829198] : [_829198 = _829196, -(c_Set_OBall(_829198) = c_Set_OBall(_829196))], (9317 ^ _775212) ^ [_926058, _926060, _926062] : [class_Orderings_Oorder(_926058), 9320 ^ _775212 : [(9329 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926058), _926060), _926062))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926058), _926060), _926062)), -(_926060 = _926062)], (9321 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926058), _926060), _926062)), 9324 ^ _775212 : [(9327 ^ _775212) ^ [] : [_926060 = _926062], (9325 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926058), _926060), _926062)))]]]]], (28606 ^ _775212) ^ [_1283109, _1283111, _1283113] : [hAPP(hAPP(c_Set_Oinsert(_1283109), _1283111), c_Orderings_Obot__class_Obot(tc_fun(_1283109, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_1283109), _1283113), c_Orderings_Obot__class_Obot(tc_fun(_1283109, tc_HOL_Obool))), -(_1283111 = _1283113)], (35843 ^ _775212) ^ [_1437514, _1437516, _1437518, _1437520, _1437522, _1437524, _1437526, _1437528, _1437530] : [c_Equiv__Relations_Oequiv(_1437514, _1437516, _1437518), c_Equiv__Relations_Oequiv(_1437520, _1437522, _1437524), c_Equiv__Relations_Ocongruent2(_1437514, _1437520, tc_fun(_1437526, tc_HOL_Obool), _1437518, _1437524, _1437528), hBOOL(hAPP(hAPP(c_member(_1437520), _1437530), _1437522)), -(c_Equiv__Relations_Ocongruent(_1437514, tc_fun(_1437526, tc_HOL_Obool), _1437518, hAPP(hAPP(c_COMBB(tc_fun(_1437520, tc_fun(_1437526, tc_HOL_Obool)), tc_fun(_1437526, tc_HOL_Obool), _1437514), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1437520, tc_fun(_1437526, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1437520, _1437520, _1437524), hAPP(hAPP(c_Set_Oinsert(_1437520), _1437530), c_Orderings_Obot__class_Obot(tc_fun(_1437520, tc_HOL_Obool)))))), _1437528)))], (7953 ^ _775212) ^ [_903037, _903039, _903041] : [class_Groups_Ogroup__add(_903037), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903037), hAPP(c_Groups_Ouminus__class_Ouminus(_903037), _903039)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903037), _903039), _903041)) = _903041)], (45862 ^ _775212) ^ [_1686344, _1686346, _1686348, _1686350] : [-(hAPP(hAPP(c_List_Oappend(_1686344), hAPP(hAPP(c_List_Oappend(_1686344), _1686346), _1686348)), _1686350) = hAPP(hAPP(c_List_Oappend(_1686344), _1686346), hAPP(hAPP(c_List_Oappend(_1686344), _1686348), _1686350)))], (31727 ^ _775212) ^ [_1349346, _1349348] : [class_Orderings_Olinorder(_1349346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349346), _1349348)), -(_1349348 = c_Orderings_Obot__class_Obot(tc_fun(_1349346, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1349346), c_Big__Operators_Olinorder__class_OMin(_1349346, _1349348)), _1349348)))], (25258 ^ _775212) ^ [_1214685, _1214687] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1214685)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1214687))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214685), _1214687)))], (30080 ^ _775212) ^ [_1314186, _1314188, _1314190, _1314192, _1314194] : [hBOOL(hAPP(hAPP(c_member(_1314186), _1314188), _1314190)), -(hAPP(hAPP(c_Set_Oinsert(_1314192), hAPP(_1314194, _1314188)), hAPP(c_Set_Oimage(_1314186, _1314192, _1314194), _1314190)) = hAPP(c_Set_Oimage(_1314186, _1314192, _1314194), _1314190))], (47710 ^ _775212) ^ [_1727228, _1727230, _1727232, _1727234] : [c_List_Olist__all2(_1727228, _1727230, _1727232, _1727234, c_List_Olist_ONil(_1727230)), -(_1727234 = c_List_Olist_ONil(_1727228))], (39347 ^ _775212) ^ [_1522487, _1522489, _1522491] : [class_Orderings_Olinorder(_1522487), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522487), _1522489)), -(_1522489 = c_Orderings_Obot__class_Obot(tc_fun(_1522487, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1522487), _1522491), c_Big__Operators_Olattice_OSup__fin(_1522487, c_Orderings_Oord__class_Omax(_1522487), _1522489)) = c_Big__Operators_Olattice_OSup__fin(_1522487, c_Orderings_Oord__class_Omax(_1522487), hAPP(c_Set_OCollect(_1522487), hAPP(hAPP(c_COMBB(tc_fun(_1522487, tc_HOL_Obool), tc_HOL_Obool, _1522487), c_HOL_OEx(_1522487)), hAPP(hAPP(c_COMBC(_1522487, tc_fun(_1522487, tc_HOL_Obool), tc_fun(_1522487, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522487, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1522487, tc_HOL_Obool), tc_fun(_1522487, tc_HOL_Obool)), _1522487), c_COMBS(_1522487, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522487, tc_HOL_Obool), tc_fun(_1522487, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1522487), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522487), c_fconj)), hAPP(hAPP(c_COMBC(_1522487, tc_fun(_1522487, _1522487), tc_fun(_1522487, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522487, tc_HOL_Obool), tc_fun(tc_fun(_1522487, _1522487), tc_fun(_1522487, tc_HOL_Obool)), _1522487), c_COMBB(_1522487, tc_HOL_Obool, _1522487)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1522487), _1522491))))), hAPP(hAPP(c_COMBC(_1522487, tc_fun(_1522487, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522487)), _1522489))))))], (3642 ^ _775212) ^ [_830225, _830227, _830229, _830231, _830233, _830235, _830237, _830239, _830241, _830243] : [-(c_Finite__Set_Ofold__graph(_830243, _830239, _830235, _830231, _830227) = c_Finite__Set_Ofold__graph(_830241, _830237, _830233, _830229, _830225)), _830243 = _830241, _830239 = _830237, _830235 = _830233, _830231 = _830229, _830227 = _830225], (34503 ^ _775212) ^ [_1408443, _1408445, _1408447, _1408449] : [class_Lattices_Odistrib__lattice(_1408443), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408443), _1408445), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408443), _1408447), _1408449)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408443), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408443), _1408445), _1408447)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408443), _1408445), _1408449)))], (26535 ^ _775212) ^ [_1241614, _1241616] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1241614, _1241616) = 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), _1241614), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241616))))], (32862 ^ _775212) ^ [_1371144, _1371146, _1371148, _1371150, _1371152] : [hAPP(_1371144, _1371146) = _1371148, -(c_Fun_Ofun__upd(_1371150, _1371152, _1371144, _1371146, _1371148) = _1371144)], (44734 ^ _775212) ^ [_1658581, _1658583, _1658585] : [c_Fun_Oinj__on(_1658581, _1658583, _1658585, c_Orderings_Otop__class_Otop(tc_fun(_1658581, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1658581), tc_List_Olist(_1658583), hAPP(c_List_Omap(_1658581, _1658583), _1658585), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1658581), tc_HOL_Obool))))], (25398 ^ _775212) ^ [_1217201, _1217203] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1217201))), _1217203)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217201), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217203))))], (42209 ^ _775212) ^ [_1591316, _1591318, _1591320, _1591322, _1591324] : [class_Complete__Lattice_Ocomplete__lattice(_1591316), class_Orderings_Olinorder(_1591316), 42216 ^ _775212 : [(42226 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1591316), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591318, _1591316), _1591320), _1591322)), _1591324))), 42227 ^ _775212 : [(42228 ^ _775212) ^ [_1591664] : [hBOOL(hAPP(hAPP(c_member(_1591318), _1591664), _1591320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1591316), hAPP(_1591322, _1591664)), _1591324))]]], (42217 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1591316), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591318, _1591316), _1591320), _1591322)), _1591324)), 42221 ^ _775212 : [(42224 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1591316), hAPP(_1591322, 42220 ^ [_1591316, _1591318, _1591320, _1591322, _1591324])), _1591324)))], (42222 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591318), 42220 ^ [_1591316, _1591318, _1591320, _1591322, _1591324]), _1591320)))]]]]], (16531 ^ _775212) ^ [_1056449, _1056451, _1056453] : [class_Rings_Olinordered__idom(_1056449), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056449), c_Groups_Ozero__class_Ozero(_1056449)), hAPP(hAPP(c_Power_Opower__class_Opower(_1056449), hAPP(c_Groups_Oabs__class_Oabs(_1056449), _1056451)), _1056453))))], (40083 ^ _775212) ^ [_1543468, _1543470] : [-(c_List_Olex(_1543468, _1543470) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1543468), tc_List_Olist(_1543468)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1543468, _1543470)))], (40343 ^ _775212) ^ [_1549693, _1549695] : [40345 ^ _775212 : [(40348 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1549695), 40344 ^ [_1549693, _1549695]))], (40346 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 40344 ^ [_1549693, _1549695]), _1549693)))]], -(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)), _1549695), _1549693))], (3386 ^ _775212) ^ [_826233, _826235, _826237, _826239, _826241, _826243, _826245, _826247] : [-(c_Random__Sequence_Omap(_826247, _826243, _826239, _826235) = c_Random__Sequence_Omap(_826245, _826241, _826237, _826233)), _826247 = _826245, _826243 = _826241, _826239 = _826237, _826235 = _826233], (29458 ^ _775212) ^ [_1299677, _1299679, _1299681, _1299683] : [hBOOL(hAPP(hAPP(c_member(_1299677), _1299679), hAPP(hAPP(c_Set_Oinsert(_1299677), _1299681), _1299683))), -(_1299679 = _1299681), -(hBOOL(hAPP(hAPP(c_member(_1299677), _1299679), _1299683)))], (7627 ^ _775212) ^ [_897207, _897209, _897211] : [class_Rings_Ocomm__semiring__1(_897207), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897207), _897209), _897211) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897207), _897211), _897209))], (31045 ^ _775212) ^ [_1336088, _1336090, _1336092, _1336094] : [hBOOL(hAPP(hAPP(_1336092, _1336094), _1336090)), -(hBOOL(hAPP(hAPP(c_member(_1336088), _1336090), c_SetInterval_Oord_OatLeast(_1336088, _1336092, _1336094))))], (32894 ^ _775212) ^ [_1371795, _1371797, _1371799, _1371801] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1371795), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371797, tc_Nat_Onat), _1371799), _1371801)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371797, _1371795), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1371795, _1371797), c_Nat_Osemiring__1__class_Oof__nat(_1371795)), _1371799)), _1371801)), class_Groups_Ocomm__monoid__mult(_1371795), class_Rings_Osemiring__1(_1371795)], (41332 ^ _775212) ^ [_1572075, _1572077, _1572079, _1572081, _1572083] : [c_Finite__Set_Ofolding__one__idem(_1572075, _1572077, _1572079), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572075), _1572081)), -(hAPP(_1572079, hAPP(hAPP(c_Set_Oinsert(_1572075), _1572083), _1572081)) = hAPP(hAPP(c_Finite__Set_Ofold(_1572075, _1572075, _1572077), _1572083), _1572081))], (36499 ^ _775212) ^ [_1452790, _1452792, _1452794, _1452796, _1452798] : [c_Fun_Oinj__on(_1452790, _1452792, _1452794, _1452796), -(c_Fun_Oinj__on(_1452790, _1452792, _1452794, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1452790, tc_HOL_Obool)), _1452796), _1452798)))], (9451 ^ _775212) ^ [_928024, _928026, _928028] : [class_Orderings_Olinorder(_928024), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928024), _928026), _928028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928024), _928028), _928026))], (18465 ^ _775212) ^ [_1088865] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1088865)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1088865)))], (52219 ^ _775212) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (33789 ^ _775212) ^ [_1391537, _1391539, _1391541] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1391537, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1391537, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1391537), _1391539)), hAPP(c_Set_OPow(_1391537), _1391541))), hAPP(c_Set_OPow(_1391537), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391537, tc_HOL_Obool)), _1391539), _1391541)))))], (1938 ^ _775212) ^ [_802311, _802313, _802315, _802317, _802319, _802321, _802323, _802325] : [-(c_Natural_Oevaln(_802323, _802319, _802315, _802311)), c_Natural_Oevaln(_802325, _802321, _802317, _802313), _802325 = _802323, _802321 = _802319, _802317 = _802315, _802313 = _802311], (37736 ^ _775212) ^ [_1479663, _1479665, _1479667, _1479669] : [-(c_Wellfounded_Omax__extp(_1479663, _1479665, _1479667, _1479669)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479663), _1479667)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479663), _1479669)), -(_1479669 = c_Orderings_Obot__class_Obot(tc_fun(_1479663, tc_HOL_Obool))), 37750 ^ _775212 : [(37753 ^ _775212) ^ [_1480008] : [hBOOL(hAPP(hAPP(c_member(_1479663), _1480008), _1479669)), hBOOL(hAPP(hAPP(_1479665, 37749 ^ [_1479663, _1479665, _1479667, _1479669]), _1480008))], (37751 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1479663), 37749 ^ [_1479663, _1479665, _1479667, _1479669]), _1479667)))]]], (43284 ^ _775212) ^ [_1620098] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620098, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1620098, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1620098, tc_HOL_Obool)))], (38383 ^ _775212) ^ [_1496734, _1496736] : [class_Orderings_Olinorder(_1496734), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496734), _1496736)), -(c_Big__Operators_Olattice_OSup__fin(_1496734, c_Orderings_Oord__class_Omax(_1496734), _1496736) = hAPP(c_Finite__Set_Ofold1(_1496734, c_Orderings_Oord__class_Omax(_1496734)), _1496736))], (28309 ^ _775212) ^ [_1277113, _1277115] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1277113, _1277115)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1277113, _1277115), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1277115), c_Orderings_Otop__class_Otop(tc_fun(_1277115, tc_HOL_Obool)))))], (23434 ^ _775212) ^ [_1181676, _1181678, _1181680, _1181682, _1181684, _1181686, _1181688] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1181676, _1181678, _1181680, _1181682), _1181684), _1181686), _1181688) = hAPP(hAPP(_1181686, hAPP(c_Product__Type_Ofst(_1181678, _1181680), hAPP(_1181684, _1181688))), hAPP(c_Product__Type_Osnd(_1181678, _1181680), hAPP(_1181684, _1181688))))], (51215 ^ _775212) ^ [_1803283, _1803285, _1803287] : [51217 ^ _775212 : [(51220 ^ _775212) ^ [] : [hBOOL(hAPP(_1803283, 51216 ^ [_1803283, _1803285, _1803287]))], (51218 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 51216 ^ [_1803283, _1803285, _1803287]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1803285, _1803287))))]], -(c_List_Oall__interval__int(_1803283, _1803285, _1803287))], (52253 ^ _775212) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (33594 ^ _775212) ^ [_1387314, _1387316, _1387318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1387314, _1387314), tc_HOL_Obool)), _1387316), _1387318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387314, tc_HOL_Obool)), hAPP(c_Relation_OField(_1387314), _1387316)), hAPP(c_Relation_OField(_1387314), _1387318))))], (19541 ^ _775212) ^ [_1108087, _1108089, _1108091, _1108093, _1108095] : [class_Fields_Ofield(_1108087), -(_1108089 = c_Groups_Ozero__class_Ozero(_1108087)), -(_1108091 = c_Groups_Ozero__class_Ozero(_1108087)), 19552 ^ _775212 : [(19559 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108087), _1108093), _1108091) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108087), _1108095), _1108089), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108087), _1108093), _1108089) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108087), _1108095), _1108091))], (19553 ^ _775212) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108087), _1108093), _1108089) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108087), _1108095), _1108091), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108087), _1108093), _1108091) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108087), _1108095), _1108089))]]], (16183 ^ _775212) ^ [_1049513, _1049515, _1049517] : [class_Groups_Oordered__ab__group__add__abs(_1049513), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049513), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049513), hAPP(c_Groups_Oabs__class_Oabs(_1049513), _1049515)), hAPP(c_Groups_Oabs__class_Oabs(_1049513), _1049517))), hAPP(c_Groups_Oabs__class_Oabs(_1049513), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049513), _1049515), _1049517)))))], (37878 ^ _775212) ^ [_1483483, _1483485, _1483487] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1483483, _1483485), c_Orderings_Obot__class_Obot(tc_fun(_1483483, tc_HOL_Obool))), _1483487) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1483483, _1483485), tc_HOL_Obool)))], (45690 ^ _775212) ^ [_1682682, _1682684, _1682686, _1682688] : [-(hAPP(hAPP(c_List_Oappend(_1682682), hAPP(hAPP(c_List_Olist_OCons(_1682682), _1682684), _1682686)), _1682688) = hAPP(hAPP(c_List_Olist_OCons(_1682682), _1682684), hAPP(hAPP(c_List_Oappend(_1682682), _1682686), _1682688)))], (14521 ^ _775212) ^ [_1017874, _1017876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017874)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1017874)), _1017876) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1017874), _1017876)))], (28273 ^ _775212) ^ [_1276467, _1276469, _1276471] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276467), _1276471)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1276467), hAPP(hAPP(c_Set_Oinsert(_1276467), _1276469), _1276471))))], (48448 ^ _775212) ^ [_1745327, _1745329] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1745327), _1745329))), -(c_List_Oupt(_1745327, _1745329) = c_List_Olist_ONil(tc_Nat_Onat))], (9999 ^ _775212) ^ [_937291, _937293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _937291), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _937291), _937293)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _937291))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _937293))))], (34569 ^ _775212) ^ [_1410157, _1410159, _1410161, _1410163] : [class_Lattices_Osemilattice__inf(_1410157), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410157), _1410159), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1410157), _1410161), _1410163))), 34576 ^ _775212 : [(34579 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410157), _1410159), _1410163)))], (34577 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410157), _1410159), _1410161)))]]], (16965 ^ _775212) ^ [_1064135, _1064137] : [class_Int_Onumber__ring(_1064135), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064135), _1064137), hAPP(c_Int_Onumber__class_Onumber__of(_1064135), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1064135), _1064137))], (42385 ^ _775212) ^ [_1596534, _1596536, _1596538, _1596540, _1596542] : [class_Complete__Lattice_Ocomplete__lattice(_1596534), 42388 ^ _775212 : [(42389 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1596534), _1596536), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596538, _1596534), _1596540), _1596542))), 42392 ^ _775212 : [(42393 ^ _775212) ^ [_1596715] : [hBOOL(hAPP(hAPP(c_member(_1596538), _1596715), _1596540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1596534), _1596536), hAPP(_1596542, _1596715))))]]], (42399 ^ _775212) ^ [] : [42401 ^ _775212 : [(42404 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1596534), _1596536), hAPP(_1596542, 42400 ^ [_1596534, _1596536, _1596538, _1596540, _1596542])))], (42402 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1596538), 42400 ^ [_1596534, _1596536, _1596538, _1596540, _1596542]), _1596540)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1596534), _1596536), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596538, _1596534), _1596540), _1596542))))]]], (45335 ^ _775212) ^ [_1674108, _1674110, _1674112] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1674108)), -(c_List_Osublist(_1674110, hAPP(hAPP(c_List_Olist_OCons(_1674110), _1674112), c_List_Olist_ONil(_1674110)), _1674108) = hAPP(hAPP(c_List_Olist_OCons(_1674110), _1674112), c_List_Olist_ONil(_1674110)))], (36497 ^ _775212) ^ [_1452767] : [-(c_Equiv__Relations_Oequivp(_1452767, c_fequal))], (11664 ^ _775212) ^ [_966705, _966707, _966709, _966711] : [class_Orderings_Oord(_966705), 11667 ^ _775212 : [(11676 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_966707, _966705)), _966709), _966711))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966707, _966705)), _966709), _966711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966707, _966705)), _966711), _966709)))], (11668 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_966707, _966705)), _966709), _966711)), 11671 ^ _775212 : [(11674 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966707, _966705)), _966711), _966709))], (11672 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966707, _966705)), _966709), _966711)))]]]]], (13443 ^ _775212) ^ [_998164, _998166, _998168] : [-(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), _998164), _998166)), _998168), _998166) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _998168, _998166))], (49281 ^ _775212) ^ [_1761329, _1761331, _1761333] : [-(hAPP(c_List_Orotate(_1761329, _1761331), hAPP(c_List_Orev(_1761329), _1761333)) = hAPP(c_List_Orev(_1761329), hAPP(c_List_Orotate(_1761329, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761329)), _1761333)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1761331, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761329)), _1761333)))), _1761333)))], (25096 ^ _775212) ^ [_1211639, _1211641, _1211643, _1211645, _1211647, _1211649, _1211651] : [-(c_New__Random__Sequence_Opos__decr__bind(_1211639, _1211641, _1211643, _1211645, _1211647, _1211649, _1211651) = c_New__DSequence_Opos__decr__bind(_1211639, _1211641, hAPP(hAPP(hAPP(_1211643, _1211647), _1211649), _1211651), hAPP(hAPP(c_COMBC(_1211639, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1211641))), hAPP(hAPP(c_COMBC(_1211639, 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(_1211641)))), hAPP(hAPP(c_COMBC(_1211639, 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(_1211641))))), _1211645), _1211647)), _1211649)), _1211651)))], (34481 ^ _775212) ^ [_1407750, _1407752, _1407754, _1407756] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407750, tc_HOL_Obool)), _1407752), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407750, tc_HOL_Obool)), _1407754), _1407756)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407750, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407750, tc_HOL_Obool)), _1407752), _1407754)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407750, tc_HOL_Obool)), _1407752), _1407756)))], (30136 ^ _775212) ^ [_1315358, _1315360, _1315362, _1315364, _1315366] : [-(hBOOL(hAPP(hAPP(c_member(_1315358), _1315360), c_SetInterval_Oord_OgreaterThanLessThan(_1315358, _1315362, _1315364, _1315366)))), hBOOL(hAPP(hAPP(_1315362, _1315364), _1315360)), hBOOL(hAPP(hAPP(_1315362, _1315360), _1315366))], (18313 ^ _775212) ^ [_1086229, _1086231] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1086229)), c_Int_OBit0(_1086231)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1086229), _1086231)))], (39083 ^ _775212) ^ [_1511402, _1511404, _1511406, _1511408, _1511410] : [class_Groups_Ocomm__monoid__add(_1511402), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511404), _1511406)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511404, _1511402), _1511408), hAPP(c_Set_OCollect(_1511404), hAPP(hAPP(c_COMBS(_1511404, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511404), c_fconj), hAPP(hAPP(c_COMBC(_1511404, tc_fun(_1511404, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511404)), _1511406))), hAPP(hAPP(c_COMBC(_1511404, tc_fun(_1511404, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511404)), _1511410)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511404, _1511402), hAPP(hAPP(c_COMBC(_1511404, _1511402, _1511402), hAPP(hAPP(c_COMBS(_1511404, _1511402, tc_fun(_1511402, _1511402)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1511402, tc_fun(_1511402, _1511402)), _1511404), c_If(_1511402)), hAPP(hAPP(c_COMBC(_1511404, tc_fun(_1511404, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511404)), _1511410))), _1511408)), c_Groups_Ozero__class_Ozero(_1511402))), _1511406))], (52063 ^ _775212) ^ [_1821380, _1821382, _1821384] : [hAPP(c_Fun_Ocomp(_1821382, _1821380, _1821380, c_Hilbert__Choice_Oinv__into(_1821380, _1821382, c_Orderings_Otop__class_Otop(tc_fun(_1821380, tc_HOL_Obool)), _1821384)), _1821384) = c_Fun_Oid(_1821380), -(c_Fun_Oinj__on(_1821380, _1821382, _1821384, c_Orderings_Otop__class_Otop(tc_fun(_1821380, tc_HOL_Obool))))], (37980 ^ _775212) ^ [_1486639, _1486641, _1486643, _1486645, _1486647, _1486649] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486639, _1486641)), hAPP(hAPP(c_Product__Type_OPair(_1486639, _1486641), _1486643), _1486645)), hAPP(hAPP(c_Product__Type_OSigma(_1486639, _1486641), _1486647), _1486649)))), hBOOL(hAPP(hAPP(c_member(_1486639), _1486643), _1486647)), hBOOL(hAPP(hAPP(c_member(_1486641), _1486645), hAPP(_1486649, _1486643)))], (30009 ^ _775212) ^ [_1312646, _1312648, _1312650, _1312652, _1312654] : [hBOOL(hAPP(hAPP(c_member(_1312646), _1312648), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312650, tc_fun(_1312646, tc_HOL_Obool)), _1312652), _1312654))), 30013 ^ _775212 : [(30016 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1312646), _1312648), hAPP(_1312654, 30012 ^ [_1312646, _1312648, _1312650, _1312652, _1312654]))))], (30014 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1312650), 30012 ^ [_1312646, _1312648, _1312650, _1312652, _1312654]), _1312652)))]]], (15949 ^ _775212) ^ [_1045363, _1045365] : [class_Int_Onumber__ring(_1045363), -(hAPP(c_Int_Oring__1__class_Oof__int(_1045363), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1045365)) = hAPP(c_Int_Onumber__class_Onumber__of(_1045363), _1045365))], (22336 ^ _775212) ^ [_1160041, _1160043] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160041), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1160043)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1160041)) = 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), _1160043), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1160041)))), 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)))], (10235 ^ _775212) ^ [_941559, _941561, _941563] : [class_Rings_Oordered__cancel__semiring(_941559), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941559), c_Groups_Ozero__class_Ozero(_941559)), _941561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941559), c_Groups_Ozero__class_Ozero(_941559)), _941563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941559), c_Groups_Ozero__class_Ozero(_941559)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941559), _941561), _941563))))], (50499 ^ _775212) ^ [_1788035, _1788037, _1788039] : [c_List_Olist__all(_1788035, _1788037, hAPP(c_List_Orev(_1788035), _1788039)), -(c_List_Olist__all(_1788035, _1788037, _1788039))], (7903 ^ _775212) ^ [_902074, _902076, _902078] : [class_Groups_Oordered__ab__group__add(_902074), 7906 ^ _775212 : [(7913 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902074), hAPP(c_Groups_Ouminus__class_Ouminus(_902074), _902078)), _902076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902074), hAPP(c_Groups_Ouminus__class_Ouminus(_902074), _902076)), _902078)))], (7907 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902074), hAPP(c_Groups_Ouminus__class_Ouminus(_902074), _902076)), _902078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902074), hAPP(c_Groups_Ouminus__class_Ouminus(_902074), _902078)), _902076)))]]], (38761 ^ _775212) ^ [_1503884, _1503886, _1503888] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503884), _1503886)), 38767 ^ _775212 : [(38770 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1503888, 38766 ^ [_1503884, _1503886, _1503888])))], (38768 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503884), 38766 ^ [_1503884, _1503886, _1503888]), _1503886)))]], -(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(_1503884, tc_Nat_Onat), _1503888), _1503886))))], (21707 ^ _775212) ^ [_1147134, _1147136, _1147138] : [_1147134 = _1147136, 21710 ^ _775212 : [(21713 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1147138, tc_HOL_Obool)), _1147136), _1147134)))], (21711 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1147138, tc_HOL_Obool)), _1147134), _1147136)))]]], (14787 ^ _775212) ^ [_1022774, _1022776, _1022778] : [class_Rings_Ocomm__semiring__1(_1022774), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1022774), _1022776), hAPP(c_Nat_OSuc, _1022778)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022774), _1022776), hAPP(hAPP(c_Power_Opower__class_Opower(_1022774), _1022776), _1022778)))], (44637 ^ _775212) ^ [_1655889, _1655891, _1655893, _1655895] : [_1655889 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1655891), hAPP(hAPP(c_List_Olist_OCons(_1655891), _1655893), _1655895)), _1655889) = _1655893)], (1564 ^ _775212) ^ [_797618, _797620] : [-(class_Groups_Ocancel__ab__semigroup__add(_797618)), _797620 = _797618, class_Groups_Ocancel__ab__semigroup__add(_797620)], (37610 ^ _775212) ^ [_1476525, _1476527, _1476529] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1476525, hAPP(hAPP(c_COMBC(_1476525, tc_fun(tc_prod(_1476525, _1476525), tc_HOL_Obool), tc_fun(_1476525, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476525, tc_fun(tc_fun(tc_prod(_1476525, _1476525), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1476525, _1476525), tc_HOL_Obool), tc_fun(_1476525, tc_HOL_Obool)), _1476525), c_COMBC(_1476525, tc_fun(tc_prod(_1476525, _1476525), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476525, tc_prod(_1476525, _1476525)), tc_fun(_1476525, tc_fun(tc_fun(tc_prod(_1476525, _1476525), tc_HOL_Obool), tc_HOL_Obool)), _1476525), hAPP(c_COMBB(tc_prod(_1476525, _1476525), tc_fun(tc_fun(tc_prod(_1476525, _1476525), tc_HOL_Obool), tc_HOL_Obool), _1476525), c_member(tc_prod(_1476525, _1476525)))), c_Product__Type_OPair(_1476525, _1476525)))), _1476527)), _1476529)), -(hBOOL(hAPP(hAPP(c_member(_1476525), _1476529), c_Wellfounded_Oacc(_1476525, _1476527))))], (5364 ^ _775212) ^ [_857046, _857048, _857050, _857052, _857054, _857056] : [-(c_Product__Type_Oprod_Oprod__case(_857056, _857052, _857048) = c_Product__Type_Oprod_Oprod__case(_857054, _857050, _857046)), _857056 = _857054, _857052 = _857050, _857048 = _857046], (3532 ^ _775212) ^ [_828592, _828594, _828596, _828598] : [-(c_New__DSequence_Opos__single(_828598, _828594) = c_New__DSequence_Opos__single(_828596, _828592)), _828598 = _828596, _828594 = _828592], (17907 ^ _775212) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (43474 ^ _775212) ^ [_1624499, _1624501, _1624503] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1624499, tc_HOL_Obool)), _1624501), _1624503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1624499, tc_HOL_Obool)), _1624501), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1624499, tc_HOL_Obool), _1624503))))], (11284 ^ _775212) ^ [_960495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _960495), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _960495) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9179 ^ _775212) ^ [_923878] : [class_Rings_Oring__1(_923878), -(hAPP(c_Int_Oring__1__class_Oof__int(_923878), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_923878))], (39617 ^ _775212) ^ [_1532037, _1532039, _1532041, _1532043] : [hBOOL(hAPP(hAPP(c_member(_1532037), _1532039), hAPP(c_Relation_ORange(_1532041, _1532037), _1532043))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532041, _1532037)), hAPP(hAPP(c_Product__Type_OPair(_1532041, _1532037), 39620 ^ [_1532037, _1532039, _1532041, _1532043]), _1532039)), _1532043)))], (22740 ^ _775212) ^ [_1168034, _1168036, _1168038, _1168040, _1168042] : [-(hAPP(c_Product__Type_Ofst(_1168034, _1168036), hAPP(c_Product__Type_Oapsnd(_1168038, _1168036, _1168034, _1168040), _1168042)) = hAPP(c_Product__Type_Ofst(_1168034, _1168038), _1168042))], (30885 ^ _775212) ^ [_1333004, _1333006, _1333008, _1333010] : [hBOOL(hAPP(hAPP(_1333008, _1333006), _1333010)), -(hBOOL(hAPP(hAPP(c_member(_1333004), _1333006), c_SetInterval_Oord_OlessThan(_1333004, _1333008, _1333010))))], (47486 ^ _775212) ^ [_1722441, _1722443, _1722445] : [-(c_List_Olistsp(_1722441, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1722441, tc_HOL_Obool)), _1722443), _1722445)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1722441), tc_HOL_Obool)), c_List_Olistsp(_1722441, _1722443)), c_List_Olistsp(_1722441, _1722445)))], (11889 ^ _775212) ^ [_970446, _970448, _970450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970446), _970448)), _970450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970448), _970450)))], (39017 ^ _775212) ^ [_1509382, _1509384, _1509386] : [hBOOL(hAPP(_1509382, _1509384)), -(hAPP(c_Set_OCollect(_1509386), hAPP(hAPP(c_COMBS(_1509386, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509386), c_fconj), hAPP(c_fequal, _1509384))), _1509382)) = hAPP(hAPP(c_Set_Oinsert(_1509386), _1509384), c_Orderings_Obot__class_Obot(tc_fun(_1509386, tc_HOL_Obool))))], (34741 ^ _775212) ^ [_1413231, _1413233, _1413235, _1413237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413231, tc_HOL_Obool)), _1413233), _1413235)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413231, tc_HOL_Obool)), _1413233), _1413237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413231, tc_HOL_Obool)), _1413233), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413231, tc_HOL_Obool)), _1413235), _1413237))))], (41279 ^ _775212) ^ [_1570958, _1570960, _1570962, _1570964] : [class_Orderings_Olinorder(_1570958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570958), _1570960)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1570958, _1570958, c_Orderings_Oord__class_Omax(_1570958)), _1570962), hAPP(hAPP(c_Set_Oinsert(_1570958), _1570964), _1570960)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1570958), _1570964), hAPP(hAPP(c_Finite__Set_Ofold(_1570958, _1570958, c_Orderings_Oord__class_Omax(_1570958)), _1570962), _1570960)))], (35589 ^ _775212) ^ [_1432476, _1432478, _1432480] : [class_Lattices_Olattice(_1432476), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432476), _1432478)), -(_1432478 = c_Orderings_Obot__class_Obot(tc_fun(_1432476, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432476), _1432480)), -(_1432480 = c_Orderings_Obot__class_Obot(tc_fun(_1432476, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432476, tc_HOL_Obool)), _1432478), _1432480) = c_Orderings_Obot__class_Obot(tc_fun(_1432476, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1432476, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1432476, tc_HOL_Obool)), _1432478), _1432480)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1432476), c_Big__Operators_Olattice__class_OSup__fin(_1432476, _1432478)), c_Big__Operators_Olattice__class_OSup__fin(_1432476, _1432480)))], (48629 ^ _775212) ^ [_1748887, _1748889] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1748887, _1748889)))], (48657 ^ _775212) ^ [_1749288, _1749290] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1749288, _1749290)))], (23892 ^ _775212) ^ [_1190470] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1190470)))], (13539 ^ _775212) ^ [_999769, _999771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _999769)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _999769), _999771)), _999769) = _999771)], (52397 ^ _775212) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (48454 ^ _775212) ^ [_1745373, _1745375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1745373), _1745375)), -(c_List_Oupt(_1745373, _1745375) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1745373), c_List_Oupt(hAPP(c_Nat_OSuc, _1745373), _1745375)))], (49412 ^ _775212) ^ [_1764226, _1764228, _1764230, _1764232, _1764234] : [-(hBOOL(hAPP(_1764226, _1764228))), -(c_List_OtakeWhile(_1764230, _1764226, hAPP(hAPP(c_List_Oappend(_1764230), _1764232), hAPP(hAPP(c_List_Olist_OCons(_1764230), _1764228), _1764234))) = c_List_OtakeWhile(_1764230, _1764226, _1764232))], (39426 ^ _775212) ^ [_1525747, _1525749] : [-(c_Product__Type_Omap__pair(_1525747, _1525747, _1525749, _1525749, c_Fun_Oid(_1525747), c_Fun_Oid(_1525749)) = c_Fun_Oid(tc_prod(_1525747, _1525749)))], (47352 ^ _775212) ^ [_1719558, _1719560, _1719562] : [class_Orderings_Olinorder(_1719558), hBOOL(hAPP(c_Finite__Set_Ofinite(_1719558), _1719560)), -(c_List_Olinorder__class_Osorted__list__of__set(_1719558, hAPP(hAPP(c_Set_Oinsert(_1719558), _1719562), _1719560)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1719558, _1719558, c_COMBI(_1719558)), _1719562), c_List_Olinorder__class_Osorted__list__of__set(_1719558, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1719558, tc_HOL_Obool)), _1719560), hAPP(hAPP(c_Set_Oinsert(_1719558), _1719562), c_Orderings_Obot__class_Obot(tc_fun(_1719558, tc_HOL_Obool)))))))], (2856 ^ _775212) ^ [_817762, _817764, _817766, _817768, _817770, _817772, _817774, _817776] : [-(c_Lazy__Sequence_Ohb__bind(_817776, _817772, _817768, _817764) = c_Lazy__Sequence_Ohb__bind(_817774, _817770, _817766, _817762)), _817776 = _817774, _817772 = _817770, _817768 = _817766, _817764 = _817762], (22826 ^ _775212) ^ [_1170065, _1170067, _1170069, _1170071, _1170073, _1170075, _1170077] : [-(hAPP(c_Product__Type_Oapfst(_1170065, _1170067, _1170069, _1170071), hAPP(c_Product__Type_Oapsnd(_1170073, _1170069, _1170065, _1170075), _1170077)) = hAPP(hAPP(c_Product__Type_OPair(_1170067, _1170069), hAPP(_1170071, hAPP(c_Product__Type_Ofst(_1170065, _1170073), _1170077))), hAPP(_1170075, hAPP(c_Product__Type_Osnd(_1170065, _1170073), _1170077))))], (40586 ^ _775212) ^ [_1555315, _1555317, _1555319, _1555321, _1555323, _1555325] : [class_Groups_Ocomm__monoid__mult(_1555315), c_Fun_Oinj__on(_1555317, _1555319, _1555321, _1555323), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555319, _1555315), _1555325), hAPP(c_Set_Oimage(_1555317, _1555319, _1555321), _1555323)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555317, _1555315), hAPP(c_Fun_Ocomp(_1555319, _1555315, _1555317, _1555325), _1555321)), _1555323))], (47108 ^ _775212) ^ [_1714397, _1714399] : [-(_1714397 = c_List_Olist_ONil(_1714399)), hBOOL(hAPP(c_List_Odistinct(_1714399), _1714397)), -(hBOOL(hAPP(c_List_Odistinct(_1714399), c_List_Obutlast(_1714399, _1714397))))], (37118 ^ _775212) ^ [_1465768, _1465770, _1465772, _1465774, _1465776] : [-(hAPP(c_Fun_Othe__inv__into(_1465768, _1465770, _1465772, _1465774), _1465776) = c_HOL_OThe(_1465768, hAPP(hAPP(c_COMBS(_1465768, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1465768), c_fconj), hAPP(hAPP(c_COMBC(_1465768, tc_fun(_1465768, tc_HOL_Obool), tc_HOL_Obool), c_member(_1465768)), _1465772))), hAPP(hAPP(c_COMBC(_1465768, _1465770, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1465770, tc_fun(_1465770, tc_HOL_Obool), _1465768), c_fequal), _1465774)), _1465776))))], (36165 ^ _775212) ^ [_1446278, _1446280, _1446282] : [class_Lattices_Olattice(_1446278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446278), _1446280)), hBOOL(hAPP(hAPP(c_member(_1446278), _1446282), _1446280)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1446278), _1446282), c_Big__Operators_Olattice__class_OInf__fin(_1446278, _1446280)) = _1446282)], (49490 ^ _775212) ^ [_1765711, _1765713] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1765711), _1765713) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1765711)), c_List_Oembed__list(_1765713))))], (24794 ^ _775212) ^ [_1205987] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1205987), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1205987 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (52241 ^ _775212) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (28249 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (33461 ^ _775212) ^ [_1383821, _1383823] : [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), _1383821), _1383823)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1383821), _1383823)))], (29985 ^ _775212) ^ [_1311841, _1311843, _1311845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1311841, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1311841, tc_fun(_1311841, tc_HOL_Obool), tc_HOL_Obool), c_member(_1311841)), _1311843)), hAPP(hAPP(c_COMBC(_1311841, tc_fun(_1311841, tc_HOL_Obool), tc_HOL_Obool), c_member(_1311841)), _1311845))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1311841, tc_HOL_Obool)), _1311843), _1311845)))], (48386 ^ _775212) ^ [_1743842, _1743844, _1743846] : [class_Groups_Oab__semigroup__add(_1743842), -(c_List_Ofoldr(_1743842, _1743842, c_Groups_Oplus__class_Oplus(_1743842), _1743844, _1743846) = hAPP(c_List_Ofoldl(_1743842, _1743842, c_Groups_Oplus__class_Oplus(_1743842), _1743846), _1743844))], (4490 ^ _775212) ^ [_843523, _843525, _843527, _843529] : [-(c_List_Olex(_843529, _843525) = c_List_Olex(_843527, _843523)), _843529 = _843527, _843525 = _843523], (35273 ^ _775212) ^ [_1425322, _1425324, _1425326, _1425328] : [class_Orderings_Olinorder(_1425322), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425322, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1425322), _1425324)), c_SetInterval_Oord__class_OatLeastAtMost(_1425322, _1425326, _1425328)) = c_SetInterval_Oord__class_OatLeastAtMost(_1425322, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1425322), _1425324), _1425326), _1425328))], (30040 ^ _775212) ^ [_1313355, _1313357, _1313359] : [_1313357 = _1313359, -(hBOOL(hAPP(hAPP(c_member(_1313355), _1313357), hAPP(hAPP(c_Set_Oinsert(_1313355), _1313359), c_Orderings_Obot__class_Obot(tc_fun(_1313355, tc_HOL_Obool))))))], (39630 ^ _775212) ^ [_1532867, _1532869, _1532871, _1532873, _1532875, _1532877, _1532879] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532867, _1532871)), hAPP(hAPP(c_Product__Type_OPair(_1532867, _1532871), _1532877), _1532879)), hAPP(hAPP(c_Relation_Orel__comp(_1532867, _1532869, _1532871), _1532873), _1532875))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1532867, _1532869, _1532871, hAPP(hAPP(c_COMBC(_1532867, tc_fun(tc_prod(_1532867, _1532869), tc_HOL_Obool), tc_fun(_1532869, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532869, tc_fun(tc_fun(tc_prod(_1532867, _1532869), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1532867, _1532869), tc_HOL_Obool), tc_fun(_1532869, tc_HOL_Obool)), _1532867), c_COMBC(_1532869, tc_fun(tc_prod(_1532867, _1532869), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532869, tc_prod(_1532867, _1532869)), tc_fun(_1532869, tc_fun(tc_fun(tc_prod(_1532867, _1532869), tc_HOL_Obool), tc_HOL_Obool)), _1532867), hAPP(c_COMBB(tc_prod(_1532867, _1532869), tc_fun(tc_fun(tc_prod(_1532867, _1532869), tc_HOL_Obool), tc_HOL_Obool), _1532869), c_member(tc_prod(_1532867, _1532869)))), c_Product__Type_OPair(_1532867, _1532869)))), _1532873), hAPP(hAPP(c_COMBC(_1532869, tc_fun(tc_prod(_1532869, _1532871), tc_HOL_Obool), tc_fun(_1532871, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532871, tc_fun(tc_fun(tc_prod(_1532869, _1532871), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1532869, _1532871), tc_HOL_Obool), tc_fun(_1532871, tc_HOL_Obool)), _1532869), c_COMBC(_1532871, tc_fun(tc_prod(_1532869, _1532871), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532871, tc_prod(_1532869, _1532871)), tc_fun(_1532871, tc_fun(tc_fun(tc_prod(_1532869, _1532871), tc_HOL_Obool), tc_HOL_Obool)), _1532869), hAPP(c_COMBB(tc_prod(_1532869, _1532871), tc_fun(tc_fun(tc_prod(_1532869, _1532871), tc_HOL_Obool), tc_HOL_Obool), _1532871), c_member(tc_prod(_1532869, _1532871)))), c_Product__Type_OPair(_1532869, _1532871)))), _1532875)), _1532877), _1532879)))], (33467 ^ _775212) ^ [_1383926, _1383928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1383926), _1383928)), -(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), _1383926), _1383928)), c_Wellfounded_Oless__than)))], (31101 ^ _775212) ^ [_1337295, _1337297, _1337299, _1337301, _1337303, _1337305, _1337307] : [hBOOL(hAPP(hAPP(c_member(_1337295), _1337297), _1337299)), c_Nitpick_Ofold__graph_H(_1337295, _1337301, _1337303, _1337305, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1337295, tc_HOL_Obool)), _1337299), hAPP(hAPP(c_Set_Oinsert(_1337295), _1337297), c_Orderings_Obot__class_Obot(tc_fun(_1337295, tc_HOL_Obool)))), _1337307), -(c_Nitpick_Ofold__graph_H(_1337295, _1337301, _1337303, _1337305, _1337299, hAPP(hAPP(_1337303, _1337297), _1337307)))], (28446 ^ _775212) ^ [_1279797, _1279799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279797), c_Orderings_Otop__class_Otop(tc_fun(_1279797, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1279797), _1279799) = hAPP(c_Finite__Set_Ocard(_1279797), c_Orderings_Otop__class_Otop(tc_fun(_1279797, tc_HOL_Obool))), -(_1279799 = c_Orderings_Otop__class_Otop(tc_fun(_1279797, tc_HOL_Obool)))], (36567 ^ _775212) ^ [_1454212, _1454214, _1454216, _1454218, _1454220, _1454222] : [c_Fun_Oinj__on(_1454212, _1454214, _1454216, _1454218), hBOOL(hAPP(hAPP(c_member(_1454212), _1454220), _1454218)), hBOOL(hAPP(hAPP(c_member(_1454212), _1454222), _1454218)), 36578 ^ _775212 : [(36585 ^ _775212) ^ [] : [_1454220 = _1454222, -(hAPP(_1454216, _1454220) = hAPP(_1454216, _1454222))], (36579 ^ _775212) ^ [] : [hAPP(_1454216, _1454220) = hAPP(_1454216, _1454222), -(_1454220 = _1454222)]]], (33360 ^ _775212) ^ [_1381299, _1381301, _1381303, _1381305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1381299), _1381301)), -(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), _1381299), _1381303)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1381301), _1381305))), c_FunDef_Opair__leq)))], (14305 ^ _775212) ^ [_1013701, _1013703, _1013705, _1013707] : [class_Divides_Oring__div(_1013701), -(c_Divides_Odiv__class_Omod(_1013701, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1013701), _1013703), _1013705), _1013707) = c_Divides_Odiv__class_Omod(_1013701, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1013701), c_Divides_Odiv__class_Omod(_1013701, _1013703, _1013707)), _1013705), _1013707))], (23666 ^ _775212) ^ [_1186691, _1186693] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1186691), _1186693) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1186691, 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)))), _1186693))))], (47234 ^ _775212) ^ [_1716903, _1716905, _1716907, _1716909] : [_1716903 = _1716905, -(c_List_Oremove1(_1716907, _1716903, hAPP(hAPP(c_List_Olist_OCons(_1716907), _1716905), _1716909)) = _1716909)], (22158 ^ _775212) ^ [_1155786, _1155788] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1155786), hAPP(c_Nat_OSuc, _1155788)) = 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), _1155786), _1155788)))], (42279 ^ _775212) ^ [_1593572, _1593574, _1593576] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1593572, _1593574)), hAPP(c_Relation_Oconverse(_1593574, _1593572), _1593576))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1593574, _1593572)), _1593576)))], (18029 ^ _775212) ^ [_1081061, _1081063] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1081061)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1081063)), _1081061) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1081063), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1081061), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (10031 ^ _775212) ^ [_937941, _937943, _937945] : [class_Rings_Ocomm__semiring__1(_937941), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937941), _937943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937941), _937945), _937943)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937941), _937945), c_Groups_Oone__class_Oone(_937941))), _937943))], (35695 ^ _775212) ^ [_1434474, _1434476, _1434478] : [class_Orderings_Olinorder(_1434474), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434474), _1434476)), -(_1434476 = c_Orderings_Obot__class_Obot(tc_fun(_1434474, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434474), _1434478)), -(_1434478 = c_Orderings_Obot__class_Obot(tc_fun(_1434474, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434474, tc_HOL_Obool)), _1434476), _1434478) = c_Orderings_Obot__class_Obot(tc_fun(_1434474, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1434474, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1434474, tc_HOL_Obool)), _1434476), _1434478)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1434474), c_Big__Operators_Olinorder__class_OMax(_1434474, _1434476)), c_Big__Operators_Olinorder__class_OMax(_1434474, _1434478)))], (21715 ^ _775212) ^ [_1147301, _1147303, _1147305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1147301, tc_HOL_Obool)), _1147303), _1147305)), 21718 ^ _775212 : [(21721 ^ _775212) ^ [] : [_1147303 = _1147305], (21719 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1147301, tc_HOL_Obool)), _1147303), _1147305)))]]], (41871 ^ _775212) ^ [_1583488, _1583490] : [-(c_Transitive__Closure_Ortrancl(_1583488, c_Transitive__Closure_Ortrancl(_1583488, _1583490)) = c_Transitive__Closure_Ortrancl(_1583488, _1583490))], (3810 ^ _775212) ^ [_832989, _832991] : [_832991 = _832989, -(c_Random_Orange(_832991) = c_Random_Orange(_832989))], (26367 ^ _775212) ^ [_1238247, _1238249] : [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)), _1238247)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238249))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1238247), _1238249)))], (47122 ^ _775212) ^ [_1714646, _1714648, _1714650] : [hBOOL(hAPP(hAPP(c_member(_1714646), _1714648), hAPP(c_List_Oset(_1714646), c_List_Obutlast(_1714646, _1714650)))), -(hBOOL(hAPP(hAPP(c_member(_1714646), _1714648), hAPP(c_List_Oset(_1714646), _1714650))))], (33600 ^ _775212) ^ [_1387459, _1387461, _1387463] : [-(hAPP(c_Relation_OField(_1387459), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1387459, _1387459), tc_HOL_Obool)), _1387461), _1387463)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1387459, tc_HOL_Obool)), hAPP(c_Relation_OField(_1387459), _1387461)), hAPP(c_Relation_OField(_1387459), _1387463)))], (20371 ^ _775212) ^ [] : [-(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))], (9987 ^ _775212) ^ [_937100] : [class_Rings_Olinordered__semidom(_937100), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937100), c_Groups_Ozero__class_Ozero(_937100)), c_Groups_Oone__class_Oone(_937100))))], (41600 ^ _775212) ^ [_1577096, _1577098] : [-(hAPP(c_Relation_ORange(_1577096, _1577096), c_Transitive__Closure_Otrancl(_1577096, _1577098)) = hAPP(c_Relation_ORange(_1577096, _1577096), _1577098))], (12843 ^ _775212) ^ [_987069, _987071, _987073] : [hBOOL(hAPP(_987069, c_Divides_Odiv__class_Omod(tc_Int_Oint, _987071, _987073))), 12846 ^ _775212 : [(12871 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987073), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 12874 ^ _775212 : [(12875 ^ _775212) ^ [_987691, _987693] : [-(hBOOL(hAPP(_987069, _987691))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987073), _987691)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _987691), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _987071 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _987073), _987693)), _987691)]]], (12853 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _987073)), 12856 ^ _775212 : [(12857 ^ _775212) ^ [_987399, _987401] : [-(hBOOL(hAPP(_987069, _987399))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _987399)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987399), _987073)), _987071 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _987073), _987401)), _987399)]]], (12847 ^ _775212) ^ [] : [_987073 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_987069, _987071)))]]], (32079 ^ _775212) ^ [_1354844, _1354846, _1354848] : [class_Lattices_Olattice(_1354844), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354844), _1354846)), 32086 ^ _775212 : [(32093 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354844, tc_HOL_Obool)), _1354846), hAPP(hAPP(c_Set_Oinsert(_1354844), _1354848), c_Orderings_Obot__class_Obot(tc_fun(_1354844, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1354844, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1354844, hAPP(hAPP(c_Set_Oinsert(_1354844), _1354848), _1354846)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1354844), _1354848), c_Big__Operators_Olattice__class_OSup__fin(_1354844, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354844, tc_HOL_Obool)), _1354846), hAPP(hAPP(c_Set_Oinsert(_1354844), _1354848), c_Orderings_Obot__class_Obot(tc_fun(_1354844, tc_HOL_Obool)))))))], (32087 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354844, tc_HOL_Obool)), _1354846), hAPP(hAPP(c_Set_Oinsert(_1354844), _1354848), c_Orderings_Obot__class_Obot(tc_fun(_1354844, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1354844, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1354844, hAPP(hAPP(c_Set_Oinsert(_1354844), _1354848), _1354846)) = _1354848)]]], (33949 ^ _775212) ^ [_1395037, _1395039, _1395041, _1395043, _1395045] : [class_Groups_Ocomm__monoid__add(_1395037), class_Groups_Oordered__cancel__ab__semigroup__add(_1395037), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395039), _1395041)), -(_1395041 = c_Orderings_Obot__class_Obot(tc_fun(_1395039, tc_HOL_Obool))), 33967 ^ _775212 : [(33970 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395037), hAPP(_1395043, 33966 ^ [_1395037, _1395039, _1395041, _1395043, _1395045])), hAPP(_1395045, 33966 ^ [_1395037, _1395039, _1395041, _1395043, _1395045])))], (33968 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1395039), 33966 ^ [_1395037, _1395039, _1395041, _1395043, _1395045]), _1395041)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395037), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1395039, _1395037), _1395043), _1395041)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1395039, _1395037), _1395045), _1395041))))], (47991 ^ _775212) ^ [_1733612, _1733614] : [-(c_List_Oremdups(_1733612, c_List_Oremdups(_1733612, _1733614)) = c_List_Oremdups(_1733612, _1733614))], (11879 ^ _775212) ^ [_970255, _970257, _970259, _970261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970255), _970257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970259), _970261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970255), _970259)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970257), _970261))))], (15153 ^ _775212) ^ [_1029924, _1029926, _1029928, _1029930, _1029932, _1029934] : [class_Rings_Oordered__ring(_1029924), 15156 ^ _775212 : [(15163 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029924), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029924), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029924), _1029926), _1029932)), _1029928)), _1029930)), _1029934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029924), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029924), _1029926), _1029928)), _1029930)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029924), _1029932), _1029928)), _1029934))))], (15157 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029924), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029924), _1029926), _1029928)), _1029930)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029924), _1029932), _1029928)), _1029934))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029924), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029924), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029924), _1029926), _1029932)), _1029928)), _1029930)), _1029934)))]]], (5707 ^ _775212) ^ [_865213, _865215, _865217, _865219] : [-(hAPP(hAPP(c_Power_Opower_Opower(_865213, _865215, _865217), _865219), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _865215)], (21895 ^ _775212) ^ [_1150635, _1150637, _1150639, _1150641, _1150643] : [-(c_Product__Type_Oprod_Oprod__size(_1150635, _1150637, _1150639, _1150641, _1150643) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1150639, hAPP(c_Product__Type_Ofst(_1150635, _1150637), _1150643))), hAPP(_1150641, hAPP(c_Product__Type_Osnd(_1150635, _1150637), _1150643)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (52315 ^ _775212) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (40417 ^ _775212) ^ [_1551589, _1551591] : [40418 ^ _775212 : [(40419 ^ _775212) ^ [_1551635] : [hBOOL(hAPP(_1551589, _1551635))]], -(hBOOL(hAPP(_1551589, c_Hilbert__Choice_OEps(_1551591, _1551589))))], (3720 ^ _775212) ^ [_831546, _831548, _831550, _831552] : [-(c_Wellfounded_Oacc(_831552, _831548) = c_Wellfounded_Oacc(_831550, _831546)), _831552 = _831550, _831548 = _831546], (23408 ^ _775212) ^ [_1181148] : [-(c_Nitpick_Oone__frac(_1181148) = c_Nitpick_OAbs__Frac(_1181148, 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))))], (52237 ^ _775212) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (12195 ^ _775212) ^ [_975784, _975786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975784)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975786)), 12202 ^ _775212 : [(12209 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _975784), _975786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _975784)), hAPP(c_Int_Onat, _975786))))], (12203 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _975784)), hAPP(c_Int_Onat, _975786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _975784), _975786)))]]], (52361 ^ _775212) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (33797 ^ _775212) ^ [_1391769, _1391771, _1391773] : [-(hAPP(c_Set_OPow(_1391769), hAPP(hAPP(c_Set_Oinsert(_1391769), _1391771), _1391773)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1391769, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1391769), _1391773)), hAPP(c_Set_Oimage(tc_fun(_1391769, tc_HOL_Obool), tc_fun(_1391769, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1391769), _1391771)), hAPP(c_Set_OPow(_1391769), _1391773))))], (32159 ^ _775212) ^ [_1356698, _1356700] : [class_Orderings_Olinorder(_1356698), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356698), _1356700)), -(_1356700 = c_Orderings_Obot__class_Obot(tc_fun(_1356698, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1356698), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1356698), 32172 ^ [_1356698, _1356700]), 32173 ^ [_1356698, _1356700])), hAPP(hAPP(c_Set_Oinsert(_1356698), 32172 ^ [_1356698, _1356700]), hAPP(hAPP(c_Set_Oinsert(_1356698), 32173 ^ [_1356698, _1356700]), c_Orderings_Obot__class_Obot(tc_fun(_1356698, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1356698), c_Big__Operators_Olinorder__class_OMin(_1356698, _1356700)), _1356700)))], (6238 ^ _775212) ^ [_873733, _873735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873733), _873735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _873733)), hAPP(c_Nat_OSuc, _873735))))], (7793 ^ _775212) ^ [_900355, _900357, _900359] : [class_Rings_Osemiring__1(_900355), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_900355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _900357), _900359)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_900355), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_900355), _900357)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_900355), _900359)))], (37042 ^ _775212) ^ [_1464236] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1464236))], (7771 ^ _775212) ^ [_899971, _899973, _899975] : [class_Groups_Ogroup__add(_899971), 7774 ^ _775212 : [(7781 ^ _775212) ^ [] : [_899973 = _899975, -(hAPP(c_Groups_Ouminus__class_Ouminus(_899971), _899973) = hAPP(c_Groups_Ouminus__class_Ouminus(_899971), _899975))], (7775 ^ _775212) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_899971), _899973) = hAPP(c_Groups_Ouminus__class_Ouminus(_899971), _899975), -(_899973 = _899975)]]], (2980 ^ _775212) ^ [_819756, _819758, _819760, _819762, _819764, _819766, _819768, _819770] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_819770, _819766, _819762, _819758) = c_SetInterval_Oord_OgreaterThanLessThan(_819768, _819764, _819760, _819756)), _819770 = _819768, _819766 = _819764, _819762 = _819760, _819758 = _819756], (18437 ^ _775212) ^ [_1088393, _1088395] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1088393)), _1088395) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1088393), _1088395))), _1088395))], (39365 ^ _775212) ^ [_1523159] : [-(c_Int_Oint__ge__less__than2(_1523159) = 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), _1523159)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (25472 ^ _775212) ^ [_1218596, _1218598] : [class_Orderings_Oorder(_1218596), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1218596, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1218598), -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1218596, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218598))], (35125 ^ _775212) ^ [_1422097, _1422099, _1422101, _1422103] : [class_Orderings_Oorder(_1422097), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422097, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1422097, _1422099, _1422101)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1422097, _1422101, _1422103)) = c_Orderings_Obot__class_Obot(tc_fun(_1422097, tc_HOL_Obool)))], (3954 ^ _775212) ^ [_835187, _835189, _835191, _835193, _835195, _835197] : [-(c_Big__Operators_Olattice_OInf__fin(_835197, _835193, _835189) = c_Big__Operators_Olattice_OInf__fin(_835195, _835191, _835187)), _835197 = _835195, _835193 = _835191, _835189 = _835187], (11808 ^ _775212) ^ [_968996, _968998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968996), _968998)), -(_968996 = _968998), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968996), _968998)))], (43156 ^ _775212) ^ [_1617413, _1617415, _1617417, _1617419, _1617421] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617413, _1617413)), hAPP(hAPP(c_Product__Type_OPair(_1617413, _1617413), _1617415), _1617417)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617413, _1617413), tc_HOL_Obool), _1617419), _1617421))), 43161 ^ _775212 : [(43164 ^ _775212) ^ [] : [-(_1617415 = _1617417)], (43162 ^ _775212) ^ [] : [-(_1617419 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 43167 ^ _775212 : [(43172 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617413, _1617413)), hAPP(hAPP(c_Product__Type_OPair(_1617413, _1617413), 43165 ^ [_1617413, _1617415, _1617417, _1617419, _1617421]), _1617417)), _1617421)))], (43170 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617413, _1617413)), hAPP(hAPP(c_Product__Type_OPair(_1617413, _1617413), _1617415), 43165 ^ [_1617413, _1617415, _1617417, _1617419, _1617421])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617413, _1617413), tc_HOL_Obool), 43166 ^ [_1617413, _1617415, _1617417, _1617419, _1617421]), _1617421))))], (43168 ^ _775212) ^ [] : [-(_1617419 = hAPP(c_Nat_OSuc, 43166 ^ [_1617413, _1617415, _1617417, _1617419, _1617421]))]]], (48546 ^ _775212) ^ [_1746973, _1746975] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1746973, _1746975)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1746973), hAPP(c_Nat_OSuc, _1746975)))], (26150 ^ _775212) ^ [_1233546, _1233548, _1233550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233546)), 26153 ^ _775212 : [(26154 ^ _775212) ^ [_1233680] : [26156 ^ _775212 : [(26162 ^ _775212) ^ [] : [-(_1233680 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26158 ^ [_1233546, _1233548, _1233550, _1233680]), 26155 ^ [_1233546, _1233548, _1233550, _1233680]))], (26160 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26158 ^ [_1233546, _1233548, _1233550, _1233680]), _1233548)))], (26157 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26155 ^ [_1233546, _1233548, _1233550, _1233680]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1233546))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233550), _1233680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1233680), _1233546))))]]], (47038 ^ _775212) ^ [_1712849, _1712851] : [-(_1712849 = c_List_Olist_ONil(_1712851)), -(c_List_Olast(_1712851, _1712849) = hAPP(hAPP(c_List_Onth(_1712851), _1712849), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712851)), _1712849)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (39057 ^ _775212) ^ [_1510323, _1510325, _1510327] : [-(hAPP(c_Set_OCollect(_1510323), hAPP(hAPP(c_COMBS(_1510323, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510323), c_fimplies), _1510325)), _1510327)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1510323, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1510323, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1510323), _1510325))), hAPP(c_Set_OCollect(_1510323), _1510327)))], (16449 ^ _775212) ^ [_1054796, _1054798, _1054800] : [class_Rings_Olinordered__idom(_1054796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054796), c_Groups_Ozero__class_Ozero(_1054796)), _1054798)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054796), hAPP(c_Groups_Oabs__class_Oabs(_1054796), _1054800)), _1054798) = hAPP(c_Groups_Oabs__class_Oabs(_1054796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054796), _1054800), _1054798)))], (1724 ^ _775212) ^ [_799618, _799620] : [-(class_Nat_Osemiring__char__0(_799618)), _799620 = _799618, class_Nat_Osemiring__char__0(_799620)], (6913 ^ _775212) ^ [_885306, _885308, _885310] : [class_Rings_Olinordered__semidom(_885306), 6916 ^ _775212 : [(6923 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885308), _885310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885306), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_885306), _885308)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_885306), _885310))))], (6917 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885306), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_885306), _885308)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_885306), _885310))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885308), _885310)))]]], (44883 ^ _775212) ^ [_1661940, _1661942, _1661944] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1661940, tc_HOL_Obool)), hAPP(c_List_Oset(_1661940), c_List_Osublist(_1661940, _1661942, _1661944))), hAPP(c_List_Oset(_1661940), _1661942))))], (50369 ^ _775212) ^ [_1785186, _1785188, _1785190, _1785192] : [c_List_Olist__ex(_1785186, _1785188, hAPP(hAPP(c_List_Oappend(_1785186), _1785190), _1785192)), -(c_List_Olist__ex(_1785186, _1785188, _1785190)), -(c_List_Olist__ex(_1785186, _1785188, _1785192))], (29302 ^ _775212) ^ [_1296195, _1296197, _1296199] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1296195), _1296197)), -(hAPP(c_Finite__Set_Ocard(_1296195), hAPP(hAPP(c_Set_Oinsert(_1296195), _1296199), _1296197)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1296195), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1296195, tc_HOL_Obool)), _1296197), hAPP(hAPP(c_Set_Oinsert(_1296195), _1296199), c_Orderings_Obot__class_Obot(tc_fun(_1296195, tc_HOL_Obool)))))))], (49175 ^ _775212) ^ [_1759114, _1759116, _1759118] : [-(hAPP(c_List_Orev(_1759114), hAPP(c_List_Ofilter(_1759114, _1759116), _1759118)) = hAPP(c_List_Ofilter(_1759114, _1759116), hAPP(c_List_Orev(_1759114), _1759118)))], (39765 ^ _775212) ^ [_1536188, _1536190, _1536192] : [c_Wellfounded_Owf(_1536188, _1536190), hBOOL(hAPP(hAPP(c_member(tc_prod(_1536188, _1536188)), hAPP(hAPP(c_Product__Type_OPair(_1536188, _1536188), _1536192), _1536192)), _1536190))], (21295 ^ _775212) ^ [_1140053, _1140055] : [-(_1140053 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1140055, _1140053) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1140055), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1140053)))], (38953 ^ _775212) ^ [_1507867, _1507869] : [-(hAPP(c_Set_OCollect(_1507867), hAPP(hAPP(c_COMBC(_1507867, tc_fun(_1507867, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507867)), _1507869)) = _1507869)], (50617 ^ _775212) ^ [_1790280, _1790282, _1790284, _1790286, _1790288] : [-(c_List_Osplice(_1790280, hAPP(hAPP(c_List_Olist_OCons(_1790280), _1790282), _1790284), hAPP(hAPP(c_List_Olist_OCons(_1790280), _1790286), _1790288)) = hAPP(hAPP(c_List_Olist_OCons(_1790280), _1790282), hAPP(hAPP(c_List_Olist_OCons(_1790280), _1790286), c_List_Osplice(_1790280, _1790284, _1790288))))], (21777 ^ _775212) ^ [_1148446, _1148448, _1148450, _1148452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1148446, tc_HOL_Obool)), _1148448), _1148450)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1148446, tc_HOL_Obool)), _1148450), _1148452)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1148446, tc_HOL_Obool)), _1148450), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1148446, tc_HOL_Obool)), _1148452), _1148448)) = _1148448)], (22688 ^ _775212) ^ [_1166854, _1166856, _1166858, _1166860] : [class_Orderings_Olinorder(_1166854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166854), _1166856), _1166858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166854), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166854), _1166856), _1166860)), _1166858)))], (35069 ^ _775212) ^ [_1420407, _1420409, _1420411, _1420413] : [hBOOL(hAPP(hAPP(c_member(_1420407), _1420409), _1420411)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420407, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1420407), _1420409), _1420413)), _1420411) = hAPP(hAPP(c_Set_Oinsert(_1420407), _1420409), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420407, tc_HOL_Obool)), _1420413), _1420411)))], (45700 ^ _775212) ^ [_1683029, _1683031, _1683033, _1683035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683029)), _1683031)), _1683033)), -(hAPP(hAPP(c_List_Olist__update(_1683029, _1683031), _1683033), _1683035) = _1683031)], (18929 ^ _775212) ^ [] : [-(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)))], (11686 ^ _775212) ^ [_967097] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _967097)))], (12085 ^ _775212) ^ [_973812] : [-(hAPP(c_Nat_OSuc, _973812) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973812), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (21869 ^ _775212) ^ [_1150182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150182)), 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), _1150182)) = 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), _1150182))))))], (49494 ^ _775212) ^ [_1765782, _1765784, _1765786] : [hBOOL(hAPP(c_List_Odistinct(_1765782), _1765784)), hBOOL(hAPP(hAPP(c_member(_1765782), _1765786), hAPP(c_List_Oset(_1765782), _1765784))), -(c_List_OtakeWhile(_1765782, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1765782), c_fNot), hAPP(hAPP(c_COMBC(_1765782, _1765782, tc_HOL_Obool), c_fequal), _1765786)), hAPP(c_List_Orev(_1765782), _1765784)) = hAPP(c_List_Orev(_1765782), hAPP(c_List_Otl(_1765782), c_List_OdropWhile(_1765782, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1765782), c_fNot), hAPP(hAPP(c_COMBC(_1765782, _1765782, tc_HOL_Obool), c_fequal), _1765786)), _1765784))))], (45355 ^ _775212) ^ [_1674467, _1674469, _1674471, _1674473] : [-(_1674467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1674469), _1674467), hAPP(hAPP(c_List_Olist_OCons(_1674469), _1674471), _1674473)) = hAPP(hAPP(c_List_Olist_OCons(_1674469), _1674471), hAPP(hAPP(c_List_Otake(_1674469), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1674467), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1674473)))], (30046 ^ _775212) ^ [_1313497, _1313499, _1313501, _1313503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313497, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1313497), _1313499), _1313501)), _1313503)), 30049 ^ _775212 : [(30052 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313497, tc_HOL_Obool)), _1313501), _1313503)))], (30050 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1313497), _1313499), _1313503)))]]], (8872 ^ _775212) ^ [_919055, _919057, _919059, _919061, _919063] : [class_Orderings_Oord(_919055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919057, _919055)), _919059), _919061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919055), hAPP(_919059, _919063)), hAPP(_919061, _919063))))], (25080 ^ _775212) ^ [_1211395, _1211397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211395)), 25083 ^ _775212 : [(25090 ^ _775212) ^ [] : [_1211397 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211397), _1211395)), _1211395)))], (25084 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211397), _1211395)), _1211395)), -(_1211397 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (6359 ^ _775212) ^ [_875696, _875698, _875700, _875702] : [class_Orderings_Oorder(_875696), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875696), hAPP(_875698, 6364 ^ [_875696, _875698, _875700, _875702])), hAPP(_875698, hAPP(c_Nat_OSuc, 6364 ^ [_875696, _875698, _875700, _875702])))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _875700), _875702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875696), hAPP(_875698, _875700)), hAPP(_875698, _875702))))], (22590 ^ _775212) ^ [_1165133, _1165135, _1165137, _1165139] : [class_Orderings_Olinorder(_1165133), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165133), _1165135), _1165137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165133), _1165135), _1165139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165133), _1165135), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165133), _1165137), _1165139))))], (9729 ^ _775212) ^ [_932577, _932579, _932581] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932577), _932579) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932577), _932581), -(_932579 = _932581), -(_932577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17277 ^ _775212) ^ [_1069002] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069002), c_Int_OPls) = _1069002)], (2488 ^ _775212) ^ [_811600, _811602, _811604, _811606] : [-(c_Nitpick_Ouminus__frac(_811606, _811602) = c_Nitpick_Ouminus__frac(_811604, _811600)), _811606 = _811604, _811602 = _811600], (50981 ^ _775212) ^ [_1798068, _1798070, _1798072, _1798074, _1798076] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1798068, _1798070, _1798072, _1798074, _1798076) = c_Option_Ooption_Ooption__case(_1798068, tc_prod(_1798070, tc_Lazy__Sequence_Olazy__sequence(_1798070)), _1798072, hAPP(c_Product__Type_Oprod_Oprod__case(_1798070, tc_Lazy__Sequence_Olazy__sequence(_1798070), _1798068), _1798074), hAPP(c_Lazy__Sequence_Oyield(_1798070), _1798076)))], (39665 ^ _775212) ^ [_1534092, _1534094, _1534096, _1534098, _1534100, _1534102, _1534104] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1534092, _1534094, _1534096, _1534098, _1534100), _1534102), _1534104)), 39669 ^ _775212 : [(39672 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1534100, 39668 ^ [_1534092, _1534094, _1534096, _1534098, _1534100, _1534102, _1534104]), _1534104)))], (39670 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1534098, _1534102), 39668 ^ [_1534092, _1534094, _1534096, _1534098, _1534100, _1534102, _1534104])))]]], (29381 ^ _775212) ^ [] : [-(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))))], (25855 ^ _775212) ^ [_1227455, _1227457, _1227459, _1227461] : [class_Orderings_Olinorder(_1227455), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1227455), _1227457), _1227459)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1227455, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1227455, _1227457), _1227461)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1227455, _1227457), _1227459)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1227455, _1227459), _1227461))], (36363 ^ _775212) ^ [_1449790, _1449792] : [c_Equiv__Relations_Oequiv(_1449790, c_Orderings_Otop__class_Otop(tc_fun(_1449790, tc_HOL_Obool)), _1449792), -(c_Equiv__Relations_Oequivp(_1449790, hAPP(hAPP(c_COMBC(_1449790, tc_fun(tc_prod(_1449790, _1449790), tc_HOL_Obool), tc_fun(_1449790, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449790, tc_fun(tc_fun(tc_prod(_1449790, _1449790), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1449790, _1449790), tc_HOL_Obool), tc_fun(_1449790, tc_HOL_Obool)), _1449790), c_COMBC(_1449790, tc_fun(tc_prod(_1449790, _1449790), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449790, tc_prod(_1449790, _1449790)), tc_fun(_1449790, tc_fun(tc_fun(tc_prod(_1449790, _1449790), tc_HOL_Obool), tc_HOL_Obool)), _1449790), hAPP(c_COMBB(tc_prod(_1449790, _1449790), tc_fun(tc_fun(tc_prod(_1449790, _1449790), tc_HOL_Obool), tc_HOL_Obool), _1449790), c_member(tc_prod(_1449790, _1449790)))), c_Product__Type_OPair(_1449790, _1449790)))), _1449792)))], (45019 ^ _775212) ^ [_1665179, _1665181] : [-(hAPP(c_List_Oset(_1665179), _1665181) = hAPP(c_Set_OCollect(_1665179), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1665179), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1665179, 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)), _1665179), 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)), _1665179), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1665179, tc_fun(tc_Nat_Onat, _1665179), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1665179, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1665179), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1665179), c_COMBB(_1665179, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1665179), _1665181))))), 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(_1665179)), _1665181))))))], (11915 ^ _775212) ^ [_970930, _970932, _970934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970930), _970932)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970930), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970932), _970934))))], (49474 ^ _775212) ^ [_1765383, _1765385, _1765387, _1765389, _1765391] : [class_Orderings_Olinorder(_1765383), c_List_Olinorder__class_Osorted(_1765383, hAPP(c_List_Orev(_1765383), hAPP(hAPP(c_List_Omap(_1765385, _1765383), _1765387), _1765389))), -(hAPP(c_List_Ofilter(_1765385, hAPP(hAPP(c_COMBB(_1765383, tc_HOL_Obool, _1765385), hAPP(c_Orderings_Oord__class_Oless(_1765383), _1765391)), _1765387)), _1765389) = c_List_OtakeWhile(_1765385, hAPP(hAPP(c_COMBB(_1765383, tc_HOL_Obool, _1765385), hAPP(c_Orderings_Oord__class_Oless(_1765383), _1765391)), _1765387), _1765389))], (12251 ^ _775212) ^ [_976673, _976675, _976677, _976679] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _976673), _976675)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _976677), _976675)), _976679)) = 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), _976673), _976677)), _976675)), _976679))], (40680 ^ _775212) ^ [_1557482, _1557484, _1557486, _1557488, _1557490, _1557492] : [c_Finite__Set_Ofolding(_1557482, _1557484, _1557486, _1557488), -(hAPP(c_Fun_Ocomp(_1557484, _1557484, _1557484, hAPP(_1557486, _1557490)), hAPP(_1557486, _1557492)) = hAPP(c_Fun_Ocomp(_1557484, _1557484, _1557484, hAPP(_1557486, _1557492)), hAPP(_1557486, _1557490)))], (46137 ^ _775212) ^ [_1693455] : [c_List_Onat__list(_1693455), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1693455)))], (47508 ^ _775212) ^ [_1722906, _1722908, _1722910] : [47510 ^ _775212 : [(47513 ^ _775212) ^ [] : [hBOOL(hAPP(_1722908, 47509 ^ [_1722906, _1722908, _1722910]))], (47511 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1722906), 47509 ^ [_1722906, _1722908, _1722910]), hAPP(c_List_Oset(_1722906), _1722910))))]], -(hBOOL(hAPP(c_List_Olistsp(_1722906, _1722908), _1722910)))], (11955 ^ _775212) ^ [_971678, _971680] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971678), _971680) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _971678 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _971680 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (34953 ^ _775212) ^ [_1417357, _1417359, _1417361, _1417363] : [class_Lattices_Osemilattice__inf(_1417357), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417357), _1417359), _1417361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417357), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1417357), _1417359), _1417363)), _1417361)))], (2962 ^ _775212) ^ [_819455, _819457, _819459, _819461, _819463, _819465, _819467, _819469] : [-(c_SetInterval_Oord_OatLeastAtMost(_819469, _819465, _819461, _819457) = c_SetInterval_Oord_OatLeastAtMost(_819467, _819463, _819459, _819455)), _819469 = _819467, _819465 = _819463, _819461 = _819459, _819457 = _819455], (1204 ^ _775212) ^ [_793118, _793120] : [-(class_Groups_Oab__group__add(_793118)), _793120 = _793118, class_Groups_Oab__group__add(_793120)], (30979 ^ _775212) ^ [_1334741, _1334743, _1334745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334741)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1334743), _1334745)), 30986 ^ _775212 : [(30987 ^ _775212) ^ [_1334931] : [30989 ^ _775212 : [(30995 ^ _775212) ^ [] : [-(_1334931 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30991 ^ [_1334741, _1334743, _1334745, _1334931]), 30988 ^ [_1334741, _1334743, _1334745, _1334931]))], (30993 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30991 ^ [_1334741, _1334743, _1334745, _1334931]), _1334745)))], (30990 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30988 ^ [_1334741, _1334743, _1334745, _1334931]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1334741))))]], -(_1334931 = _1334743), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1334931), _1334741) = _1334743]]], (14377 ^ _775212) ^ [_1015160, _1015162] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015160), _1015162))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1015160, _1015162) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015160), _1015162), _1015162))], (39803 ^ _775212) ^ [_1536959, _1536961, _1536963] : [c_Wellfounded_Owf(_1536959, _1536961), -(c_Wellfounded_Owf(_1536959, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1536959, _1536959), tc_HOL_Obool)), _1536963), _1536961)))], (13881 ^ _775212) ^ [_1005834, _1005836, _1005838] : [-(hBOOL(hAPP(_1005834, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1005836), _1005838)))), 13884 ^ _775212 : [(13887 ^ _775212) ^ [] : [hBOOL(hAPP(_1005834, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13885 ^ _775212) ^ [] : [-(_1005838 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 13888 ^ _775212 : [(13893 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13891 ^ [_1005834, _1005836, _1005838]), _1005838)))], (13895 ^ _775212) ^ [] : [-(_1005836 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005838), 13890 ^ [_1005834, _1005836, _1005838])), 13891 ^ [_1005834, _1005836, _1005838]))], (13897 ^ _775212) ^ [] : [hBOOL(hAPP(_1005834, 13890 ^ [_1005834, _1005836, _1005838]))], (13889 ^ _775212) ^ [] : [_1005838 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43388 ^ _775212) ^ [_1622461, _1622463, _1622465] : [-(hAPP(c_Relation_ODomain(_1622461, _1622463), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1622461, _1622463), tc_HOL_Obool), _1622465)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1622461, _1622463), tc_HOL_Obool), tc_fun(_1622461, tc_HOL_Obool)), _1622465), c_Relation_ODomain(_1622461, _1622463)))], (40478 ^ _775212) ^ [_1552877, _1552879, _1552881, _1552883, _1552885, _1552887, _1552889] : [-(hAPP(c_Product__Type_Oapsnd(_1552877, _1552879, _1552881, _1552883), hAPP(c_Product__Type_Oapsnd(_1552885, _1552877, _1552881, _1552887), _1552889)) = hAPP(c_Product__Type_Oapsnd(_1552885, _1552879, _1552881, hAPP(c_Fun_Ocomp(_1552877, _1552879, _1552885, _1552883), _1552887)), _1552889))], (48230 ^ _775212) ^ [_1739467, _1739469, _1739471] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1739467), tc_List_Olist(_1739467)), c_List_Opartition(_1739467, _1739469, _1739471)) = hAPP(c_List_Ofilter(_1739467, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1739467, c_fNot), _1739469)), _1739471))], (49283 ^ _775212) ^ [_1761402, _1761404, _1761406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761402), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761404)), _1761406))), -(hAPP(hAPP(c_List_Onth(_1761404), hAPP(c_List_Orev(_1761404), _1761406)), _1761402) = hAPP(hAPP(c_List_Onth(_1761404), _1761406), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761404)), _1761406)), hAPP(c_Nat_OSuc, _1761402))))], (52319 ^ _775212) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (22856 ^ _775212) ^ [_1170556, _1170558, _1170560, _1170562, _1170564] : [hBOOL(hAPP(hAPP(_1170556, _1170558), _1170560)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1170562, _1170564, tc_HOL_Obool), _1170556), hAPP(hAPP(c_Product__Type_OPair(_1170562, _1170564), _1170558), _1170560))))], (23478 ^ _775212) ^ [_1182645, _1182647, _1182649] : [-(c_Product__Type_Ointernal__split(_1182645, _1182647, _1182649) = c_Product__Type_Oprod_Oprod__case(_1182645, _1182647, _1182649))], (30788 ^ _775212) ^ [_1331080, _1331082, _1331084, _1331086, _1331088, _1331090] : [hBOOL(hAPP(hAPP(_1331080, _1331082), _1331084)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1331086, tc_fun(_1331088, tc_HOL_Obool))), _1331080), _1331090), _1331082), _1331084)))], (19773 ^ _775212) ^ [_1112079, _1112081, _1112083] : [class_Fields_Olinordered__field(_1112079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112079), _1112081), c_Groups_Ozero__class_Ozero(_1112079))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112079), c_Groups_Ozero__class_Ozero(_1112079)), _1112083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112079), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112079), _1112081), _1112083)), c_Groups_Ozero__class_Ozero(_1112079))))], (13833 ^ _775212) ^ [_1004813, _1004815, _1004817, _1004819] : [class_Divides_Osemiring__div(_1004813), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004813), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004813), _1004815), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1004813), _1004817), _1004815))), c_Divides_Odiv__class_Omod(_1004813, _1004817, _1004815))), _1004819) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004813), _1004817), _1004819))], (7344 ^ _775212) ^ [_891822, _891824] : [_891822 = _891824, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _891822) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _891824))], (44041 ^ _775212) ^ [_1638202, _1638204, _1638206, _1638208] : [class_Rings_Olinordered__semidom(_1638202), 44047 ^ _775212 : [(44050 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1638202), c_Groups_Ozero__class_Ozero(_1638202)), hAPP(_1638208, 44046 ^ [_1638202, _1638204, _1638206, _1638208])))], (44048 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1638204), 44046 ^ [_1638202, _1638204, _1638206, _1638208]), _1638206)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1638202), c_Groups_Ozero__class_Ozero(_1638202)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1638204, _1638202), _1638208), _1638206))))], (21435 ^ _775212) ^ [_1142426, _1142428, _1142430, _1142432, _1142434, _1142436] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1142426, _1142428), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1142430), _1142432))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1142426, _1142428), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1142434), _1142436))), -(_1142428 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1142430 = _1142434)], (1864 ^ _775212) ^ [_801368, _801370] : [-(class_Groups_Ozero(_801368)), _801370 = _801368, class_Groups_Ozero(_801370)], (16201 ^ _775212) ^ [_1049928, _1049930, _1049932] : [class_Groups_Oordered__ab__group__add__abs(_1049928), 16204 ^ _775212 : [(16213 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049928), hAPP(c_Groups_Oabs__class_Oabs(_1049928), _1049930)), _1049932))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049928), _1049930), _1049932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049928), hAPP(c_Groups_Ouminus__class_Ouminus(_1049928), _1049930)), _1049932))], (16205 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049928), hAPP(c_Groups_Oabs__class_Oabs(_1049928), _1049930)), _1049932)), 16208 ^ _775212 : [(16211 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049928), hAPP(c_Groups_Ouminus__class_Ouminus(_1049928), _1049930)), _1049932)))], (16209 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049928), _1049930), _1049932)))]]]]], (33322 ^ _775212) ^ [_1380534, _1380536, _1380538, _1380540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1380534), _1380536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1380538), _1380540)), -(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), _1380534), _1380538)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1380536), _1380540))), c_FunDef_Opair__leq)))], (43282 ^ _775212) ^ [_1620037, _1620039, _1620041] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620037, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1620037, tc_HOL_Obool)), _1620039), _1620041)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620037, tc_HOL_Obool)), _1620039), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620037, tc_HOL_Obool), _1620041)))], (8820 ^ _775212) ^ [_918303, _918305] : [_918303 = hAPP(c_Int_Onat, _918305), 8823 ^ _775212 : [(8830 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _918305))), -(_918303 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8824 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _918305)), -(_918305 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918303))]]], (29860 ^ _775212) ^ [_1307235, _1307237, _1307239, _1307241, _1307243] : [hBOOL(hAPP(hAPP(c_member(_1307235), _1307237), hAPP(c_Set_Oimage(_1307239, _1307235, _1307241), _1307243))), 29864 ^ _775212 : [(29867 ^ _775212) ^ [] : [-(_1307237 = hAPP(_1307241, 29863 ^ [_1307235, _1307237, _1307239, _1307241, _1307243]))], (29865 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1307239), 29863 ^ [_1307235, _1307237, _1307239, _1307241, _1307243]), _1307243)))]]], (46724 ^ _775212) ^ [_1706488, _1706490, _1706492] : [-(_1706488 = c_List_Olist_ONil(_1706490)), -(hAPP(c_List_Ohd(_1706490), hAPP(c_List_Orotate(_1706490, _1706492), _1706488)) = hAPP(hAPP(c_List_Onth(_1706490), _1706488), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1706492, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706490)), _1706488))))], (26505 ^ _775212) ^ [_1241037, _1241039] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1241037), _1241039) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1241037, _1241039))], (29560 ^ _775212) ^ [_1301551, _1301553, _1301555, _1301557, _1301559, _1301561, _1301563] : [hBOOL(hAPP(hAPP(c_member(_1301551), _1301553), hAPP(hAPP(_1301555, _1301557), _1301559))), -(hBOOL(hAPP(hAPP(c_member(_1301551), _1301553), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1301561, _1301563, tc_fun(_1301551, tc_HOL_Obool)), _1301555), hAPP(hAPP(c_Product__Type_OPair(_1301561, _1301563), _1301557), _1301559)))))], (14823 ^ _775212) ^ [_1023524, _1023526] : [class_Power_Opower(_1023524), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1023524), _1023526), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1023524))], (34895 ^ _775212) ^ [_1416156, _1416158, _1416160, _1416162] : [class_Lattices_Osemilattice__inf(_1416156), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416156), _1416158), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416156), _1416160), _1416162)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416156), _1416160), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416156), _1416158), _1416162)))], (40113 ^ _775212) ^ [_1544275, _1544277] : [c_Wellfounded_Owf(_1544275, hAPP(c_Set_OCollect(tc_prod(_1544275, _1544275)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544275, _1544275, tc_HOL_Obool), _1544277))), -(c_Wellfounded_OwfP(_1544275, _1544277))], (16989 ^ _775212) ^ [_1064551] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1064551), hAPP(c_Int_Onumber__class_Onumber__of(_1064551), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1064551)), class_Int_Onumber__ring(_1064551), class_Rings_Olinordered__idom(_1064551)], (15169 ^ _775212) ^ [_1030363, _1030365, _1030367, _1030369, _1030371, _1030373] : [class_Rings_Oordered__ring(_1030363), 15172 ^ _775212 : [(15179 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030363), _1030369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030363), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1030363), _1030371), _1030365)), _1030367)), _1030373))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030363), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030363), _1030365), _1030367)), _1030369)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030363), _1030371), _1030367)), _1030373))))], (15173 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030363), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030363), _1030365), _1030367)), _1030369)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030363), _1030371), _1030367)), _1030373))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030363), _1030369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030363), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1030363), _1030371), _1030365)), _1030367)), _1030373))))]]], (12490 ^ _775212) ^ [_980819, _980821, _980823, _980825] : [class_Divides_Osemiring__div(_980819), -(c_Divides_Odiv__class_Omod(_980819, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980819), _980821), _980823), _980825) = c_Divides_Odiv__class_Omod(_980819, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980819), _980821), c_Divides_Odiv__class_Omod(_980819, _980823, _980825)), _980825))], (11700 ^ _775212) ^ [_967311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967311)), _967311))], (46500 ^ _775212) ^ [_1701744] : [-(hBOOL(hAPP(c_List_Odistinct(_1701744), c_List_Olist_ONil(_1701744))))], (12586 ^ _775212) ^ [_982753] : [class_Groups_Osgn__if(_982753), -(c_Groups_Osgn__class_Osgn(_982753, c_Groups_Ozero__class_Ozero(_982753)) = c_Groups_Ozero__class_Ozero(_982753))], (35962 ^ _775212) ^ [_1441789, _1441791, _1441793] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1441789), _1441791)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441789), _1441793)), 35972 ^ _775212 : [(35975 ^ _775212) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (35973 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1441789), 35971 ^ [_1441789, _1441791, _1441793]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441789, tc_HOL_Obool)), _1441791), _1441793))))]], -(hAPP(c_Finite__Set_Ocard(_1441789), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441789, tc_HOL_Obool)), _1441791), _1441793)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1441789), _1441791)), hAPP(c_Finite__Set_Ocard(_1441789), _1441793)))], (46668 ^ _775212) ^ [_1705322, _1705324, _1705326, _1705328] : [class_Groups_Ocomm__monoid__add(_1705322), hBOOL(hAPP(c_List_Odistinct(_1705324), _1705326)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1705322), hAPP(hAPP(c_List_Omap(_1705324, _1705322), _1705328), _1705326)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1705324, _1705322), _1705328), hAPP(c_List_Oset(_1705324), _1705326)))], (25522 ^ _775212) ^ [_1219637, _1219639, _1219641] : [25523 ^ _775212 : [(25524 ^ _775212) ^ [_1219718, _1219720] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1219637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1219639), _1219720)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1219641), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1219639), _1219718))]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1219637, _1219639) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1219641, _1219639))], (17585 ^ _775212) ^ [_1073736, _1073738] : [class_Int_Onumber__ring(_1073736), -(hAPP(c_Int_Onumber__class_Onumber__of(_1073736), c_Int_Osucc(_1073738)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073736), c_Groups_Oone__class_Oone(_1073736)), hAPP(c_Int_Onumber__class_Onumber__of(_1073736), _1073738)))], (17073 ^ _775212) ^ [_1065765, _1065767] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1065765) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1065767), 17076 ^ _775212 : [(17083 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065765)))), 17086 ^ _775212 : [(17093 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065767)))), -(_1065765 = _1065767)], (17087 ^ _775212) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065767))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065765) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (17077 ^ _775212) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065765))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065767)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (7599 ^ _775212) ^ [_896628, _896630] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896628), _896630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _896628)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _896630)))], (23704 ^ _775212) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (44098 ^ _775212) ^ [] : [-(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))))], (30630 ^ _775212) ^ [_1327562, _1327564, _1327566, _1327568] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327562), _1327564)), hBOOL(hAPP(hAPP(c_member(_1327562), _1327566), _1327564)), hBOOL(hAPP(hAPP(c_member(_1327562), _1327568), _1327564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1327562), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327562, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327562, tc_HOL_Obool)), _1327564), hAPP(hAPP(c_Set_Oinsert(_1327562), _1327566), c_Orderings_Obot__class_Obot(tc_fun(_1327562, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1327562), _1327568), c_Orderings_Obot__class_Obot(tc_fun(_1327562, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1327562), _1327564))))], (34937 ^ _775212) ^ [_1417067, _1417069, _1417071, _1417073] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417067, tc_HOL_Obool)), _1417069), _1417071), _1417073)), -(hBOOL(hAPP(_1417071, _1417073)))], (42037 ^ _775212) ^ [_1587409, _1587411, _1587413, _1587415] : [c_Wellfounded_Owf(_1587409, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1587409, _1587409)), hAPP(hAPP(c_Product__Type_OPair(_1587409, _1587409), _1587411), _1587413)), _1587415)), 42040 ^ _775212 : [(42043 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587409, _1587409)), hAPP(hAPP(c_Product__Type_OPair(_1587409, _1587409), _1587413), _1587411)), c_Transitive__Closure_Ortrancl(_1587409, _1587415)))], (42041 ^ _775212) ^ [] : [-(c_Wellfounded_Owf(_1587409, _1587415))]]], (3152 ^ _775212) ^ [_822560, _822562] : [_822562 = _822560, -(c_SetInterval_Oord__class_OatLeast(_822562) = c_SetInterval_Oord__class_OatLeast(_822560))], (1714 ^ _775212) ^ [_799493, _799495] : [-(class_Rings_Ocomm__semiring(_799493)), _799495 = _799493, class_Rings_Ocomm__semiring(_799495)], (1194 ^ _775212) ^ [_792993, _792995] : [-(class_Rings_Olinordered__idom(_792993)), _792995 = _792993, class_Rings_Olinordered__idom(_792995)], (43298 ^ _775212) ^ [_1620375, _1620377] : [class_Complete__Lattice_Ocomplete__lattice(_1620375), -(c_Complete__Lattice_OInf__class_OInf(_1620375, hAPP(hAPP(c_Set_Oinsert(_1620375), _1620377), c_Orderings_Obot__class_Obot(tc_fun(_1620375, tc_HOL_Obool)))) = _1620377)], (15261 ^ _775212) ^ [_1032274, _1032276] : [class_Power_Opower(_1032274), class_Rings_Osemiring__0(_1032274), 15268 ^ _775212 : [(15275 ^ _775212) ^ [] : [-(_1032276 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1032274), c_Groups_Ozero__class_Ozero(_1032274)), _1032276) = c_Groups_Ozero__class_Ozero(_1032274))], (15269 ^ _775212) ^ [] : [_1032276 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1032274), c_Groups_Ozero__class_Ozero(_1032274)), _1032276) = c_Groups_Oone__class_Oone(_1032274))]]], (13065 ^ _775212) ^ [_991296, _991298, _991300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991296)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _991298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _991300), _991296)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _991300), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _991298), _991300), _991296))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _991298, _991300)))], (3314 ^ _775212) ^ [_825075, _825077, _825079, _825081, _825083, _825085, _825087, _825089] : [-(c_Product__Type_Oapfst(_825089, _825085, _825081, _825077) = c_Product__Type_Oapfst(_825087, _825083, _825079, _825075)), _825089 = _825087, _825085 = _825083, _825081 = _825079, _825077 = _825075], (12055 ^ _775212) ^ [_973269, _973271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973269), _973271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973269)), _973271)))], (48125 ^ _775212) ^ [_1736198, _1736200] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736198)), c_List_Oconcat(_1736198, _1736200)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1736198), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1736198))), _1736200)))], (18039 ^ _775212) ^ [_1081280, _1081282] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1081280, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1081282)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1081280, 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)))), _1081282)))], (28604 ^ _775212) ^ [_1283077] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283077), c_Orderings_Obot__class_Obot(tc_fun(_1283077, tc_HOL_Obool)))))], (52075 ^ _775212) ^ [_1821648, _1821650, _1821652, _1821654, _1821656] : [c_Fun_Oinj__on(_1821648, _1821650, _1821652, _1821654), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1821648, tc_HOL_Obool)), _1821656), _1821654)), -(hAPP(c_Set_Oimage(_1821650, _1821648, c_Hilbert__Choice_Oinv__into(_1821648, _1821650, _1821654, _1821652)), hAPP(c_Set_Oimage(_1821648, _1821650, _1821652), _1821656)) = _1821656)], (49724 ^ _775212) ^ [_1770802, _1770804, _1770806, _1770808, _1770810] : [c_Fun_Oinj__on(_1770802, _1770804, _1770806, hAPP(hAPP(c_Set_Oinsert(_1770802), _1770808), hAPP(c_List_Oset(_1770802), _1770810))), -(hAPP(hAPP(c_List_Omap(_1770802, _1770804), _1770806), hAPP(c_List_OremoveAll(_1770802, _1770808), _1770810)) = hAPP(c_List_OremoveAll(_1770804, hAPP(_1770806, _1770808)), hAPP(hAPP(c_List_Omap(_1770802, _1770804), _1770806), _1770810)))], (4892 ^ _775212) ^ [_849766, _849768] : [_849768 = _849766, -(c_Groups_Oplus__class_Oplus(_849768) = c_Groups_Oplus__class_Oplus(_849766))], (38210 ^ _775212) ^ [_1493004, _1493006, _1493008, _1493010, _1493012, _1493014, _1493016] : [-(hAPP(c_Product__Type_Ofst(_1493004, _1493006), hAPP(c_Product__Type_Omap__pair(_1493008, _1493004, _1493010, _1493006, _1493012, _1493014), _1493016)) = hAPP(_1493012, hAPP(c_Product__Type_Ofst(_1493008, _1493010), _1493016)))], (4288 ^ _775212) ^ [_840404, _840406, _840408, _840410] : [-(c_List_Olinorder__class_Osorted__list__of__set(_840410, _840406) = c_List_Olinorder__class_Osorted__list__of__set(_840408, _840404)), _840410 = _840408, _840406 = _840404], (2660 ^ _775212) ^ [_814436, _814438, _814440, _814442] : [-(c_Quickcheck_Obeyond(_814442, _814438) = c_Quickcheck_Obeyond(_814440, _814436)), _814442 = _814440, _814438 = _814436], (44138 ^ _775212) ^ [_1640247, _1640249] : [-(c_List_Olenlex(_1640247, _1640249) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1640247), tc_List_Olist(_1640247))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1640247), tc_List_Olist(_1640247), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1640247), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1640247), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool)), tc_List_Olist(_1640247)), c_COMBS(tc_List_Olist(_1640247), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool), tc_fun(tc_List_Olist(_1640247), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1640247)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1640247)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1640247), tc_fun(tc_List_Olist(_1640247), tc_Nat_Onat), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1640247), tc_Nat_Onat), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool)), tc_List_Olist(_1640247)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1640247))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1640247)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1640247))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1640247)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1640247), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1640247), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool)), tc_List_Olist(_1640247)), c_COMBS(tc_List_Olist(_1640247), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool), tc_fun(tc_List_Olist(_1640247), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1640247)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1640247)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1640247), tc_fun(tc_List_Olist(_1640247), tc_Nat_Onat), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1640247), tc_Nat_Onat), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool)), tc_List_Olist(_1640247)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1640247))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1640247)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1640247))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1640247)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1640247), tc_fun(tc_prod(tc_List_Olist(_1640247), tc_List_Olist(_1640247)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1640247), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1640247), tc_List_Olist(_1640247)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1640247), tc_List_Olist(_1640247)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1640247), tc_HOL_Obool)), tc_List_Olist(_1640247)), c_COMBC(tc_List_Olist(_1640247), tc_fun(tc_prod(tc_List_Olist(_1640247), tc_List_Olist(_1640247)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1640247), tc_prod(tc_List_Olist(_1640247), tc_List_Olist(_1640247))), tc_fun(tc_List_Olist(_1640247), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1640247), tc_List_Olist(_1640247)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1640247)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1640247), tc_List_Olist(_1640247)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1640247), tc_List_Olist(_1640247)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1640247)), c_member(tc_prod(tc_List_Olist(_1640247), tc_List_Olist(_1640247))))), c_Product__Type_OPair(tc_List_Olist(_1640247), tc_List_Olist(_1640247))))), c_List_Olex(_1640247, _1640249)))))))], (26228 ^ _775212) ^ [_1235056, _1235058, _1235060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235056)), 26231 ^ _775212 : [(26232 ^ _775212) ^ [_1235190] : [26234 ^ _775212 : [(26240 ^ _775212) ^ [] : [-(_1235190 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26236 ^ [_1235056, _1235058, _1235060, _1235190]), 26233 ^ [_1235056, _1235058, _1235060, _1235190]))], (26238 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26236 ^ [_1235056, _1235058, _1235060, _1235190]), _1235058)))], (26235 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26233 ^ [_1235056, _1235058, _1235060, _1235190]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1235056))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235190), _1235060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1235190), _1235056)), _1235060)))]]], (46035 ^ _775212) ^ [_1690451, _1690453, _1690455, _1690457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690451), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690453)), _1690455))), -(hAPP(hAPP(c_List_Onth(_1690453), hAPP(hAPP(c_List_Oappend(_1690453), _1690455), _1690457)), _1690451) = hAPP(hAPP(c_List_Onth(_1690453), _1690455), _1690451))], (25150 ^ _775212) ^ [_1212805, _1212807, _1212809] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212805), _1212807)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212805), _1212809)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212805), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212807, _1212809))))], (42615 ^ _775212) ^ [_1603250, _1603252, _1603254, _1603256, _1603258] : [-(_1603250 = c_Orderings_Obot__class_Obot(tc_fun(_1603252, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1603254, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603252, tc_fun(_1603254, tc_HOL_Obool)), _1603250), _1603256)), _1603258) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603252, tc_fun(_1603254, tc_HOL_Obool)), _1603250), hAPP(hAPP(c_COMBC(_1603252, tc_fun(_1603254, tc_HOL_Obool), tc_fun(_1603254, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603254, tc_HOL_Obool), tc_fun(tc_fun(_1603254, tc_HOL_Obool), tc_fun(_1603254, tc_HOL_Obool)), _1603252), c_Groups_Ominus__class_Ominus(tc_fun(_1603254, tc_HOL_Obool))), _1603256)), _1603258)))], (31415 ^ _775212) ^ [_1343693, _1343695] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1343693, _1343695) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343693), _1343695)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343695), _1343693)))], (44389 ^ _775212) ^ [_1648662, _1648664, _1648666, _1648668] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648662), tc_List_Olist(_1648662))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648662), tc_List_Olist(_1648662)), _1648664), _1648666)), c_List_Olistrel(_1648662, _1648668))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648662)), _1648664) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648662)), _1648666))], (42889 ^ _775212) ^ [_1610671, _1610673, _1610675, _1610677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1610671, _1610673), tc_HOL_Obool)), _1610675), _1610677)), c_Relation_Osingle__valued(_1610671, _1610673, _1610677), -(c_Relation_Osingle__valued(_1610671, _1610673, _1610675))], (360 ^ _775212) ^ [_780704, _780706, _780708, _780710, _780712, _780714, _780716, _780718, _780720, _780722, _780724, _780726] : [-(c_Finite__Set_Ofolding__image__simple(_780724, _780720, _780716, _780712, _780708, _780704)), c_Finite__Set_Ofolding__image__simple(_780726, _780722, _780718, _780714, _780710, _780706), _780726 = _780724, _780722 = _780720, _780718 = _780716, _780714 = _780712, _780710 = _780708, _780706 = _780704], (34437 ^ _775212) ^ [_1406892, _1406894, _1406896, _1406898] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406892, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1406892), _1406894), _1406896)), hAPP(hAPP(c_Set_Oinsert(_1406892), _1406894), _1406898)) = hAPP(hAPP(c_Set_Oinsert(_1406892), _1406894), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406892, tc_HOL_Obool)), _1406896), _1406898)))], (3590 ^ _775212) ^ [_829451, _829453] : [_829453 = _829451, -(c_HOL_OAll(_829453) = c_HOL_OAll(_829451))], (3596 ^ _775212) ^ [_829536, _829538, _829540, _829542, _829544, _829546] : [-(c_Set_Ovimage(_829546, _829542, _829538) = c_Set_Ovimage(_829544, _829540, _829536)), _829546 = _829544, _829542 = _829540, _829538 = _829536], (50937 ^ _775212) ^ [_1797067, _1797069, _1797071] : [_1797067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1797069), c_List_Oreplicate(_1797069, _1797067, _1797071)) = c_Orderings_Obot__class_Obot(tc_fun(_1797069, tc_HOL_Obool)))], (42236 ^ _775212) ^ [_1591852, _1591854, _1591856] : [c_Relation_Orefl__on(_1591852, _1591854, hAPP(c_Relation_Oconverse(_1591852, _1591852), _1591856)), -(c_Relation_Orefl__on(_1591852, _1591854, _1591856))], (16929 ^ _775212) ^ [_1063704] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1063704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1063704)))], (2590 ^ _775212) ^ [_813275, _813277, _813279, _813281, _813283, _813285, _813287, _813289, _813291, _813293] : [-(c_Nitpick_Opair__box_Opair__box__case(_813293, _813289, _813285, _813281, _813277) = c_Nitpick_Opair__box_Opair__box__case(_813291, _813287, _813283, _813279, _813275)), _813293 = _813291, _813289 = _813287, _813285 = _813283, _813281 = _813279, _813277 = _813275], (6128 ^ _775212) ^ [_872165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872165), _872165))], (48932 ^ _775212) ^ [_1754042, _1754044, _1754046, _1754048, _1754050, _1754052] : [class_Orderings_Olinorder(_1754042), c_List_Olinorder__class_Osorted(_1754042, hAPP(hAPP(c_List_Omap(_1754044, _1754042), _1754046), _1754048)), hBOOL(hAPP(_1754050, _1754052)), -(hAPP(c_List_Ofilter(_1754044, _1754050), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754044, _1754042, _1754046), _1754052), _1754048)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754044, _1754042, _1754046), _1754052), hAPP(c_List_Ofilter(_1754044, _1754050), _1754048)))], (52585 ^ _775212) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (27964 ^ _775212) ^ [_1270639] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1270639)), -(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)), _1270639))))], (37844 ^ _775212) ^ [_1482390, _1482392, _1482394, _1482396, _1482398, _1482400] : [-(hAPP(c_Set_Oimage(_1482390, tc_prod(_1482392, _1482394), hAPP(hAPP(c_COMBS(_1482390, _1482394, tc_prod(_1482392, _1482394)), hAPP(hAPP(c_COMBB(_1482392, tc_fun(_1482394, tc_prod(_1482392, _1482394)), _1482390), c_Product__Type_OPair(_1482392, _1482394)), _1482396)), _1482398)), _1482400) = hAPP(hAPP(c_Product__Type_OSigma(_1482392, _1482394), hAPP(c_Set_Oimage(_1482390, _1482392, _1482396), _1482400)), hAPP(hAPP(c_COMBB(tc_fun(_1482390, tc_HOL_Obool), tc_fun(_1482394, tc_HOL_Obool), _1482392), c_Set_Oimage(_1482390, _1482394, _1482398)), hAPP(hAPP(c_COMBC(_1482392, tc_fun(_1482390, tc_HOL_Obool), tc_fun(_1482390, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1482390, tc_HOL_Obool), tc_fun(tc_fun(_1482390, tc_HOL_Obool), tc_fun(_1482390, tc_HOL_Obool)), _1482392), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482390, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1482392, tc_HOL_Obool), tc_fun(_1482390, tc_HOL_Obool), _1482392), c_Set_Ovimage(_1482390, _1482392, _1482396)), hAPP(hAPP(c_COMBC(_1482392, tc_fun(_1482392, tc_HOL_Obool), tc_fun(_1482392, tc_HOL_Obool)), c_Set_Oinsert(_1482392)), c_Orderings_Obot__class_Obot(tc_fun(_1482392, tc_HOL_Obool)))))), _1482400))))], (49754 ^ _775212) ^ [_1771393, _1771395, _1771397, _1771399] : [-(_1771393 = _1771395), -(hAPP(c_List_OremoveAll(_1771397, _1771393), hAPP(hAPP(c_List_Olist_OCons(_1771397), _1771395), _1771399)) = hAPP(hAPP(c_List_Olist_OCons(_1771397), _1771395), hAPP(c_List_OremoveAll(_1771397, _1771393), _1771399)))], (42489 ^ _775212) ^ [_1599862, _1599864, _1599866, _1599868, _1599870] : [_1599862 = c_Orderings_Obot__class_Obot(tc_fun(_1599864, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599866, tc_HOL_Obool)), _1599868), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599864, tc_fun(_1599866, tc_HOL_Obool)), _1599862), _1599870)) = _1599868)], (52581 ^ _775212) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (20621 ^ _775212) ^ [_1127364, _1127366, _1127368, _1127370] : [class_Fields_Olinordered__field__inverse__zero(_1127364), class_Int_Onumber(_1127364), 20628 ^ _775212 : [(20629 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), _1127366), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127364), _1127368), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370)))), 20632 ^ _775212 : [(20639 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), c_Groups_Ozero__class_Ozero(_1127364)), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370)))), 20642 ^ _775212 : [(20649 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370)), c_Groups_Ozero__class_Ozero(_1127364)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), _1127366), c_Groups_Ozero__class_Ozero(_1127364))))], (20643 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370)), c_Groups_Ozero__class_Ozero(_1127364))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), _1127368), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127364), _1127366), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370)))))]]], (20633 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), c_Groups_Ozero__class_Ozero(_1127364)), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127364), _1127366), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370))), _1127368)))]]], (20655 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), _1127366), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127364), _1127368), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370))))), 20658 ^ _775212 : [(20661 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127364), _1127366), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370))), _1127368))], (20659 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), c_Groups_Ozero__class_Ozero(_1127364)), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370))))]], 20662 ^ _775212 : [(20665 ^ _775212) ^ [] : [20666 ^ _775212 : [(20669 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), _1127368), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127364), _1127366), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370))))], (20667 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370)), c_Groups_Ozero__class_Ozero(_1127364))))]], 20670 ^ _775212 : [(20673 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), _1127366), c_Groups_Ozero__class_Ozero(_1127364)))], (20671 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370)), c_Groups_Ozero__class_Ozero(_1127364)))]]], (20663 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127364), c_Groups_Ozero__class_Ozero(_1127364)), hAPP(c_Int_Onumber__class_Onumber__of(_1127364), _1127370)))]]]]], (12558 ^ _775212) ^ [_982271] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _982271, _982271) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45812 ^ _775212) ^ [_1685220, _1685222, _1685224] : [_1685220 = hAPP(hAPP(c_List_Oappend(_1685222), _1685220), _1685224), -(_1685224 = c_List_Olist_ONil(_1685222))], (49203 ^ _775212) ^ [_1759771, _1759773, _1759775, _1759777, _1759779] : [c_List_Olist__all2(_1759771, _1759773, _1759775, _1759777, _1759779), -(c_List_Olist__all2(_1759771, _1759773, _1759775, hAPP(c_List_Orev(_1759771), _1759777), hAPP(c_List_Orev(_1759773), _1759779)))], (50949 ^ _775212) ^ [_1797230, _1797232, _1797234] : [-(hAPP(c_List_Oset(_1797230), c_List_Oreplicate(_1797230, hAPP(c_Nat_OSuc, _1797232), _1797234)) = hAPP(hAPP(c_Set_Oinsert(_1797230), _1797234), c_Orderings_Obot__class_Obot(tc_fun(_1797230, tc_HOL_Obool))))], (10984 ^ _775212) ^ [_954912, _954914, _954916, _954918] : [class_Rings_Olinordered__semiring__strict(_954912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954912), _954914), _954916)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954912), _954914), _954918))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954912), c_Groups_Ozero__class_Ozero(_954912)), _954914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954912), _954916), _954918)))], (10873 ^ _775212) ^ [_952874, _952876] : [10874 ^ _775212 : [(10877 ^ _775212) ^ [] : [_952874 = _952876], (10875 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _952874), _952876))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _952874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _952876), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (15840 ^ _775212) ^ [_1043383, _1043385, _1043387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1043383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1043385), 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), _1043385), _1043387))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1043383))), _1043387)))], (13320 ^ _775212) ^ [_996246, _996248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996246)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _996246), _996248)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _996246)), hAPP(c_Int_Onat, _996248)))], (28418 ^ _775212) ^ [_1279232, _1279234, _1279236, _1279238, _1279240] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279232), _1279234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1279236, tc_HOL_Obool)), _1279238), hAPP(c_Set_Oimage(_1279232, _1279236, _1279240), _1279234))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279236), _1279238)))], (52229 ^ _775212) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (17885 ^ _775212) ^ [_1078841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1078841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1078841))))], (22122 ^ _775212) ^ [_1155045] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1155045)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1155045)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16895 ^ _775212) ^ [_1063237, _1063239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1063237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1063237), _1063239)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1063237), _1063239) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (5656 ^ _775212) ^ [_864336, _864338, _864340, _864342, _864344] : [-(c_Natural_Oevaln(c_Com_Ocom_OSemi(_864336, _864338), _864340, _864342, _864344)), 5657 ^ _775212 : [(5658 ^ _775212) ^ [_864391] : [c_Natural_Oevaln(_864336, _864340, _864342, _864391), c_Natural_Oevaln(_864338, _864391, _864342, _864344)]]], (4612 ^ _775212) ^ [_845520, _845522, _845524, _845526, _845528, _845530] : [-(c_New__DSequence_Opos__union(_845530, _845526, _845522) = c_New__DSequence_Opos__union(_845528, _845524, _845520)), _845530 = _845528, _845526 = _845524, _845522 = _845520], (13517 ^ _775212) ^ [_999378, _999380, _999382] : [class_Divides_Osemiring__div(_999378), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_999378), c_Divides_Odiv__class_Omod(_999378, _999380, _999382)), _999382) = c_Groups_Ozero__class_Ozero(_999378))], (42099 ^ _775212) ^ [_1588777, _1588779, _1588781] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1588777, _1588777), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1588777, _1588777), _1588779)), c_Transitive__Closure_Ortrancl(_1588777, _1588779)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1588777, _1588777), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588777, _1588777)), hAPP(hAPP(c_Product__Type_OPair(_1588777, _1588777), _1588781), _1588781)), c_Transitive__Closure_Otrancl(_1588777, _1588779)))], (42752 ^ _775212) ^ [_1607388] : [-(hAPP(c_Relation_Oconverse(_1607388, _1607388), c_Relation_OId(_1607388)) = c_Relation_OId(_1607388))], (12013 ^ _775212) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11422 ^ _775212) ^ [_962621, _962623] : [hAPP(c_Int_Onat, _962621) = _962623, 11425 ^ _775212 : [(11432 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _962621))), -(_962623 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11426 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _962621)), -(_962621 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _962623))]]], (48733 ^ _775212) ^ [_1750459, _1750461, _1750463, _1750465] : [class_Orderings_Olinorder(_1750459), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1750459), _1750461), _1750463)), c_List_Olinorder__class_Osorted(_1750459, hAPP(hAPP(c_List_Olist_OCons(_1750459), _1750463), _1750465)), -(c_List_Olinorder__class_Osorted(_1750459, hAPP(hAPP(c_List_Olist_OCons(_1750459), _1750461), hAPP(hAPP(c_List_Olist_OCons(_1750459), _1750463), _1750465))))], (2450 ^ _775212) ^ [_811009, _811011, _811013, _811015, _811017, _811019] : [-(c_Random_Ominus__shift(_811019, _811015, _811011) = c_Random_Ominus__shift(_811017, _811013, _811009)), _811019 = _811017, _811015 = _811013, _811011 = _811009], (29498 ^ _775212) ^ [_1300397, _1300399, _1300401, _1300403] : [29499 ^ _775212 : [(29502 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1300397), _1300399), _1300403))], (29500 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1300397), _1300399), _1300401))]], -(hBOOL(hAPP(hAPP(c_member(_1300397), _1300399), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1300397, tc_HOL_Obool)), _1300403), _1300401))))], (6274 ^ _775212) ^ [_874286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _874286)), -(_874286 = hAPP(c_Nat_OSuc, 6277 ^ [_874286]))], (48424 ^ _775212) ^ [_1744886, _1744888] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1744886), _1744888))), -(c_List_Oupt(_1744886, hAPP(c_Nat_OSuc, _1744888)) = c_List_Olist_ONil(tc_Nat_Onat))], (42433 ^ _775212) ^ [_1597847, _1597849, _1597851, _1597853, _1597855] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597847, tc_HOL_Obool)), _1597849), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597851, tc_fun(_1597847, tc_HOL_Obool)), _1597853), _1597855)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597851, tc_fun(_1597847, tc_HOL_Obool)), _1597853), hAPP(hAPP(c_COMBB(tc_fun(_1597847, tc_HOL_Obool), tc_fun(_1597847, tc_HOL_Obool), _1597851), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597847, tc_HOL_Obool)), _1597849)), _1597855)))], (27505 ^ _775212) ^ [_1260368, _1260370, _1260372, _1260374] : [class_Orderings_Olinorder(_1260368), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260368), _1260370), _1260372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260368), _1260372), _1260374)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260368, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1260368, _1260370, _1260372)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1260368, _1260372, _1260374)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1260368, _1260370, _1260374))], (28339 ^ _775212) ^ [_1277742] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1277742), c_Orderings_Otop__class_Otop(tc_fun(_1277742, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1277742)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1277742), tc_HOL_Obool)))))], (33903 ^ _775212) ^ [_1394042, _1394044, _1394046, _1394048, _1394050] : [c_Finite__Set_Ofolding__one__idem(_1394042, _1394044, _1394046), hBOOL(hAPP(c_Finite__Set_Ofinite(_1394042), _1394048)), -(_1394050 = c_Orderings_Obot__class_Obot(tc_fun(_1394042, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1394042, tc_HOL_Obool)), _1394050), _1394048)), -(hAPP(hAPP(_1394044, hAPP(_1394046, _1394050)), hAPP(_1394046, _1394048)) = hAPP(_1394046, _1394048))], (22460 ^ _775212) ^ [_1162843, _1162845, _1162847, _1162849] : [class_Orderings_Olinorder(_1162843), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162843), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162843), _1162845), _1162847)), _1162849) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162843), _1162845), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162843), _1162847), _1162849)))], (2292 ^ _775212) ^ [_808598, _808600, _808602, _808604] : [-(c_Orderings_Oord_Omax(_808604, _808600) = c_Orderings_Oord_Omax(_808602, _808598)), _808604 = _808602, _808600 = _808598], (46426 ^ _775212) ^ [_1700436, _1700438] : [-(_1700436 = c_List_Olist_ONil(_1700438)), -(hBOOL(hAPP(hAPP(c_member(_1700438), hAPP(c_List_Ohd(_1700438), _1700436)), hAPP(c_List_Oset(_1700438), _1700436))))], (49408 ^ _775212) ^ [_1764091, _1764093, _1764095, _1764097, _1764099] : [-(hAPP(hAPP(c_List_Ozip(_1764091, _1764093), c_List_OtakeWhile(_1764091, _1764095, _1764097)), _1764099) = c_List_OtakeWhile(tc_prod(_1764091, _1764093), hAPP(c_Fun_Ocomp(_1764091, tc_HOL_Obool, tc_prod(_1764091, _1764093), _1764095), c_Product__Type_Ofst(_1764091, _1764093)), hAPP(hAPP(c_List_Ozip(_1764091, _1764093), _1764097), _1764099)))], (1584 ^ _775212) ^ [_797868, _797870] : [-(class_Rings_Oordered__comm__semiring(_797868)), _797870 = _797868, class_Rings_Oordered__comm__semiring(_797870)], (43316 ^ _775212) ^ [_1620668, _1620670, _1620672] : [class_Complete__Lattice_Ocomplete__lattice(_1620668), -(c_Complete__Lattice_OInf__class_OInf(_1620668, hAPP(hAPP(c_Set_Oinsert(_1620668), _1620670), _1620672)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1620668), _1620670), c_Complete__Lattice_OInf__class_OInf(_1620668, _1620672)))], (49585 ^ _775212) ^ [_1767706, _1767708, _1767710, _1767712, _1767714] : [c_List_OdropWhile(_1767706, _1767708, _1767710) = hAPP(hAPP(c_List_Olist_OCons(_1767706), _1767712), _1767714), 49588 ^ _775212 : [(49591 ^ _775212) ^ [] : [hBOOL(hAPP(_1767708, _1767712))], (49589 ^ _775212) ^ [] : [-(_1767710 = hAPP(hAPP(c_List_Oappend(_1767706), c_List_OtakeWhile(_1767706, _1767708, _1767710)), hAPP(hAPP(c_List_Olist_OCons(_1767706), _1767712), _1767714)))]]], (39213 ^ _775212) ^ [_1516597, _1516599] : [-(c_Fun_Oinj__on(tc_fun(_1516597, _1516599), tc_fun(tc_prod(_1516597, _1516599), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1516597, _1516599), tc_HOL_Obool), tc_fun(tc_prod(_1516597, _1516599), tc_HOL_Obool), tc_fun(_1516597, _1516599)), c_Set_OCollect(tc_prod(_1516597, _1516599))), hAPP(hAPP(c_COMBB(tc_fun(_1516597, tc_fun(_1516599, tc_HOL_Obool)), tc_fun(tc_prod(_1516597, _1516599), tc_HOL_Obool), tc_fun(_1516597, _1516599)), c_Product__Type_Oprod_Oprod__case(_1516597, _1516599, tc_HOL_Obool)), hAPP(c_COMBB(_1516599, tc_fun(_1516599, tc_HOL_Obool), _1516597), hAPP(c_COMBC(_1516599, _1516599, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1516597, _1516599), tc_HOL_Obool))))], (41474 ^ _775212) ^ [_1574920, _1574922, _1574924, _1574926, _1574928] : [c_Finite__Set_Ofolding__one(_1574920, _1574922, _1574924), hBOOL(hAPP(c_Finite__Set_Ofinite(_1574920), _1574926)), -(hBOOL(hAPP(hAPP(c_member(_1574920), _1574928), _1574926))), -(hAPP(_1574924, hAPP(hAPP(c_Set_Oinsert(_1574920), _1574928), _1574926)) = hAPP(hAPP(c_Finite__Set_Ofold(_1574920, _1574920, _1574922), _1574928), _1574926))], (26525 ^ _775212) ^ [_1241394, _1241396, _1241398, _1241400] : [class_Rings_Osemiring__1(_1241394), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1241396, _1241394), hAPP(c_COMBK(_1241394, _1241396), _1241398)), _1241400) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241394), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1241394), hAPP(c_Finite__Set_Ocard(_1241396), _1241400))), _1241398))], (37505 ^ _775212) ^ [_1474039, _1474041, _1474043, _1474045] : [c_Fun_Oinj__on(_1474039, _1474041, _1474043, c_Orderings_Otop__class_Otop(tc_fun(_1474039, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1474039, _1474041, _1474043), hAPP(c_Set_Oimage(_1474039, _1474041, _1474043), _1474045)) = _1474045)], (46923 ^ _775212) ^ [_1710833, _1710835, _1710837] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710833), tc_List_Olist(_1710833))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710833), tc_List_Olist(_1710833)), c_List_Olist_ONil(_1710833)), _1710835)), c_List_Olexord(_1710833, _1710837))), -(_1710835 = hAPP(hAPP(c_List_Olist_OCons(_1710833), 46926 ^ [_1710833, _1710835, _1710837]), 46927 ^ [_1710833, _1710835, _1710837]))], (48382 ^ _775212) ^ [_1743724, _1743726, _1743728, _1743730, _1743732, _1743734] : [-(c_List_Ofoldr(_1743724, _1743726, _1743728, hAPP(hAPP(c_List_Olist_OCons(_1743724), _1743730), _1743732), _1743734) = hAPP(hAPP(_1743728, _1743730), c_List_Ofoldr(_1743724, _1743726, _1743728, _1743732, _1743734)))], (33097 ^ _775212) ^ [_1375629, _1375631, _1375633, _1375635, _1375637] : [class_Groups_Ocomm__monoid__mult(_1375629), class_Rings_Odvd(_1375629), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375631), _1375633)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375631, tc_HOL_Obool)), _1375635), _1375633)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1375629), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1375631, _1375629), _1375637), _1375635)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1375631, _1375629), _1375637), _1375633))))], (37216 ^ _775212) ^ [_1467948, _1467950] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467948), _1467950)), -(hAPP(c_Finite__Set_Ocard(_1467948), _1467950) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1467948, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1467948), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1467950))], (14145 ^ _775212) ^ [_1010807, _1010809, _1010811] : [class_Rings_Osemiring__1(_1010807), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1010807), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1010809), _1010811)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1010807), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1010807), _1010809)), _1010811))], (6731 ^ _775212) ^ [_882317, _882319, _882321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882317), _882319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882317), _882321)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882319), _882321))))], (22788 ^ _775212) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (45242 ^ _775212) ^ [_1671189, _1671191, _1671193, _1671195, _1671197, _1671199] : [-(hAPP(hAPP(c_List_Ozip(_1671189, _1671191), hAPP(hAPP(c_List_Olist_OCons(_1671189), _1671193), _1671195)), hAPP(hAPP(c_List_Olist_OCons(_1671191), _1671197), _1671199)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1671189, _1671191)), hAPP(hAPP(c_Product__Type_OPair(_1671189, _1671191), _1671193), _1671197)), hAPP(hAPP(c_List_Ozip(_1671189, _1671191), _1671195), _1671199)))], (38208 ^ _775212) ^ [_1492933, _1492935, _1492937, _1492939, _1492941, _1492943, _1492945, _1492947] : [-(hAPP(c_Product__Type_Omap__pair(_1492933, _1492935, _1492937, _1492939, _1492941, _1492943), hAPP(hAPP(c_Product__Type_OPair(_1492933, _1492937), _1492945), _1492947)) = hAPP(hAPP(c_Product__Type_OPair(_1492935, _1492939), hAPP(_1492941, _1492945)), hAPP(_1492943, _1492947)))], (9695 ^ _775212) ^ [_931979, _931981, _931983, _931985] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_931979), 9698 ^ _775212 : [(9705 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931979), _931981), _931985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931979), _931981), _931983)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931979), _931985), _931983))))], (9699 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931979), _931981), _931983)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931979), _931985), _931983))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931979), _931981), _931985)))]]], (5831 ^ _775212) ^ [_867406] : [hAPP(c_Nat_OSuc, _867406) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10863 ^ _775212) ^ [_952756, _952758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _952756), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _952758), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _952756), _952758))), -(_952756 = _952758)], (23176 ^ _775212) ^ [_1176451, _1176453, _1176455, _1176457] : [class_Orderings_Olinorder(_1176451), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176451), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176451), _1176453), _1176455)), _1176457) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176451), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176451), _1176453), _1176457)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176451), _1176455), _1176457)))], (25230 ^ _775212) ^ [_1214103, _1214105, _1214107] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1214103), _1214105)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1214103), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1214103), _1214107)))))], (37022 ^ _775212) ^ [_1463763, _1463765, _1463767, _1463769, _1463771] : [class_Groups_Ocomm__monoid__mult(_1463763), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463765), _1463767)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463765), _1463769)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463765, tc_HOL_Obool)), _1463767), _1463769) = c_Orderings_Obot__class_Obot(tc_fun(_1463765, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1463763, _1463765, c_Groups_Otimes__class_Otimes(_1463763)), _1463771), c_Groups_Oone__class_Oone(_1463763)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463765, tc_HOL_Obool)), _1463767), _1463769)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1463763), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1463763, _1463765, c_Groups_Otimes__class_Otimes(_1463763)), _1463771), c_Groups_Oone__class_Oone(_1463763)), _1463767)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1463763, _1463765, c_Groups_Otimes__class_Otimes(_1463763)), _1463771), c_Groups_Oone__class_Oone(_1463763)), _1463769)))], (52609 ^ _775212) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (19043 ^ _775212) ^ [_1099582, _1099584, _1099586, _1099588] : [class_Rings_Odivision__ring(_1099582), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099582), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099582), _1099584), _1099586)), _1099588) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099582), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099582), _1099584), _1099588)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099582), _1099586), _1099588)))], (12253 ^ _775212) ^ [] : [-(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))))], (31111 ^ _775212) ^ [_1337534, _1337536, _1337538, _1337540, _1337542] : [class_Groups_Oordered__comm__monoid__add(_1337534), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337536), _1337538)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1337536, tc_HOL_Obool)), _1337540), _1337538)), 31125 ^ _775212 : [(31128 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337534), c_Groups_Ozero__class_Ozero(_1337534)), hAPP(_1337542, 31124 ^ [_1337534, _1337536, _1337538, _1337540, _1337542])))], (31126 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1337536), 31124 ^ [_1337534, _1337536, _1337538, _1337540, _1337542]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1337536, tc_HOL_Obool)), _1337538), _1337540))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337534), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1337536, _1337534), _1337542), _1337540)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1337536, _1337534), _1337542), _1337538))))], (6200 ^ _775212) ^ [_873130, _873132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873130), _873132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873130), hAPP(c_Nat_OSuc, _873132))))], (48348 ^ _775212) ^ [_1742101, _1742103, _1742105] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742101)), hAPP(c_List_Ofilter(_1742101, _1742103), _1742105)) = 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(_1742101)), _1742105)))), hAPP(hAPP(c_COMBB(_1742101, tc_HOL_Obool, tc_Nat_Onat), _1742103), hAPP(c_List_Onth(_1742101), _1742105))))))], (2302 ^ _775212) ^ [_808747, _808749, _808751, _808753] : [-(c_Nitpick_Onat__gcd(_808753, _808749) = c_Nitpick_Onat__gcd(_808751, _808747)), _808753 = _808751, _808749 = _808747], (12564 ^ _775212) ^ [_982400, _982402] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _982400, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _982402)) = 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), _982400), _982402)))], (39239 ^ _775212) ^ [_1517714, _1517716, _1517718] : [class_Groups_Olinordered__ab__semigroup__add(_1517714), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517714), _1517716)), -(_1517716 = c_Orderings_Obot__class_Obot(tc_fun(_1517714, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1517714), _1517718), c_Big__Operators_Olinorder__class_OMin(_1517714, _1517716)) = c_Big__Operators_Olinorder__class_OMin(_1517714, hAPP(c_Set_OCollect(_1517714), hAPP(hAPP(c_COMBB(tc_fun(_1517714, tc_HOL_Obool), tc_HOL_Obool, _1517714), c_HOL_OEx(_1517714)), hAPP(hAPP(c_COMBC(_1517714, tc_fun(_1517714, tc_HOL_Obool), tc_fun(_1517714, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517714, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1517714, tc_HOL_Obool), tc_fun(_1517714, tc_HOL_Obool)), _1517714), c_COMBS(_1517714, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517714, tc_HOL_Obool), tc_fun(_1517714, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1517714), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1517714), c_fconj)), hAPP(hAPP(c_COMBC(_1517714, tc_fun(_1517714, _1517714), tc_fun(_1517714, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517714, tc_HOL_Obool), tc_fun(tc_fun(_1517714, _1517714), tc_fun(_1517714, tc_HOL_Obool)), _1517714), c_COMBB(_1517714, tc_HOL_Obool, _1517714)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1517714), _1517718))))), hAPP(hAPP(c_COMBC(_1517714, tc_fun(_1517714, tc_HOL_Obool), tc_HOL_Obool), c_member(_1517714)), _1517716))))))], (23894 ^ _775212) ^ [_1190495, _1190497, _1190499] : [class_Rings_Olinordered__idom(_1190495), hAPP(c_Groups_Oabs__class_Oabs(_1190495), _1190497) = hAPP(c_Groups_Oabs__class_Oabs(_1190495), _1190499), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1190495), _1190497), _1190499)))], (7919 ^ _775212) ^ [_902357, _902359, _902361] : [class_Groups_Oordered__ab__group__add(_902357), 7922 ^ _775212 : [(7929 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902357), _902361), hAPP(c_Groups_Ouminus__class_Ouminus(_902357), _902359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902357), _902359), hAPP(c_Groups_Ouminus__class_Ouminus(_902357), _902361))))], (7923 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902357), _902359), hAPP(c_Groups_Ouminus__class_Ouminus(_902357), _902361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902357), _902361), hAPP(c_Groups_Ouminus__class_Ouminus(_902357), _902359))))]]], (7603 ^ _775212) ^ [_896703, _896705] : [class_Rings_Oring__1(_896703), -(hAPP(c_Int_Oring__1__class_Oof__int(_896703), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _896705)) = hAPP(c_Groups_Ouminus__class_Ouminus(_896703), hAPP(c_Int_Oring__1__class_Oof__int(_896703), _896705)))], (7318 ^ _775212) ^ [_891484] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _891484) = _891484)], (45100 ^ _775212) ^ [_1668117, _1668119, _1668121, _1668123] : [hAPP(hAPP(c_List_Omap(_1668117, _1668119), _1668121), _1668123) = c_List_Olist_ONil(_1668119), -(_1668123 = c_List_Olist_ONil(_1668117))], (11732 ^ _775212) ^ [_967799, _967801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967799)), hAPP(c_Nat_OSuc, _967801))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967799), _967801)))], (30298 ^ _775212) ^ [_1319316, _1319318, _1319320, _1319322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319316, tc_fun(_1319318, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1319316, tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_fun(_1319318, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319318, tc_fun(tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_fun(_1319318, tc_HOL_Obool)), _1319316), c_COMBC(_1319318, tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319318, tc_prod(_1319316, _1319318)), tc_fun(_1319318, tc_fun(tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_HOL_Obool)), _1319316), hAPP(c_COMBB(tc_prod(_1319316, _1319318), tc_fun(tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_HOL_Obool), _1319318), c_member(tc_prod(_1319316, _1319318)))), c_Product__Type_OPair(_1319316, _1319318)))), _1319320)), hAPP(hAPP(c_COMBC(_1319316, tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_fun(_1319318, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319318, tc_fun(tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_fun(_1319318, tc_HOL_Obool)), _1319316), c_COMBC(_1319318, tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319318, tc_prod(_1319316, _1319318)), tc_fun(_1319318, tc_fun(tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_HOL_Obool)), _1319316), hAPP(c_COMBB(tc_prod(_1319316, _1319318), tc_fun(tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool), tc_HOL_Obool), _1319318), c_member(tc_prod(_1319316, _1319318)))), c_Product__Type_OPair(_1319316, _1319318)))), _1319322))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1319316, _1319318), tc_HOL_Obool)), _1319320), _1319322)))], (34685 ^ _775212) ^ [_1412209, _1412211, _1412213] : [class_Lattices_Osemilattice__inf(_1412209), 34688 ^ _775212 : [(34695 ^ _775212) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1412209), _1412211), _1412213) = _1412211, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412209), _1412211), _1412213)))], (34689 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412209), _1412211), _1412213)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1412209), _1412211), _1412213) = _1412211)]]], (51741 ^ _775212) ^ [_1815558, _1815560, _1815562, _1815564] : [c_Relation_Osym(_1815558, _1815560), -(c_Relation_Osym(_1815562, hAPP(hAPP(c_Relation_Oinv__image(_1815558, _1815562), _1815560), _1815564)))], (48442 ^ _775212) ^ [_1745216, _1745218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1745216), _1745218)), -(c_List_Oupt(_1745216, _1745218) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1745216), c_List_Oupt(hAPP(c_Nat_OSuc, _1745216), _1745218)))], (23444 ^ _775212) ^ [_1182035, _1182037, _1182039, _1182041, _1182043, _1182045, _1182047] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1182035, _1182037, _1182039, _1182041), _1182043), _1182045), _1182047) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1182037, _1182039, _1182041), _1182045), hAPP(_1182043, _1182047)))], (49549 ^ _775212) ^ [_1767092, _1767094, _1767096, _1767098] : [hBOOL(hAPP(_1767092, _1767094)), -(c_List_OdropWhile(_1767096, _1767092, hAPP(hAPP(c_List_Olist_OCons(_1767096), _1767094), _1767098)) = c_List_OdropWhile(_1767096, _1767092, _1767098))], (17423 ^ _775212) ^ [] : [-(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))))], (114 ^ _775212) ^ [_776787, _776789, _776791, _776793, _776795, _776797] : [-(c_Nitpick_Oless__eq__frac(_776795, _776791, _776787)), c_Nitpick_Oless__eq__frac(_776797, _776793, _776789), _776797 = _776795, _776793 = _776791, _776789 = _776787], (51010 ^ _775212) ^ [_1798776] : [-(c_List_Omember(_1798776) = c_List_Oset(_1798776))], (47228 ^ _775212) ^ [_1716725, _1716727, _1716729] : [hBOOL(hAPP(c_List_Odistinct(_1716725), _1716727)), -(hAPP(c_List_Oset(_1716725), c_List_Oremove1(_1716725, _1716729, _1716727)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1716725, tc_HOL_Obool)), hAPP(c_List_Oset(_1716725), _1716727)), hAPP(hAPP(c_Set_Oinsert(_1716725), _1716729), c_Orderings_Obot__class_Obot(tc_fun(_1716725, tc_HOL_Obool)))))], (44788 ^ _775212) ^ [_1659842, _1659844, _1659846, _1659848, _1659850] : [hAPP(hAPP(c_List_Omap(_1659842, _1659844), _1659846), _1659848) = hAPP(hAPP(c_List_Omap(_1659842, _1659844), _1659850), _1659848), 44791 ^ _775212 : [(44792 ^ _775212) ^ [_1659965] : [hBOOL(hAPP(hAPP(c_member(_1659842), _1659965), hAPP(c_List_Oset(_1659842), _1659848))), -(hAPP(_1659846, _1659965) = hAPP(_1659850, _1659965))]]], (39952 ^ _775212) ^ [_1539999, _1540001, _1540003, _1540005] : [hBOOL(hAPP(hAPP(c_member(_1539999), _1540001), hAPP(c_Relation_ODomain(_1539999, _1540003), _1540005))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539999, _1540003)), hAPP(hAPP(c_Product__Type_OPair(_1539999, _1540003), _1540001), 39955 ^ [_1539999, _1540001, _1540003, _1540005])), _1540005)))], (25871 ^ _775212) ^ [_1227825, _1227827, _1227829, _1227831, _1227833] : [class_Groups_Ocomm__monoid__add(_1227825), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227825), _1227827), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227829), _1227831), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227833), _1227831))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227825), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1227825, tc_Nat_Onat), _1227827), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1227831))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1227829, _1227833)))], (23652 ^ _775212) ^ [_1186294, _1186296, _1186298, _1186300, _1186302, _1186304, _1186306] : [hBOOL(hAPP(hAPP(_1186294, hAPP(c_Product__Type_Osnd(_1186296, _1186298), _1186300)), hAPP(c_Product__Type_Ofst(_1186296, _1186298), _1186300))), 23659 ^ _775212 : [(23662 ^ _775212) ^ [] : [hBOOL(hAPP(_1186302, hAPP(hAPP(_1186304, 23657 ^ [_1186294, _1186296, _1186298, _1186300, _1186302, _1186304, _1186306]), 23658 ^ [_1186294, _1186296, _1186298, _1186300, _1186302, _1186304, _1186306])))], (23660 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1186294, 23658 ^ [_1186294, _1186296, _1186298, _1186300, _1186302, _1186304, _1186306]), 23657 ^ [_1186294, _1186296, _1186298, _1186300, _1186302, _1186304, _1186306])))]], -(hBOOL(hAPP(_1186302, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186296, _1186298, _1186306), _1186304), _1186300))))], (3164 ^ _775212) ^ [_822730, _822732, _822734, _822736, _822738, _822740] : [-(c_Finite__Set_Ofold1Set(_822740, _822736, _822732) = c_Finite__Set_Ofold1Set(_822738, _822734, _822730)), _822740 = _822738, _822736 = _822734, _822732 = _822730], (52069 ^ _775212) ^ [_1821515, _1821517, _1821519] : [c_Fun_Oinj__on(_1821515, _1821517, _1821519, c_Orderings_Otop__class_Otop(tc_fun(_1821515, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1821517, _1821515, _1821515, c_Hilbert__Choice_Oinv__into(_1821515, _1821517, c_Orderings_Otop__class_Otop(tc_fun(_1821515, tc_HOL_Obool)), _1821519)), _1821519) = c_Fun_Oid(_1821515))], (37240 ^ _775212) ^ [_1468368, _1468370, _1468372, _1468374, _1468376] : [c_Typedef_Otype__definition(_1468368, _1468370, _1468372, _1468374, _1468376), -(hAPP(c_Set_Oimage(_1468370, _1468368, _1468374), _1468376) = c_Orderings_Otop__class_Otop(tc_fun(_1468368, tc_HOL_Obool)))], (5212 ^ _775212) ^ [_854702, _854704] : [_854704 = _854702, -(c_Finite__Set_Ofinite(_854704) = c_Finite__Set_Ofinite(_854702))], (52465 ^ _775212) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (52475 ^ _775212) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (27261 ^ _775212) ^ [_1255443, _1255445, _1255447] : [class_Lattices_Osemilattice__sup(_1255443), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255443), _1255445), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255443), _1255447), _1255445))))], (9711 ^ _775212) ^ [_932304, _932306, _932308] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932304), _932306) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932308), _932306), -(_932304 = _932308), -(_932306 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14413 ^ _775212) ^ [_1015801, _1015803] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015801), _1015803)), _1015801) = _1015803)], (52185 ^ _775212) ^ [_1823294, _1823296] : [class_Orderings_Oord(_1823294), -(class_Orderings_Oord(tc_fun(_1823296, _1823294)))], (42828 ^ _775212) ^ [_1609138, _1609140] : [-(c_Transitive__Closure_Otrancl(_1609138, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1609138, _1609138), tc_HOL_Obool)), _1609140), c_Relation_OId(_1609138))) = c_Transitive__Closure_Ortrancl(_1609138, _1609140))], (45007 ^ _775212) ^ [_1664865, _1664867, _1664869] : [-(hBOOL(hAPP(hAPP(c_member(_1664865), _1664867), hAPP(c_List_Oset(_1664865), _1664869)))), 45008 ^ _775212 : [(45009 ^ _775212) ^ [_1664939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1664939), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664865)), _1664869))), hAPP(hAPP(c_List_Onth(_1664865), _1664869), _1664939) = _1664867]]], (45068 ^ _775212) ^ [_1667484, _1667486, _1667488] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667484), tc_List_Olist(_1667484))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667484), tc_List_Olist(_1667484)), c_List_Olist_ONil(_1667484)), _1667486)), c_List_Olistrel(_1667484, _1667488))), -(_1667486 = c_List_Olist_ONil(_1667484))], (46212 ^ _775212) ^ [_1695368, _1695370] : [_1695370 = c_List_Olist_ONil(_1695368), -(hAPP(c_List_Orotate1(_1695368), _1695370) = c_List_Olist_ONil(_1695368))], (25514 ^ _775212) ^ [_1219470, _1219472, _1219474] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1219470, _1219472) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1219474, _1219472), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1219470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1219472), 25517 ^ [_1219470, _1219472, _1219474])) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1219474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1219472), 25518 ^ [_1219470, _1219472, _1219474])))], (14263 ^ _775212) ^ [_1012888, _1012890, _1012892] : [class_Groups_Ogroup__add(_1012888), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012888), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1012888), _1012890), _1012892)), _1012892) = _1012890)], (46526 ^ _775212) ^ [_1702193, _1702195, _1702197] : [hBOOL(hAPP(c_List_Odistinct(_1702193), hAPP(hAPP(c_List_Olist_OCons(_1702193), _1702195), _1702197))), 46529 ^ _775212 : [(46532 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1702193), _1702197)))], (46530 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1702193), _1702195), hAPP(c_List_Oset(_1702193), _1702197)))]]], (14713 ^ _775212) ^ [_1021605, _1021607, _1021609] : [class_Power_Opower(_1021605), class_Rings_Omult__zero(_1021605), class_Rings_Ono__zero__divisors(_1021605), class_Rings_Ozero__neq__one(_1021605), 14728 ^ _775212 : [(14737 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1021605), _1021607), _1021609) = c_Groups_Ozero__class_Ozero(_1021605)), _1021607 = c_Groups_Ozero__class_Ozero(_1021605), -(_1021609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14729 ^ _775212) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1021605), _1021607), _1021609) = c_Groups_Ozero__class_Ozero(_1021605), 14732 ^ _775212 : [(14735 ^ _775212) ^ [] : [_1021609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14733 ^ _775212) ^ [] : [-(_1021607 = c_Groups_Ozero__class_Ozero(_1021605))]]]]], (49379 ^ _775212) ^ [_1763448, _1763450, _1763452, _1763454] : [hBOOL(hAPP(hAPP(c_member(_1763448), _1763450), hAPP(c_List_Oset(_1763448), c_List_OtakeWhile(_1763448, _1763452, _1763454)))), 49382 ^ _775212 : [(49385 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1763452, _1763450)))], (49383 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763448), _1763450), hAPP(c_List_Oset(_1763448), _1763454))))]]], (17381 ^ _775212) ^ [_1070470] : [-(c_Int_Opred(_1070470) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1070470), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (40119 ^ _775212) ^ [_1544384] : [-(c_Wellfounded_OwfP(_1544384, hAPP(c_COMBK(tc_fun(_1544384, tc_HOL_Obool), _1544384), hAPP(c_COMBK(tc_HOL_Obool, _1544384), c_fFalse))))], (30772 ^ _775212) ^ [_1330694, _1330696, _1330698, _1330700, _1330702, _1330704, _1330706] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330694, tc_fun(_1330696, tc_fun(_1330698, tc_HOL_Obool))), _1330700), _1330702), _1330704), _1330706))), 30773 ^ _775212 : [(30774 ^ _775212) ^ [_1330779] : [hBOOL(hAPP(hAPP(c_member(_1330694), _1330779), _1330700)), hBOOL(hAPP(hAPP(hAPP(_1330702, _1330779), _1330704), _1330706))]]], (48647 ^ _775212) ^ [_1749151, _1749153] : [class_Orderings_Olinorder(_1749151), c_List_Olinorder__class_Osorted(_1749151, _1749153), -(c_List_Olinorder__class_Osorted(_1749151, hAPP(c_List_Otl(_1749151), _1749153)))], (49171 ^ _775212) ^ [_1758999, _1759001] : [-(hAPP(c_List_Orev(_1758999), c_List_Oconcat(_1758999, _1759001)) = c_List_Oconcat(_1758999, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1758999), tc_List_Olist(_1758999)), c_List_Orev(_1758999)), hAPP(c_List_Orev(tc_List_Olist(_1758999)), _1759001))))], (27628 ^ _775212) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (22066 ^ _775212) ^ [_1153934, _1153936, _1153938] : [hBOOL(hAPP(_1153934, hAPP(hAPP(c_Product__Type_OPair(_1153936, _1153938), 22067 ^ [_1153934, _1153936, _1153938]), 22068 ^ [_1153934, _1153936, _1153938]))), 22071 ^ _775212 : [(22072 ^ _775212) ^ [_1154081] : [-(hBOOL(hAPP(_1153934, _1154081)))]]], (27519 ^ _775212) ^ [_1260633, _1260635, _1260637] : [class_Orderings_Olinorder(_1260633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260633), _1260635), _1260637)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260633, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1260633), _1260635)), c_SetInterval_Oord__class_OatLeastAtMost(_1260633, _1260635, _1260637)) = hAPP(c_SetInterval_Oord__class_OatMost(_1260633), _1260637))], (28886 ^ _775212) ^ [_1288468, _1288470, _1288472] : [class_Orderings_Oorder(_1288468), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288468), _1288470), _1288472)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1288468, _1288472, _1288470) = c_Orderings_Obot__class_Obot(tc_fun(_1288468, tc_HOL_Obool)))], (29172 ^ _775212) ^ [_1293703, _1293705, _1293707, _1293709, _1293711] : [-(_1293703 = c_Orderings_Obot__class_Obot(tc_fun(_1293705, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293705, tc_fun(_1293707, tc_HOL_Obool)), _1293703), hAPP(hAPP(c_COMBB(tc_fun(_1293707, tc_HOL_Obool), tc_fun(_1293707, tc_HOL_Obool), _1293705), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293707, tc_HOL_Obool)), _1293709)), _1293711)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293707, tc_HOL_Obool)), _1293709), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293705, tc_fun(_1293707, tc_HOL_Obool)), _1293703), _1293711)))], (23826 ^ _775212) ^ [_1189371, _1189373, _1189375, _1189377, _1189379] : [_1189371 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1189373, _1189375, _1189377, _1189379), _1189371) = c_Lazy__Sequence_Ohit__bound(_1189375))], (40326 ^ _775212) ^ [_1549343] : [-(_1549343 = hAPP(c_Int_OAbs__Integ, 40324 ^ [_1549343]))], (10025 ^ _775212) ^ [_937796, _937798, _937800] : [class_Rings_Ocomm__semiring__1(_937796), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937796), _937798), _937800)), _937800) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937796), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937796), _937798), c_Groups_Oone__class_Oone(_937796))), _937800))], (41302 ^ _775212) ^ [_1571398, _1571400, _1571402, _1571404, _1571406, _1571408] : [c_Finite__Set_Ofun__left__comm__idem(_1571398, _1571400, _1571402), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571398), _1571404)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1571398, _1571400, _1571402), _1571406), hAPP(hAPP(c_Set_Oinsert(_1571398), _1571408), _1571404)) = hAPP(hAPP(_1571402, _1571408), hAPP(hAPP(c_Finite__Set_Ofold(_1571398, _1571400, _1571402), _1571406), _1571404)))], (48003 ^ _775212) ^ [_1733834, _1733836] : [_1733836 = c_List_Olist_ONil(_1733834), -(c_List_Olist_ONil(_1733834) = c_List_Oremdups(_1733834, _1733836))], (47867 ^ _775212) ^ [_1730761, _1730763, _1730765, _1730767] : [-(hAPP(c_List_Oset(tc_prod(_1730761, _1730763)), c_Enum_Oproduct(_1730761, _1730763, _1730765, _1730767)) = hAPP(hAPP(c_Product__Type_OSigma(_1730761, _1730763), hAPP(c_List_Oset(_1730761), _1730765)), hAPP(c_COMBK(tc_fun(_1730763, tc_HOL_Obool), _1730761), hAPP(c_List_Oset(_1730763), _1730767))))], (49442 ^ _775212) ^ [_1764708, _1764710, _1764712, _1764714, _1764716] : [hBOOL(hAPP(hAPP(c_member(_1764708), _1764710), hAPP(c_List_Oset(_1764708), _1764712))), -(hBOOL(hAPP(_1764714, _1764710))), -(c_List_OtakeWhile(_1764708, _1764714, hAPP(hAPP(c_List_Oappend(_1764708), _1764712), _1764716)) = c_List_OtakeWhile(_1764708, _1764714, _1764712))], (6491 ^ _775212) ^ [_877950, _877952, _877954] : [class_Rings_Osemiring__1(_877950), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_877950), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _877952), _877954)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877950), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_877950), _877952)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_877950), _877954)))], (13785 ^ _775212) ^ [_1003915, _1003917] : [-(_1003915 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003917), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1003915), _1003917))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1003915, _1003917)))], (30304 ^ _775212) ^ [_1319917, _1319919, _1319921, _1319923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool)), _1319921), _1319923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319917, tc_fun(_1319919, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1319917, tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_fun(_1319919, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319919, tc_fun(tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_fun(_1319919, tc_HOL_Obool)), _1319917), c_COMBC(_1319919, tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319919, tc_prod(_1319917, _1319919)), tc_fun(_1319919, tc_fun(tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_HOL_Obool)), _1319917), hAPP(c_COMBB(tc_prod(_1319917, _1319919), tc_fun(tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_HOL_Obool), _1319919), c_member(tc_prod(_1319917, _1319919)))), c_Product__Type_OPair(_1319917, _1319919)))), _1319921)), hAPP(hAPP(c_COMBC(_1319917, tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_fun(_1319919, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319919, tc_fun(tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_fun(_1319919, tc_HOL_Obool)), _1319917), c_COMBC(_1319919, tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319919, tc_prod(_1319917, _1319919)), tc_fun(_1319919, tc_fun(tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_HOL_Obool)), _1319917), hAPP(c_COMBB(tc_prod(_1319917, _1319919), tc_fun(tc_fun(tc_prod(_1319917, _1319919), tc_HOL_Obool), tc_HOL_Obool), _1319919), c_member(tc_prod(_1319917, _1319919)))), c_Product__Type_OPair(_1319917, _1319919)))), _1319923))))], (12079 ^ _775212) ^ [_973707, _973709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973707)), _973709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973707), _973709)))], (37960 ^ _775212) ^ [_1486099, _1486101, _1486103, _1486105, _1486107, _1486109] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486099, _1486101)), hAPP(hAPP(c_Product__Type_OPair(_1486099, _1486101), _1486103), _1486105)), hAPP(hAPP(c_Product__Type_OSigma(_1486099, _1486101), _1486107), _1486109))), -(hBOOL(hAPP(hAPP(c_member(_1486101), _1486105), hAPP(_1486109, _1486103))))], (18879 ^ _775212) ^ [_1096442, _1096444, _1096446] : [class_Rings_Olinordered__idom(_1096442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096442), _1096444), c_Groups_Ozero__class_Ozero(_1096442))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096442), hAPP(hAPP(c_Power_Opower__class_Opower(_1096442), _1096444), 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)))), _1096446)))), c_Groups_Ozero__class_Ozero(_1096442))))], (23182 ^ _775212) ^ [_1176610, _1176612, _1176614, _1176616] : [class_Orderings_Olinorder(_1176610), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176610), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176610), _1176612), _1176614)), _1176616) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176610), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176610), _1176612), _1176616)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176610), _1176614), _1176616)))], (38074 ^ _775212) ^ [_1488840, _1488842, _1488844, _1488846, _1488848, _1488850, _1488852, _1488854] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1488840, _1488842), tc_fun(tc_prod(_1488844, _1488846), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1488840, _1488842), _1488848), hAPP(c_COMBK(tc_fun(_1488842, tc_HOL_Obool), _1488840), _1488850))), hAPP(c_Product__Type_Oprod_Oprod__case(_1488840, _1488842, tc_fun(tc_prod(_1488844, _1488846), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1488840, tc_fun(_1488842, tc_fun(_1488844, tc_fun(_1488846, tc_HOL_Obool))), tc_fun(_1488842, tc_fun(tc_prod(_1488844, _1488846), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1488844, tc_fun(_1488846, tc_HOL_Obool)), tc_fun(tc_prod(_1488844, _1488846), tc_HOL_Obool)), tc_fun(tc_fun(_1488842, tc_fun(_1488844, tc_fun(_1488846, tc_HOL_Obool))), tc_fun(_1488842, tc_fun(tc_prod(_1488844, _1488846), tc_HOL_Obool))), _1488840), c_COMBB(tc_fun(_1488844, tc_fun(_1488846, tc_HOL_Obool)), tc_fun(tc_prod(_1488844, _1488846), tc_HOL_Obool), _1488842)), hAPP(hAPP(c_COMBB(tc_fun(_1488844, tc_HOL_Obool), tc_fun(tc_fun(_1488844, tc_fun(_1488846, tc_HOL_Obool)), tc_fun(tc_prod(_1488844, _1488846), tc_HOL_Obool)), _1488840), c_Product__Type_OSigma(_1488844, _1488846)), _1488852))), hAPP(hAPP(c_COMBB(tc_fun(_1488846, tc_HOL_Obool), tc_fun(_1488844, tc_fun(_1488846, tc_HOL_Obool)), _1488842), c_COMBK(tc_fun(_1488846, tc_HOL_Obool), _1488844)), _1488854)))) = hAPP(hAPP(c_Product__Type_OSigma(_1488844, _1488846), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1488840, tc_fun(_1488844, tc_HOL_Obool)), _1488848), _1488852)), hAPP(c_COMBK(tc_fun(_1488846, tc_HOL_Obool), _1488844), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1488842, tc_fun(_1488846, tc_HOL_Obool)), _1488850), _1488854))))], (46390 ^ _775212) ^ [_1699902, _1699904, _1699906] : [-(_1699902 = c_List_Olist_ONil(_1699904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1699906), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699904)), _1699902))), -(hAPP(c_List_Ohd(_1699904), hAPP(hAPP(c_List_Odrop(_1699904), _1699906), _1699902)) = hAPP(hAPP(c_List_Onth(_1699904), _1699902), _1699906))], (16119 ^ _775212) ^ [_1048309, _1048311] : [class_Groups_Oordered__ab__group__add__abs(_1048309), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048309), c_Groups_Ozero__class_Ozero(_1048309)), hAPP(c_Groups_Oabs__class_Oabs(_1048309), _1048311))))], (13523 ^ _775212) ^ [_999483, _999485, _999487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _999483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999483), _999485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _999487), _999485)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _999487), _999483))))], (31273 ^ _775212) ^ [_1341026, _1341028, _1341030] : [-(hAPP(c_Finite__Set_Ocard(_1341026), _1341028) = hAPP(c_Nat_OSuc, _1341030)), 31274 ^ _775212 : [(31275 ^ _775212) ^ [_1341126, _1341128] : [_1341028 = hAPP(hAPP(c_Set_Oinsert(_1341026), _1341128), _1341126), -(hBOOL(hAPP(hAPP(c_member(_1341026), _1341128), _1341126))), hAPP(c_Finite__Set_Ocard(_1341026), _1341126) = _1341030, 31286 ^ _775212 : [(31289 ^ _775212) ^ [] : [_1341126 = c_Orderings_Obot__class_Obot(tc_fun(_1341026, tc_HOL_Obool))], (31287 ^ _775212) ^ [] : [-(_1341030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (37451 ^ _775212) ^ [_1472760, _1472762, _1472764, _1472766] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472760, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1472762, _1472760, _1472764), hAPP(c_Set_Ovimage(_1472762, _1472760, _1472764), _1472766))), _1472766)))], (10709 ^ _775212) ^ [] : [-(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))))], (5864 ^ _775212) ^ [_868016, _868018, _868020, _868022, _868024] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_868016, _868018), _868020, _868022, _868024), 5869 ^ _775212 : [(5872 ^ _775212) ^ [] : [hBOOL(hAPP(_868016, _868020))], (5870 ^ _775212) ^ [] : [-(_868024 = _868020)]], 5873 ^ _775212 : [(5879 ^ _775212) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_868016, _868018), 5875 ^ [_868016, _868018, _868020, _868022, _868024], _868022, _868024))], (5877 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_868018, _868020, _868022, 5875 ^ [_868016, _868018, _868020, _868022, _868024]))], (5874 ^ _775212) ^ [] : [-(hBOOL(hAPP(_868016, _868020)))]]], (18347 ^ _775212) ^ [_1086824] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086824))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1086824)))))], (35033 ^ _775212) ^ [_1419752, _1419754, _1419756, _1419758] : [-(hBOOL(hAPP(hAPP(c_member(_1419752), _1419754), _1419756))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419752, tc_HOL_Obool)), _1419756), hAPP(hAPP(c_Set_Oinsert(_1419752), _1419754), _1419758)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419752, tc_HOL_Obool)), _1419756), _1419758))], (26593 ^ _775212) ^ [_1242694, _1242696] : [c_Nat__Transfer_Onat__set(_1242694), c_Nat__Transfer_Onat__set(_1242696), 26600 ^ _775212 : [(26607 ^ _775212) ^ [] : [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), _1242694)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1242696))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1242694), _1242696)))], (26601 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1242694), _1242696)), -(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), _1242694)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1242696))))]]], (41764 ^ _775212) ^ [_1580904, _1580906, _1580908, _1580910, _1580912] : [c_Finite__Set_Ofun__left__comm(_1580904, _1580906, _1580908), hBOOL(hAPP(c_Finite__Set_Ofinite(_1580904), _1580910)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1580904, _1580906, _1580908, _1580912, _1580910), hAPP(hAPP(c_Finite__Set_Ofold(_1580904, _1580906, _1580908), _1580912), _1580910))))], (27880 ^ _775212) ^ [_1269019] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1269019)), 27884 ^ _775212 : [(27885 ^ _775212) ^ [_1269099] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1269099), _1269019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1269099), 27883 ^ [_1269019])))]]], (45441 ^ _775212) ^ [_1676792, _1676794, _1676796, _1676798] : [class_Groups_Oab__group__add(_1676792), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1676792), hAPP(c_List_Omonoid__add__class_Olistsum(_1676792), hAPP(hAPP(c_List_Omap(_1676794, _1676792), _1676796), _1676798))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1676792), hAPP(hAPP(c_List_Omap(_1676794, _1676792), hAPP(c_Fun_Ocomp(_1676792, _1676792, _1676794, c_Groups_Ouminus__class_Ouminus(_1676792)), _1676796)), _1676798)))], (49816 ^ _775212) ^ [_1772459, _1772461, _1772463, _1772465] : [-(c_List_Omaps(_1772459, _1772461, _1772463, _1772465) = c_List_Oconcat(_1772461, hAPP(hAPP(c_List_Omap(_1772459, tc_List_Olist(_1772461)), _1772463), _1772465)))], (18747 ^ _775212) ^ [_1093687, _1093689, _1093691] : [class_Rings_Olinordered__idom(_1093687), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093687), c_Groups_Ozero__class_Ozero(_1093687)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093687), hAPP(hAPP(c_Power_Opower__class_Opower(_1093687), _1093689), 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(_1093687), _1093691), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (25909 ^ _775212) ^ [_1228770, _1228772, _1228774, _1228776, _1228778] : [class_Orderings_Oorder(_1228770), 25912 ^ _775212 : [(25933 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1228770, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1228770, _1228772, _1228774)), c_SetInterval_Oord__class_OatLeastAtMost(_1228770, _1228776, _1228778)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228770), _1228776), _1228778)), 25936 ^ _775212 : [(25939 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228770), _1228776), _1228772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228770), _1228774), _1228778)), 25946 ^ _775212 : [(25949 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228770), _1228774), _1228778))], (25947 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228770), _1228776), _1228772))]]], (25937 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228770), _1228772), _1228774)))]]], (25913 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1228770, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1228770, _1228772, _1228774)), c_SetInterval_Oord__class_OatLeastAtMost(_1228770, _1228776, _1228778))), 25916 ^ _775212 : [(25917 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228770), _1228772), _1228774)), 25920 ^ _775212 : [(25925 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228770), _1228776), _1228772))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228770), _1228774), _1228778)))], (25923 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228770), _1228774), _1228778)))], (25921 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228770), _1228776), _1228772)))]]], (25931 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228770), _1228776), _1228778)))]]]]], (11156 ^ _775212) ^ [_958218, _958220, _958222, _958224] : [class_Rings_Olinordered__ring__strict(_958218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958218), _958220), c_Groups_Ozero__class_Ozero(_958218))), 11163 ^ _775212 : [(11170 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958218), _958224), _958222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958218), _958220), _958222)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958218), _958220), _958224))))], (11164 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958218), _958220), _958222)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958218), _958220), _958224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958218), _958224), _958222)))]]], (40694 ^ _775212) ^ [_1557879, _1557881, _1557883, _1557885, _1557887, _1557889] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1557879, _1557881), _1557879, tc_prod(_1557883, _1557885), c_Product__Type_Ofst(_1557879, _1557881)), c_Product__Type_Omap__pair(_1557883, _1557879, _1557885, _1557881, _1557887, _1557889)) = hAPP(c_Fun_Ocomp(_1557883, _1557879, tc_prod(_1557883, _1557885), _1557887), c_Product__Type_Ofst(_1557883, _1557885)))], (7144 ^ _775212) ^ [_888974, _888976, _888978] : [class_Orderings_Olinorder(_888974), -(_888976 = _888978), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888974), _888976), _888978))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888974), _888978), _888976)))], (13467 ^ _775212) ^ [_998684, _998686, _998688] : [class_Divides_Osemiring__div(_998684), -(_998686 = c_Groups_Ozero__class_Ozero(_998684)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_998684), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998684), _998688), _998686)), _998686) = _998688)], (17307 ^ _775212) ^ [_1069427, _1069429] : [class_Int_Onumber__ring(_1069427), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069427), hAPP(c_Int_Onumber__class_Onumber__of(_1069427), c_Int_OPls)), _1069429) = _1069429)], (10744 ^ _775212) ^ [_950774] : [10745 ^ _775212 : [(10746 ^ _775212) ^ [_950831] : [hBOOL(hAPP(_950774, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _950831)))]], 10748 ^ _775212 : [(10751 ^ _775212) ^ [] : [-(hBOOL(hAPP(_950774, 10747 ^ [_950774])))], (10749 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10747 ^ [_950774])))]]], (23348 ^ _775212) ^ [_1180105] : [class_Orderings_Olinorder(_1180105), -(c_Orderings_Oord_Omax(_1180105, hAPP(c_COMBC(_1180105, _1180105, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1180105))) = c_Orderings_Oord__class_Omin(_1180105))], (12520 ^ _775212) ^ [_981518, _981520, _981522, _981524] : [class_Divides_Osemiring__div(_981518), -(c_Divides_Odiv__class_Omod(_981518, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981518), c_Divides_Odiv__class_Omod(_981518, _981520, _981522)), _981524), _981522) = c_Divides_Odiv__class_Omod(_981518, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981518), _981520), _981524), _981522))], (40440 ^ _775212) ^ [_1551969, _1551971] : [40441 ^ _775212 : [(40442 ^ _775212) ^ [_1552015] : [hBOOL(hAPP(_1551969, _1552015))]], -(hBOOL(hAPP(_1551969, c_Hilbert__Choice_OEps(_1551971, _1551969))))], (29399 ^ _775212) ^ [_1298317, _1298319, _1298321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1298317, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1298317, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29400 ^ [_1298317, _1298319, _1298321])), _1298319)), _1298321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1298317, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1298317, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1298319)), _1298321)))], (26082 ^ _775212) ^ [_1232107, _1232109] : [26090 ^ _775212 : [(26093 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1232109, 26089 ^ [_1232107, _1232109])))], (26091 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26089 ^ [_1232107, _1232109]), _1232107)))]], 26083 ^ _775212 : [(26084 ^ _775212) ^ [_1232175] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1232175), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232107))), hBOOL(hAPP(_1232109, _1232175))]]], (40328 ^ _775212) ^ [_1549371] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40324 ^ [_1549371]), c_Int_OInteg)))], (18395 ^ _775212) ^ [_1087617, _1087619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087617), _1087619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1087617)), c_Int_OBit0(_1087619))))], (45383 ^ _775212) ^ [_1674986, _1674988, _1674990, _1674992] : [-(hAPP(c_List_Oset(tc_prod(_1674986, _1674988)), hAPP(hAPP(c_List_Ozip(_1674986, _1674988), _1674990), _1674992)) = hAPP(c_Set_OCollect(tc_prod(_1674986, _1674988)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1674986, _1674988)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1674986, _1674988), 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(_1674986, _1674988)), 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(_1674986, _1674988)), 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(_1674986, _1674988), tc_fun(tc_Nat_Onat, tc_prod(_1674986, _1674988)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1674986, _1674988), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1674986, _1674988)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1674986, _1674988)), c_COMBB(tc_prod(_1674986, _1674988), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1674988, tc_prod(_1674986, _1674988)), hAPP(hAPP(c_COMBB(_1674986, tc_fun(_1674988, tc_prod(_1674986, _1674988)), tc_Nat_Onat), c_Product__Type_OPair(_1674986, _1674988)), hAPP(c_List_Onth(_1674986), _1674990))), hAPP(c_List_Onth(_1674988), _1674992)))))), 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(_1674986)), _1674990)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674988)), _1674992)))))))], (45534 ^ _775212) ^ [_1679331, _1679333] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1679331, _1679333)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1679331, _1679333))], (43061 ^ _775212) ^ [_1614842, _1614844, _1614846, _1614848, _1614850, _1614852] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614842, _1614842)), hAPP(hAPP(c_Product__Type_OPair(_1614842, _1614842), _1614844), _1614846)), _1614848)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1614842, _1614842)), hAPP(hAPP(c_Product__Type_OPair(_1614842, _1614842), _1614846), _1614850)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1614842, _1614842), tc_HOL_Obool), _1614852), _1614848))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614842, _1614842)), hAPP(hAPP(c_Product__Type_OPair(_1614842, _1614842), _1614844), _1614850)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1614842, _1614842), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1614852)), _1614848))))], (34067 ^ _775212) ^ [_1398121, _1398123] : [-(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), _1398121), _1398123)), 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), _1398121), _1398123))], (25569 ^ _775212) ^ [_1220746, _1220748, _1220750, _1220752] : [class_Rings_Oring__1(_1220746), -(hAPP(c_Int_Oring__1__class_Oof__int(_1220746), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1220748, tc_Int_Oint), _1220750), _1220752)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1220748, _1220746), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1220746, _1220748), c_Int_Oring__1__class_Oof__int(_1220746)), _1220750)), _1220752))], (46258 ^ _775212) ^ [_1696393, _1696395, _1696397, _1696399] : [-(hAPP(hAPP(c_List_Odrop(_1696393), _1696395), hAPP(hAPP(c_List_Oappend(_1696393), _1696397), _1696399)) = hAPP(hAPP(c_List_Oappend(_1696393), hAPP(hAPP(c_List_Odrop(_1696393), _1696395), _1696397)), hAPP(hAPP(c_List_Odrop(_1696393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1696395), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696393)), _1696397))), _1696399)))], (51036 ^ _775212) ^ [_1799254, _1799256, _1799258] : [hBOOL(hAPP(hAPP(c_member(_1799254), _1799258), hAPP(c_List_Oset(_1799254), _1799256))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1799254), _1799256), _1799258)))], (31425 ^ _775212) ^ [_1343854, _1343856] : [31426 ^ _775212 : [(31429 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343856), _1343854))], (31427 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343854), _1343856)))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1343854, _1343856) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (50135 ^ _775212) ^ [_1780098, _1780100, _1780102, _1780104, _1780106] : [hAPP(hAPP(c_List_Olist_OCons(_1780098), _1780100), _1780102) = hAPP(c_List_Ofilter(_1780098, _1780104), _1780106), 50140 ^ _775212 : [(50149 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1780104, _1780100)))], (50151 ^ _775212) ^ [] : [-(_1780102 = hAPP(c_List_Ofilter(_1780098, _1780104), 50139 ^ [_1780098, _1780100, _1780102, _1780104, _1780106]))], (50143 ^ _775212) ^ [_1780412] : [hBOOL(hAPP(hAPP(c_member(_1780098), _1780412), hAPP(c_List_Oset(_1780098), 50138 ^ [_1780098, _1780100, _1780102, _1780104, _1780106]))), hBOOL(hAPP(_1780104, _1780412))], (50141 ^ _775212) ^ [] : [-(_1780106 = hAPP(hAPP(c_List_Oappend(_1780098), 50138 ^ [_1780098, _1780100, _1780102, _1780104, _1780106]), hAPP(hAPP(c_List_Olist_OCons(_1780098), _1780100), 50139 ^ [_1780098, _1780100, _1780102, _1780104, _1780106])))]]], (18309 ^ _775212) ^ [_1086153] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1086153)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1086153)))], (23800 ^ _775212) ^ [_1188853, _1188855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1188853), _1188855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1188853)), hAPP(c_Code__Numeral_Onat__of, _1188855))))], (17369 ^ _775212) ^ [_1070270, _1070272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070270), _1070272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1070270)), _1070272)))], (40924 ^ _775212) ^ [_1563094, _1563096, _1563098, _1563100, _1563102, _1563104] : [c_Finite__Set_Ofolding__idem(_1563094, _1563096, _1563098, _1563100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563094), _1563102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1563094, tc_HOL_Obool)), _1563104), _1563102)), -(hAPP(c_Fun_Ocomp(_1563096, _1563096, _1563096, hAPP(_1563100, _1563102)), hAPP(_1563100, _1563104)) = hAPP(_1563100, _1563102))], (22436 ^ _775212) ^ [_1162307, _1162309, _1162311] : [class_Orderings_Olinorder(_1162307), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162307), _1162309), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162307), _1162309), _1162311)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162307), _1162309), _1162311))], (32627 ^ _775212) ^ [_1366564, _1366566, _1366568] : [class_Orderings_Olinorder(_1366564), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366564), _1366566)), -(_1366566 = c_Orderings_Obot__class_Obot(tc_fun(_1366564, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1366564, c_Orderings_Oord__class_Omin(_1366564), hAPP(hAPP(c_Set_Oinsert(_1366564), _1366568), _1366566)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1366564), _1366568), c_Big__Operators_Olattice_OInf__fin(_1366564, c_Orderings_Oord__class_Omin(_1366564), _1366566)))], (50548 ^ _775212) ^ [_1788937, _1788939, _1788941, _1788943] : [c_List_Olist__all(_1788937, _1788939, hAPP(hAPP(c_List_Olist_OCons(_1788937), _1788941), _1788943)), 50551 ^ _775212 : [(50554 ^ _775212) ^ [] : [-(c_List_Olist__all(_1788937, _1788939, _1788943))], (50552 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1788939, _1788941)))]]], (3470 ^ _775212) ^ [_827607, _827609, _827611, _827613, _827615, _827617, _827619, _827621] : [-(c_New__Random__Sequence_Opos__map(_827621, _827617, _827613, _827609) = c_New__Random__Sequence_Opos__map(_827619, _827615, _827611, _827607)), _827621 = _827619, _827617 = _827615, _827613 = _827611, _827609 = _827607], (2050 ^ _775212) ^ [_804797, _804799, _804801, _804803] : [-(c_SMT_Oz3mod(_804803, _804799) = c_SMT_Oz3mod(_804801, _804797)), _804803 = _804801, _804799 = _804797], (39184 ^ _775212) ^ [_1515588, _1515590, _1515592, _1515594] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515588), hAPP(c_Set_OCollect(_1515588), _1515590))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1515592), hAPP(c_Set_OCollect(_1515592), hAPP(hAPP(c_COMBB(tc_fun(_1515588, tc_HOL_Obool), tc_HOL_Obool, _1515592), c_HOL_OEx(_1515588)), hAPP(hAPP(c_COMBC(_1515592, tc_fun(_1515588, tc_HOL_Obool), tc_fun(_1515588, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515588, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1515588, tc_HOL_Obool), tc_fun(_1515588, tc_HOL_Obool)), _1515592), c_COMBS(_1515588, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515588, tc_HOL_Obool), tc_fun(_1515588, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1515592), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515588), c_fconj)), hAPP(hAPP(c_COMBC(_1515592, tc_fun(_1515588, _1515592), tc_fun(_1515588, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515592, tc_HOL_Obool), tc_fun(tc_fun(_1515588, _1515592), tc_fun(_1515588, tc_HOL_Obool)), _1515592), c_COMBB(_1515592, tc_HOL_Obool, _1515588)), c_fequal)), _1515594)))), _1515590))))))], (27874 ^ _775212) ^ [_1268827, _1268829] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1268827, tc_HOL_Obool)), _1268829), c_Orderings_Otop__class_Otop(tc_fun(_1268827, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1268827, tc_HOL_Obool)))], (24510 ^ _775212) ^ [_1200724, _1200726, _1200728, _1200730, _1200732] : [class_Rings_Ocomm__semiring__1(_1200724), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1200724), _1200726), _1200728)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1200724), _1200730), _1200732)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1200724), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200724), _1200726), _1200730)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200724), _1200728), _1200732))))], (46829 ^ _775212) ^ [_1708644, _1708646, _1708648] : [-(c_List_Orotate(_1708644, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1708646), _1708648)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1708644), tc_List_Olist(_1708644), tc_List_Olist(_1708644), c_List_Orotate(_1708644, _1708646)), c_List_Orotate(_1708644, _1708648)))], (43950 ^ _775212) ^ [_1636097, _1636099, _1636101, _1636103, _1636105, _1636107, _1636109] : [c_Finite__Set_Ofolding__image__simple__idem(_1636097, _1636099, _1636101, _1636103, _1636105, _1636107), -(hAPP(hAPP(_1636101, _1636109), _1636109) = _1636109)], (52151 ^ _775212) ^ [_1822849, _1822851] : [class_Orderings_Opreorder(_1822849), -(class_Orderings_Opreorder(tc_fun(_1822851, _1822849)))], (44798 ^ _775212) ^ [_1660086, _1660088, _1660090, _1660092, _1660094] : [44800 ^ _775212 : [(44803 ^ _775212) ^ [] : [hAPP(_1660090, 44799 ^ [_1660086, _1660088, _1660090, _1660092, _1660094]) = hAPP(_1660094, 44799 ^ [_1660086, _1660088, _1660090, _1660092, _1660094])], (44801 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1660086), 44799 ^ [_1660086, _1660088, _1660090, _1660092, _1660094]), hAPP(c_List_Oset(_1660086), _1660092))))]], -(hAPP(hAPP(c_List_Omap(_1660086, _1660088), _1660090), _1660092) = hAPP(hAPP(c_List_Omap(_1660086, _1660088), _1660094), _1660092))], (2508 ^ _775212) ^ [_811898, _811900, _811902, _811904, _811906, _811908, _811910, _811912, _811914, _811916] : [-(c_Nitpick_Opair__box_Opair__box__size(_811916, _811912, _811908, _811904, _811900) = c_Nitpick_Opair__box_Opair__box__size(_811914, _811910, _811906, _811902, _811898)), _811916 = _811914, _811912 = _811910, _811908 = _811906, _811904 = _811902, _811900 = _811898], (27343 ^ _775212) ^ [_1257044, _1257046, _1257048, _1257050, _1257052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257044, tc_HOL_Obool)), _1257046), _1257048)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257044, tc_HOL_Obool)), _1257050), _1257052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257044, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257044, tc_HOL_Obool)), _1257046), _1257050)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257044, tc_HOL_Obool)), _1257048), _1257052))))], (14977 ^ _775212) ^ [_1026219, _1026221, _1026223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026219), _1026221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026219), _1026223)), 14984 ^ _775212 : [(14991 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026221), _1026223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026221), _1026219)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026223), _1026219))))], (14985 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026221), _1026219)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026223), _1026219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026221), _1026223)))]]], (13163 ^ _775212) ^ [_993290, _993292, _993294, _993296] : [_993290 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _993292), _993294)), _993296), -(_993292 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _993290), _993292) = _993294), 13170 ^ _775212 : [(13173 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _993296)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _993296), _993292))], (13171 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _993292)))]], 13178 ^ _775212 : [(13181 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _993292), _993296)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _993296), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (13179 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _993292))]]], (22790 ^ _775212) ^ [_1169248, _1169250] : [-(c_Divides_Odivmod__int__rel(_1169248, _1169250) = 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, _1169248))), 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), _1169250)))))), 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)), _1169250))), 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)), _1169250))))), 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)), _1169250)))), 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), _1169250))), 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))))))))], (23680 ^ _775212) ^ [_1186858, _1186860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1186858), _1186860)), -(c_Quickcheck_Obeyond(_1186858, _1186860) = _1186860)], (33217 ^ _775212) ^ [_1378303, _1378305, _1378307, _1378309, _1378311] : [class_Fields_Ofield(_1378303), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378305), _1378307)), -(hAPP(_1378309, _1378311) = c_Groups_Ozero__class_Ozero(_1378303)), 33228 ^ _775212 : [(33235 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1378305), _1378311), _1378307))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378305, _1378303), _1378309), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378305, tc_HOL_Obool)), _1378307), hAPP(hAPP(c_Set_Oinsert(_1378305), _1378311), c_Orderings_Obot__class_Obot(tc_fun(_1378305, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378305, _1378303), _1378309), _1378307))], (33229 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1378305), _1378311), _1378307)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378305, _1378303), _1378309), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378305, tc_HOL_Obool)), _1378307), hAPP(hAPP(c_Set_Oinsert(_1378305), _1378311), c_Orderings_Obot__class_Obot(tc_fun(_1378305, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1378303), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378305, _1378303), _1378309), _1378307)), hAPP(_1378309, _1378311)))]]], (47176 ^ _775212) ^ [_1715748, _1715750, _1715752, _1715754] : [_1715748 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715750)), _1715752)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1715750, hAPP(hAPP(c_List_Olist__update(_1715750, _1715752), _1715748), _1715754)) = c_List_Obutlast(_1715750, _1715752))], (49904 ^ _775212) ^ [_1775001, _1775003, _1775005, _1775007] : [class_Orderings_Oorder(_1775001), class_Enum_Oenum(_1775003), 49911 ^ _775212 : [(49920 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1775003, _1775001)), _1775005), _1775007))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1775003, _1775001)), _1775005), _1775007)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1775003), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1775003), c_fNot), hAPP(hAPP(c_COMBS(_1775003, _1775001, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1775001, tc_fun(_1775001, tc_HOL_Obool), _1775003), c_fequal), _1775005)), _1775007))))], (49912 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1775003, _1775001)), _1775005), _1775007)), 49915 ^ _775212 : [(49918 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1775003), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1775003), c_fNot), hAPP(hAPP(c_COMBS(_1775003, _1775001, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1775001, tc_fun(_1775001, tc_HOL_Obool), _1775003), c_fequal), _1775005)), _1775007)))))], (49916 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1775003, _1775001)), _1775005), _1775007)))]]]]], (18775 ^ _775212) ^ [_1094226, _1094228, _1094230] : [class_Rings_Olinordered__idom(_1094226), 18778 ^ _775212 : [(18779 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094226), c_Groups_Ozero__class_Ozero(_1094226)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094226), hAPP(hAPP(c_Power_Opower__class_Opower(_1094226), _1094228), 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(_1094226), _1094230), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1094228 = c_Groups_Ozero__class_Ozero(_1094226), _1094230 = c_Groups_Ozero__class_Ozero(_1094226)], (18789 ^ _775212) ^ [] : [18790 ^ _775212 : [(18793 ^ _775212) ^ [] : [-(_1094230 = c_Groups_Ozero__class_Ozero(_1094226))], (18791 ^ _775212) ^ [] : [-(_1094228 = c_Groups_Ozero__class_Ozero(_1094226))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094226), c_Groups_Ozero__class_Ozero(_1094226)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094226), hAPP(hAPP(c_Power_Opower__class_Opower(_1094226), _1094228), 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(_1094226), _1094230), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (52257 ^ _775212) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (19667 ^ _775212) ^ [_1110084, _1110086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110084), 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)), _1110086)), -(c_Divides_OnegDivAlg(_1110084, _1110086) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1110084), _1110086)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1110084, _1110086)))], (12562 ^ _775212) ^ [_982349, _982351, _982353] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _982349), c_Divides_Odiv__class_Omod(tc_Int_Oint, _982351, _982353)), _982353) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _982349), _982351), _982353))], (49253 ^ _775212) ^ [_1760784, _1760786, _1760788, _1760790] : [_1760786 = hAPP(hAPP(c_List_Oappend(_1760784), hAPP(c_List_Orev(_1760784), _1760790)), hAPP(hAPP(c_List_Olist_OCons(_1760784), _1760788), c_List_Olist_ONil(_1760784))), -(hAPP(c_List_Orev(_1760784), _1760786) = hAPP(hAPP(c_List_Olist_OCons(_1760784), _1760788), _1760790))], (27267 ^ _775212) ^ [_1255550, _1255552, _1255554] : [class_Lattices_Olattice(_1255550), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255550), _1255552), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255550), _1255554), _1255552))))], (38123 ^ _775212) ^ [_1490609, _1490611, _1490613, _1490615, _1490617, _1490619] : [class_Groups_Ocomm__monoid__mult(_1490609), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490611), _1490613)), 38133 ^ _775212 : [(38136 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490615), hAPP(_1490617, 38132 ^ [_1490609, _1490611, _1490613, _1490615, _1490617, _1490619])))], (38134 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490611), 38132 ^ [_1490609, _1490611, _1490613, _1490615, _1490617, _1490619]), _1490613)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490611, _1490609), hAPP(hAPP(c_COMBS(_1490611, tc_fun(_1490615, tc_HOL_Obool), _1490609), hAPP(hAPP(c_COMBB(tc_fun(_1490615, _1490609), tc_fun(tc_fun(_1490615, tc_HOL_Obool), _1490609), _1490611), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490615, _1490609)), _1490619)), _1490617)), _1490613) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1490611, _1490615), _1490609), hAPP(c_Product__Type_Oprod_Oprod__case(_1490611, _1490615, _1490609), _1490619)), hAPP(hAPP(c_Product__Type_OSigma(_1490611, _1490615), _1490613), _1490617)))], (22370 ^ _775212) ^ [_1161059] : [-(c_Divides_Oadjust(_1161059) = 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)), _1161059))))), 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)), _1161059))))), 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))))))))], (38413 ^ _775212) ^ [_1497287, _1497289, _1497291, _1497293] : [c_Relation_Orefl__on(_1497287, _1497289, _1497291), hBOOL(hAPP(hAPP(c_member(_1497287), _1497293), _1497289)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1497287, _1497287)), hAPP(hAPP(c_Product__Type_OPair(_1497287, _1497287), _1497293), _1497293)), _1497291)))], (36591 ^ _775212) ^ [_1454613, _1454615, _1454617, _1454619, _1454621, _1454623] : [c_Fun_Oinj__on(_1454613, _1454615, _1454617, _1454619), hAPP(_1454617, _1454621) = hAPP(_1454617, _1454623), hBOOL(hAPP(hAPP(c_member(_1454613), _1454621), _1454619)), hBOOL(hAPP(hAPP(c_member(_1454613), _1454623), _1454619)), -(_1454621 = _1454623)], (52729 ^ _775212) ^ [_1828930, _1828932] : [hBOOL(hAPP(hAPP(c_fconj, _1828930), _1828932)), -(hBOOL(_1828932))], (14601 ^ _775212) ^ [_1019312, _1019314, _1019316] : [class_Groups_Oordered__ab__group__add(_1019312), 14604 ^ _775212 : [(14611 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019312), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1019312), _1019314), _1019316)), c_Groups_Ozero__class_Ozero(_1019312))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019312), _1019314), _1019316)))], (14605 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019312), _1019314), _1019316)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019312), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1019312), _1019314), _1019316)), c_Groups_Ozero__class_Ozero(_1019312))))]]], (50530 ^ _775212) ^ [_1788630, _1788632, _1788634, _1788636] : [c_List_Olist__all(_1788630, _1788632, hAPP(hAPP(c_List_Oappend(_1788630), _1788634), _1788636)), 50533 ^ _775212 : [(50536 ^ _775212) ^ [] : [-(c_List_Olist__all(_1788630, _1788632, _1788636))], (50534 ^ _775212) ^ [] : [-(c_List_Olist__all(_1788630, _1788632, _1788634))]]], (35079 ^ _775212) ^ [_1420716, _1420718, _1420720] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420716, tc_HOL_Obool)), _1420718), _1420720) = c_Orderings_Obot__class_Obot(tc_fun(_1420716, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1420716, tc_HOL_Obool)), _1420718), _1420720) = _1420718)], (48631 ^ _775212) ^ [_1748915, _1748917] : [class_Orderings_Olinorder(_1748915), -(c_List_Olinorder__class_Osorted(_1748915, c_List_Olinorder__class_Osort__key(_1748915, _1748915, c_COMBI(_1748915), _1748917)))], (7178 ^ _775212) ^ [_889368, _889370, _889372] : [class_Orderings_Olinorder(_889368), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889368), _889370), _889372))), -(_889370 = _889372), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889368), _889372), _889370)))], (17271 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (33980 ^ _775212) ^ [_1395714, _1395716] : [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)), _1395714), _1395716)), 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)), _1395714), 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)), _1395716), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (14945 ^ _775212) ^ [_1025629, _1025631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025629), _1025631)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025629), _1025631) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38949 ^ _775212) ^ [_1507743] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1507743, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1507743), hAPP(c_COMBK(tc_HOL_Obool, _1507743), c_fFalse)))], (29090 ^ _775212) ^ [_1292053, _1292055, _1292057, _1292059, _1292061] : [-(_1292053 = c_Orderings_Obot__class_Obot(tc_fun(_1292055, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1292057), _1292059), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292055, tc_fun(_1292057, tc_HOL_Obool)), _1292053), _1292061)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292055, tc_fun(_1292057, tc_HOL_Obool)), _1292053), hAPP(hAPP(c_COMBB(tc_fun(_1292057, tc_HOL_Obool), tc_fun(_1292057, tc_HOL_Obool), _1292055), hAPP(c_Set_Oinsert(_1292057), _1292059)), _1292061)))], (11480 ^ _775212) ^ [_963495, _963497, _963499, _963501, _963503, _963505] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _963495), _963497)), _963499) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _963501), _963503)), _963505), 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), _963501), _963503)), _963505)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _963499), _963495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _963505)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _963501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _963501), _963495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _963503), _963497)))], (35979 ^ _775212) ^ [_1442133, _1442135, _1442137, _1442139, _1442141] : [class_Fields_Ofield(_1442133), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442135), _1442137)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442135), _1442139)), 35993 ^ _775212 : [(35996 ^ _775212) ^ [] : [-(hAPP(_1442141, 35992 ^ [_1442133, _1442135, _1442137, _1442139, _1442141]) = c_Groups_Ozero__class_Ozero(_1442133))], (35994 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1442135), 35992 ^ [_1442133, _1442135, _1442137, _1442139, _1442141]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442135, tc_HOL_Obool)), _1442137), _1442139))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1442135, _1442133), _1442141), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442135, tc_HOL_Obool)), _1442137), _1442139)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1442133), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442133), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1442135, _1442133), _1442141), _1442137)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1442135, _1442133), _1442141), _1442139))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1442135, _1442133), _1442141), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442135, tc_HOL_Obool)), _1442137), _1442139))))], (36737 ^ _775212) ^ [_1457398, _1457400, _1457402] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1457398), _1457400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1457398, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1457398, _1457398, _1457402), _1457400)), _1457400)), c_Fun_Oinj__on(_1457398, _1457398, _1457402, _1457400), -(hAPP(c_Set_Oimage(_1457398, _1457398, _1457402), _1457400) = _1457400)], (46702 ^ _775212) ^ [_1706050, _1706052] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1706050), _1706052)), -(c_Nitpick_Ocard_H(_1706050, _1706052) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706050)), c_Hilbert__Choice_OEps(tc_List_Olist(_1706050), hAPP(hAPP(c_COMBS(tc_List_Olist(_1706050), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1706050)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1706050), tc_fun(_1706050, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1706050, tc_HOL_Obool), tc_fun(tc_fun(_1706050, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1706050)), c_fequal), c_List_Oset(_1706050))), _1706052))), c_List_Odistinct(_1706050)))))], (39589 ^ _775212) ^ [_1530402, _1530404, _1530406, _1530408] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1530402, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1530404, _1530402), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1530404, _1530402), tc_HOL_Obool)), _1530406), _1530408))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1530402, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1530404, _1530402), _1530406)), hAPP(c_Relation_ORange(_1530404, _1530402), _1530408)))))], (48295 ^ _775212) ^ [_1740704, _1740706, _1740708, _1740710, _1740712] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740704)), hAPP(c_List_Ofilter(_1740704, _1740706), hAPP(hAPP(c_List_Omap(_1740708, _1740704), _1740710), _1740712))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740708)), hAPP(c_List_Ofilter(_1740708, hAPP(c_Fun_Ocomp(_1740704, tc_HOL_Obool, _1740708, _1740706), _1740710)), _1740712)))], (3516 ^ _775212) ^ [_828358, _828360, _828362, _828364] : [-(c_Lazy__Sequence_Ohb__single(_828364, _828360) = c_Lazy__Sequence_Ohb__single(_828362, _828358)), _828364 = _828362, _828360 = _828358], (5336 ^ _775212) ^ [_856642, _856644] : [_856644 = _856642, -(c_Lattices_Osemilattice__sup__class_Osup(_856644) = c_Lattices_Osemilattice__sup__class_Osup(_856642))], (15007 ^ _775212) ^ [_1026759, _1026761, _1026763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026759), _1026761)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026761), _1026763)), _1026759) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026761), _1026759)), _1026763))], (176 ^ _775212) ^ [_777762, _777764, _777766, _777768] : [-(c_Nitpick_Orefl_H(_777766, _777762)), c_Nitpick_Orefl_H(_777768, _777764), _777768 = _777766, _777764 = _777762], (21425 ^ _775212) ^ [_1142310, _1142312, _1142314] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1142310, _1142310), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1142312), _1142314))), -(_1142310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1142314 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43280 ^ _775212) ^ [_1619909, _1619911] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619909, tc_HOL_Obool), _1619911) = hAPP(c_Set_OCollect(_1619909), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1619909, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1619909), c_HOL_OAll(tc_fun(_1619909, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1619909, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1619909, tc_HOL_Obool), tc_HOL_Obool), _1619909), hAPP(c_COMBS(tc_fun(_1619909, 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(_1619909, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1619909, tc_HOL_Obool), tc_fun(tc_fun(_1619909, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1619909, tc_HOL_Obool))), _1619911)))), c_member(_1619909)))))], (5224 ^ _775212) ^ [_854872, _854874] : [_854874 = _854872, -(c_Orderings_Obot__class_Obot(_854874) = c_Orderings_Obot__class_Obot(_854872))], (8966 ^ _775212) ^ [_920570, _920572, _920574, _920576] : [class_Orderings_Oorder(_920570), _920572 = _920574, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920570), _920576), _920574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920570), _920576), _920572)))], (40894 ^ _775212) ^ [_1562501, _1562503, _1562505, _1562507, _1562509] : [c_Finite__Set_Ofolding__idem(_1562501, _1562503, _1562505, _1562507), -(hAPP(c_Fun_Ocomp(_1562503, _1562503, _1562503, hAPP(_1562505, _1562509)), hAPP(_1562505, _1562509)) = hAPP(_1562505, _1562509))], (17775 ^ _775212) ^ [_1077052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1077052))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1077052)))], (52283 ^ _775212) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (36142 ^ _775212) ^ [_1445806, _1445808, _1445810, _1445812] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1445806), _1445808)), c_Equiv__Relations_Oequiv(_1445806, _1445808, _1445810), 36152 ^ _775212 : [(36155 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1445812), hAPP(c_Finite__Set_Ocard(_1445806), 36151 ^ [_1445806, _1445808, _1445810, _1445812])))], (36153 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1445806, tc_HOL_Obool)), 36151 ^ [_1445806, _1445808, _1445810, _1445812]), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1445806), _1445808), _1445810))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1445812), hAPP(c_Finite__Set_Ocard(_1445806), _1445808))))], (10085 ^ _775212) ^ [_938978, _938980, _938982] : [class_Groups_Oordered__comm__monoid__add(_938978), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938978), c_Groups_Ozero__class_Ozero(_938978)), _938980)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938978), c_Groups_Ozero__class_Ozero(_938978)), _938982)), 10096 ^ _775212 : [(10105 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938978), _938980), _938982) = c_Groups_Ozero__class_Ozero(_938978)), _938980 = c_Groups_Ozero__class_Ozero(_938978), _938982 = c_Groups_Ozero__class_Ozero(_938978)], (10097 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938978), _938980), _938982) = c_Groups_Ozero__class_Ozero(_938978), 10100 ^ _775212 : [(10103 ^ _775212) ^ [] : [-(_938982 = c_Groups_Ozero__class_Ozero(_938978))], (10101 ^ _775212) ^ [] : [-(_938980 = c_Groups_Ozero__class_Ozero(_938978))]]]]], (7593 ^ _775212) ^ [_896483, _896485, _896487] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _896483), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896485), _896487)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _896483), _896485)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _896483), _896487)))], (9139 ^ _775212) ^ [] : [-(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))))], (27223 ^ _775212) ^ [_1254807, _1254809, _1254811, _1254813] : [class_Lattices_Osemilattice__sup(_1254807), 27226 ^ _775212 : [(27235 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254807), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254807), _1254809), _1254811)), _1254813))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254807), _1254809), _1254813)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254807), _1254811), _1254813))], (27227 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254807), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254807), _1254809), _1254811)), _1254813)), 27230 ^ _775212 : [(27233 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254807), _1254811), _1254813)))], (27231 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254807), _1254809), _1254813)))]]]]], (40352 ^ _775212) ^ [_1549868, _1549870, _1549872] : [c_Wellfounded_OwfP(_1549868, hAPP(_1549870, 40353 ^ [_1549868, _1549870, _1549872])), 40360 ^ _775212 : [(40363 ^ _775212) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1549868, tc_HOL_Obool)), c_Predicate_ODomainP(_1549868, _1549868, hAPP(_1549870, 40358 ^ [_1549868, _1549870, _1549872]))), c_Predicate_ORangeP(_1549868, _1549868, hAPP(_1549870, 40359 ^ [_1549868, _1549870, _1549872]))) = c_Orderings_Obot__class_Obot(tc_fun(_1549868, tc_HOL_Obool))], (40361 ^ _775212) ^ [] : [hAPP(_1549870, 40358 ^ [_1549868, _1549870, _1549872]) = hAPP(_1549870, 40359 ^ [_1549868, _1549870, _1549872])]], -(c_Wellfounded_OwfP(_1549868, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1549872, tc_fun(_1549868, tc_fun(_1549868, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1549872, tc_HOL_Obool))), _1549870)))], (31180 ^ _775212) ^ [_1338809, _1338811, _1338813, _1338815, _1338817, _1338819, _1338821, _1338823] : [c_Finite__Set_Ofolding__image__simple(_1338809, _1338811, _1338813, _1338815, _1338817, _1338819), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338811), _1338821)), -(hAPP(_1338819, hAPP(hAPP(c_Set_Oinsert(_1338811), _1338823), _1338821)) = hAPP(hAPP(_1338813, hAPP(_1338817, _1338823)), hAPP(_1338819, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1338811, tc_HOL_Obool)), _1338821), hAPP(hAPP(c_Set_Oinsert(_1338811), _1338823), c_Orderings_Obot__class_Obot(tc_fun(_1338811, tc_HOL_Obool)))))))], (11987 ^ _775212) ^ [_972145, _972147, _972149, _972151, _972153] : [c_Natural_Oevaln(_972145, _972147, _972149, _972151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972149), _972153)), -(c_Natural_Oevaln(_972145, _972147, _972153, _972151))], (29184 ^ _775212) ^ [_1293902] : [class_Lattices_Oboolean__algebra(_1293902), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1293902), c_Orderings_Otop__class_Otop(_1293902)) = c_Orderings_Obot__class_Obot(_1293902))], (36159 ^ _775212) ^ [_1446171, _1446173] : [class_Lattices_Olattice(_1446171), -(c_Big__Operators_Olattice__class_OInf__fin(_1446171, hAPP(hAPP(c_Set_Oinsert(_1446171), _1446173), c_Orderings_Obot__class_Obot(tc_fun(_1446171, tc_HOL_Obool)))) = _1446173)], (32305 ^ _775212) ^ [_1360219, _1360221, _1360223, _1360225] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1360219, _1360221)), c_Sum__Type_OPlus(_1360219, _1360221, _1360223, _1360225))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1360219), _1360223)))], (48339 ^ _775212) ^ [_1741906, _1741908] : [48341 ^ _775212 : [(48344 ^ _775212) ^ [] : [48340 ^ [_1741906, _1741908] = c_List_Olist_ONil(_1741906)], (48342 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1741906)), 48340 ^ [_1741906, _1741908]), hAPP(c_List_Oset(tc_List_Olist(_1741906)), _1741908))))]], -(c_List_Otranspose(_1741906, _1741908) = c_List_Olist_ONil(tc_List_Olist(_1741906)))], (35119 ^ _775212) ^ [_1421910, _1421912, _1421914] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1421910, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421910, tc_HOL_Obool)), _1421912), _1421914)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421910, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1421910, tc_HOL_Obool)), _1421912)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1421910, tc_HOL_Obool)), _1421914)))], (37040 ^ _775212) ^ [_1464206, _1464208] : [-(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)), _1464206), _1464208))], (18561 ^ _775212) ^ [_1090526] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1090526), 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), _1090526), _1090526))], (32607 ^ _775212) ^ [_1366204, _1366206, _1366208] : [class_Orderings_Olinorder(_1366204), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366204), _1366206)), hBOOL(hAPP(hAPP(c_member(_1366204), _1366208), _1366206)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1366204), _1366208), c_Big__Operators_Olattice_OInf__fin(_1366204, c_Orderings_Oord__class_Omin(_1366204), _1366206)) = c_Big__Operators_Olattice_OInf__fin(_1366204, c_Orderings_Oord__class_Omin(_1366204), _1366206))], (41873 ^ _775212) ^ [_1583522, _1583524, _1583526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583522, _1583522), tc_HOL_Obool)), _1583524), c_Transitive__Closure_Ortrancl(_1583522, _1583526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583522, _1583522), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1583522, _1583524)), c_Transitive__Closure_Ortrancl(_1583522, _1583526))))], (42571 ^ _775212) ^ [_1601903, _1601905, _1601907, _1601909] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601903, tc_fun(_1601905, tc_HOL_Obool)), _1601907), _1601909) = hAPP(c_Set_OCollect(_1601905), hAPP(hAPP(c_COMBB(tc_fun(_1601903, tc_HOL_Obool), tc_HOL_Obool, _1601905), c_HOL_OAll(_1601903)), hAPP(hAPP(c_COMBB(tc_fun(_1601903, tc_HOL_Obool), tc_fun(_1601903, tc_HOL_Obool), _1601905), hAPP(c_COMBS(_1601903, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1601903), c_fimplies), hAPP(hAPP(c_COMBC(_1601903, tc_fun(_1601903, tc_HOL_Obool), tc_HOL_Obool), c_member(_1601903)), _1601907)))), hAPP(hAPP(c_COMBC(_1601905, tc_fun(_1601903, tc_fun(_1601905, tc_HOL_Obool)), tc_fun(_1601903, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1601905, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1601903, tc_fun(_1601905, tc_HOL_Obool)), tc_fun(_1601903, tc_HOL_Obool)), _1601905), c_COMBB(tc_fun(_1601905, tc_HOL_Obool), tc_HOL_Obool, _1601903)), c_member(_1601905))), _1601909)))))], (42315 ^ _775212) ^ [_1594539, _1594541, _1594543, _1594545] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594539, tc_fun(_1594541, tc_HOL_Obool)), _1594543), _1594545) = c_Orderings_Otop__class_Otop(tc_fun(_1594541, tc_HOL_Obool)), 42318 ^ _775212 : [(42319 ^ _775212) ^ [_1594655] : [hBOOL(hAPP(hAPP(c_member(_1594539), _1594655), _1594543)), -(hAPP(_1594545, _1594655) = c_Orderings_Otop__class_Otop(tc_fun(_1594541, tc_HOL_Obool)))]]], (42295 ^ _775212) ^ [_1593939, _1593941, _1593943, _1593945, _1593947, _1593949] : [class_Complete__Lattice_Ocomplete__lattice(_1593939), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593941, _1593939), _1593943), hAPP(hAPP(c_COMBB(tc_fun(_1593945, _1593939), _1593939, _1593941), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593945, _1593939), _1593947)), _1593949)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593945, _1593939), _1593947), hAPP(hAPP(c_COMBB(tc_fun(_1593941, _1593939), _1593939, _1593945), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593941, _1593939), _1593943)), hAPP(c_COMBC(_1593941, _1593945, _1593939), _1593949))))], (16785 ^ _775212) ^ [_1061405, _1061407] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1061405)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1061407)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1061405), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1061407))))], (22344 ^ _775212) ^ [_1160146, _1160148] : [class_Rings_Oring__1(_1160146), 22347 ^ _775212 : [(22354 ^ _775212) ^ [] : [-(_1160148 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22357 ^ _775212 : [(22364 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160148), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1160146), _1160148) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1160146), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1160146, _1160146)), tc_fun(tc_Int_Oint, _1160146)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1160146, _1160146), _1160146), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1160146, _1160146)), tc_fun(tc_Int_Oint, _1160146)), tc_Int_Oint), c_COMBB(tc_fun(_1160146, _1160146), _1160146, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1160146, tc_fun(tc_fun(_1160146, _1160146), _1160146), tc_Int_Oint), c_HOL_OLet(_1160146, _1160146)), c_Int_Oring__1__class_Oof__int(_1160146)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1160146, _1160146), tc_fun(_1160146, _1160146)), hAPP(hAPP(c_COMBB(tc_fun(_1160146, tc_fun(_1160146, _1160146)), tc_fun(tc_fun(_1160146, _1160146), tc_fun(_1160146, _1160146)), tc_Int_Oint), c_COMBS(_1160146, _1160146, _1160146)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1160146, _1160146), tc_fun(_1160146, tc_fun(_1160146, _1160146))), hAPP(hAPP(c_COMBB(tc_fun(_1160146, tc_fun(_1160146, _1160146)), tc_fun(tc_fun(_1160146, _1160146), tc_fun(_1160146, tc_fun(_1160146, _1160146))), tc_Int_Oint), c_COMBB(_1160146, tc_fun(_1160146, _1160146), _1160146)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1160146, tc_fun(_1160146, _1160146)), tc_Int_Oint), c_If(_1160146)), 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(_1160146, _1160146, _1160146), c_Groups_Oplus__class_Oplus(_1160146)), c_COMBI(_1160146))))), hAPP(hAPP(c_COMBC(_1160146, _1160146, _1160146), hAPP(hAPP(c_COMBB(_1160146, tc_fun(_1160146, _1160146), _1160146), c_Groups_Oplus__class_Oplus(_1160146)), hAPP(hAPP(c_COMBS(_1160146, _1160146, _1160146), c_Groups_Oplus__class_Oplus(_1160146)), c_COMBI(_1160146)))), c_Groups_Oone__class_Oone(_1160146))))), c_Divides_Odivmod__int(_1160148, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (22358 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160148), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1160146), _1160148) = hAPP(c_Groups_Ouminus__class_Ouminus(_1160146), hAPP(c_Int_Oring__1__class_Oof__int(_1160146), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1160148))))]]], (22348 ^ _775212) ^ [] : [_1160148 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1160146), _1160148) = c_Groups_Ozero__class_Ozero(_1160146))]]], (14861 ^ _775212) ^ [_1024197, _1024199, _1024201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1024197), _1024199)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1024197), _1024201))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1024199), _1024201)))], (28478 ^ _775212) ^ [_1280429, _1280431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1280429), _1280431))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1280429), _1280431)))], (16157 ^ _775212) ^ [_1048886, _1048888, _1048890] : [class_Groups_Oordered__ab__group__add__abs(_1048886), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048886), hAPP(c_Groups_Oabs__class_Oabs(_1048886), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048886), _1048888), _1048890))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048886), hAPP(c_Groups_Oabs__class_Oabs(_1048886), _1048888)), hAPP(c_Groups_Oabs__class_Oabs(_1048886), _1048890)))))], (27980 ^ _775212) ^ [_1270951, _1270953] : [class_Orderings_Otop(_1270951), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270951), _1270953), c_Orderings_Otop__class_Otop(_1270951))))], (6499 ^ _775212) ^ [_878122, _878124, _878126] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878122), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878124), _878126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878124), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878122), _878126)))], (32892 ^ _775212) ^ [_1371737, _1371739, _1371741] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371737, tc_Nat_Onat), _1371739), _1371741) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371737, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1371737), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1371739)), _1371741)))], (5931 ^ _775212) ^ [_869205, _869207, _869209, _869211, _869213, _869215] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_869205, _869207, _869209), _869211, _869213, _869215), 5936 ^ _775212 : [(5939 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_869207, _869211, _869213, _869215))], (5937 ^ _775212) ^ [] : [-(hBOOL(hAPP(_869205, _869211)))]], 5940 ^ _775212 : [(5943 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_869209, _869211, _869213, _869215))], (5941 ^ _775212) ^ [] : [hBOOL(hAPP(_869205, _869211))]]], (40914 ^ _775212) ^ [_1562887, _1562889, _1562891, _1562893, _1562895, _1562897] : [c_Finite__Set_Ofolding__idem(_1562887, _1562889, _1562891, _1562893), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562887), _1562895)), -(hAPP(_1562893, hAPP(hAPP(c_Set_Oinsert(_1562887), _1562897), _1562895)) = hAPP(c_Fun_Ocomp(_1562889, _1562889, _1562889, hAPP(_1562893, _1562895)), hAPP(_1562891, _1562897)))], (23458 ^ _775212) ^ [_1182309, _1182311] : [23459 ^ _775212 : [(23462 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1182311), _1182309))], (23460 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1182309), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1182309, _1182311) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (4534 ^ _775212) ^ [_844207, _844209] : [_844209 = _844207, -(c_If(_844209) = c_If(_844207))], (7395 ^ _775212) ^ [_892818, _892820, _892822, _892824, _892826, _892828] : [c_Com_Ocom_OCond(_892818, _892820, _892822) = c_Com_Ocom_OLocal(_892824, _892826, _892828)], (37284 ^ _775212) ^ [_1469113, _1469115, _1469117, _1469119, _1469121, _1469123, _1469125] : [c_Big__Operators_Ocomm__monoid__big(_1469113, _1469115, _1469117, _1469119, _1469121), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1469115), _1469123))), -(hAPP(hAPP(_1469121, _1469125), _1469123) = _1469119)], (26684 ^ _775212) ^ [_1244094] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1244094) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1244094))], (9907 ^ _775212) ^ [_935651, _935653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935653)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _935651)), hAPP(c_Int_Onat, _935653)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _935651), _935653)))], (50979 ^ _775212) ^ [_1797875, _1797877, _1797879] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1797875, _1797877), _1797879) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1797875, tc_Lazy__Sequence_Olazy__sequence(_1797875)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1797875, tc_Lazy__Sequence_Olazy__sequence(_1797875), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1797875, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1797875), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1797875), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1797875), tc_Nat_Onat)), _1797875), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1797875), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1797875), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1797875), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1797875), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1797875)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1797875, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1797875), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1797875), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1797875), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1797875), tc_Nat_Onat)), _1797875), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1797875))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1797875), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1797877))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1797875, _1797877))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1797875), _1797879)))], (34063 ^ _775212) ^ [_1397976] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1397976) = 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), _1397976), 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))))))], (17335 ^ _775212) ^ [] : [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)], (26943 ^ _775212) ^ [_1249234, _1249236, _1249238, _1249240] : [26944 ^ _775212 : [(26945 ^ _775212) ^ [_1249344] : [hBOOL(hAPP(hAPP(c_member(_1249234), _1249344), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249234, tc_HOL_Obool)), _1249236), _1249238))), hBOOL(hAPP(_1249240, _1249344))]], 26953 ^ _775212 : [(26956 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1249240, 26952 ^ [_1249234, _1249236, _1249238, _1249240])))], (26954 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1249234), 26952 ^ [_1249234, _1249236, _1249238, _1249240]), _1249236)))]], 26958 ^ _775212 : [(26961 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1249240, 26957 ^ [_1249234, _1249236, _1249238, _1249240])))], (26959 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1249234), 26957 ^ [_1249234, _1249236, _1249238, _1249240]), _1249238)))]]], (48368 ^ _775212) ^ [_1743231, _1743233] : [-(c_Random_Oselect__weight(_1743231, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1743231), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1743231, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1743231, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1743231)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1743233)) = c_Random_Oselect__weight(_1743231, _1743233))], (17127 ^ _775212) ^ [_1066701, _1066703, _1066705] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066701)))), 17130 ^ _775212 : [(17137 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066703)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066701)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066703)), _1066705)) = 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), _1066701), _1066703))), _1066705))], (17131 ^ _775212) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066703))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066701)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066703)), _1066705)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066701)), _1066705))]]], (28777 ^ _775212) ^ [_1286603, _1286605, _1286607, _1286609] : [c_Orderings_Obot__class_Obot(tc_fun(_1286603, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1286605, tc_fun(_1286603, tc_HOL_Obool)), _1286607), _1286609), 28780 ^ _775212 : [(28781 ^ _775212) ^ [_1286719] : [hBOOL(hAPP(hAPP(c_member(_1286605), _1286719), _1286607)), -(hAPP(_1286609, _1286719) = c_Orderings_Obot__class_Obot(tc_fun(_1286603, tc_HOL_Obool)))]]], (11218 ^ _775212) ^ [_959376, _959378, _959380] : [class_Rings_Olinordered__ring(_959376), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959376), c_Groups_Ozero__class_Ozero(_959376)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959376), _959378), _959378)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959376), _959380), _959380)))))], (36247 ^ _775212) ^ [_1447613, _1447615] : [class_Lattices_Olattice(_1447613), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447613), _1447615)), -(_1447615 = c_Orderings_Obot__class_Obot(tc_fun(_1447613, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1447613), c_Big__Operators_Olattice__class_OInf__fin(_1447613, _1447615)), c_Big__Operators_Olattice__class_OSup__fin(_1447613, _1447615))))], (22082 ^ _775212) ^ [_1154256, _1154258, _1154260, _1154262] : [-(hAPP(c_Product__Type_Ofst(_1154256, _1154258), hAPP(hAPP(c_Product__Type_OPair(_1154256, _1154258), _1154260), _1154262)) = _1154260)], (30054 ^ _775212) ^ [_1313670, _1313672, _1313674, _1313676] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313670, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1313670), _1313672), _1313674)), _1313676))), hBOOL(hAPP(hAPP(c_member(_1313670), _1313672), _1313676)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313670, tc_HOL_Obool)), _1313674), _1313676))], (52329 ^ _775212) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (34729 ^ _775212) ^ [_1412989, _1412991, _1412993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412989, tc_HOL_Obool)), _1412991), _1412993)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412989, tc_HOL_Obool)), _1412991), _1412993) = _1412991)], (40031 ^ _775212) ^ [_1542300, _1542302, _1542304, _1542306] : [hBOOL(hAPP(hAPP(c_member(_1542300), _1542306), hAPP(c_Relation_ODomain(_1542300, _1542302), _1542304))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1542300, _1542302, hAPP(hAPP(c_COMBC(_1542300, tc_fun(tc_prod(_1542300, _1542302), tc_HOL_Obool), tc_fun(_1542302, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542302, tc_fun(tc_fun(tc_prod(_1542300, _1542302), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1542300, _1542302), tc_HOL_Obool), tc_fun(_1542302, tc_HOL_Obool)), _1542300), c_COMBC(_1542302, tc_fun(tc_prod(_1542300, _1542302), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542302, tc_prod(_1542300, _1542302)), tc_fun(_1542302, tc_fun(tc_fun(tc_prod(_1542300, _1542302), tc_HOL_Obool), tc_HOL_Obool)), _1542300), hAPP(c_COMBB(tc_prod(_1542300, _1542302), tc_fun(tc_fun(tc_prod(_1542300, _1542302), tc_HOL_Obool), tc_HOL_Obool), _1542302), c_member(tc_prod(_1542300, _1542302)))), c_Product__Type_OPair(_1542300, _1542302)))), _1542304)), _1542306)))], (4100 ^ _775212) ^ [_837436, _837438, _837440, _837442, _837444, _837446] : [-(c_Enum_On__lists(_837446, _837442, _837438) = c_Enum_On__lists(_837444, _837440, _837436)), _837446 = _837444, _837442 = _837440, _837438 = _837436], (41588 ^ _775212) ^ [_1576820, _1576822] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1576820, _1576820), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1576820, _1576822)), hAPP(hAPP(c_Product__Type_OSigma(_1576820, _1576820), hAPP(c_Relation_OField(_1576820), _1576822)), hAPP(c_COMBK(tc_fun(_1576820, tc_HOL_Obool), _1576820), hAPP(c_Relation_OField(_1576820), _1576822))))))], (39866 ^ _775212) ^ [_1538010, _1538012] : [hAPP(hAPP(c_Relation_Orel__comp(_1538010, _1538010, _1538010), _1538012), _1538012) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1538010, _1538010), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1538010, _1538012))], (35956 ^ _775212) ^ [_1441126, _1441128, _1441130, _1441132, _1441134, _1441136] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1441126, _1441128)), hAPP(hAPP(c_Product__Type_OPair(_1441126, _1441128), _1441134), _1441136)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool)), _1441130), _1441132))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441126, tc_fun(_1441128, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1441126, tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_fun(_1441128, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441128, tc_fun(tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_fun(_1441128, tc_HOL_Obool)), _1441126), c_COMBC(_1441128, tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441128, tc_prod(_1441126, _1441128)), tc_fun(_1441128, tc_fun(tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_HOL_Obool)), _1441126), hAPP(c_COMBB(tc_prod(_1441126, _1441128), tc_fun(tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_HOL_Obool), _1441128), c_member(tc_prod(_1441126, _1441128)))), c_Product__Type_OPair(_1441126, _1441128)))), _1441130)), hAPP(hAPP(c_COMBC(_1441126, tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_fun(_1441128, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441128, tc_fun(tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_fun(_1441128, tc_HOL_Obool)), _1441126), c_COMBC(_1441128, tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441128, tc_prod(_1441126, _1441128)), tc_fun(_1441128, tc_fun(tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_HOL_Obool)), _1441126), hAPP(c_COMBB(tc_prod(_1441126, _1441128), tc_fun(tc_fun(tc_prod(_1441126, _1441128), tc_HOL_Obool), tc_HOL_Obool), _1441128), c_member(tc_prod(_1441126, _1441128)))), c_Product__Type_OPair(_1441126, _1441128)))), _1441132)), _1441134), _1441136)))], (38058 ^ _775212) ^ [_1488380, _1488382, _1488384, _1488386, _1488388, _1488390] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1488380, _1488382), hAPP(hAPP(c_Set_Oinsert(_1488380), _1488384), _1488386)), hAPP(c_COMBK(tc_fun(_1488382, tc_HOL_Obool), _1488380), hAPP(hAPP(c_Set_Oinsert(_1488382), _1488388), _1488390))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1488380, _1488382)), hAPP(hAPP(c_Product__Type_OPair(_1488380, _1488382), _1488384), _1488388)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1488380, _1488382), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1488380, _1488382), _1488386), hAPP(c_COMBK(tc_fun(_1488382, tc_HOL_Obool), _1488380), hAPP(hAPP(c_Set_Oinsert(_1488382), _1488388), _1488390)))), hAPP(hAPP(c_Product__Type_OSigma(_1488380, _1488382), hAPP(hAPP(c_Set_Oinsert(_1488380), _1488384), _1488386)), hAPP(c_COMBK(tc_fun(_1488382, tc_HOL_Obool), _1488380), _1488390)))))], (18221 ^ _775212) ^ [_1084611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1084611))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1084611)))], (49424 ^ _775212) ^ [_1764436, _1764438, _1764440, _1764442] : [-(hBOOL(hAPP(_1764436, _1764438))), -(c_List_OtakeWhile(_1764440, _1764436, hAPP(hAPP(c_List_Olist_OCons(_1764440), _1764438), _1764442)) = c_List_Olist_ONil(_1764440))], (13439 ^ _775212) ^ [_998109] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _998109), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25300 ^ _775212) ^ [_1215487] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1215487) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1215487), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (6713 ^ _775212) ^ [_881970, _881972, _881974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _881972), _881974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881970), _881972)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881970), _881974))))], (10998 ^ _775212) ^ [_955181, _955183, _955185, _955187] : [class_Rings_Olinordered__semiring__strict(_955181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955181), _955183), _955185)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955181), _955187), _955185))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955181), c_Groups_Ozero__class_Ozero(_955181)), _955185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955181), _955183), _955187)))], (15479 ^ _775212) ^ [_1036485, _1036487, _1036489, _1036491, _1036493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036485), _1036487)), -(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), _1036487), _1036489)), _1036491)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036485), _1036489)), _1036493)) = 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), _1036487), _1036485)), _1036489)), _1036491)), _1036493))], (43051 ^ _775212) ^ [_1614529, _1614531, _1614533, _1614535, _1614537, _1614539] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614529, _1614529)), hAPP(hAPP(c_Product__Type_OPair(_1614529, _1614529), _1614531), _1614533)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1614529, _1614529), tc_HOL_Obool), _1614535), _1614537))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1614529, _1614529)), hAPP(hAPP(c_Product__Type_OPair(_1614529, _1614529), _1614533), _1614539)), _1614537)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614529, _1614529)), hAPP(hAPP(c_Product__Type_OPair(_1614529, _1614529), _1614531), _1614539)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1614529, _1614529), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1614535)), _1614537))))], (42764 ^ _775212) ^ [_1607663, _1607665, _1607667, _1607669, _1607671] : [42766 ^ _775212 : [(42769 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1607669, 42765 ^ [_1607663, _1607665, _1607667, _1607669, _1607671]), _1607671))], (42767 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1607663), 42765 ^ [_1607663, _1607665, _1607667, _1607669, _1607671]), _1607667)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607663, tc_fun(_1607665, tc_HOL_Obool)), _1607667), _1607669), _1607671)))], (23602 ^ _775212) ^ [_1184978, _1184980, _1184982] : [-(c_HOL_OThe(tc_prod(_1184978, _1184980), _1184982) = c_HOL_OThe(tc_prod(_1184978, _1184980), hAPP(c_Product__Type_Oprod_Oprod__case(_1184978, _1184980, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1184980, tc_prod(_1184978, _1184980)), tc_fun(_1184980, tc_HOL_Obool), _1184978), hAPP(c_COMBB(tc_prod(_1184978, _1184980), tc_HOL_Obool, _1184980), _1184982)), c_Product__Type_OPair(_1184978, _1184980)))))], (2148 ^ _775212) ^ [_806322, _806324, _806326, _806328] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_806328, _806324) = c_Code__Numeral_Odiv__mod__code__numeral(_806326, _806322)), _806328 = _806326, _806324 = _806322], (47474 ^ _775212) ^ [_1722175, _1722177, _1722179, _1722181] : [class_Orderings_Olinorder(_1722175), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1722175, _1722175, c_COMBI(_1722175)), _1722177), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1722175, _1722175, c_COMBI(_1722175)), _1722179), _1722181)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1722175, _1722175, c_COMBI(_1722175)), _1722179), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1722175, _1722175, c_COMBI(_1722175)), _1722177), _1722181)))], (51723 ^ _775212) ^ [_1815075, _1815077] : [c_Wellfounded_Oacyclic(_1815075, _1815077), -(c_Relation_Oantisym(_1815075, c_Transitive__Closure_Ortrancl(_1815075, _1815077)))], (39174 ^ _775212) ^ [_1515092, _1515094] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515092), _1515094)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1515092, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1515092, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1515092, tc_HOL_Obool), tc_fun(_1515092, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1515092, tc_HOL_Obool))), _1515094)))))], (26718 ^ _775212) ^ [_1244685, _1244687] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1244685, _1244687)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1244687)), _1244685))], (16783 ^ _775212) ^ [_1061372, _1061374] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1061372, _1061374), c_Divides_Odivmod__nat(_1061372, _1061374))))], (15545 ^ _775212) ^ [_1038102, _1038104] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038102, _1038104) = 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), _1038102), _1038104) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1038104), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038102, _1038104)))], (33616 ^ _775212) ^ [_1387817, _1387819, _1387821, _1387823] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1387817, _1387817)), hAPP(hAPP(c_Product__Type_OPair(_1387817, _1387817), _1387819), _1387821)), c_Relation_OId__on(_1387817, _1387823)))), _1387819 = _1387821, hBOOL(hAPP(hAPP(c_member(_1387817), _1387819), _1387823))], (23524 ^ _775212) ^ [_1183562, _1183564, _1183566] : [c_Nitpick_Oless__eq__frac(_1183562, _1183564, _1183566), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1183562), c_Nitpick_Oplus__frac(_1183562, _1183564, c_Nitpick_Ouminus__frac(_1183562, _1183566)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40748 ^ _775212) ^ [] : [-(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))], (20677 ^ _775212) ^ [_1128478, _1128480, _1128482, _1128484] : [class_Fields_Olinordered__field__inverse__zero(_1128478), class_Int_Onumber(_1128478), 20684 ^ _775212 : [(20685 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), hAPP(c_Int_Onumber__class_Onumber__of(_1128478), _1128480)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128478), _1128482), _1128484))), 20688 ^ _775212 : [(20695 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), c_Groups_Ozero__class_Ozero(_1128478)), _1128484))), 20698 ^ _775212 : [(20705 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), _1128484), c_Groups_Ozero__class_Ozero(_1128478)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), hAPP(c_Int_Onumber__class_Onumber__of(_1128478), _1128480)), c_Groups_Ozero__class_Ozero(_1128478))))], (20699 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), _1128484), c_Groups_Ozero__class_Ozero(_1128478))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), _1128482), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128478), hAPP(c_Int_Onumber__class_Onumber__of(_1128478), _1128480)), _1128484))))]]], (20689 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), c_Groups_Ozero__class_Ozero(_1128478)), _1128484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128478), hAPP(c_Int_Onumber__class_Onumber__of(_1128478), _1128480)), _1128484)), _1128482)))]]], (20711 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), hAPP(c_Int_Onumber__class_Onumber__of(_1128478), _1128480)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128478), _1128482), _1128484)))), 20714 ^ _775212 : [(20717 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128478), hAPP(c_Int_Onumber__class_Onumber__of(_1128478), _1128480)), _1128484)), _1128482))], (20715 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), c_Groups_Ozero__class_Ozero(_1128478)), _1128484)))]], 20718 ^ _775212 : [(20721 ^ _775212) ^ [] : [20722 ^ _775212 : [(20725 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), _1128482), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128478), hAPP(c_Int_Onumber__class_Onumber__of(_1128478), _1128480)), _1128484)))], (20723 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), _1128484), c_Groups_Ozero__class_Ozero(_1128478))))]], 20726 ^ _775212 : [(20729 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), hAPP(c_Int_Onumber__class_Onumber__of(_1128478), _1128480)), c_Groups_Ozero__class_Ozero(_1128478)))], (20727 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), _1128484), c_Groups_Ozero__class_Ozero(_1128478)))]]], (20719 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128478), c_Groups_Ozero__class_Ozero(_1128478)), _1128484))]]]]], (18535 ^ _775212) ^ [_1090088, _1090090] : [class_Groups_Omonoid__mult(_1090088), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1090088), _1090090), 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(_1090088), _1090090), _1090090))], (48323 ^ _775212) ^ [_1741526, _1741528, _1741530] : [hBOOL(hAPP(c_List_Odistinct(_1741526), _1741528)), -(hAPP(c_List_Ofilter(_1741526, hAPP(hAPP(c_COMBC(_1741526, tc_fun(_1741526, tc_HOL_Obool), tc_HOL_Obool), c_member(_1741526)), hAPP(c_List_Oset(_1741526), c_List_Osublist(_1741526, _1741528, _1741530)))), _1741528) = c_List_Osublist(_1741526, _1741528, _1741530))], (42579 ^ _775212) ^ [_1602255, _1602257, _1602259, _1602261, _1602263] : [-(_1602255 = c_Orderings_Obot__class_Obot(tc_fun(_1602257, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602257, tc_fun(_1602259, tc_HOL_Obool)), _1602255), hAPP(hAPP(c_COMBB(tc_fun(_1602259, tc_HOL_Obool), tc_fun(_1602259, tc_HOL_Obool), _1602257), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602259, tc_HOL_Obool)), _1602261)), _1602263)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602259, tc_HOL_Obool)), _1602261), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602257, tc_fun(_1602259, tc_HOL_Obool)), _1602255), _1602263)))], (52461 ^ _775212) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (18559 ^ _775212) ^ [_1090494] : [-(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)))), _1090494) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1090494), _1090494))], (40738 ^ _775212) ^ [_1558961, _1558963, _1558965, _1558967, _1558969, _1558971] : [c_Finite__Set_Ofolding(_1558961, _1558963, _1558965, _1558967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558961), _1558969)), -(hAPP(c_Fun_Ocomp(_1558963, _1558963, _1558963, hAPP(_1558965, _1558971)), hAPP(_1558967, _1558969)) = hAPP(c_Fun_Ocomp(_1558963, _1558963, _1558963, hAPP(_1558967, _1558969)), hAPP(_1558965, _1558971)))], (12410 ^ _775212) ^ [_979277, _979279] : [class_Rings_Olinordered__idom(_979277), -(c_Groups_Osgn__class_Osgn(_979277, c_Groups_Osgn__class_Osgn(_979277, _979279)) = c_Groups_Osgn__class_Osgn(_979277, _979279))], (29108 ^ _775212) ^ [_1292325, _1292327] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292325, _1292327) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292325), _1292327))], (46149 ^ _775212) ^ [_1693607, _1693609, _1693611, _1693613] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693607), tc_List_Olist(_1693607))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693607), tc_List_Olist(_1693607)), _1693609), _1693611)), c_List_Olistrel1(_1693607, _1693613))), 46154 ^ _775212 : [(46161 ^ _775212) ^ [] : [-(_1693611 = hAPP(hAPP(c_List_Oappend(_1693607), 46156 ^ [_1693607, _1693609, _1693611, _1693613]), hAPP(hAPP(c_List_Olist_OCons(_1693607), 46153 ^ [_1693607, _1693609, _1693611, _1693613]), 46157 ^ [_1693607, _1693609, _1693611, _1693613])))], (46159 ^ _775212) ^ [] : [-(_1693609 = hAPP(hAPP(c_List_Oappend(_1693607), 46156 ^ [_1693607, _1693609, _1693611, _1693613]), hAPP(hAPP(c_List_Olist_OCons(_1693607), 46152 ^ [_1693607, _1693609, _1693611, _1693613]), 46157 ^ [_1693607, _1693609, _1693611, _1693613])))], (46155 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1693607, _1693607)), hAPP(hAPP(c_Product__Type_OPair(_1693607, _1693607), 46152 ^ [_1693607, _1693609, _1693611, _1693613]), 46153 ^ [_1693607, _1693609, _1693611, _1693613])), _1693613)))]]], (36657 ^ _775212) ^ [_1455786, _1455788, _1455790, _1455792, _1455794] : [c_Fun_Oinj__on(_1455786, _1455788, _1455790, _1455792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1455786, tc_HOL_Obool)), _1455794), _1455792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1455788, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1455786, _1455788, _1455790), _1455794)), hAPP(c_Set_Oimage(_1455786, _1455788, _1455790), _1455792))))], (27105 ^ _775212) ^ [_1252685, _1252687, _1252689, _1252691, _1252693] : [class_Lattices_Olattice(_1252685), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252687, _1252685)), _1252689), _1252691), _1252693) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252685), hAPP(_1252689, _1252693)), hAPP(_1252691, _1252693)))], (11292 ^ _775212) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (52649 ^ _775212) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (31015 ^ _775212) ^ [_1335527, _1335529] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1335527), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335529))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335529), _1335527)))], (49859 ^ _775212) ^ [_1773641, _1773643] : [-(c_Wellfounded_Owf(_1773641, c_List_Omeasures(_1773641, _1773643)))], (45347 ^ _775212) ^ [_1674291] : [-(c_List_Olists(_1674291, c_Orderings_Obot__class_Obot(tc_fun(_1674291, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1674291)), c_List_Olist_ONil(_1674291)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1674291), tc_HOL_Obool))))], (46742 ^ _775212) ^ [_1706788, _1706790, _1706792] : [-(hAPP(c_List_Oset(_1706788), hAPP(c_List_Orotate(_1706788, _1706790), _1706792)) = hAPP(c_List_Oset(_1706788), _1706792))], (47752 ^ _775212) ^ [_1727970, _1727972, _1727974, _1727976, _1727978, _1727980, _1727982] : [c_List_Olist__all2(_1727970, _1727972, _1727974, hAPP(hAPP(c_List_Omap(_1727976, _1727970), _1727978), _1727980), _1727982), -(c_List_Olist__all2(_1727976, _1727972, hAPP(hAPP(c_COMBB(_1727970, tc_fun(_1727972, tc_HOL_Obool), _1727976), _1727974), _1727978), _1727980, _1727982))], (49169 ^ _775212) ^ [_1758941, _1758943, _1758945] : [-(hAPP(c_List_Orev(_1758941), hAPP(hAPP(c_List_Oappend(_1758941), _1758943), _1758945)) = hAPP(hAPP(c_List_Oappend(_1758941), hAPP(c_List_Orev(_1758941), _1758945)), hAPP(c_List_Orev(_1758941), _1758943)))], (23640 ^ _775212) ^ [_1185784, _1185786, _1185788, _1185790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1185784), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1185786, _1185788, _1185784, _1185790) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185786)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1185786)))], (46814 ^ _775212) ^ [_1708388, _1708390] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1708388), _1708390) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1708388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 46820 ^ _775212 : [(46823 ^ _775212) ^ [] : [46819 ^ [_1708388, _1708390] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46821 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 46819 ^ [_1708388, _1708390]), hAPP(c_List_Oset(tc_Nat_Onat), _1708390))))]]], (7817 ^ _775212) ^ [_900784, _900786] : [class_Groups_Olinordered__ab__group__add(_900784), 7820 ^ _775212 : [(7827 ^ _775212) ^ [] : [_900786 = c_Groups_Ozero__class_Ozero(_900784), -(hAPP(c_Groups_Ouminus__class_Ouminus(_900784), _900786) = _900786)], (7821 ^ _775212) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_900784), _900786) = _900786, -(_900786 = c_Groups_Ozero__class_Ozero(_900784))]]], (22892 ^ _775212) ^ [_1171386, _1171388, _1171390] : [class_Orderings_Olinorder(_1171386), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171386), _1171388), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171386), _1171388), _1171390)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171386), _1171388), _1171390))], (23726 ^ _775212) ^ [_1187539, _1187541] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1187539)), hAPP(c_Code__Numeral_Oof__nat, _1187541)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1187539), _1187541)))], (17279 ^ _775212) ^ [_1069031] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1069031) = c_Int_OPls)], (11290 ^ _775212) ^ [] : [-(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))], (23414 ^ _775212) ^ [_1181254, _1181256, _1181258] : [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), _1181254), _1181256))), -(hBOOL(hAPP(hAPP(_1181258, _1181254), _1181256))), 23421 ^ _775212 : [(23424 ^ _775212) ^ [] : [-(23420 ^ [_1181254, _1181256, _1181258] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1181258, 23420 ^ [_1181254, _1181256, _1181258]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 23419 ^ [_1181254, _1181256, _1181258], 23420 ^ [_1181254, _1181256, _1181258]))))], (23430 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1181258, 23419 ^ [_1181254, _1181256, _1181258]), 23420 ^ [_1181254, _1181256, _1181258]))], (23422 ^ _775212) ^ [] : [-(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), 23419 ^ [_1181254, _1181256, _1181258]), 23420 ^ [_1181254, _1181256, _1181258]))))]]], (11965 ^ _775212) ^ [_971821] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971821), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _971821)], (47440 ^ _775212) ^ [_1721476, _1721478, _1721480, _1721482, _1721484] : [class_Orderings_Olinorder(_1721476), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1721478, _1721476, _1721480), _1721482), _1721484) = c_List_Olist_ONil(_1721478)], (7609 ^ _775212) ^ [_896814, _896816, _896818] : [class_Rings_Oring(_896814), -(hAPP(c_Groups_Ouminus__class_Ouminus(_896814), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896814), _896816), _896818)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896814), _896816), hAPP(c_Groups_Ouminus__class_Ouminus(_896814), _896818)))], (40433 ^ _775212) ^ [_1551870, _1551872] : [hBOOL(hAPP(_1551870, c_Hilbert__Choice_OEps(_1551872, _1551870))), -(hBOOL(hAPP(_1551870, 40436 ^ [_1551870, _1551872])))], (34403 ^ _775212) ^ [_1406208, _1406210, _1406212, _1406214] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406208, tc_HOL_Obool)), _1406210), _1406212), _1406214)), 34406 ^ _775212 : [(34409 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1406212, _1406214)))], (34407 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1406210, _1406214)))]]], (4788 ^ _775212) ^ [_848148, _848150, _848152, _848154] : [-(c_List_Ozip(_848154, _848150) = c_List_Ozip(_848152, _848148)), _848154 = _848152, _848150 = _848148], (14173 ^ _775212) ^ [_1011397, _1011399, _1011401, _1011403, _1011405] : [class_Groups_Oordered__ab__group__add(_1011397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1011397), _1011399), _1011401) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1011397), _1011403), _1011405), 14180 ^ _775212 : [(14187 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1011397), _1011403), _1011405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1011397), _1011399), _1011401)))], (14181 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1011397), _1011399), _1011401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1011397), _1011403), _1011405)))]]], (50027 ^ _775212) ^ [_1777804, _1777806] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1777804), _1777806))), -(c_Lazy__Sequence_Osmall__lazy_H(_1777804, _1777806) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1777806), c_Lazy__Sequence_Osmall__lazy_H(_1777804, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1777806), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (19751 ^ _775212) ^ [_1111656, _1111658, _1111660, _1111662, _1111664] : [class_Fields_Olinordered__field(_1111656), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111656), c_Groups_Ozero__class_Ozero(_1111656)), _1111658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111656), _1111658), _1111660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111656), c_Groups_Ozero__class_Ozero(_1111656)), _1111662)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111656), _1111662), _1111664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111656), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111656), _1111658), _1111664)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111656), _1111660), _1111662))))], (51271 ^ _775212) ^ [_1804521, _1804523, _1804525] : [-(c_List_Olist__ex(_1804521, _1804525, _1804523)), 51272 ^ _775212 : [(51273 ^ _775212) ^ [_1804578] : [hBOOL(hAPP(hAPP(c_member(_1804521), _1804578), hAPP(c_List_Oset(_1804521), _1804523))), hBOOL(hAPP(_1804525, _1804578))]]], (46680 ^ _775212) ^ [_1705576, _1705578, _1705580] : [-(_1705576 = c_List_Olist_ONil(_1705578)), -(hAPP(hAPP(c_List_Otake(_1705578), hAPP(c_Nat_OSuc, _1705580)), _1705576) = hAPP(hAPP(c_List_Olist_OCons(_1705578), hAPP(c_List_Ohd(_1705578), _1705576)), hAPP(hAPP(c_List_Otake(_1705578), _1705580), hAPP(c_List_Otl(_1705578), _1705576))))], (49432 ^ _775212) ^ [_1764527, _1764529, _1764531] : [-(c_List_OtakeWhile(_1764527, _1764529, _1764531) = hAPP(hAPP(c_List_Otake(_1764527), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764527)), c_List_OtakeWhile(_1764527, _1764529, _1764531))), _1764531))], (19993 ^ _775212) ^ [_1116176, _1116178, _1116180, _1116182] : [class_Fields_Olinordered__field(_1116176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116176), _1116178), c_Groups_Ozero__class_Ozero(_1116176))), 20000 ^ _775212 : [(20007 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116176), _1116182), _1116178)), _1116180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116176), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116176), _1116180), _1116178)), _1116182)))], (20001 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116176), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116176), _1116180), _1116178)), _1116182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116176), _1116182), _1116178)), _1116180)))]]], (13310 ^ _775212) ^ [_996067, _996069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996067)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996069)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _996067)), hAPP(c_Int_Onat, _996069)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _996067), _996069)))], (6481 ^ _775212) ^ [_877783, _877785, _877787, _877789] : [class_Groups_Ocancel__semigroup__add(_877783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877783), _877785), _877787) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877783), _877789), _877787), -(_877785 = _877789)], (15371 ^ _775212) ^ [_1034278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1034278)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034278), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1034278)], (48578 ^ _775212) ^ [_1747663, _1747665, _1747667, _1747669, _1747671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747663), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1747665), _1747667))), -(hAPP(hAPP(c_List_Onth(_1747669), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1747669), _1747671), c_List_Oupt(_1747667, _1747665))), _1747663) = hAPP(_1747671, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1747667), _1747663)))], (17641 ^ _775212) ^ [_1074756, _1074758] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1074756), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1074758)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1074756), 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)))), _1074758)))], (52269 ^ _775212) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (13779 ^ _775212) ^ [_1003720, _1003722, _1003724] : [-(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), _1003720), _1003722)), _1003722)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1003720, _1003722))), _1003724) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1003720), _1003724))], (31641 ^ _775212) ^ [_1347877, _1347879, _1347881] : [class_Rings_Oring__1(_1347877), hBOOL(hAPP(hAPP(c_member(_1347877), _1347879), c_Int_Oring__1__class_OInts(_1347877))), hBOOL(hAPP(hAPP(c_member(_1347877), _1347881), c_Int_Oring__1__class_OInts(_1347877))), -(hBOOL(hAPP(hAPP(c_member(_1347877), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1347877), _1347879), _1347881)), c_Int_Oring__1__class_OInts(_1347877))))], (47320 ^ _775212) ^ [_1718447, _1718449, _1718451, _1718453, _1718455] : [c_List_Opartition(_1718447, _1718449, _1718451) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1718447), tc_List_Olist(_1718447)), _1718453), _1718455), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1718447, tc_HOL_Obool)), hAPP(c_List_Oset(_1718447), _1718453)), hAPP(c_List_Oset(_1718447), _1718455)) = hAPP(c_List_Oset(_1718447), _1718451))], (29668 ^ _775212) ^ [_1303681, _1303683, _1303685, _1303687] : [hBOOL(hAPP(hAPP(c_member(_1303681), _1303683), hAPP(hAPP(c_Set_Oinsert(_1303681), _1303685), _1303687))), -(_1303683 = _1303685), -(hBOOL(hAPP(hAPP(c_member(_1303681), _1303683), _1303687)))], (42541 ^ _775212) ^ [_1601249, _1601251, _1601253, _1601255, _1601257] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1601249, tc_HOL_Obool)), _1601251), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601253, tc_fun(_1601249, tc_HOL_Obool)), _1601255), _1601257)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1601253, tc_fun(_1601249, tc_HOL_Obool)), _1601255), hAPP(hAPP(c_COMBB(tc_fun(_1601249, tc_HOL_Obool), tc_fun(_1601249, tc_HOL_Obool), _1601253), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1601249, tc_HOL_Obool)), _1601251)), _1601257)))], (10689 ^ _775212) ^ [_949804, _949806, _949808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949806), _949808)), -(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, _949804)), _949806)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _949804)), _949808))))], (23668 ^ _775212) ^ [_1186735] : [-(_1186735 = 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)), _1186735)))], (23354 ^ _775212) ^ [_1180215, _1180217] : [_1180215 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1180217, _1180215) = _1180217)], (24582 ^ _775212) ^ [_1202017] : [_1202017 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202017), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (49387 ^ _775212) ^ [_1763633, _1763635, _1763637] : [c_List_OtakeWhile(_1763633, _1763635, _1763637) = _1763637, 49390 ^ _775212 : [(49391 ^ _775212) ^ [_1763720] : [hBOOL(hAPP(hAPP(c_member(_1763633), _1763720), hAPP(c_List_Oset(_1763633), _1763637))), -(hBOOL(hAPP(_1763635, _1763720)))]]], (15705 ^ _775212) ^ [_1040900, _1040902, _1040904] : [class_Rings_Olinordered__semidom(_1040900), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040900), c_Groups_Oone__class_Oone(_1040900)), _1040902)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040900), c_Groups_Oone__class_Oone(_1040900)), hAPP(hAPP(c_Power_Opower__class_Opower(_1040900), _1040902), _1040904))))], (25865 ^ _775212) ^ [_1227662, _1227664, _1227666, _1227668] : [class_Groups_Ocomm__monoid__add(_1227662), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227662), _1227664), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1227666), hAPP(c_Nat_OSuc, _1227668))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227662), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1227662, tc_Nat_Onat), _1227664), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1227666, _1227668)))], (44663 ^ _775212) ^ [_1656392, _1656394, _1656396, _1656398] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656392), tc_List_Olist(_1656392))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656392), tc_List_Olist(_1656392)), _1656394), _1656396)), c_List_Olexord(_1656392, _1656398))), 44668 ^ _775212 : [(44671 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1656392), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656392)), _1656394)), _1656396) = _1656394)], (44669 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656392)), _1656394)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656392)), _1656396))))]], 44673 ^ _775212 : [(44678 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1656392, _1656392)), hAPP(hAPP(c_Product__Type_OPair(_1656392, _1656392), hAPP(hAPP(c_List_Onth(_1656392), _1656394), 44672 ^ [_1656392, _1656394, _1656396, _1656398])), hAPP(hAPP(c_List_Onth(_1656392), _1656396), 44672 ^ [_1656392, _1656394, _1656396, _1656398]))), _1656398)))], (44676 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1656392), 44672 ^ [_1656392, _1656394, _1656396, _1656398]), _1656394) = hAPP(hAPP(c_List_Otake(_1656392), 44672 ^ [_1656392, _1656394, _1656396, _1656398]), _1656396))], (44674 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44672 ^ [_1656392, _1656394, _1656396, _1656398]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656392)), _1656394)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656392)), _1656396)))))]]], (25386 ^ _775212) ^ [_1216958, _1216960] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216958), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1216960)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216958)), _1216960)))], (51871 ^ _775212) ^ [_1817859, _1817861, _1817863] : [c_Equiv__Relations_Oequiv(_1817859, _1817861, _1817863), 51874 ^ _775212 : [(51879 ^ _775212) ^ [] : [-(c_Relation_Otrans(_1817859, _1817863))], (51877 ^ _775212) ^ [] : [-(c_Relation_Osym(_1817859, _1817863))], (51875 ^ _775212) ^ [] : [-(c_Relation_Orefl__on(_1817859, _1817861, _1817863))]]], (33495 ^ _775212) ^ [_1384557, _1384559, _1384561] : [class_Orderings_Olinorder(_1384557), hAPP(_1384559, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1384557), 33500 ^ [_1384557, _1384559, _1384561]), 33501 ^ [_1384557, _1384559, _1384561])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1384557), hAPP(_1384559, 33500 ^ [_1384557, _1384559, _1384561])), hAPP(_1384559, 33501 ^ [_1384557, _1384559, _1384561])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384557), _1384561)), -(_1384561 = c_Orderings_Obot__class_Obot(tc_fun(_1384557, tc_HOL_Obool))), -(hAPP(_1384559, c_Big__Operators_Olinorder__class_OMax(_1384557, _1384561)) = c_Big__Operators_Olinorder__class_OMax(_1384557, hAPP(c_Set_Oimage(_1384557, _1384557, _1384559), _1384561)))], (43970 ^ _775212) ^ [_1636481, _1636483, _1636485, _1636487, _1636489, _1636491, _1636493, _1636495] : [c_Finite__Set_Ofolding__image__simple__idem(_1636481, _1636483, _1636485, _1636487, _1636489, _1636491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1636483), _1636493)), -(hAPP(_1636491, hAPP(hAPP(c_Set_Oinsert(_1636483), _1636495), _1636493)) = hAPP(hAPP(_1636485, hAPP(_1636489, _1636495)), hAPP(_1636491, _1636493)))], (28113 ^ _775212) ^ [_1273338, _1273340, _1273342] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1273338), _1273340)), 28116 ^ _775212 : [(28136 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1273338, tc_Nat_Onat), _1273342), _1273340) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 28137 ^ _775212 : [(28138 ^ _775212) ^ [_1273819] : [hBOOL(hAPP(hAPP(c_member(_1273338), _1273819), _1273340)), hAPP(_1273342, _1273819) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28146 ^ _775212 : [(28151 ^ _775212) ^ [] : [hAPP(_1273342, 28145 ^ [_1273338, _1273340, _1273342, _1273819]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28149 ^ _775212) ^ [] : [_1273819 = 28145 ^ [_1273338, _1273340, _1273342, _1273819]], (28147 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1273338), 28145 ^ [_1273338, _1273340, _1273342, _1273819]), _1273340)))]]]]], (28117 ^ _775212) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1273338, tc_Nat_Onat), _1273342), _1273340) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28121 ^ _775212 : [(28126 ^ _775212) ^ [_1273658] : [hBOOL(hAPP(hAPP(c_member(_1273338), _1273658), _1273340)), -(28120 ^ [_1273338, _1273340, _1273342] = _1273658), -(hAPP(_1273342, _1273658) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28124 ^ _775212) ^ [] : [-(hAPP(_1273342, 28120 ^ [_1273338, _1273340, _1273342]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (28122 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1273338), 28120 ^ [_1273338, _1273340, _1273342]), _1273340)))]]]]], (34777 ^ _775212) ^ [_1413967, _1413969, _1413971] : [class_Lattices_Obounded__lattice__top(_1413967), 34780 ^ _775212 : [(34789 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1413967), _1413969), _1413971) = c_Orderings_Otop__class_Otop(_1413967)), _1413969 = c_Orderings_Otop__class_Otop(_1413967), _1413971 = c_Orderings_Otop__class_Otop(_1413967)], (34781 ^ _775212) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1413967), _1413969), _1413971) = c_Orderings_Otop__class_Otop(_1413967), 34784 ^ _775212 : [(34787 ^ _775212) ^ [] : [-(_1413971 = c_Orderings_Otop__class_Otop(_1413967))], (34785 ^ _775212) ^ [] : [-(_1413969 = c_Orderings_Otop__class_Otop(_1413967))]]]]], (49121 ^ _775212) ^ [_1758002, _1758004] : [c_List_Olist_ONil(_1758002) = hAPP(c_List_Orev(_1758002), _1758004), -(_1758004 = c_List_Olist_ONil(_1758002))], (50619 ^ _775212) ^ [_1790351, _1790353] : [-(c_List_Osplice(_1790351, _1790353, c_List_Olist_ONil(_1790351)) = _1790353)], (9263 ^ _775212) ^ [_925358] : [class_Rings_Ozero__neq__one(_925358), c_Groups_Oone__class_Oone(_925358) = c_Groups_Ozero__class_Ozero(_925358)], (10722 ^ _775212) ^ [_950401] : [hBOOL(hAPP(_950401, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 10723 ^ [_950401]))), 10726 ^ _775212 : [(10727 ^ _775212) ^ [_950501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950501)), -(hBOOL(hAPP(_950401, _950501)))]]], (44224 ^ _775212) ^ [_1643565, _1643567, _1643569, _1643571, _1643573, _1643575] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643565), tc_List_Olist(_1643565))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643565), tc_List_Olist(_1643565)), hAPP(hAPP(c_List_Olist_OCons(_1643565), _1643567), _1643569)), hAPP(hAPP(c_List_Olist_OCons(_1643565), _1643571), _1643573))), c_List_Olexord(_1643565, _1643575))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643565, _1643565)), hAPP(hAPP(c_Product__Type_OPair(_1643565, _1643565), _1643567), _1643571)), _1643575))), 44231 ^ _775212 : [(44234 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643565), tc_List_Olist(_1643565))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643565), tc_List_Olist(_1643565)), _1643569), _1643573)), c_List_Olexord(_1643565, _1643575))))], (44232 ^ _775212) ^ [] : [-(_1643567 = _1643571)]]], (21575 ^ _775212) ^ [] : [-(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))], (38301 ^ _775212) ^ [_1495344, _1495346, _1495348, _1495350] : [c_Finite__Set_Ofolding__one(_1495344, _1495346, _1495348), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495344), _1495350)), -(hAPP(_1495348, _1495350) = hAPP(c_Finite__Set_Ofold1(_1495344, _1495346), _1495350))], (15457 ^ _775212) ^ [_1035945, _1035947, _1035949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035945), _1035947)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035949), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035947), _1035945))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035949), _1035945)), hAPP(c_Nat_OSuc, _1035947)))], (3684 ^ _775212) ^ [_830912, _830914, _830916, _830918, _830920, _830922, _830924, _830926, _830928, _830930, _830932, _830934] : [-(c_Product__Type_Omap__pair(_830934, _830930, _830926, _830922, _830918, _830914) = c_Product__Type_Omap__pair(_830932, _830928, _830924, _830920, _830916, _830912)), _830934 = _830932, _830930 = _830928, _830926 = _830924, _830922 = _830920, _830918 = _830916, _830914 = _830912], (23476 ^ _775212) ^ [_1182514, _1182516, _1182518] : [-(c_Nitpick_Oplus__frac(_1182514, _1182516, _1182518) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1182514), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1182514), _1182516), hAPP(c_Nitpick_Odenom(_1182514), _1182518))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1182514), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1182514), tc_Int_Oint), c_Nitpick_Ofrac(_1182514)), 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(_1182514), _1182516))), 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(_1182514), _1182516))))), 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(_1182514), _1182518))), 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(_1182514), _1182518)))))), c_COMBI(tc_Int_Oint))))], (9613 ^ _775212) ^ [_930431, _930433] : [class_Rings_Ocomm__semiring__1(_930431), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930431), _930433), c_Groups_Oone__class_Oone(_930431)) = _930433)], (44340 ^ _775212) ^ [_1647303, _1647305, _1647307, _1647309, _1647311, _1647313] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647303), tc_List_Olist(_1647303))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647303), tc_List_Olist(_1647303)), hAPP(hAPP(c_List_Olist_OCons(_1647303), _1647305), _1647307)), hAPP(hAPP(c_List_Olist_OCons(_1647303), _1647309), _1647311))), c_List_Olistrel1(_1647303, _1647313))), 44345 ^ _775212 : [(44348 ^ _775212) ^ [] : [-(_1647307 = _1647311)], (44346 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1647303, _1647303)), hAPP(hAPP(c_Product__Type_OPair(_1647303, _1647303), _1647305), _1647309)), _1647313)))]], 44349 ^ _775212 : [(44352 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647303), tc_List_Olist(_1647303))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647303), tc_List_Olist(_1647303)), _1647307), _1647311)), c_List_Olistrel1(_1647303, _1647313))))], (44350 ^ _775212) ^ [] : [-(_1647305 = _1647309)]]], (36435 ^ _775212) ^ [_1451650, _1451652, _1451654, _1451656, _1451658] : [c_Equiv__Relations_Oequivp(_1451650, _1451652), hBOOL(hAPP(hAPP(_1451652, _1451654), _1451656)), hBOOL(hAPP(hAPP(_1451652, _1451656), _1451658)), -(hBOOL(hAPP(hAPP(_1451652, _1451654), _1451658)))], (12099 ^ _775212) ^ [_973993, _973995, _973997] : [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, _973993)), _973995)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973993)), _973997))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973995), _973997)))], (13232 ^ _775212) ^ [_994465, _994467, _994469] : [-(hBOOL(hAPP(_994465, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _994467), _994469)))), 13233 ^ _775212 : [(13240 ^ _775212) ^ [_994633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994469), _994633)), _994467)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994469), hAPP(c_Nat_OSuc, _994633)))), hBOOL(hAPP(_994465, _994633))], (13234 ^ _775212) ^ [] : [_994469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_994465, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (4926 ^ _775212) ^ [_850325, _850327] : [_850327 = _850325, -(c_Lazy__Sequence_Oyieldn(_850327) = c_Lazy__Sequence_Oyieldn(_850325))], (39504 ^ _775212) ^ [_1528080, _1528082, _1528084, _1528086, _1528088, _1528090] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1528080, _1528082, _1528084), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528080, _1528082), tc_HOL_Obool)), _1528086), _1528088)), _1528090) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528080, _1528084), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1528080, _1528082, _1528084), _1528086), _1528090)), hAPP(hAPP(c_Relation_Orel__comp(_1528080, _1528082, _1528084), _1528088), _1528090)))], (2334 ^ _775212) ^ [_809215, _809217, _809219, _809221] : [-(c_Nitpick_Onumber__of__frac(_809221, _809217) = c_Nitpick_Onumber__of__frac(_809219, _809215)), _809221 = _809219, _809217 = _809215], (37800 ^ _775212) ^ [_1481100, _1481102, _1481104, _1481106] : [_1481104 = _1481106, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1481100, _1481102, hAPP(hAPP(c_Set_Oinsert(_1481100), _1481104), c_Orderings_Obot__class_Obot(tc_fun(_1481100, tc_HOL_Obool)))), _1481106)))], (50405 ^ _775212) ^ [_1785739, _1785741, _1785743] : [hBOOL(hAPP(hAPP(c_member(_1785739), _1785741), hAPP(c_List_Oset(_1785739), _1785743))), 50410 ^ _775212 : [(50413 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1785739), _1785741), hAPP(c_List_Oset(_1785739), 50408 ^ [_1785739, _1785741, _1785743])))], (50411 ^ _775212) ^ [] : [-(_1785743 = hAPP(hAPP(c_List_Oappend(_1785739), 50408 ^ [_1785739, _1785741, _1785743]), hAPP(hAPP(c_List_Olist_OCons(_1785739), _1785741), 50409 ^ [_1785739, _1785741, _1785743])))]]], (6092 ^ _775212) ^ [_871786, _871788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871786), _871788)), _871788 = _871786], (8477 ^ _775212) ^ [_912442, _912444, _912446, _912448] : [class_Rings_Olinordered__comm__semiring__strict(_912442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912442), _912444), _912446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912442), c_Groups_Ozero__class_Ozero(_912442)), _912448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912442), _912448), _912444)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912442), _912448), _912446))))], (51042 ^ _775212) ^ [_1799391, _1799393, _1799395] : [c_List_Olist__ex1(_1799391, _1799393, _1799395), 51046 ^ _775212 : [(51051 ^ _775212) ^ [_1799637] : [-(_1799637 = 51045 ^ [_1799391, _1799393, _1799395]), hBOOL(hAPP(hAPP(c_member(_1799391), _1799637), hAPP(c_List_Oset(_1799391), _1799395))), hBOOL(hAPP(_1799393, _1799637))], (51049 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1799393, 51045 ^ [_1799391, _1799393, _1799395])))], (51047 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1799391), 51045 ^ [_1799391, _1799393, _1799395]), hAPP(c_List_Oset(_1799391), _1799395))))]]], (50317 ^ _775212) ^ [_1784165, _1784167, _1784169] : [c_List_Olist__ex(_1784165, _1784167, _1784169), 50321 ^ _775212 : [(50324 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1784167, hAPP(hAPP(c_List_Onth(_1784165), _1784169), 50320 ^ [_1784165, _1784167, _1784169]))))], (50322 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50320 ^ [_1784165, _1784167, _1784169]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784165)), _1784169))))]]], (23744 ^ _775212) ^ [_1187911, _1187913, _1187915, _1187917] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1187911), _1187913), _1187915), _1187917) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1187911)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1187911), _1187913)))], (34975 ^ _775212) ^ [_1418131, _1418133, _1418135, _1418137, _1418139] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418131, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418133, tc_fun(_1418131, tc_HOL_Obool)), _1418135), _1418137)), _1418139) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418133, tc_fun(_1418131, tc_HOL_Obool)), _1418135), hAPP(hAPP(c_COMBC(_1418133, tc_fun(_1418131, tc_HOL_Obool), tc_fun(_1418131, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1418131, tc_HOL_Obool), tc_fun(tc_fun(_1418131, tc_HOL_Obool), tc_fun(_1418131, tc_HOL_Obool)), _1418133), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418131, tc_HOL_Obool))), _1418137)), _1418139)))], (47416 ^ _775212) ^ [_1720927, _1720929, _1720931, _1720933, _1720935, _1720937] : [class_Orderings_Olinorder(_1720927), 47419 ^ _775212 : [(47426 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1720927), hAPP(_1720929, _1720931)), hAPP(_1720929, _1720933)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1720935, _1720927, _1720929), _1720931), hAPP(hAPP(c_List_Olist_OCons(_1720935), _1720933), _1720937)) = hAPP(hAPP(c_List_Olist_OCons(_1720935), _1720933), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1720935, _1720927, _1720929), _1720931), _1720937)))], (47420 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1720927), hAPP(_1720929, _1720931)), hAPP(_1720929, _1720933))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1720935, _1720927, _1720929), _1720931), hAPP(hAPP(c_List_Olist_OCons(_1720935), _1720933), _1720937)) = hAPP(hAPP(c_List_Olist_OCons(_1720935), _1720931), hAPP(hAPP(c_List_Olist_OCons(_1720935), _1720933), _1720937)))]]], (29804 ^ _775212) ^ [_1306248, _1306250, _1306252, _1306254] : [_1306248 = _1306250, 29807 ^ _775212 : [(29814 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1306252), _1306250), _1306254)), -(hBOOL(hAPP(hAPP(c_member(_1306252), _1306248), _1306254)))], (29808 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1306252), _1306248), _1306254)), -(hBOOL(hAPP(hAPP(c_member(_1306252), _1306250), _1306254)))]]], (42794 ^ _775212) ^ [_1608462, _1608464, _1608466] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1608462, _1608462, _1608464), c_Relation_OId(_1608462)), _1608466) = _1608466)], (40429 ^ _775212) ^ [_1551786, _1551788] : [-(c_Hilbert__Choice_OEps(_1551786, hAPP(c_fequal, _1551788)) = _1551788)], (4438 ^ _775212) ^ [_842703, _842705, _842707, _842709] : [-(c_List_OremoveAll(_842709, _842705) = c_List_OremoveAll(_842707, _842703)), _842709 = _842707, _842705 = _842703], (45688 ^ _775212) ^ [_1682614, _1682616, _1682618, _1682620, _1682622] : [-(hAPP(hAPP(c_List_Olist__update(_1682614, hAPP(hAPP(c_List_Olist_OCons(_1682614), _1682616), _1682618)), hAPP(c_Nat_OSuc, _1682620)), _1682622) = hAPP(hAPP(c_List_Olist_OCons(_1682614), _1682616), hAPP(hAPP(c_List_Olist__update(_1682614, _1682618), _1682620), _1682622)))], (6763 ^ _775212) ^ [_882923, _882925] : [class_Groups_Olinordered__ab__group__add(_882923), 6766 ^ _775212 : [(6773 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882923), c_Groups_Ozero__class_Ozero(_882923)), _882925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882923), c_Groups_Ozero__class_Ozero(_882923)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_882923), _882925), _882925))))], (6767 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882923), c_Groups_Ozero__class_Ozero(_882923)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_882923), _882925), _882925))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882923), c_Groups_Ozero__class_Ozero(_882923)), _882925)))]]], (7104 ^ _775212) ^ [_888362, _888364, _888366] : [class_Orderings_Oorder(_888362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888362), _888364), _888366)), _888364 = _888366], (12149 ^ _775212) ^ [_974915, _974917] : [-(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), _974915), _974917)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _974915)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _974917))], (6058 ^ _775212) ^ [_871212, _871214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871212), _871214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _871212)), hAPP(c_Nat_OSuc, _871214))))], (3578 ^ _775212) ^ [_829281, _829283] : [_829283 = _829281, -(c_SetInterval_Oord__class_OgreaterThan(_829283) = c_SetInterval_Oord__class_OgreaterThan(_829281))], (18037 ^ _775212) ^ [_1081235, _1081237] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1081235))), _1081237) = 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)))), _1081235), _1081237))], (12546 ^ _775212) ^ [_982057, _982059, _982061, _982063] : [class_Divides_Oring__div(_982057), c_Divides_Odiv__class_Omod(_982057, _982059, _982061) = c_Divides_Odiv__class_Omod(_982057, _982063, _982061), -(c_Divides_Odiv__class_Omod(_982057, hAPP(c_Groups_Ouminus__class_Ouminus(_982057), _982059), _982061) = c_Divides_Odiv__class_Omod(_982057, hAPP(c_Groups_Ouminus__class_Ouminus(_982057), _982063), _982061))], (1634 ^ _775212) ^ [_798493, _798495] : [-(class_Groups_Ocomm__monoid__mult(_798493)), _798495 = _798493, class_Groups_Ocomm__monoid__mult(_798495)], (27203 ^ _775212) ^ [_1254449, _1254451, _1254453, _1254455] : [class_Lattices_Osemilattice__sup(_1254449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254449), _1254451), _1254453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254449), _1254451), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254449), _1254455), _1254453))))], (33429 ^ _775212) ^ [] : [-(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)))))], (17597 ^ _775212) ^ [_1073984, _1073986] : [class_Int_Onumber__ring(_1073984), 17600 ^ _775212 : [(17607 ^ _775212) ^ [] : [c_Int_Oiszero(_1073984, hAPP(c_Int_Onumber__class_Onumber__of(_1073984), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1073986), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1073984), _1073986) = c_Groups_Oone__class_Oone(_1073984))], (17601 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1073984), _1073986) = c_Groups_Oone__class_Oone(_1073984), -(c_Int_Oiszero(_1073984, hAPP(c_Int_Onumber__class_Onumber__of(_1073984), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1073986), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (14119 ^ _775212) ^ [_1010365, _1010367, _1010369, _1010371, _1010373] : [class_Groups_Oab__group__add(_1010365), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1010365), _1010367), _1010369) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1010365), _1010371), _1010373), 14126 ^ _775212 : [(14133 ^ _775212) ^ [] : [_1010371 = _1010373, -(_1010367 = _1010369)], (14127 ^ _775212) ^ [] : [_1010367 = _1010369, -(_1010371 = _1010373)]]], (30028 ^ _775212) ^ [_1313103, _1313105, _1313107] : [hBOOL(hAPP(hAPP(c_member(_1313103), _1313105), hAPP(hAPP(c_Set_Oinsert(_1313103), _1313107), c_Orderings_Obot__class_Obot(tc_fun(_1313103, tc_HOL_Obool))))), -(_1313105 = _1313107)], (22284 ^ _775212) ^ [_1158793, _1158795, _1158797, _1158799, _1158801] : [-(hAPP(c_Nat_Onat_Onat__rec(_1158793, _1158795, _1158797), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158799)), _1158801)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1158793), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1158799))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1158793, _1158793), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1158793, tc_fun(_1158793, _1158793)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1158793, tc_fun(_1158793, _1158793)), tc_Int_Oint), c_If(_1158793)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1158793, _1158795, _1158797), _1158801))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1158793, _1158793), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1158793, _1158793), tc_Int_Oint), _1158797), 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)), _1158801))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1158793, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1158793, _1158795, _1158797)), 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)), _1158801))))))], (43021 ^ _775212) ^ [_1613888, _1613890, _1613892] : [43022 ^ _775212 : [(43023 ^ _775212) ^ [_1613964] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613888, _1613888)), _1613890), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613888, _1613888), tc_HOL_Obool), _1613964), _1613892)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613888, _1613888)), _1613890), c_Transitive__Closure_Ortrancl(_1613888, _1613892))))], (3768 ^ _775212) ^ [_832318, _832320, _832322, _832324, _832326, _832328] : [-(c_List_Oset__Cons(_832328, _832324, _832320) = c_List_Oset__Cons(_832326, _832322, _832318)), _832328 = _832326, _832324 = _832322, _832320 = _832318], (40828 ^ _775212) ^ [_1560793, _1560795, _1560797, _1560799, _1560801, _1560803] : [class_Groups_Ocomm__monoid__add(_1560793), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560795), _1560797)), 40838 ^ _775212 : [(40839 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560795), 40837 ^ [_1560793, _1560795, _1560797, _1560799, _1560801, _1560803]), _1560797)))], (40844 ^ _775212) ^ [] : [40837 ^ [_1560793, _1560795, _1560797, _1560799, _1560801, _1560803] = 40840 ^ [_1560793, _1560795, _1560797, _1560799, _1560801, _1560803]], (40848 ^ _775212) ^ [] : [hAPP(_1560801, hAPP(_1560799, 40837 ^ [_1560793, _1560795, _1560797, _1560799, _1560801, _1560803])) = c_Groups_Ozero__class_Ozero(_1560793)], (40846 ^ _775212) ^ [] : [-(hAPP(_1560799, 40837 ^ [_1560793, _1560795, _1560797, _1560799, _1560801, _1560803]) = hAPP(_1560799, 40840 ^ [_1560793, _1560795, _1560797, _1560799, _1560801, _1560803]))], (40842 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560795), 40840 ^ [_1560793, _1560795, _1560797, _1560799, _1560801, _1560803]), _1560797)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560803, _1560793), _1560801), hAPP(c_Set_Oimage(_1560795, _1560803, _1560799), _1560797)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560795, _1560793), hAPP(c_Fun_Ocomp(_1560803, _1560793, _1560795, _1560801), _1560799)), _1560797))], (18187 ^ _775212) ^ [_1083998, _1084000] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1083998)), _1084000) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1083998), _1084000)))], (42519 ^ _775212) ^ [_1600438, _1600440, _1600442, _1600444] : [-(_1600438 = c_Orderings_Obot__class_Obot(tc_fun(_1600440, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600440, tc_fun(_1600442, tc_HOL_Obool)), _1600438), hAPP(c_COMBK(tc_fun(_1600442, tc_HOL_Obool), _1600440), _1600444)) = _1600444)], (42437 ^ _775212) ^ [_1598027, _1598029, _1598031, _1598033, _1598035] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1598027, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598029, tc_fun(_1598027, tc_HOL_Obool)), _1598031), _1598033)), _1598035) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598029, tc_fun(_1598027, tc_HOL_Obool)), _1598031), hAPP(hAPP(c_COMBC(_1598029, tc_fun(_1598027, tc_HOL_Obool), tc_fun(_1598027, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598027, tc_HOL_Obool), tc_fun(tc_fun(_1598027, tc_HOL_Obool), tc_fun(_1598027, tc_HOL_Obool)), _1598029), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1598027, tc_HOL_Obool))), _1598033)), _1598035)))], (7300 ^ _775212) ^ [_891181, _891183] : [class_Rings_Ocomm__semiring__1(_891181), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_891181), _891183), c_Groups_Ozero__class_Ozero(_891181)) = _891183)], (45126 ^ _775212) ^ [_1668602, _1668604, _1668606] : [-(hAPP(hAPP(c_List_Ozip(_1668602, _1668604), hAPP(hAPP(c_List_Omap(tc_prod(_1668602, _1668604), _1668602), c_Product__Type_Ofst(_1668602, _1668604)), _1668606)), hAPP(hAPP(c_List_Omap(tc_prod(_1668602, _1668604), _1668604), c_Product__Type_Osnd(_1668602, _1668604)), _1668606)) = _1668606)], (5560 ^ _775212) ^ [_860042, _860044, _860046, _860048, _860050, _860052] : [-(c_COMBS(_860052, _860048, _860044) = c_COMBS(_860050, _860046, _860042)), _860052 = _860050, _860048 = _860046, _860044 = _860042], (14415 ^ _775212) ^ [_1015838, _1015840] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015838), _1015840)), _1015840) = _1015838)], (26613 ^ _775212) ^ [_1242997] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1242997) = 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), _1242997))))], (15763 ^ _775212) ^ [_1042126, _1042128] : [_1042126 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042126), _1042128) = _1042128)], (6016 ^ _775212) ^ [_870658] : [-(_870658 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_870658 = hAPP(c_Nat_OSuc, 6019 ^ [_870658]))], (26789 ^ _775212) ^ [_1246042, _1246044, _1246046, _1246048] : [class_Orderings_Olinorder(_1246042), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246042), _1246044), _1246046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246042), _1246046), _1246048)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1246042, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1246042, _1246044, _1246046)), c_SetInterval_Oord__class_OatLeastAtMost(_1246042, _1246046, _1246048)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1246042, _1246044, _1246048))], (52263 ^ _775212) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (22968 ^ _775212) ^ [_1172817, _1172819, _1172821, _1172823] : [class_Orderings_Olinorder(_1172817), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172817), _1172819), _1172821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172817), _1172823), _1172821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172817), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1172817), _1172819), _1172823)), _1172821)))], (38660 ^ _775212) ^ [_1501734, _1501736, _1501738] : [class_Orderings_Olinorder(_1501734), -(_1501736 = c_Orderings_Obot__class_Obot(tc_fun(_1501734, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501734, tc_HOL_Obool)), _1501736), _1501738)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1501734), _1501738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1501734), hAPP(c_Finite__Set_Ofold1(_1501734, c_Orderings_Oord__class_Omin(_1501734)), _1501738)), hAPP(c_Finite__Set_Ofold1(_1501734, c_Orderings_Oord__class_Omin(_1501734)), _1501736))))], (23158 ^ _775212) ^ [_1176032, _1176034, _1176036, _1176038] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1176032), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176032), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176032), _1176034), _1176036)), _1176038) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176032), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176032), _1176034), _1176038)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176032), _1176036), _1176038)))], (8577 ^ _775212) ^ [_914255, _914257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914255)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914257))))], (34985 ^ _775212) ^ [_1418619, _1418621, _1418623, _1418625] : [class_Lattices_Olattice(_1418619), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1418619), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1418619), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418619), _1418621), _1418623)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418619), _1418621), _1418625))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418619), _1418621), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1418619), _1418623), _1418625)))))], (52203 ^ _775212) ^ [_1823531, _1823533] : [class_Groups_Ominus(_1823531), -(class_Groups_Ominus(tc_fun(_1823533, _1823531)))], (8980 ^ _775212) ^ [_920789, _920791, _920793, _920795] : [class_Orderings_Oord(_920789), _920791 = _920793, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920789), _920793), _920795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920789), _920791), _920795)))], (38046 ^ _775212) ^ [_1488145, _1488147, _1488149, _1488151] : [_1488145 = c_Orderings_Obot__class_Obot(tc_fun(_1488147, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1488147, _1488149), _1488149, c_Product__Type_Osnd(_1488147, _1488149)), hAPP(hAPP(c_Product__Type_OSigma(_1488147, _1488149), _1488145), hAPP(c_COMBK(tc_fun(_1488149, tc_HOL_Obool), _1488147), _1488151))) = c_Orderings_Obot__class_Obot(tc_fun(_1488149, tc_HOL_Obool)))], (25116 ^ _775212) ^ [_1212211, _1212213] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212211), _1212213)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1212211)), _1212213)))], (34835 ^ _775212) ^ [_1414986, _1414988] : [class_Lattices_Osemilattice__inf(_1414986), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1414986), _1414988), _1414988) = _1414988)], (51835 ^ _775212) ^ [_1817307, _1817309] : [-(c_Relation_Osym(_1817307, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1817307, _1817307), tc_HOL_Obool)), _1817309), hAPP(c_Relation_Oconverse(_1817307, _1817307), _1817309))))], (4636 ^ _775212) ^ [_845890, _845892] : [_845892 = _845890, -(c_Groups_Ouminus__class_Ouminus(_845892) = c_Groups_Ouminus__class_Ouminus(_845890))], (19729 ^ _775212) ^ [_1111233, _1111235, _1111237, _1111239, _1111241] : [class_Fields_Olinordered__field(_1111233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111233), c_Groups_Ozero__class_Ozero(_1111233)), _1111235)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111233), _1111235), _1111237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111233), c_Groups_Ozero__class_Ozero(_1111233)), _1111239)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111233), _1111239), _1111241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111233), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111233), _1111235), _1111241)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111233), _1111237), _1111239))))], (10291 ^ _775212) ^ [_942579, _942581, _942583] : [class_Rings_Oordered__ring(_942579), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942579), _942581), c_Groups_Ozero__class_Ozero(_942579))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942579), _942583), c_Groups_Ozero__class_Ozero(_942579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942579), c_Groups_Ozero__class_Ozero(_942579)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942579), _942581), _942583))))], (38887 ^ _775212) ^ [_1506340] : [-(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)), _1506340)))))], (19585 ^ _775212) ^ [_1108838, _1108840] : [class_Rings_Odivision__ring(_1108838), -(_1108840 = c_Groups_Ozero__class_Ozero(_1108838)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108838), _1108840), _1108840) = c_Groups_Oone__class_Oone(_1108838))], (8786 ^ _775212) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38814 ^ _775212) ^ [_1504867] : [class_Lattices_Osemilattice__inf(_1504867), -(c_Finite__Set_Ofun__left__comm__idem(_1504867, _1504867, c_Lattices_Osemilattice__inf__class_Oinf(_1504867)))], (33346 ^ _775212) ^ [_1381018, _1381020, _1381022, _1381024] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1381018), _1381020)), 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)), _1381018), _1381022)), 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)), _1381020), _1381024)), 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)), _1381020), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1381022), _1381024))), c_FunDef_Omin__strict)))], (40568 ^ _775212) ^ [_1554966, _1554968, _1554970, _1554972, _1554974, _1554976, _1554978, _1554980] : [class_Groups_Ocomm__monoid__mult(_1554966), c_Fun_Oinj__on(_1554968, _1554970, _1554972, _1554974), _1554976 = hAPP(c_Set_Oimage(_1554968, _1554970, _1554972), _1554974), _1554978 = hAPP(c_Fun_Ocomp(_1554970, _1554966, _1554968, _1554980), _1554972), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1554970, _1554966), _1554980), _1554976) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1554968, _1554966), _1554978), _1554974))], (27529 ^ _775212) ^ [_1260828, _1260830, _1260832] : [class_Orderings_Olinorder(_1260828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260828), _1260830), _1260832)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260828, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1260828), _1260830)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1260828, _1260830, _1260832)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1260828), _1260832))], (14527 ^ _775212) ^ [_1017991, _1017993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017991)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1017991), _1017993)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1017991)), _1017993))], (49221 ^ _775212) ^ [_1760120, _1760122, _1760124] : [hAPP(c_List_Orev(_1760120), _1760122) = _1760124, -(_1760122 = hAPP(c_List_Orev(_1760120), _1760124))], (38052 ^ _775212) ^ [_1488302, _1488304, _1488306, _1488308] : [-(_1488302 = c_Orderings_Obot__class_Obot(tc_fun(_1488304, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1488304, _1488306), _1488306, c_Product__Type_Osnd(_1488304, _1488306)), hAPP(hAPP(c_Product__Type_OSigma(_1488304, _1488306), _1488302), hAPP(c_COMBK(tc_fun(_1488306, tc_HOL_Obool), _1488304), _1488308))) = _1488308)], (33586 ^ _775212) ^ [_1387016, _1387018] : [-(c_Relation_OId__on(_1387016, _1387018) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387016, tc_fun(tc_prod(_1387016, _1387016), tc_HOL_Obool)), _1387018), hAPP(hAPP(c_COMBC(_1387016, tc_fun(tc_prod(_1387016, _1387016), tc_HOL_Obool), tc_fun(tc_prod(_1387016, _1387016), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1387016, _1387016), tc_fun(tc_fun(tc_prod(_1387016, _1387016), tc_HOL_Obool), tc_fun(tc_prod(_1387016, _1387016), tc_HOL_Obool)), _1387016), c_Set_Oinsert(tc_prod(_1387016, _1387016))), hAPP(hAPP(c_COMBS(_1387016, _1387016, tc_prod(_1387016, _1387016)), c_Product__Type_OPair(_1387016, _1387016)), c_COMBI(_1387016)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1387016, _1387016), tc_HOL_Obool)))))], (48566 ^ _775212) ^ [_1747377, _1747379, _1747381, _1747383] : [class_Groups_Ocomm__monoid__add(_1747377), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1747377), _1747379), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1747381, _1747383))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1747377), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1747377), _1747379), c_List_Oupt(_1747381, _1747383))))], (45435 ^ _775212) ^ [_1676651, _1676653] : [class_Groups_Oordered__ab__group__add__abs(_1676651), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676651), hAPP(c_Groups_Oabs__class_Oabs(_1676651), hAPP(c_List_Omonoid__add__class_Olistsum(_1676651), _1676653))), hAPP(c_List_Omonoid__add__class_Olistsum(_1676651), hAPP(hAPP(c_List_Omap(_1676651, _1676651), c_Groups_Oabs__class_Oabs(_1676651)), _1676653)))))], (46827 ^ _775212) ^ [_1708614] : [-(c_List_Orotate(_1708614, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1708614)))], (45746 ^ _775212) ^ [_1684038, _1684040, _1684042, _1684044] : [hAPP(hAPP(c_List_Olist__update(_1684038, _1684040), _1684042), _1684044) = c_List_Olist_ONil(_1684038), -(_1684040 = c_List_Olist_ONil(_1684038))], (41568 ^ _775212) ^ [_1576437, _1576439, _1576441] : [class_Orderings_Olinorder(_1576437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576437), _1576439)), -(hBOOL(hAPP(hAPP(c_member(_1576437), _1576441), _1576439))), -(c_Big__Operators_Olattice_OInf__fin(_1576437, c_Orderings_Oord__class_Omin(_1576437), hAPP(hAPP(c_Set_Oinsert(_1576437), _1576441), _1576439)) = hAPP(hAPP(c_Finite__Set_Ofold(_1576437, _1576437, c_Orderings_Oord__class_Omin(_1576437)), _1576441), _1576439))], (48297 ^ _775212) ^ [_1740778, _1740780, _1740782] : [-(c_List_Oremdups(_1740778, hAPP(c_List_Ofilter(_1740778, _1740780), _1740782)) = hAPP(c_List_Ofilter(_1740778, _1740780), c_List_Oremdups(_1740778, _1740782)))], (34347 ^ _775212) ^ [_1404852, _1404854, _1404856, _1404858, _1404860, _1404862] : [c_Equiv__Relations_Oequiv(_1404852, _1404854, _1404856), c_Equiv__Relations_Ocongruent(_1404852, tc_fun(_1404858, tc_HOL_Obool), _1404856, _1404860), hBOOL(hAPP(hAPP(c_member(_1404852), _1404862), _1404854)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404852, tc_fun(_1404858, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404852, _1404852, _1404856), hAPP(hAPP(c_Set_Oinsert(_1404852), _1404862), c_Orderings_Obot__class_Obot(tc_fun(_1404852, tc_HOL_Obool))))), _1404860) = hAPP(_1404860, _1404862))], (50683 ^ _775212) ^ [_1791753, _1791755, _1791757, _1791759] : [hBOOL(hAPP(_1791753, _1791755)), -(hAPP(c_List_Ofilter(_1791757, _1791753), c_List_Oreplicate(_1791757, _1791759, _1791755)) = c_List_Oreplicate(_1791757, _1791759, _1791755))], (960 ^ _775212) ^ [_789838, _789840, _789842, _789844, _789846, _789848] : [-(c_Relation_Orefl__on(_789846, _789842, _789838)), c_Relation_Orefl__on(_789848, _789844, _789840), _789848 = _789846, _789844 = _789842, _789840 = _789838], (290 ^ _775212) ^ [_779545, _779547, _779549, _779551, _779553, _779555, _779557, _779559, _779561, _779563] : [-(c_Big__Operators_Ocomm__monoid__big(_779561, _779557, _779553, _779549, _779545)), c_Big__Operators_Ocomm__monoid__big(_779563, _779559, _779555, _779551, _779547), _779563 = _779561, _779559 = _779557, _779555 = _779553, _779551 = _779549, _779547 = _779545], (44661 ^ _775212) ^ [_1656283, _1656285] : [-(c_Random_Oselect(_1656283, _1656285) = 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(_1656283, 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(_1656283)), _1656285)))), hAPP(hAPP(c_COMBB(_1656283, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1656283, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1656283, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1656283, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1656283), _1656285)), c_Code__Numeral_Onat__of))))], (43368 ^ _775212) ^ [_1621911, _1621913] : [class_Complete__Lattice_Ocomplete__lattice(_1621911), -(c_Complete__Lattice_OSup__class_OSup(_1621911, _1621913) = c_Complete__Lattice_OInf__class_OInf(_1621911, hAPP(c_Set_OCollect(_1621911), hAPP(hAPP(c_COMBB(tc_fun(_1621911, tc_HOL_Obool), tc_HOL_Obool, _1621911), c_HOL_OAll(_1621911)), hAPP(hAPP(c_COMBB(tc_fun(_1621911, tc_HOL_Obool), tc_fun(_1621911, tc_HOL_Obool), _1621911), hAPP(c_COMBS(_1621911, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1621911), c_fimplies), hAPP(hAPP(c_COMBC(_1621911, tc_fun(_1621911, tc_HOL_Obool), tc_HOL_Obool), c_member(_1621911)), _1621913)))), hAPP(c_COMBC(_1621911, _1621911, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1621911)))))))], (50745 ^ _775212) ^ [_1792713, _1792715, _1792717] : [-(c_List_Oreplicate(_1792713, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792713)), hAPP(c_List_Ofilter(_1792713, hAPP(c_fequal, _1792715)), _1792717)), _1792715) = hAPP(c_List_Ofilter(_1792713, hAPP(c_fequal, _1792715)), _1792717))], (52287 ^ _775212) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (38859 ^ _775212) ^ [_1505684, _1505686] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1505684)), -(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)), _1505684))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1505686))))) = 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)), _1505684))), 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, _1505686))))))], (34441 ^ _775212) ^ [_1407013, _1407015] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407013, tc_HOL_Obool)), _1407015), c_Orderings_Obot__class_Obot(tc_fun(_1407013, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1407013, tc_HOL_Obool)))], (42627 ^ _775212) ^ [_1603528, _1603530, _1603532, _1603534, _1603536] : [-(_1603528 = c_Orderings_Obot__class_Obot(tc_fun(_1603530, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1603532, tc_HOL_Obool)), _1603534), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1603530, tc_fun(_1603532, tc_HOL_Obool)), _1603528), _1603536)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603530, tc_fun(_1603532, tc_HOL_Obool)), _1603528), hAPP(hAPP(c_COMBB(tc_fun(_1603532, tc_HOL_Obool), tc_fun(_1603532, tc_HOL_Obool), _1603530), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1603532, tc_HOL_Obool)), _1603534)), _1603536)))], (51306 ^ _775212) ^ [_1805447, _1805449] : [c_Relation_Otrans(_1805447, _1805449), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1805447, _1805447), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1805447, _1805447, _1805447), _1805449), _1805449)), _1805449)))], (31397 ^ _775212) ^ [_1343369, _1343371] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1343369, _1343371) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343369), _1343371)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343371), _1343369)))], (45399 ^ _775212) ^ [_1675549, _1675551, _1675553] : [class_Groups_Omonoid__add(_1675549), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1675549), hAPP(hAPP(c_List_Olist_OCons(_1675549), _1675551), _1675553)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1675549), _1675551), hAPP(c_List_Omonoid__add__class_Olistsum(_1675549), _1675553)))], (16593 ^ _775212) ^ [_1057572, _1057574, _1057576] : [class_Int_Onumber__ring(_1057572), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057572), hAPP(c_Int_Onumber__class_Onumber__of(_1057572), _1057574)), hAPP(c_Int_Onumber__class_Onumber__of(_1057572), _1057576)) = hAPP(c_Int_Onumber__class_Onumber__of(_1057572), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1057574), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1057576))))], (23692 ^ _775212) ^ [_1187006, _1187008] : [hAPP(c_Code__Numeral_Oof__nat, _1187006) = hAPP(c_Code__Numeral_Oof__nat, _1187008), -(_1187006 = _1187008)], (18469 ^ _775212) ^ [_1088943, _1088945] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1088943)), c_Int_OBit1(_1088945)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088943), c_Int_Osucc(_1088945))))], (5852 ^ _775212) ^ [_867772, _867774, _867776, _867778] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_867772, _867774), _867776, _867778, _867776)), 5853 ^ _775212 : [(5856 ^ _775212) ^ [_867859] : [c_Natural_Oevaln(_867774, _867776, _867778, _867859), c_Natural_Oevaln(c_Com_Ocom_OWhile(_867772, _867774), _867859, _867778, _867776)], (5854 ^ _775212) ^ [] : [-(hBOOL(hAPP(_867772, _867776)))]]], (44523 ^ _775212) ^ [_1652831, _1652833, _1652835] : [c_Relation_Orefl__on(_1652831, _1652833, _1652835), -(c_Relation_Orefl__on(tc_List_Olist(_1652831), c_List_Olists(_1652831, _1652833), c_List_Olistrel(_1652831, _1652835)))], (42796 ^ _775212) ^ [_1608501, _1608503] : [-(hAPP(c_Relation_OImage(_1608501, _1608501, c_Relation_OId(_1608501)), _1608503) = _1608503)], (22170 ^ _775212) ^ [_1156090, _1156092, _1156094] : [class_Int_Onumber__ring(_1156090), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1156090), hAPP(c_Int_Onumber__class_Onumber__of(_1156090), _1156092)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1156094))) = hAPP(hAPP(c_HOL_OLet(_1156090, _1156090), hAPP(hAPP(c_Power_Opower__class_Opower(_1156090), hAPP(c_Int_Onumber__class_Onumber__of(_1156090), _1156092)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156094))), hAPP(hAPP(c_COMBS(_1156090, _1156090, _1156090), c_Groups_Otimes__class_Otimes(_1156090)), c_COMBI(_1156090))))], (17683 ^ _775212) ^ [_1075553, _1075555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1075553)), c_Int_OBit1(_1075555))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075553), _1075555)))], (16971 ^ _775212) ^ [_1064246, _1064248] : [class_Int_Onumber__ring(_1064246), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064246), hAPP(c_Int_Onumber__class_Onumber__of(_1064246), c_Int_OMin)), _1064248) = hAPP(c_Groups_Ouminus__class_Ouminus(_1064246), _1064248))], (21959 ^ _775212) ^ [_1151971] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1151971)], (18339 ^ _775212) ^ [_1086664, _1086666] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1086664))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1086666))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086664)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086666)))], (10509 ^ _775212) ^ [_946626, _946628] : [class_Rings_Ocomm__ring__1(_946626), -(hAPP(c_Groups_Ouminus__class_Ouminus(_946626), _946628) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946626), hAPP(c_Groups_Ouminus__class_Ouminus(_946626), c_Groups_Oone__class_Oone(_946626))), _946628))], (6593 ^ _775212) ^ [_879725, _879727, _879729, _879731] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_879725), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879725), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879725), _879727), _879729)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879725), _879731), _879729))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879725), _879727), _879731)))], (36299 ^ _775212) ^ [_1448506, _1448508, _1448510] : [class_Lattices_Olattice(_1448506), hBOOL(hAPP(c_Finite__Set_Ofinite(_1448506), _1448508)), -(_1448508 = c_Orderings_Obot__class_Obot(tc_fun(_1448506, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1448506), _1448510)), -(_1448510 = c_Orderings_Obot__class_Obot(tc_fun(_1448506, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448506, tc_HOL_Obool)), _1448508), _1448510) = c_Orderings_Obot__class_Obot(tc_fun(_1448506, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1448506, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448506, tc_HOL_Obool)), _1448508), _1448510)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1448506), c_Big__Operators_Olattice__class_OInf__fin(_1448506, _1448508)), c_Big__Operators_Olattice__class_OInf__fin(_1448506, _1448510)))], (40470 ^ _775212) ^ [_1552647, _1552649, _1552651, _1552653, _1552655, _1552657, _1552659, _1552661, _1552663, _1552665, _1552667] : [hAPP(_1552647, hAPP(_1552649, _1552651)) = hAPP(_1552653, hAPP(_1552655, _1552657)), -(hAPP(hAPP(c_Fun_Ocomp(_1552659, _1552661, _1552663, _1552647), _1552649), _1552651) = hAPP(hAPP(c_Fun_Ocomp(_1552665, _1552661, _1552667, _1552653), _1552655), _1552657))], (5176 ^ _775212) ^ [_854170, _854172, _854174, _854176] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_854176, _854172) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_854174, _854170)), _854176 = _854174, _854172 = _854170], (49730 ^ _775212) ^ [_1770981, _1770983, _1770985] : [-(hAPP(c_List_Oset(_1770981), hAPP(c_List_OremoveAll(_1770981, _1770983), _1770985)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1770981, tc_HOL_Obool)), hAPP(c_List_Oset(_1770981), _1770985)), hAPP(hAPP(c_Set_Oinsert(_1770981), _1770983), c_Orderings_Obot__class_Obot(tc_fun(_1770981, tc_HOL_Obool)))))], (40367 ^ _775212) ^ [_1550308, _1550310, _1550312, _1550314, _1550316, _1550318] : [40370 ^ _775212 : [(40373 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1550314), _1550316), hAPP(hAPP(_1550318, 40368 ^ [_1550308, _1550310, _1550312, _1550314, _1550316, _1550318]), 40369 ^ [_1550308, _1550310, _1550312, _1550314, _1550316, _1550318])))], (40371 ^ _775212) ^ [] : [-(_1550308 = hAPP(hAPP(c_Product__Type_OPair(_1550310, _1550312), 40368 ^ [_1550308, _1550310, _1550312, _1550314, _1550316, _1550318]), 40369 ^ [_1550308, _1550310, _1550312, _1550314, _1550316, _1550318]))]], -(hBOOL(hAPP(hAPP(c_member(_1550314), _1550316), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550310, _1550312, tc_fun(_1550314, tc_HOL_Obool)), _1550318), _1550308))))], (35267 ^ _775212) ^ [_1425195, _1425197, _1425199] : [class_Orderings_Oorder(_1425195), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425195, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1425195, _1425197, _1425199)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1425195), _1425199)) = c_Orderings_Obot__class_Obot(tc_fun(_1425195, tc_HOL_Obool)))], (25312 ^ _775212) ^ [_1215709, _1215711] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1215709), _1215711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215709), _1215711)))], (41438 ^ _775212) ^ [_1574086, _1574088, _1574090] : [class_Orderings_Olinorder(_1574086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1574086), _1574088)), -(c_Big__Operators_Olinorder__class_OMax(_1574086, hAPP(hAPP(c_Set_Oinsert(_1574086), _1574090), _1574088)) = hAPP(hAPP(c_Finite__Set_Ofold(_1574086, _1574086, c_Orderings_Oord__class_Omax(_1574086)), _1574090), _1574088))], (23256 ^ _775212) ^ [_1178346, _1178348, _1178350, _1178352] : [class_Orderings_Olinorder(_1178346), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178346), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178346), _1178348), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1178346), _1178350), _1178352))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1178346), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178346), _1178348), _1178350)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178346), _1178348), _1178352)))))], (14817 ^ _775212) ^ [_1023429, _1023431] : [class_Rings_Ocomm__semiring__1(_1023429), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1023429), _1023431), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1023429))], (35101 ^ _775212) ^ [_1421414, _1421416, _1421418] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421414, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421414, tc_HOL_Obool)), _1421416), _1421418)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421414, tc_HOL_Obool)), _1421416), _1421418)) = _1421416)], (36771 ^ _775212) ^ [_1458019, _1458021] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1458019), c_Orderings_Otop__class_Otop(tc_fun(_1458019, tc_HOL_Obool)))), c_Fun_Oinj__on(_1458019, _1458019, _1458021, c_Orderings_Otop__class_Otop(tc_fun(_1458019, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1458019, _1458019, _1458021), c_Orderings_Otop__class_Otop(tc_fun(_1458019, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1458019, tc_HOL_Obool)))], (860 ^ _775212) ^ [_788368, _788370, _788372, _788374, _788376, _788378] : [-(c_List_Olist__ex(_788376, _788372, _788368)), c_List_Olist__ex(_788378, _788374, _788370), _788378 = _788376, _788374 = _788372, _788370 = _788368], (37262 ^ _775212) ^ [_1468749, _1468751, _1468753, _1468755, _1468757, _1468759] : [c_Typedef_Otype__definition(_1468749, _1468751, _1468753, _1468755, _1468757), -(hAPP(_1468755, hAPP(_1468753, _1468759)) = _1468759)], (16091 ^ _775212) ^ [_1047857, _1047859] : [-(c_Divides_Odivmod__nat(_1047857, _1047859) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1047857), _1047859)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1047857, _1047859)))], (44867 ^ _775212) ^ [_1661647, _1661649, _1661651, _1661653, _1661655] : [c_Fun_Oinj__on(_1661647, _1661649, _1661651, c_Orderings_Otop__class_Otop(tc_fun(_1661647, tc_HOL_Obool))), 44870 ^ _775212 : [(44877 ^ _775212) ^ [] : [_1661653 = _1661655, -(hAPP(hAPP(c_List_Omap(_1661647, _1661649), _1661651), _1661653) = hAPP(hAPP(c_List_Omap(_1661647, _1661649), _1661651), _1661655))], (44871 ^ _775212) ^ [] : [hAPP(hAPP(c_List_Omap(_1661647, _1661649), _1661651), _1661653) = hAPP(hAPP(c_List_Omap(_1661647, _1661649), _1661651), _1661655), -(_1661653 = _1661655)]]], (2344 ^ _775212) ^ [_809364, _809366, _809368, _809370] : [-(c_Nitpick_Onorm__frac(_809370, _809366) = c_Nitpick_Onorm__frac(_809368, _809364)), _809370 = _809368, _809366 = _809364], (29885 ^ _775212) ^ [_1307768, _1307770, _1307772, _1307774, _1307776, _1307778] : [hBOOL(hAPP(hAPP(c_member(_1307768), _1307770), _1307772)), _1307774 = hAPP(_1307776, _1307770), -(hBOOL(hAPP(hAPP(c_member(_1307778), _1307774), hAPP(c_Set_Oimage(_1307768, _1307778, _1307776), _1307772))))], (19101 ^ _775212) ^ [_1100717, _1100719] : [c_Nat__Transfer_Ois__nat(_1100717), c_Nat__Transfer_Ois__nat(_1100719), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1100717), _1100719)))], (10857 ^ _775212) ^ [_952603, _952605] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952603)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952605)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952603), _952605)))], (33863 ^ _775212) ^ [_1393347, _1393349, _1393351, _1393353] : [c_Finite__Set_Ofolding__one__idem(_1393347, _1393349, _1393351), -(hAPP(hAPP(_1393349, _1393353), _1393353) = _1393353)], (29082 ^ _775212) ^ [_1291822, _1291824] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291822, tc_fun(_1291822, tc_HOL_Obool)), _1291824), hAPP(hAPP(c_COMBC(_1291822, tc_fun(_1291822, tc_HOL_Obool), tc_fun(_1291822, tc_HOL_Obool)), c_Set_Oinsert(_1291822)), c_Orderings_Obot__class_Obot(tc_fun(_1291822, tc_HOL_Obool)))) = _1291824)], (27912 ^ _775212) ^ [_1269675, _1269677, _1269679] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269675, tc_HOL_Obool)), _1269677), hAPP(hAPP(c_Set_Oinsert(_1269675), _1269679), _1269677))))], (39223 ^ _775212) ^ [_1517187] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1517187) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Int_Oint), _1517187), c_Int_Onat)))))], (46228 ^ _775212) ^ [_1695695, _1695697, _1695699] : [-(hAPP(hAPP(c_List_Odrop(_1695695), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1695695), _1695697), _1695699)) = _1695699)], (47893 ^ _775212) ^ [_1731544, _1731546] : [_1731544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1731546, _1731544, c_List_Olist_ONil(_1731546)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1731546)), c_List_Olist_ONil(_1731546)), c_List_Olist_ONil(tc_List_Olist(_1731546))))], (45800 ^ _775212) ^ [_1685006, _1685008, _1685010] : [_1685006 = hAPP(hAPP(c_List_Oappend(_1685008), _1685010), _1685006), -(_1685010 = c_List_Olist_ONil(_1685008))], (23886 ^ _775212) ^ [_1190377, _1190379] : [class_Rings_Ocomm__semiring__1(_1190377), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1190377), _1190379), c_Groups_Ozero__class_Ozero(_1190377))))], (51173 ^ _775212) ^ [_1802570, _1802572, _1802574, _1802576] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1802570, _1802572, _1802574, _1802576, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1802572)) = _1802574)], (39904 ^ _775212) ^ [_1538990, _1538992, _1538994, _1538996] : [-(hAPP(c_Relation_ODomain(_1538990, _1538992), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1538990, _1538992), tc_HOL_Obool)), _1538994), _1538996)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1538990, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1538990, _1538992), _1538994)), hAPP(c_Relation_ODomain(_1538990, _1538992), _1538996)))], (22618 ^ _775212) ^ [_1165631, _1165633, _1165635, _1165637, _1165639] : [class_Orderings_Olinorder(_1165631), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165631), _1165633), _1165635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165631), _1165637), _1165639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165631), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165631), _1165633), _1165637)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165631), _1165635), _1165639))))], (44162 ^ _775212) ^ [_1641557, _1641559, _1641561, _1641563, _1641565] : [-(hAPP(hAPP(c_List_Olist_OCons(_1641557), _1641559), _1641561) = hAPP(hAPP(c_List_Olist_OCons(_1641557), _1641563), _1641565)), _1641559 = _1641563, _1641561 = _1641565], (23200 ^ _775212) ^ [_1177087, _1177089, _1177091] : [class_Orderings_Olinorder(_1177087), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1177087), _1177089), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177087), _1177089), _1177091)) = _1177089)], (7389 ^ _775212) ^ [_892616, _892618, _892620] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _892616)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _892618)), _892620)) = 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), _892616), _892618))), _892620))], (52499 ^ _775212) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (4370 ^ _775212) ^ [_841695, _841697, _841699, _841701] : [-(c_Product__Type_Osnd(_841701, _841697) = c_Product__Type_Osnd(_841699, _841695)), _841701 = _841699, _841697 = _841695], (28014 ^ _775212) ^ [] : [-(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)))], (30596 ^ _775212) ^ [_1326775, _1326777, _1326779, _1326781, _1326783] : [class_Rings_Oring(_1326775), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326777), _1326779)), hBOOL(hAPP(hAPP(c_member(_1326777), _1326781), _1326779)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1326777, _1326775), _1326783), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326777, tc_HOL_Obool)), _1326779), hAPP(hAPP(c_Set_Oinsert(_1326777), _1326781), c_Orderings_Obot__class_Obot(tc_fun(_1326777, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1326775), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1326777, _1326775), _1326783), _1326779)), hAPP(_1326783, _1326781)))], (42940 ^ _775212) ^ [_1611883, _1611885, _1611887, _1611889, _1611891] : [c_Relation_Osingle__valued(_1611883, _1611883, _1611885), hBOOL(hAPP(hAPP(c_member(tc_prod(_1611883, _1611883)), hAPP(hAPP(c_Product__Type_OPair(_1611883, _1611883), _1611887), _1611889)), c_Transitive__Closure_Ortrancl(_1611883, _1611885))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1611883, _1611883)), hAPP(hAPP(c_Product__Type_OPair(_1611883, _1611883), _1611887), _1611891)), c_Transitive__Closure_Ortrancl(_1611883, _1611885))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611883, _1611883)), hAPP(hAPP(c_Product__Type_OPair(_1611883, _1611883), _1611889), _1611891)), c_Transitive__Closure_Ortrancl(_1611883, _1611885)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611883, _1611883)), hAPP(hAPP(c_Product__Type_OPair(_1611883, _1611883), _1611891), _1611889)), c_Transitive__Closure_Ortrancl(_1611883, _1611885))))], (52481 ^ _775212) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (45074 ^ _775212) ^ [_1667631] : [-(hAPP(c_List_Oset(_1667631), c_List_Olist_ONil(_1667631)) = c_Orderings_Obot__class_Obot(tc_fun(_1667631, tc_HOL_Obool)))], (8938 ^ _775212) ^ [_920132, _920134, _920136, _920138] : [class_Orderings_Oorder(_920132), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920132), _920134), _920136)), _920134 = _920138, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920132), _920138), _920136)))], (10655 ^ _775212) ^ [_949179, _949181, _949183] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949179), _949181)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949179), _949183)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _949179)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949181), _949183))], (5280 ^ _775212) ^ [_855812, _855814, _855816, _855818] : [-(c_List_Olistrel(_855818, _855814) = c_List_Olistrel(_855816, _855812)), _855818 = _855816, _855814 = _855812], (14871 ^ _775212) ^ [_1024393, _1024395] : [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), _1024393), _1024395))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024393))), -(_1024395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31148 ^ _775212) ^ [_1338320, _1338322, _1338324, _1338326, _1338328, _1338330, _1338332, _1338334] : [c_Finite__Set_Ofolding__image__simple(_1338320, _1338322, _1338324, _1338326, _1338328, _1338330), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338322), _1338332)), -(hBOOL(hAPP(hAPP(c_member(_1338322), _1338334), _1338332))), -(hAPP(_1338330, hAPP(hAPP(c_Set_Oinsert(_1338322), _1338334), _1338332)) = hAPP(hAPP(_1338324, hAPP(_1338328, _1338334)), hAPP(_1338330, _1338332)))], (34969 ^ _775212) ^ [_1417777, _1417779, _1417781, _1417783] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417777, tc_HOL_Obool)), _1417779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417777, tc_HOL_Obool)), _1417781), _1417783)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417777, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417777, tc_HOL_Obool)), _1417779), _1417781)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417777, tc_HOL_Obool)), _1417779), _1417783)))], (33332 ^ _775212) ^ [_1380737, _1380739, _1380741, _1380743] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1380737), _1380739)), 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)), _1380741), _1380737)), 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)), _1380743), _1380739)), 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)), _1380741), _1380743)), _1380739)), c_FunDef_Omax__strict)))], (1654 ^ _775212) ^ [_798743, _798745] : [-(class_Rings_Oordered__semiring(_798743)), _798745 = _798743, class_Rings_Oordered__semiring(_798745)], (24588 ^ _775212) ^ [_1202104, _1202106, _1202108, _1202110] : [class_Rings_Oidom(_1202104), 24591 ^ _775212 : [(24592 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1202104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202104), _1202106), _1202108)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202104), _1202106), _1202110))), -(_1202106 = c_Groups_Ozero__class_Ozero(_1202104)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1202104), _1202108), _1202110)))], (24602 ^ _775212) ^ [] : [24603 ^ _775212 : [(24606 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1202104), _1202108), _1202110))], (24604 ^ _775212) ^ [] : [_1202106 = c_Groups_Ozero__class_Ozero(_1202104)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1202104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202104), _1202106), _1202108)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202104), _1202106), _1202110))))]]], (13725 ^ _775212) ^ [_1002749, _1002751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002749), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002751), _1002749)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1002749), _1002751) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6705 ^ _775212) ^ [_881797, _881799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881797), _881799)), _881799))], (14469 ^ _775212) ^ [_1016843, _1016845, _1016847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016843), _1016845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016843), _1016847)), 14476 ^ _775212 : [(14483 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016845), _1016847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016845), _1016843)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016847), _1016843))))], (14477 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016845), _1016843)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016847), _1016843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016845), _1016847)))]]], (20341 ^ _775212) ^ [_1122197, _1122199] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122197), _1122199), hAPP(c_Int_Onumber__class_Onumber__of(_1122197), c_Int_OBit1(c_Int_OPls))) = _1122199), class_Fields_Ofield(_1122197), class_Int_Onumber__ring(_1122197)], (41913 ^ _775212) ^ [_1584519, _1584521] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1584519, _1584519, _1584519), c_Transitive__Closure_Ortrancl(_1584519, _1584521)), c_Transitive__Closure_Ortrancl(_1584519, _1584521)) = c_Transitive__Closure_Ortrancl(_1584519, _1584521))], (570 ^ _775212) ^ [_783995, _783997, _783999, _784001] : [-(c_Relation_Oirrefl(_783999, _783995)), c_Relation_Oirrefl(_784001, _783997), _784001 = _783999, _783997 = _783995], (42707 ^ _775212) ^ [_1605496, _1605498, _1605500, _1605502, _1605504] : [_1605496 = c_Orderings_Obot__class_Obot(tc_fun(_1605498, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605498, tc_fun(_1605500, tc_HOL_Obool)), _1605496), hAPP(hAPP(c_COMBB(tc_fun(_1605500, tc_HOL_Obool), tc_fun(_1605500, tc_HOL_Obool), _1605498), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1605500, tc_HOL_Obool)), _1605502)), _1605504)) = c_Orderings_Otop__class_Otop(tc_fun(_1605500, tc_HOL_Obool)))], (10 ^ _775212) ^ [_775335, _775337, _775339] : [-(_775339 = _775335), _775339 = _775337, _775337 = _775335], (26537 ^ _775212) ^ [_1241656, _1241658, _1241660] : [class_Groups_Oordered__ab__group__add(_1241656), -(hAPP(c_Set_Oimage(_1241656, _1241656, c_Groups_Ouminus__class_Ouminus(_1241656)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1241656, _1241658, _1241660)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241656, hAPP(c_Groups_Ouminus__class_Ouminus(_1241656), _1241660)), hAPP(c_Groups_Ouminus__class_Ouminus(_1241656), _1241658)))], (36833 ^ _775212) ^ [_1459357, _1459359, _1459361, _1459363] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1459357), _1459359)), hAPP(c_Finite__Set_Ocard(_1459361), hAPP(c_Set_Oimage(_1459357, _1459361, _1459363), _1459359)) = hAPP(c_Finite__Set_Ocard(_1459357), _1459359), -(c_Fun_Oinj__on(_1459357, _1459361, _1459363, _1459359))], (5631 ^ _775212) ^ [_863912, _863914, _863916] : [c_Natural_Oevaln(c_Com_Ocom_OSKIP, _863912, _863914, _863916), -(_863916 = _863912)], (23570 ^ _775212) ^ [_1184338, _1184340, _1184342, _1184344, _1184346, _1184348] : [hBOOL(hAPP(hAPP(_1184338, _1184340), _1184342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1184344, tc_fun(_1184346, tc_HOL_Obool))), _1184338), _1184348)), -(hBOOL(hAPP(hAPP(_1184348, _1184340), _1184342)))], (9923 ^ _775212) ^ [_935953, _935955] : [class_Rings_Olinordered__idom(_935953), 9926 ^ _775212 : [(9933 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935953), c_Groups_Ozero__class_Ozero(_935953)), hAPP(c_Int_Oring__1__class_Oof__int(_935953), _935955))))], (9927 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935953), c_Groups_Ozero__class_Ozero(_935953)), hAPP(c_Int_Oring__1__class_Oof__int(_935953), _935955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935955)))]]], (41247 ^ _775212) ^ [_1570271, _1570273, _1570275, _1570277] : [class_Lattices_Osemilattice__sup(_1570271), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570271), _1570273)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1570271, _1570271, c_Lattices_Osemilattice__sup__class_Osup(_1570271)), _1570275), hAPP(hAPP(c_Set_Oinsert(_1570271), _1570277), _1570273)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1570271), _1570277), hAPP(hAPP(c_Finite__Set_Ofold(_1570271, _1570271, c_Lattices_Osemilattice__sup__class_Osup(_1570271)), _1570275), _1570273)))], (32061 ^ _775212) ^ [_1354607, _1354609, _1354611] : [class_Orderings_Olinorder(_1354607), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354607), _1354609)), -(hBOOL(hAPP(hAPP(c_member(_1354607), _1354611), _1354609))), -(_1354609 = c_Orderings_Obot__class_Obot(tc_fun(_1354607, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1354607, hAPP(hAPP(c_Set_Oinsert(_1354607), _1354611), _1354609)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1354607), _1354611), c_Big__Operators_Olinorder__class_OMax(_1354607, _1354609)))], (52479 ^ _775212) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (35525 ^ _775212) ^ [_1431026, _1431028, _1431030, _1431032, _1431034] : [class_Groups_Oab__group__add(_1431026), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431028), _1431030)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431028), _1431032)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1431028, _1431026), _1431034), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431028, tc_HOL_Obool)), _1431030), _1431032)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1431026), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1431026), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1431028, _1431026), _1431034), _1431030)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1431028, _1431026), _1431034), _1431032))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1431028, _1431026), _1431034), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431028, tc_HOL_Obool)), _1431030), _1431032))))], (7685 ^ _775212) ^ [_898375, _898377, _898379, _898381] : [class_Rings_Ocomm__semiring__1(_898375), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898375), _898377), _898379)), _898381) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898375), _898377), _898381)), _898379))], (28682 ^ _775212) ^ [_1284690, _1284692] : [_1284692 = c_Orderings_Obot__class_Obot(tc_fun(_1284690, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284690, tc_HOL_Obool)), _1284692), c_Orderings_Obot__class_Obot(tc_fun(_1284690, tc_HOL_Obool)))))], (43310 ^ _775212) ^ [_1620575] : [class_Complete__Lattice_Ocomplete__lattice(_1620575), -(c_Complete__Lattice_OInf__class_OInf(_1620575, c_Orderings_Otop__class_Otop(tc_fun(_1620575, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1620575))], (48205 ^ _775212) ^ [_1738894, _1738896, _1738898] : [hAPP(c_List_Ofilter(_1738894, _1738896), _1738898) = _1738898, 48208 ^ _775212 : [(48209 ^ _775212) ^ [_1738985] : [hBOOL(hAPP(hAPP(c_member(_1738894), _1738985), hAPP(c_List_Oset(_1738894), _1738898))), -(hBOOL(hAPP(_1738896, _1738985)))]]], (1754 ^ _775212) ^ [_799993, _799995] : [-(class_Orderings_Olinorder(_799993)), _799995 = _799993, class_Orderings_Olinorder(_799995)], (25364 ^ _775212) ^ [_1216585, _1216587] : [-(_1216585 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25367 ^ _775212 : [(25374 ^ _775212) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1216587) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1216585), _1216587)), _1216585)))], (25368 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1216585), _1216587)), _1216585)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1216587) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (14361 ^ _775212) ^ [_1014866, _1014868, _1014870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1014866), _1014868)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1014866), _1014870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014870), _1014868)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014870), _1014866))))], (46055 ^ _775212) ^ [_1690915, _1690917, _1690919, _1690921, _1690923, _1690925, _1690927, _1690929] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1690915, _1690915)), hAPP(hAPP(c_Product__Type_OPair(_1690915, _1690915), _1690917), _1690919)), _1690921)), _1690923 = hAPP(hAPP(c_List_Oappend(_1690915), _1690925), hAPP(hAPP(c_List_Olist_OCons(_1690915), _1690917), _1690927)), _1690929 = hAPP(hAPP(c_List_Oappend(_1690915), _1690925), hAPP(hAPP(c_List_Olist_OCons(_1690915), _1690919), _1690927)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1690915), tc_List_Olist(_1690915))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1690915), tc_List_Olist(_1690915)), _1690923), _1690929)), c_List_Olistrel1(_1690915, _1690921))))], (47875 ^ _775212) ^ [_1730981, _1730983, _1730985] : [-(c_Enum_Osublists(_1730981, hAPP(hAPP(c_List_Olist_OCons(_1730981), _1730983), _1730985)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1730981)), tc_List_Olist(tc_List_Olist(_1730981))), c_Enum_Osublists(_1730981, _1730985)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1730981)), tc_List_Olist(tc_List_Olist(_1730981)), tc_List_Olist(tc_List_Olist(_1730981))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1730981)), tc_fun(tc_List_Olist(tc_List_Olist(_1730981)), tc_List_Olist(tc_List_Olist(_1730981))), tc_List_Olist(tc_List_Olist(_1730981))), c_List_Oappend(tc_List_Olist(_1730981))), hAPP(c_List_Omap(tc_List_Olist(_1730981), tc_List_Olist(_1730981)), hAPP(c_List_Olist_OCons(_1730981), _1730983)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1730981))))))], (6517 ^ _775212) ^ [_878414, _878416, _878418] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878414), _878416)), _878418) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878414), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878416), _878418)))], (20061 ^ _775212) ^ [_1117439, _1117441, _1117443, _1117445, _1117447] : [class_Fields_Ofield(_1117439), -(_1117441 = c_Groups_Ozero__class_Ozero(_1117439)), -(_1117443 = c_Groups_Ozero__class_Ozero(_1117439)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117439), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117439), _1117445), _1117441)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117439), _1117447), _1117443)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117439), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117439), _1117445), _1117443)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117439), _1117447), _1117441))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117439), _1117441), _1117443)))], (22644 ^ _775212) ^ [_1166125, _1166127, _1166129, _1166131] : [class_Orderings_Olinorder(_1166125), 22647 ^ _775212 : [(22648 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166125), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166125), _1166127), _1166129)), _1166131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166125), _1166127), _1166131))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166125), _1166129), _1166131)))], (22658 ^ _775212) ^ [] : [22659 ^ _775212 : [(22662 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166125), _1166129), _1166131))], (22660 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166125), _1166127), _1166131))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166125), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166125), _1166127), _1166129)), _1166131)))]]], (4586 ^ _775212) ^ [_845035, _845037, _845039, _845041, _845043, _845045, _845047, _845049, _845051, _845053, _845055, _845057] : [-(c_New__Random__Sequence_Opos__union(_845057, _845053, _845049, _845045, _845041, _845037) = c_New__Random__Sequence_Opos__union(_845055, _845051, _845047, _845043, _845039, _845035)), _845057 = _845055, _845053 = _845051, _845049 = _845047, _845045 = _845043, _845041 = _845039, _845037 = _845035], (17283 ^ _775212) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (41899 ^ _775212) ^ [_1584161, _1584163, _1584165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1584161, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1584161, _1584161, _1584163), _1584165)), _1584165)), -(hAPP(c_Relation_OImage(_1584161, _1584161, c_Transitive__Closure_Ortrancl(_1584161, _1584163)), _1584165) = _1584165)], (26334 ^ _775212) ^ [_1237439, _1237441, _1237443, _1237445, _1237447, _1237449] : [-(hAPP(c_Set_Oimage(_1237439, _1237441, _1237443), hAPP(c_Set_Oimage(_1237445, _1237439, _1237447), _1237449)) = hAPP(c_Set_Oimage(_1237445, _1237441, hAPP(hAPP(c_COMBB(_1237439, _1237441, _1237445), _1237443), _1237447)), _1237449))], (29879 ^ _775212) ^ [_1307637, _1307639, _1307641, _1307643, _1307645] : [hBOOL(hAPP(hAPP(c_member(_1307637), _1307639), _1307641)), -(hBOOL(hAPP(hAPP(c_member(_1307643), hAPP(_1307645, _1307639)), hAPP(c_Set_Oimage(_1307637, _1307643, _1307645), _1307641))))], (18383 ^ _775212) ^ [_1087356, _1087358] : [class_Int_Onumber__ring(_1087356), -(hAPP(c_Int_Onumber__class_Onumber__of(_1087356), c_Int_OBit0(_1087358)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087356), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087356), c_Groups_Ozero__class_Ozero(_1087356)), hAPP(c_Int_Onumber__class_Onumber__of(_1087356), _1087358))), hAPP(c_Int_Onumber__class_Onumber__of(_1087356), _1087358)))], (1314 ^ _775212) ^ [_794493, _794495] : [-(class_Rings_Oring(_794493)), _794495 = _794493, class_Rings_Oring(_794495)], (42443 ^ _775212) ^ [_1598423, _1598425, _1598427, _1598429, _1598431] : [-(hAPP(hAPP(c_Set_Oinsert(_1598423), _1598425), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598427, tc_fun(_1598423, tc_HOL_Obool)), _1598429), _1598431)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598427, tc_fun(_1598423, tc_HOL_Obool)), _1598429), hAPP(hAPP(c_COMBB(tc_fun(_1598423, tc_HOL_Obool), tc_fun(_1598423, tc_HOL_Obool), _1598427), hAPP(c_Set_Oinsert(_1598423), _1598425)), _1598431)))], (37648 ^ _775212) ^ [_1477728, _1477730, _1477732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1477728, _1477728), tc_HOL_Obool)), _1477730), _1477732)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477728, tc_HOL_Obool)), c_Wellfounded_Oacc(_1477728, _1477732)), c_Wellfounded_Oacc(_1477728, _1477730))))], (48035 ^ _775212) ^ [_1734378, _1734380] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734378)), c_List_Oremdups(_1734378, c_List_Oconcat(_1734378, _1734380))) = hAPP(c_Finite__Set_Ocard(_1734378), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1734378), tc_fun(_1734378, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1734378)), _1734380)), c_List_Oset(_1734378))))], (29220 ^ _775212) ^ [_1294612, _1294614] : [_1294612 = _1294614, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1294612, _1294614) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1294612), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (43449 ^ _775212) ^ [_1624002, _1624004] : [-(hAPP(c_Relation_OField(_1624002), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1624002, _1624002), tc_HOL_Obool), _1624004)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1624002, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1624002, _1624002), tc_HOL_Obool), tc_fun(_1624002, tc_HOL_Obool), c_Relation_OField(_1624002)), _1624004)))], (44451 ^ _775212) ^ [_1650960, _1650962, _1650964, _1650966, _1650968] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650960), tc_List_Olist(_1650960))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650960), tc_List_Olist(_1650960)), _1650962), hAPP(hAPP(c_List_Olist_OCons(_1650960), _1650964), _1650966))), c_List_Olistrel(_1650960, _1650968))), 44456 ^ _775212 : [(44461 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650960), tc_List_Olist(_1650960))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650960), tc_List_Olist(_1650960)), 44455 ^ [_1650960, _1650962, _1650964, _1650966, _1650968]), _1650966)), c_List_Olistrel(_1650960, _1650968))))], (44459 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1650960, _1650960)), hAPP(hAPP(c_Product__Type_OPair(_1650960, _1650960), 44454 ^ [_1650960, _1650962, _1650964, _1650966, _1650968]), _1650964)), _1650968)))], (44457 ^ _775212) ^ [] : [-(_1650962 = hAPP(hAPP(c_List_Olist_OCons(_1650960), 44454 ^ [_1650960, _1650962, _1650964, _1650966, _1650968]), 44455 ^ [_1650960, _1650962, _1650964, _1650966, _1650968]))]]], (7316 ^ _775212) ^ [_891455] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _891455), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _891455)], (16401 ^ _775212) ^ [_1053820, _1053822, _1053824] : [class_Int_Onumber__ring(_1053820), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053820), hAPP(c_Int_Onumber__class_Onumber__of(_1053820), _1053822)), hAPP(c_Int_Onumber__class_Onumber__of(_1053820), _1053824)) = hAPP(c_Int_Onumber__class_Onumber__of(_1053820), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1053822), _1053824)))], (14419 ^ _775212) ^ [_1015926, _1015928] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015926), _1015928)), _1015926)))], (48711 ^ _775212) ^ [_1750073, _1750075, _1750077, _1750079] : [class_Orderings_Olinorder(_1750073), 48714 ^ _775212 : [(48723 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1750073, hAPP(hAPP(c_List_Olist_OCons(_1750073), _1750075), hAPP(hAPP(c_List_Olist_OCons(_1750073), _1750077), _1750079)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1750073), _1750075), _1750077)), c_List_Olinorder__class_Osorted(_1750073, hAPP(hAPP(c_List_Olist_OCons(_1750073), _1750077), _1750079))], (48715 ^ _775212) ^ [] : [c_List_Olinorder__class_Osorted(_1750073, hAPP(hAPP(c_List_Olist_OCons(_1750073), _1750075), hAPP(hAPP(c_List_Olist_OCons(_1750073), _1750077), _1750079))), 48718 ^ _775212 : [(48721 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1750073, hAPP(hAPP(c_List_Olist_OCons(_1750073), _1750077), _1750079)))], (48719 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1750073), _1750075), _1750077)))]]]]], (18047 ^ _775212) ^ [_1081481, _1081483] : [-(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), _1081481)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1081483)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1081481))) = 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), _1081483)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081481)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (47374 ^ _775212) ^ [_1720127, _1720129, _1720131, _1720133] : [hBOOL(hAPP(c_List_Olistsp(_1720127, _1720129), hAPP(hAPP(c_List_Oappend(_1720127), _1720131), _1720133))), 47377 ^ _775212 : [(47380 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1720127, _1720129), _1720133)))], (47378 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1720127, _1720129), _1720131)))]]], (32904 ^ _775212) ^ [_1371998, _1372000, _1372002] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371998, tc_Nat_Onat), _1372000), _1372002)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371998, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1371998), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1372000)), _1372002))], (47943 ^ _775212) ^ [_1732696, _1732698, _1732700, _1732702, _1732704] : [c_Finite__Set_Ofun__left__comm(_1732696, _1732698, _1732700), -(hAPP(hAPP(c_Finite__Set_Ofold(_1732696, _1732698, _1732700), _1732702), hAPP(c_List_Oset(_1732696), _1732704)) = hAPP(c_List_Ofoldl(_1732698, _1732696, hAPP(c_COMBC(_1732696, _1732698, _1732698), _1732700), _1732702), c_List_Oremdups(_1732696, _1732704)))], (52685 ^ _775212) ^ [_1828373, _1828375] : [hBOOL(hAPP(hAPP(c_fequal, _1828373), _1828375)), -(_1828373 = _1828375)], (15047 ^ _775212) ^ [_1027540, _1027542, _1027544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027540), _1027542)), 15050 ^ _775212 : [(15057 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027544), _1027540)), _1027542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027544), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027542), _1027540))))], (15051 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027544), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027542), _1027540))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027544), _1027540)), _1027542)))]]], (18017 ^ _775212) ^ [_1080813, _1080815] : [class_Int_Onumber__ring(_1080813), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080813), c_Groups_Oone__class_Oone(_1080813)), hAPP(c_Int_Onumber__class_Onumber__of(_1080813), _1080815)) = hAPP(c_Int_Onumber__class_Onumber__of(_1080813), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1080815)))], (11750 ^ _775212) ^ [_968118, _968120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968118), hAPP(c_Nat_OSuc, _968120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968118), _968120))), -(_968118 = hAPP(c_Nat_OSuc, _968120))], (46362 ^ _775212) ^ [_1698977, _1698979, _1698981, _1698983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1698977), _1698979)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698981)), _1698983))), -(hAPP(hAPP(c_List_Otake(_1698981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1698977), _1698979)), _1698983) = hAPP(hAPP(c_List_Oappend(_1698981), hAPP(hAPP(c_List_Otake(_1698981), _1698977), _1698983)), hAPP(hAPP(c_List_Otake(_1698981), _1698979), hAPP(hAPP(c_List_Odrop(_1698981), _1698977), _1698983))))], (42307 ^ _775212) ^ [_1594299, _1594301] : [-(hAPP(c_Relation_Oconverse(_1594299, _1594299), c_Relation_OId__on(_1594299, _1594301)) = c_Relation_OId__on(_1594299, _1594301))], (38393 ^ _775212) ^ [_1496897, _1496899, _1496901, _1496903, _1496905] : [c_Relation_Orefl__on(_1496897, _1496899, _1496901), hBOOL(hAPP(hAPP(c_member(tc_prod(_1496897, _1496897)), hAPP(hAPP(c_Product__Type_OPair(_1496897, _1496897), _1496903), _1496905)), _1496901)), -(hBOOL(hAPP(hAPP(c_member(_1496897), _1496905), _1496899)))], (14969 ^ _775212) ^ [_1026039, _1026041, _1026043] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1026039), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026041), _1026043)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1026039), _1026041)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1026039), _1026043)))], (47292 ^ _775212) ^ [_1717935, _1717937, _1717939, _1717941] : [-(hBOOL(hAPP(hAPP(c_member(_1717935), _1717937), hAPP(c_List_Oset(_1717935), _1717939)))), -(c_List_Oremove1(_1717935, _1717937, hAPP(hAPP(c_List_Oappend(_1717935), _1717939), _1717941)) = hAPP(hAPP(c_List_Oappend(_1717935), _1717939), c_List_Oremove1(_1717935, _1717937, _1717941)))], (26935 ^ _775212) ^ [_1248958, _1248960, _1248962] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248958, tc_HOL_Obool)), _1248960), _1248962) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248958, tc_HOL_Obool)), _1248962), _1248960))], (19111 ^ _775212) ^ [_1100852, _1100854] : [c_Nat__Transfer_Ois__nat(_1100852), c_Nat__Transfer_Ois__nat(_1100854), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1100852, _1100854)))], (9239 ^ _775212) ^ [_924907, _924909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _924907), _924909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _924907), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _924909), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (43272 ^ _775212) ^ [_1619718, _1619720, _1619722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1619718, tc_HOL_Obool), tc_HOL_Obool)), _1619720), _1619722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619718, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619718, tc_HOL_Obool), _1619722)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619718, tc_HOL_Obool), _1619720))))], (37856 ^ _775212) ^ [_1482822, _1482824, _1482826, _1482828, _1482830] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1482822, _1482824), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1482822, tc_HOL_Obool)), _1482826), _1482828)), _1482830) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1482822, _1482824), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1482822, _1482824), _1482826), _1482830)), hAPP(hAPP(c_Product__Type_OSigma(_1482822, _1482824), _1482828), _1482830)))], (23510 ^ _775212) ^ [_1183248, _1183250] : [-(c_Nitpick_Ouminus__frac(_1183248, _1183250) = c_Nitpick_OAbs__Frac(_1183248, 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(_1183248), _1183250))), hAPP(c_Nitpick_Odenom(_1183248), _1183250))))], (22150 ^ _775212) ^ [_1155645, _1155647] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1155645), _1155647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1155645)), _1155647)))], (45473 ^ _775212) ^ [_1678012] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1678012) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 45476 ^ _775212 : [(45477 ^ _775212) ^ [_1678087] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1678087), hAPP(c_List_Oset(tc_Nat_Onat), _1678012))), -(_1678087 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (45178 ^ _775212) ^ [_1669692, _1669694] : [_1669694 = c_List_Olist_ONil(_1669692), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669692)), _1669694) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3404 ^ _775212) ^ [_826534, _826536, _826538, _826540, _826542, _826544, _826546, _826548] : [-(c_Random__Sequence_Obind(_826548, _826544, _826540, _826536) = c_Random__Sequence_Obind(_826546, _826542, _826538, _826534)), _826548 = _826546, _826544 = _826542, _826540 = _826538, _826536 = _826534], (21519 ^ _775212) ^ [_1143571, _1143573, _1143575, _1143577, _1143579, _1143581, _1143583] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1143571, _1143573), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1143575), _1143577))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1143579, _1143573), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1143581), _1143583))), -(_1143573 = 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), _1143571), _1143579), _1143573), 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), _1143575), _1143581)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1143577), _1143583)), _1143573))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1143577), _1143583), _1143573)))))], (15013 ^ _775212) ^ [_1026896, _1026898, _1026900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026896), _1026898)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026898), _1026896)), _1026900) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026898), _1026900)), _1026896))], (21261 ^ _775212) ^ [_1139379, _1139381, _1139383] : [21263 ^ _775212 : [(21266 ^ _775212) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1139379, _1139381), 21262 ^ [_1139379, _1139381, _1139383]))], (21264 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1139381, 21262 ^ [_1139379, _1139381, _1139383]), _1139383)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1139379, _1139381), _1139383)))], (4766 ^ _775212) ^ [_847829, _847831] : [_847831 = _847829, -(c_List_Ohd(_847831) = c_List_Ohd(_847829))], (39011 ^ _775212) ^ [_1509288, _1509290, _1509292] : [-(hBOOL(hAPP(_1509288, _1509290))), -(hAPP(c_Set_OCollect(_1509292), hAPP(hAPP(c_COMBS(_1509292, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509292), c_fconj), hAPP(hAPP(c_COMBC(_1509292, _1509292, tc_HOL_Obool), c_fequal), _1509290))), _1509288)) = c_Orderings_Obot__class_Obot(tc_fun(_1509292, tc_HOL_Obool)))], (18967 ^ _775212) ^ [_1097971, _1097973, _1097975, _1097977] : [18969 ^ _775212 : [(18974 ^ _775212) ^ [] : [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(_1097975, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 18968 ^ [_1097971, _1097973, _1097975, _1097977]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1097975, 18968 ^ [_1097971, _1097973, _1097975, _1097977])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18972 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18968 ^ [_1097971, _1097973, _1097975, _1097977]), _1097973)))], (18970 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1097971), 18968 ^ [_1097971, _1097973, _1097975, _1097977])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1097971), _1097973)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1097975, _1097971)), _1097977)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097977), hAPP(_1097975, _1097973))), 18988 ^ _775212 : [(18993 ^ _775212) ^ [] : [-(hAPP(_1097975, 18987 ^ [_1097971, _1097973, _1097975, _1097977]) = _1097977)], (18991 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18987 ^ [_1097971, _1097973, _1097975, _1097977]), _1097973)))], (18989 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1097971), 18987 ^ [_1097971, _1097973, _1097975, _1097977])))]]], (25098 ^ _775212) ^ [_1211750, _1211752, _1211754, _1211756, _1211758, _1211760, _1211762] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1211750, _1211752, _1211754, _1211756, _1211758, _1211760, _1211762) = c_New__DSequence_Oneg__decr__bind(_1211750, _1211752, hAPP(hAPP(hAPP(_1211754, _1211758), _1211760), _1211762), hAPP(hAPP(c_COMBC(_1211750, 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(_1211752)))), hAPP(hAPP(c_COMBC(_1211750, 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(_1211752))))), hAPP(hAPP(c_COMBC(_1211750, 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(_1211752)))))), _1211756), _1211758)), _1211760)), _1211762)))], (22550 ^ _775212) ^ [_1164453, _1164455, _1164457, _1164459] : [class_Orderings_Olinorder(_1164453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164453), _1164455), _1164457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164453), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1164453), _1164455), _1164459)), _1164457)))], (10397 ^ _775212) ^ [_944602, _944604, _944606, _944608, _944610] : [class_Rings_Oordered__semiring(_944602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944602), _944604), _944606)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944602), _944608), _944610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944602), c_Groups_Ozero__class_Ozero(_944602)), _944606)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944602), c_Groups_Ozero__class_Ozero(_944602)), _944608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944602), _944604), _944608)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944602), _944606), _944610))))], (38291 ^ _775212) ^ [_1495142, _1495144, _1495146] : [-(hAPP(c_Finite__Set_Ofold1(_1495142, _1495144), hAPP(hAPP(c_Set_Oinsert(_1495142), _1495146), c_Orderings_Obot__class_Obot(tc_fun(_1495142, tc_HOL_Obool)))) = _1495146)], (45961 ^ _775212) ^ [_1688628, _1688630, _1688632, _1688634, _1688636, _1688638] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1688628), tc_List_Olist(_1688628))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1688628), tc_List_Olist(_1688628)), hAPP(hAPP(c_List_Oappend(_1688628), _1688630), _1688636)), hAPP(hAPP(c_List_Oappend(_1688628), _1688632), _1688638))), c_List_Olistrel1(_1688628, _1688634)))), 45962 ^ _775212 : [(45969 ^ _775212) ^ [] : [_1688630 = _1688632, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1688628), tc_List_Olist(_1688628))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1688628), tc_List_Olist(_1688628)), _1688636), _1688638)), c_List_Olistrel1(_1688628, _1688634)))], (45963 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1688628), tc_List_Olist(_1688628))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1688628), tc_List_Olist(_1688628)), _1688630), _1688632)), c_List_Olistrel1(_1688628, _1688634))), _1688636 = _1688638]]], (45170 ^ _775212) ^ [_1669554] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669554)), c_List_Olist_ONil(_1669554)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24800 ^ _775212) ^ [_1206068] : [_1206068 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206068), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (22220 ^ _775212) ^ [_1157222, _1157224, _1157226, _1157228] : [-(hAPP(c_Nat_Onat_Onat__rec(_1157222, _1157224, _1157226), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157228)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1157222), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1157228))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1157222, _1157222), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1157222, tc_fun(_1157222, _1157222)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1157222, tc_fun(_1157222, _1157222)), tc_Int_Oint), c_If(_1157222)), c_Nat__Numeral_Oneg)), _1157224)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1157222, _1157222), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1157222, _1157222), tc_Int_Oint), _1157226), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1157222, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1157222, _1157224, _1157226)), c_Int_Onat)))))], (43348 ^ _775212) ^ [_1621512, _1621514] : [class_Complete__Lattice_Ocomplete__lattice(_1621512), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621512), _1621514)), -(_1621514 = c_Orderings_Obot__class_Obot(tc_fun(_1621512, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1621512, _1621514) = c_Complete__Lattice_OInf__class_OInf(_1621512, _1621514))], (17551 ^ _775212) ^ [_1073166] : [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), _1073166))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1073166)))], (8717 ^ _775212) ^ [_916574, _916576, _916578] : [class_Rings_Olinordered__ring(_916574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916574), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916574), _916576), _916576)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916574), _916578), _916578))), c_Groups_Ozero__class_Ozero(_916574)))], (35557 ^ _775212) ^ [_1431782, _1431784, _1431786, _1431788, _1431790] : [class_Groups_Ocomm__monoid__mult(_1431782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431784), _1431786)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431784), _1431788)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431784, tc_HOL_Obool)), _1431786), _1431788) = c_Orderings_Obot__class_Obot(tc_fun(_1431784, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1431784, _1431782), _1431790), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431784, tc_HOL_Obool)), _1431786), _1431788)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1431782), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1431784, _1431782), _1431790), _1431786)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1431784, _1431782), _1431790), _1431788)))], (30843 ^ _775212) ^ [_1332179, _1332181, _1332183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332179)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1332181), _1332183)), 30850 ^ _775212 : [(30851 ^ _775212) ^ [_1332369] : [30853 ^ _775212 : [(30859 ^ _775212) ^ [] : [-(_1332369 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30855 ^ [_1332179, _1332181, _1332183, _1332369]), 30852 ^ [_1332179, _1332181, _1332183, _1332369]))], (30857 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30855 ^ [_1332179, _1332181, _1332183, _1332369]), _1332183)))], (30854 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30852 ^ [_1332179, _1332181, _1332183, _1332369]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1332179))))]], -(_1332369 = _1332181), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1332369), _1332179) = _1332181]]], (29385 ^ _775212) ^ [_1298127, _1298129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1298127), _1298129)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1298129, _1298127) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (47456 ^ _775212) ^ [_1721793, _1721795, _1721797, _1721799] : [hBOOL(hAPP(c_List_Olistsp(_1721793, hAPP(hAPP(c_COMBS(_1721793, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1721793), c_fconj), _1721795)), _1721797)), _1721799)), 47459 ^ _775212 : [(47462 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1721793, _1721797), _1721799)))], (47460 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1721793, _1721795), _1721799)))]]], (44977 ^ _775212) ^ [_1664175, _1664177, _1664179] : [44979 ^ _775212 : [(44982 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1664175), 44978 ^ [_1664175, _1664177, _1664179]), _1664179))], (44980 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1664175), 44978 ^ [_1664175, _1664177, _1664179]), hAPP(c_List_Oset(_1664175), _1664177))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664175)), _1664177), c_List_Olists(_1664175, _1664179))))], (48516 ^ _775212) ^ [_1746448, _1746450, _1746452, _1746454] : [c_List_Oupt(_1746448, _1746450) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1746452), _1746454), 48519 ^ _775212 : [(48524 ^ _775212) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1746448), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1746450) = _1746454)], (48522 ^ _775212) ^ [] : [-(_1746448 = _1746452)], (48520 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746448), _1746450)))]]], (18177 ^ _775212) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (45112 ^ _775212) ^ [_1668329, _1668331, _1668333] : [-(hAPP(hAPP(c_List_Omap(_1668329, _1668331), _1668333), c_List_Olist_ONil(_1668329)) = c_List_Olist_ONil(_1668331))], (37794 ^ _775212) ^ [_1480985, _1480987, _1480989, _1480991] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1480985, _1480987, hAPP(hAPP(c_Set_Oinsert(_1480985), _1480989), c_Orderings_Obot__class_Obot(tc_fun(_1480985, tc_HOL_Obool)))), _1480991)), -(_1480989 = _1480991)], (42639 ^ _775212) ^ [_1603817, _1603819, _1603821, _1603823] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603817, _1603817)), hAPP(hAPP(c_Product__Type_OPair(_1603817, _1603817), _1603819), _1603821)), c_Transitive__Closure_Ortrancl(_1603817, _1603823))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603817, _1603817)), hAPP(hAPP(c_Product__Type_OPair(_1603817, _1603817), _1603821), _1603819)), c_Transitive__Closure_Ortrancl(_1603817, hAPP(c_Relation_Oconverse(_1603817, _1603817), _1603823)))))], (16913 ^ _775212) ^ [_1063497] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1063497)))], (8747 ^ _775212) ^ [_917097, _917099] : [-(c_Int_Onat__aux(_917097, _917099) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _917097)), _917099))], (24658 ^ _775212) ^ [_1203227, _1203229, _1203231, _1203233] : [class_Divides_Osemiring__div(_1203227), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1203227), _1203229), _1203231)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1203227), _1203229), _1203233)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1203227), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1203227), _1203231), _1203233)), _1203229) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1203227), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1203227), _1203231), _1203229)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1203227), _1203233), _1203229)))], (7158 ^ _775212) ^ [_889109, _889111, _889113] : [class_Orderings_Olinorder(_889109), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889109), _889111), _889113))), 7165 ^ _775212 : [(7172 ^ _775212) ^ [] : [_889113 = _889111, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889109), _889113), _889111))], (7166 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889109), _889113), _889111))), -(_889113 = _889111)]]], (46260 ^ _775212) ^ [_1696496, _1696498, _1696500, _1696502] : [hAPP(hAPP(c_List_Oappend(_1696496), _1696498), _1696500) = _1696502, 46263 ^ _775212 : [(46266 ^ _775212) ^ [] : [-(_1696500 = hAPP(hAPP(c_List_Odrop(_1696496), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696496)), _1696498)), _1696502))], (46264 ^ _775212) ^ [] : [-(_1696498 = hAPP(hAPP(c_List_Otake(_1696496), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696496)), _1696498)), _1696502))]]], (38311 ^ _775212) ^ [_1495509, _1495511, _1495513, _1495515, _1495517] : [c_Relation_Orefl__on(_1495509, _1495511, _1495513), c_Relation_Orefl__on(_1495509, _1495515, _1495517), -(c_Relation_Orefl__on(_1495509, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1495509, tc_HOL_Obool)), _1495511), _1495515), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1495509, _1495509), tc_HOL_Obool)), _1495513), _1495517)))], (2212 ^ _775212) ^ [_807382, _807384, _807386, _807388, _807390, _807392, _807394, _807396] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_807396, _807392, _807388, _807384) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_807394, _807390, _807386, _807382)), _807396 = _807394, _807392 = _807390, _807388 = _807386, _807384 = _807382], (29000 ^ _775212) ^ [_1290478] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290478, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1290478, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1290478, tc_HOL_Obool)))], (24868 ^ _775212) ^ [_1207225, _1207227, _1207229, _1207231, _1207233] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1207225, _1207227, tc_HOL_Obool, _1207229), _1207231), _1207233)), -(hBOOL(hAPP(_1207229, hAPP(hAPP(c_Product__Type_OPair(_1207225, _1207227), _1207231), _1207233))))], (33592 ^ _775212) ^ [_1387273] : [-(hAPP(c_Relation_OField(_1387273), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1387273, _1387273), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1387273, tc_HOL_Obool)))], (40874 ^ _775212) ^ [_1562063, _1562065, _1562067, _1562069, _1562071, _1562073] : [c_Finite__Set_Ofolding__idem(_1562063, _1562065, _1562067, _1562069), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562063), _1562071)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562063), _1562073)), -(hAPP(_1562069, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1562063, tc_HOL_Obool)), _1562071), _1562073)) = hAPP(c_Fun_Ocomp(_1562065, _1562065, _1562065, hAPP(_1562069, _1562071)), hAPP(_1562069, _1562073)))], (50008 ^ _775212) ^ [_1777382, _1777384, _1777386, _1777388] : [-(hAPP(c_New__DSequence_Opos__union(_1777382, _1777384, _1777386), _1777388) = c_Lazy__Sequence_Oappend(_1777382, hAPP(_1777384, _1777388), hAPP(_1777386, _1777388)))], (9843 ^ _775212) ^ [] : [-(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))))], (40227 ^ _775212) ^ [_1547357, _1547359, _1547361] : [c_Wellfounded_Oacyclic(_1547357, _1547359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547357, _1547357), tc_HOL_Obool)), _1547361), _1547359)), -(c_Wellfounded_Oacyclic(_1547357, _1547361))], (49119 ^ _775212) ^ [_1757955] : [-(hAPP(c_List_Orev(_1757955), c_List_Olist_ONil(_1757955)) = c_List_Olist_ONil(_1757955))], (47280 ^ _775212) ^ [_1717670, _1717672, _1717674] : [hBOOL(hAPP(c_List_Odistinct(_1717670), _1717672)), -(hBOOL(hAPP(c_List_Odistinct(_1717670), c_List_Oremove1(_1717670, _1717674, _1717672))))], (3968 ^ _775212) ^ [_835408, _835410, _835412, _835414, _835416, _835418] : [-(c_Big__Operators_Olattice_OSup__fin(_835418, _835414, _835410) = c_Big__Operators_Olattice_OSup__fin(_835416, _835412, _835408)), _835418 = _835416, _835414 = _835412, _835410 = _835408], (45429 ^ _775212) ^ [_1676420, _1676422, _1676424, _1676426, _1676428] : [class_Groups_Oab__group__add(_1676420), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676420), hAPP(hAPP(c_List_Omap(_1676422, _1676420), hAPP(hAPP(c_COMBS(_1676422, _1676420, _1676420), hAPP(hAPP(c_COMBB(_1676420, tc_fun(_1676420, _1676420), _1676422), c_Groups_Ominus__class_Ominus(_1676420)), _1676424)), _1676426)), _1676428)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1676420), hAPP(c_List_Omonoid__add__class_Olistsum(_1676420), hAPP(hAPP(c_List_Omap(_1676422, _1676420), _1676424), _1676428))), hAPP(c_List_Omonoid__add__class_Olistsum(_1676420), hAPP(hAPP(c_List_Omap(_1676422, _1676420), _1676426), _1676428))))], (30737 ^ _775212) ^ [_1329924, _1329926, _1329928, _1329930, _1329932, _1329934] : [30738 ^ _775212 : [(30741 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1329930, _1329926), _1329928))], (30739 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1329924, _1329926), _1329928))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329932, tc_fun(_1329934, tc_HOL_Obool))), _1329930), _1329924), _1329926), _1329928)))], (29446 ^ _775212) ^ [_1299405, _1299407, _1299409, _1299411, _1299413, _1299415, _1299417, _1299419] : [hBOOL(hAPP(hAPP(c_member(_1299405), _1299407), _1299409)), hBOOL(hAPP(hAPP(hAPP(_1299411, _1299407), _1299413), _1299415)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1299405, tc_fun(_1299417, tc_fun(_1299419, tc_HOL_Obool))), _1299409), _1299411), _1299413), _1299415)))], (47722 ^ _775212) ^ [_1727437, _1727439, _1727441, _1727443] : [c_List_Olist__all2(_1727437, _1727439, _1727441, c_List_Olist_ONil(_1727437), _1727443), -(_1727443 = c_List_Olist_ONil(_1727439))], (16775 ^ _775212) ^ [_1061245] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1061245)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061245))], (22442 ^ _775212) ^ [_1162432, _1162434, _1162436] : [class_Orderings_Olinorder(_1162432), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162432), _1162434), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162432), _1162434), _1162436)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162432), _1162434), _1162436))], (25436 ^ _775212) ^ [_1217825, _1217827, _1217829, _1217831, _1217833, _1217835, _1217837] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1217825, _1217827, _1217829, _1217831), _1217833), _1217835), _1217837) = c_New__DSequence_Oneg__bind(_1217825, _1217827, hAPP(hAPP(hAPP(_1217829, _1217833), _1217835), _1217837), hAPP(hAPP(c_COMBC(_1217825, 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(_1217827)))), hAPP(hAPP(c_COMBC(_1217825, 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(_1217827))))), hAPP(hAPP(c_COMBC(_1217825, 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(_1217827)))))), _1217831), _1217833)), _1217835)), _1217837)))], (36393 ^ _775212) ^ [_1450904, _1450906, _1450908, _1450910, _1450912] : [c_Fun_Oinj__on(_1450904, _1450906, _1450908, _1450910), c_Fun_Oinj__on(_1450904, _1450906, _1450908, _1450912), -(c_Fun_Oinj__on(_1450904, _1450906, _1450908, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450904, tc_HOL_Obool)), _1450910), _1450912)))], (35659 ^ _775212) ^ [_1433778, _1433780, _1433782] : [class_Orderings_Olinorder(_1433778), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433778), _1433780)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433778), _1433782)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1433778, tc_HOL_Obool)), _1433780), _1433782) = c_Orderings_Obot__class_Obot(tc_fun(_1433778, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1433778), c_Big__Operators_Olinorder__class_OMin(_1433778, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1433778, tc_HOL_Obool)), _1433780), _1433782))), c_Big__Operators_Olinorder__class_OMin(_1433778, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1433778, tc_HOL_Obool)), _1433780), _1433782))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1433778), c_Big__Operators_Olinorder__class_OMin(_1433778, _1433780)), c_Big__Operators_Olinorder__class_OMin(_1433778, _1433782)))], (43919 ^ _775212) ^ [_1635483, _1635485, _1635487, _1635489, _1635491, _1635493, _1635495, _1635497] : [c_Finite__Set_Ofolding__image__simple__idem(_1635483, _1635485, _1635487, _1635489, _1635491, _1635493), hBOOL(hAPP(c_Finite__Set_Ofinite(_1635485), _1635495)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1635485), _1635497)), -(hAPP(_1635493, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1635485, tc_HOL_Obool)), _1635495), _1635497)) = hAPP(hAPP(_1635487, hAPP(_1635493, _1635495)), hAPP(_1635493, _1635497)))], (22124 ^ _775212) ^ [_1155082, _1155084, _1155086, _1155088, _1155090, _1155092] : [-(c_Product__Type_Oprod_Oprod__rec(_1155082, _1155084, _1155086, _1155088, hAPP(hAPP(c_Product__Type_OPair(_1155082, _1155084), _1155090), _1155092)) = hAPP(hAPP(_1155088, _1155090), _1155092))], (22734 ^ _775212) ^ [_1167872, _1167874, _1167876, _1167878, _1167880, _1167882] : [-(hAPP(c_Product__Type_Oapsnd(_1167872, _1167874, _1167876, _1167878), hAPP(hAPP(c_Product__Type_OPair(_1167876, _1167872), _1167880), _1167882)) = hAPP(hAPP(c_Product__Type_OPair(_1167876, _1167874), _1167880), hAPP(_1167878, _1167882)))], (52579 ^ _775212) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (10861 ^ _775212) ^ [_952695, _952697] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952695)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952697)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952695), _952697)))], (28992 ^ _775212) ^ [_1290312, _1290314] : [_1290314 = c_Orderings_Obot__class_Obot(tc_fun(_1290312, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290312, tc_HOL_Obool)), _1290314), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290312, tc_HOL_Obool)), _1290314))))], (4510 ^ _775212) ^ [_843821, _843823, _843825, _843827, _843829, _843831, _843833, _843835] : [-(c_List_Ofoldl(_843835, _843831, _843827, _843823) = c_List_Ofoldl(_843833, _843829, _843825, _843821)), _843835 = _843833, _843831 = _843829, _843827 = _843825, _843823 = _843821], (18353 ^ _775212) ^ [_1086925] : [-(c_Int_Opred(c_Int_OBit1(_1086925)) = c_Int_OBit0(_1086925))], (4418 ^ _775212) ^ [_842397, _842399] : [_842399 = _842397, -(c_List_Omonoid__add__class_Olistsum(_842399) = c_List_Omonoid__add__class_Olistsum(_842397))], (51454 ^ _775212) ^ [_1808728, _1808730] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1808728, tc_HOL_Obool), _1808730) = hAPP(c_Set_OCollect(_1808728), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1808728, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1808728), c_HOL_OEx(tc_fun(_1808728, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1808728, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1808728, tc_HOL_Obool), tc_HOL_Obool), _1808728), hAPP(c_COMBS(tc_fun(_1808728, 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(_1808728, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1808728, tc_HOL_Obool), tc_fun(tc_fun(_1808728, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1808728, tc_HOL_Obool))), _1808730)))), c_member(_1808728)))))], (23632 ^ _775212) ^ [_1185600, _1185602, _1185604, _1185606, _1185608, _1185610] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1185600, _1185602, _1185604, _1185606, c_Nitpick_Opair__box_OPairBox(_1185600, _1185602, _1185608, _1185610)) = hAPP(hAPP(_1185606, _1185608), _1185610))], (50233 ^ _775212) ^ [_1782600, _1782602, _1782604, _1782606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1782600), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782602)), _1782604))), 50239 ^ _775212 : [(50242 ^ _775212) ^ [] : [hBOOL(hAPP(_1782606, 50238 ^ [_1782600, _1782602, _1782604, _1782606]))], (50240 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1782602), 50238 ^ [_1782600, _1782602, _1782604, _1782606]), hAPP(c_List_Oset(_1782602), _1782604))))]], -(hBOOL(hAPP(_1782606, hAPP(hAPP(c_List_Onth(_1782602), _1782604), _1782600))))], (52259 ^ _775212) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (32836 ^ _775212) ^ [_1370810, _1370812, _1370814, _1370816, _1370818] : [-(hAPP(c_Fun_Ofun__upd(_1370810, _1370812, _1370814, _1370816, _1370818), _1370816) = _1370818)], (7134 ^ _775212) ^ [_888828, _888830, _888832] : [class_Orderings_Oorder(_888828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888828), _888830), _888832)), _888830 = _888832], (33155 ^ _775212) ^ [_1377010, _1377012, _1377014, _1377016] : [class_Groups_Ocomm__monoid__mult(_1377010), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377012), _1377014)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377012, _1377010), hAPP(c_COMBK(_1377010, _1377012), _1377016)), _1377014) = hAPP(hAPP(c_Power_Opower__class_Opower(_1377010), _1377016), hAPP(c_Finite__Set_Ocard(_1377012), _1377014)))], (50867 ^ _775212) ^ [_1795103, _1795105, _1795107, _1795109, _1795111] : [-(c_List_Oreplicate(_1795103, _1795105, _1795107) = c_List_Oreplicate(_1795103, _1795109, _1795111)), _1795105 = _1795109, 50872 ^ _775212 : [(50875 ^ _775212) ^ [] : [_1795107 = _1795111], (50873 ^ _775212) ^ [] : [_1795105 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (45423 ^ _775212) ^ [_1676217, _1676219, _1676221, _1676223, _1676225] : [class_Rings_Osemiring__0(_1676217), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676217), hAPP(hAPP(c_List_Omap(_1676219, _1676217), hAPP(hAPP(c_COMBC(_1676219, _1676217, _1676217), hAPP(hAPP(c_COMBB(_1676217, tc_fun(_1676217, _1676217), _1676219), c_Groups_Otimes__class_Otimes(_1676217)), _1676221)), _1676223)), _1676225)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1676217), hAPP(c_List_Omonoid__add__class_Olistsum(_1676217), hAPP(hAPP(c_List_Omap(_1676219, _1676217), _1676221), _1676225))), _1676223))], (33869 ^ _775212) ^ [_1393442, _1393444, _1393446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1393442, tc_HOL_Obool)), _1393444), _1393446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1393442, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1393442, _1393444)), c_Predicate_OPowp(_1393442, _1393446))))], (52501 ^ _775212) ^ [_1826277] : [class_Lazy__Sequence_Osmall__lazy(_1826277), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1826277)))], (35111 ^ _775212) ^ [_1421655, _1421657] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421655, tc_HOL_Obool)), _1421657), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1421655, tc_HOL_Obool)), _1421657)) = c_Orderings_Obot__class_Obot(tc_fun(_1421655, tc_HOL_Obool)))], (46350 ^ _775212) ^ [_1698761, _1698763, _1698765, _1698767] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1698761) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1698763), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1698761)), hAPP(hAPP(c_List_Olist_OCons(_1698763), _1698765), _1698767)) = hAPP(hAPP(c_List_Olist_OCons(_1698763), _1698765), _1698767))], (14895 ^ _775212) ^ [_1024748, _1024750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024748), _1024750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1024748), _1024750)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20031 ^ _775212) ^ [_1116916, _1116918, _1116920, _1116922] : [class_Fields_Olinordered__field(_1116916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116916), _1116918), _1116920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116916), _1116922), c_Groups_Ozero__class_Ozero(_1116916))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116916), c_Groups_Ozero__class_Ozero(_1116916)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116916), _1116918), _1116920))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116916), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116916), _1116922), _1116918)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116916), _1116922), _1116920))))], (46095 ^ _775212) ^ [_1692173, _1692175, _1692177, _1692179, _1692181, _1692183] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692173), tc_List_Olist(_1692173))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692173), tc_List_Olist(_1692173)), hAPP(hAPP(c_List_Oappend(_1692173), _1692175), hAPP(hAPP(c_List_Olist_OCons(_1692173), _1692177), c_List_Olist_ONil(_1692173)))), hAPP(hAPP(c_List_Oappend(_1692173), _1692179), hAPP(hAPP(c_List_Olist_OCons(_1692173), _1692181), c_List_Olist_ONil(_1692173))))), c_List_Olistrel1(_1692173, _1692183)))), 46096 ^ _775212 : [(46103 ^ _775212) ^ [] : [_1692175 = _1692179, hBOOL(hAPP(hAPP(c_member(tc_prod(_1692173, _1692173)), hAPP(hAPP(c_Product__Type_OPair(_1692173, _1692173), _1692177), _1692181)), _1692183))], (46097 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692173), tc_List_Olist(_1692173))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692173), tc_List_Olist(_1692173)), _1692175), _1692179)), c_List_Olistrel1(_1692173, _1692183))), _1692177 = _1692181]]], (23752 ^ _775212) ^ [_1188019, _1188021, _1188023, _1188025] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1188019, _1188021, _1188023, _1188025) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1188019, _1188021), _1188023), _1188025)))], (49215 ^ _775212) ^ [_1760001, _1760003, _1760005] : [_1760003 = _1760005, -(hAPP(c_List_Orev(_1760001), _1760003) = hAPP(c_List_Orev(_1760001), _1760005))], (22059 ^ _775212) ^ [_1153787, _1153789, _1153791] : [hBOOL(hAPP(_1153787, 22060 ^ [_1153787, _1153789, _1153791])), 22063 ^ _775212 : [(22064 ^ _775212) ^ [_1153898, _1153900] : [-(hBOOL(hAPP(_1153787, hAPP(hAPP(c_Product__Type_OPair(_1153789, _1153791), _1153900), _1153898))))]]], (18321 ^ _775212) ^ [_1086379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086379), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1086379)), c_Int_OMin)))], (17171 ^ _775212) ^ [_1067422, _1067424] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1067422))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067422)), _1067424)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1067424))], (48679 ^ _775212) ^ [_1749610, _1749612, _1749614] : [class_Orderings_Olinorder(_1749610), c_List_Olinorder__class_Osorted(_1749610, _1749612), -(c_List_Olinorder__class_Osorted(_1749610, c_List_Oremove1(_1749610, _1749614, _1749612)))], (22240 ^ _775212) ^ [_1157645, _1157647] : [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(_1157645))), 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)), _1157647)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157645)), hAPP(c_Nat_OSuc, _1157647))))], (46897 ^ _775212) ^ [_1710089, _1710091, _1710093, _1710095] : [class_Complete__Lattice_Ocomplete__lattice(_1710089), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1710091, _1710089), hAPP(c_List_Oset(_1710091), _1710093)), _1710095) = hAPP(c_List_Ofoldl(_1710089, _1710091, hAPP(c_COMBC(_1710091, _1710089, _1710089), hAPP(hAPP(c_COMBB(_1710089, tc_fun(_1710089, _1710089), _1710091), c_Lattices_Osemilattice__sup__class_Osup(_1710089)), _1710095)), c_Orderings_Obot__class_Obot(_1710089)), _1710093))], (36032 ^ _775212) ^ [_1443289] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1443289)), c_Int_OInteg)))], (27986 ^ _775212) ^ [_1271044, _1271046] : [class_Lattices_Obounded__lattice__top(_1271044), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271044), _1271046), c_Orderings_Otop__class_Otop(_1271044)) = c_Orderings_Otop__class_Otop(_1271044))], (19073 ^ _775212) ^ [_1100223, _1100225, _1100227, _1100229] : [class_Fields_Ofield__inverse__zero(_1100223), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1100223), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100223), _1100225), _1100227)), _1100229) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100223), hAPP(hAPP(c_Power_Opower__class_Opower(_1100223), _1100225), _1100229)), hAPP(hAPP(c_Power_Opower__class_Opower(_1100223), _1100227), _1100229)))], (17385 ^ _775212) ^ [_1070532] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1070532) = c_Int_Opred(_1070532))], (15579 ^ _775212) ^ [_1038570] : [class_Power_Opower(_1038570), -(c_Power_Opower__class_Opower(_1038570) = c_Power_Opower_Opower(_1038570, c_Groups_Oone__class_Oone(_1038570), c_Groups_Otimes__class_Otimes(_1038570)))], (27698 ^ _775212) ^ [_1264363, _1264365, _1264367, _1264369, _1264371] : [27700 ^ _775212 : [(27703 ^ _775212) ^ [] : [hBOOL(hAPP(_1264371, 27699 ^ [_1264363, _1264365, _1264367, _1264369, _1264371]))], (27701 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1264363), 27699 ^ [_1264363, _1264365, _1264367, _1264369, _1264371]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1264365, tc_fun(_1264363, tc_HOL_Obool)), _1264367), _1264369))))]], 27704 ^ _775212 : [(27705 ^ _775212) ^ [_1264585] : [hBOOL(hAPP(hAPP(c_member(_1264365), _1264585), _1264367)), 27708 ^ _775212 : [(27709 ^ _775212) ^ [_1264682] : [hBOOL(hAPP(hAPP(c_member(_1264363), _1264682), hAPP(_1264369, _1264585))), -(hBOOL(hAPP(_1264371, _1264682)))]]]]], (40750 ^ _775212) ^ [_1559192, _1559194, _1559196, _1559198] : [c_Finite__Set_Ofolding(_1559192, _1559194, _1559196, _1559198), -(hAPP(_1559198, c_Orderings_Obot__class_Obot(tc_fun(_1559192, tc_HOL_Obool))) = c_Fun_Oid(_1559194))], (13376 ^ _775212) ^ [_997128, _997130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997128)), 13379 ^ _775212 : [(13386 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _997130), 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), _997130), _997128)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13380 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _997130), _997128)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _997130), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (11656 ^ _775212) ^ [_966631, _966633] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966631), _966633))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966633), _966631)))], (928 ^ _775212) ^ [_789376, _789378, _789380, _789382] : [-(c_Relation_Oantisym(_789380, _789376)), c_Relation_Oantisym(_789382, _789378), _789382 = _789380, _789378 = _789376], (3872 ^ _775212) ^ [_833974, _833976, _833978, _833980] : [-(c_Nitpick_Ocard_H(_833980, _833976) = c_Nitpick_Ocard_H(_833978, _833974)), _833980 = _833978, _833976 = _833974], (34014 ^ _775212) ^ [_1396618, _1396620, _1396622, _1396624, _1396626] : [hBOOL(hAPP(hAPP(c_member(_1396618), _1396620), hAPP(c_Relation_OImage(_1396622, _1396618, _1396624), _1396626))), 34018 ^ _775212 : [(34021 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1396622, _1396618)), hAPP(hAPP(c_Product__Type_OPair(_1396622, _1396618), 34017 ^ [_1396618, _1396620, _1396622, _1396624, _1396626]), _1396620)), _1396624)))], (34019 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1396622), 34017 ^ [_1396618, _1396620, _1396622, _1396624, _1396626]), _1396626)))]]], (1034 ^ _775212) ^ [_790879, _790881, _790883, _790885] : [-(c_Predicate_Otransp(_790883, _790879)), c_Predicate_Otransp(_790885, _790881), _790885 = _790883, _790881 = _790879], (16017 ^ _775212) ^ [_1046609] : [class_Rings_Olinordered__idom(_1046609), -(hAPP(c_Groups_Oabs__class_Oabs(_1046609), c_Groups_Oone__class_Oone(_1046609)) = c_Groups_Oone__class_Oone(_1046609))], (25288 ^ _775212) ^ [_1215269, _1215271, _1215273] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1215271), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1215269), _1215273))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215269, _1215271) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215273, _1215271))], (27093 ^ _775212) ^ [_1252399, _1252401, _1252403, _1252405] : [class_Lattices_Olattice(_1252399), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252399), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252399), _1252401), _1252403)), _1252405) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252399), _1252401), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252399), _1252403), _1252405)))], (50344 ^ _775212) ^ [_1784702, _1784704, _1784706] : [c_List_Olist__ex(_1784702, _1784704, _1784706), -(c_List_Olist__ex(_1784702, _1784704, hAPP(c_List_Orev(_1784702), _1784706)))], (31373 ^ _775212) ^ [_1342958] : [class_Rings_Osemiring__1(_1342958), -(hBOOL(hAPP(hAPP(c_member(_1342958), c_Groups_Oone__class_Oone(_1342958)), c_Nat_Osemiring__1__class_ONats(_1342958))))], (39225 ^ _775212) ^ [_1517228, _1517230, _1517232] : [class_Groups_Olinordered__ab__semigroup__add(_1517228), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517228), _1517230)), -(_1517230 = c_Orderings_Obot__class_Obot(tc_fun(_1517228, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1517228), _1517232), c_Big__Operators_Olinorder__class_OMax(_1517228, _1517230)) = c_Big__Operators_Olinorder__class_OMax(_1517228, hAPP(c_Set_OCollect(_1517228), hAPP(hAPP(c_COMBB(tc_fun(_1517228, tc_HOL_Obool), tc_HOL_Obool, _1517228), c_HOL_OEx(_1517228)), hAPP(hAPP(c_COMBC(_1517228, tc_fun(_1517228, tc_HOL_Obool), tc_fun(_1517228, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517228, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1517228, tc_HOL_Obool), tc_fun(_1517228, tc_HOL_Obool)), _1517228), c_COMBS(_1517228, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517228, tc_HOL_Obool), tc_fun(_1517228, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1517228), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1517228), c_fconj)), hAPP(hAPP(c_COMBC(_1517228, tc_fun(_1517228, _1517228), tc_fun(_1517228, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517228, tc_HOL_Obool), tc_fun(tc_fun(_1517228, _1517228), tc_fun(_1517228, tc_HOL_Obool)), _1517228), c_COMBB(_1517228, tc_HOL_Obool, _1517228)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1517228), _1517232))))), hAPP(hAPP(c_COMBC(_1517228, tc_fun(_1517228, tc_HOL_Obool), tc_HOL_Obool), c_member(_1517228)), _1517230))))))], (13264 ^ _775212) ^ [_995210, _995212, _995214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995210), _995212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _995210), _995214)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _995212), _995214))))], (13981 ^ _775212) ^ [_1007779, _1007781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007779)), -(c_SMT_Oz3div(_1007781, _1007779) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1007781), _1007779))], (43086 ^ _775212) ^ [_1615533, _1615535, _1615537] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615533, _1615533)), _1615535), c_Transitive__Closure_Otrancl(_1615533, _1615537)))), 43087 ^ _775212 : [(43088 ^ _775212) ^ [_1615612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1615612)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1615533, _1615533)), _1615535), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1615533, _1615533), tc_HOL_Obool), _1615612), _1615537)))]]], (44939 ^ _775212) ^ [_1663313, _1663315, _1663317, _1663319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1663313), _1663315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1663317, tc_HOL_Obool)), hAPP(c_List_Oset(_1663317), hAPP(hAPP(c_List_Otake(_1663317), _1663313), _1663319))), hAPP(c_List_Oset(_1663317), hAPP(hAPP(c_List_Otake(_1663317), _1663315), _1663319)))))], (8421 ^ _775212) ^ [_911394, _911396, _911398] : [class_Rings_Olinordered__semiring__strict(_911394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911394), _911396), c_Groups_Ozero__class_Ozero(_911394))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911394), c_Groups_Ozero__class_Ozero(_911394)), _911398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911394), _911396), _911398)), c_Groups_Ozero__class_Ozero(_911394))))], (16947 ^ _775212) ^ [_1063921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1063921), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1063921)))], (42254 ^ _775212) ^ [_1592550, _1592552, _1592554, _1592556, _1592558, _1592560] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592552, _1592554)), hAPP(hAPP(c_Product__Type_OPair(_1592552, _1592554), _1592558), _1592560)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592550, tc_fun(tc_prod(_1592552, _1592554), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1592550, tc_HOL_Obool))), _1592556))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592550, tc_fun(_1592552, tc_fun(_1592554, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1592550, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1592552, _1592554), tc_HOL_Obool), tc_fun(_1592552, tc_fun(_1592554, tc_HOL_Obool)), _1592550), hAPP(c_COMBC(_1592552, tc_fun(tc_prod(_1592552, _1592554), tc_HOL_Obool), tc_fun(_1592554, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1592554, tc_fun(tc_fun(tc_prod(_1592552, _1592554), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1592552, _1592554), tc_HOL_Obool), tc_fun(_1592554, tc_HOL_Obool)), _1592552), c_COMBC(_1592554, tc_fun(tc_prod(_1592552, _1592554), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1592554, tc_prod(_1592552, _1592554)), tc_fun(_1592554, tc_fun(tc_fun(tc_prod(_1592552, _1592554), tc_HOL_Obool), tc_HOL_Obool)), _1592552), hAPP(c_COMBB(tc_prod(_1592552, _1592554), tc_fun(tc_fun(tc_prod(_1592552, _1592554), tc_HOL_Obool), tc_HOL_Obool), _1592554), c_member(tc_prod(_1592552, _1592554)))), c_Product__Type_OPair(_1592552, _1592554))))), _1592556)), _1592558), _1592560)))], (12598 ^ _775212) ^ [_982967, _982969, _982971] : [class_Divides_Osemiring__div(_982967), -(c_Divides_Odiv__class_Omod(_982967, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982967), _982969), _982971), _982969) = c_Groups_Ozero__class_Ozero(_982967))], (27900 ^ _775212) ^ [_1269385, _1269387, _1269389, _1269391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269385, tc_HOL_Obool)), _1269387), _1269389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269385, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1269385), _1269391), _1269387)), hAPP(hAPP(c_Set_Oinsert(_1269385), _1269391), _1269389))))], (23646 ^ _775212) ^ [_1185915, _1185917, _1185919, _1185921] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1185915), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1185917, _1185919, _1185915, _1185921) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1185917, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm)), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1185919, _1185921)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1185917, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1185917, _1185919, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1185915), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1185921))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1185917, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917))))), tc_prod(_1185917, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1185917)), hAPP(hAPP(c_COMBB(_1185917, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1185917)))), tc_prod(_1185917, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1185917)), c_Product__Type_Ofst(_1185917, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (23366 ^ _775212) ^ [_1180340, _1180342] : [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), _1180340), _1180342))), 23369 ^ _775212 : [(23376 ^ _775212) ^ [] : [-(_1180342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1180340, _1180342) = c_Nitpick_Onat__gcd(_1180342, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1180340, _1180342)))], (23370 ^ _775212) ^ [] : [_1180342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1180340, _1180342) = _1180340)]]], (9423 ^ _775212) ^ [_927592, _927594, _927596] : [class_Orderings_Oorder(_927592), -(_927594 = _927596), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927592), _927594), _927596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927592), _927594), _927596)))], (21751 ^ _775212) ^ [_1147933, _1147935, _1147937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1147933, tc_HOL_Obool)), _1147935), _1147937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1147933, tc_HOL_Obool)), _1147935), _1147937)))], (4642 ^ _775212) ^ [_845975, _845977] : [_845977 = _845975, -(c_Lazy__Sequence_Oempty(_845977) = c_Lazy__Sequence_Oempty(_845975))], (38877 ^ _775212) ^ [_1506098, _1506100, _1506102] : [38878 ^ _775212 : [(38881 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506098), hAPP(c_Set_OCollect(_1506098), _1506102)))], (38879 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506098), hAPP(c_Set_OCollect(_1506098), _1506100)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506098), hAPP(c_Set_OCollect(_1506098), hAPP(hAPP(c_COMBS(_1506098, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506098), c_fconj), _1506100)), _1506102)))))], (20497 ^ _775212) ^ [_1125077, _1125079, _1125081, _1125083] : [class_Fields_Olinordered__field(_1125077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125077), c_Groups_Ozero__class_Ozero(_1125077)), _1125079)), 20504 ^ _775212 : [(20511 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125077), _1125081), _1125079)), _1125083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125077), _1125081), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125077), _1125083), _1125079))))], (20505 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125077), _1125081), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125077), _1125083), _1125079))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125077), _1125081), _1125079)), _1125083)))]]], (5607 ^ _775212) ^ [_863494, _863496] : [_863494 = _863496, -(hAPP(c_Nat_OSuc, _863494) = hAPP(c_Nat_OSuc, _863496))], (14199 ^ _775212) ^ [_1011847, _1011849] : [class_Groups_Ogroup__add(_1011847), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1011847), _1011849), _1011849) = c_Groups_Ozero__class_Ozero(_1011847))], (48946 ^ _775212) ^ [_1754331, _1754333, _1754335] : [class_Orderings_Olinorder(_1754331), 48949 ^ _775212 : [(48962 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1754331, hAPP(hAPP(c_List_Olist_OCons(_1754331), _1754333), _1754335))), 48966 ^ _775212 : [(48969 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1754331), _1754333), 48965 ^ [_1754331, _1754333, _1754335]))], (48967 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754331), 48965 ^ [_1754331, _1754333, _1754335]), hAPP(c_List_Oset(_1754331), _1754335))))]], c_List_Olinorder__class_Osorted(_1754331, _1754335)], (48950 ^ _775212) ^ [] : [c_List_Olinorder__class_Osorted(_1754331, hAPP(hAPP(c_List_Olist_OCons(_1754331), _1754333), _1754335)), 48953 ^ _775212 : [(48954 ^ _775212) ^ [_1754499] : [hBOOL(hAPP(hAPP(c_member(_1754331), _1754499), hAPP(c_List_Oset(_1754331), _1754335))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1754331), _1754333), _1754499)))], (48960 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1754331, _1754335))]]]]], (4898 ^ _775212) ^ [_849851, _849853] : [_849853 = _849851, -(c_Groups_Oone__class_Oone(_849853) = c_Groups_Oone__class_Oone(_849851))], (34491 ^ _775212) ^ [_1408225, _1408227, _1408229] : [class_Lattices_Olattice(_1408225), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408225), _1408227), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408225), _1408227), _1408229)) = _1408227)], (39450 ^ _775212) ^ [_1526227, _1526229, _1526231, _1526233] : [class_Groups_Ocomm__monoid__mult(_1526227), c_Fun_Oinj__on(_1526229, _1526227, _1526231, _1526233), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1526229, _1526227), _1526231), _1526233) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1526227, _1526227), c_Fun_Oid(_1526227)), hAPP(c_Set_Oimage(_1526229, _1526227, _1526231), _1526233)))], (47997 ^ _775212) ^ [_1733747, _1733749] : [c_List_Olist_ONil(_1733747) = c_List_Oremdups(_1733747, _1733749), -(_1733749 = c_List_Olist_ONil(_1733747))], (52455 ^ _775212) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (43390 ^ _775212) ^ [_1622524, _1622526, _1622528] : [-(hAPP(c_Relation_ORange(_1622524, _1622526), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1622524, _1622526), tc_HOL_Obool), _1622528)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1622524, _1622526), tc_HOL_Obool), tc_fun(_1622526, tc_HOL_Obool)), _1622528), c_Relation_ORange(_1622524, _1622526)))], (31391 ^ _775212) ^ [_1343255, _1343257] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343255), _1343257)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1343257, _1343255) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (35927 ^ _775212) ^ [_1439913, _1439915, _1439917, _1439919, _1439921, _1439923, _1439925] : [c_Equiv__Relations_Oequiv(_1439913, _1439915, _1439917), c_Equiv__Relations_Ocongruent(_1439913, tc_fun(_1439919, tc_HOL_Obool), _1439917, _1439921), hBOOL(hAPP(hAPP(c_member(tc_fun(_1439913, tc_HOL_Obool)), _1439923), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1439913), _1439915), _1439917))), 35941 ^ _775212 : [(35944 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1439919, tc_HOL_Obool)), hAPP(_1439921, 35940 ^ [_1439913, _1439915, _1439917, _1439919, _1439921, _1439923, _1439925])), _1439925))], (35942 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1439913), 35940 ^ [_1439913, _1439915, _1439917, _1439919, _1439921, _1439923, _1439925]), _1439915)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1439919, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1439913, tc_fun(_1439919, tc_HOL_Obool)), _1439923), _1439921)), _1439925)))], (18563 ^ _775212) ^ [_1090561, _1090563, _1090565] : [class_Groups_Omonoid__mult(_1090561), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1090561), _1090563), 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)))), _1090565)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1090561), hAPP(hAPP(c_Power_Opower__class_Opower(_1090561), _1090563), _1090565)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (25102 ^ _775212) ^ [_1211928, _1211930] : [-(hAPP(c_New__DSequence_Opos__empty(_1211928), _1211930) = c_Lazy__Sequence_Oempty(_1211928))], (52537 ^ _775212) ^ [_1826736] : [class_Enum_Oenum(_1826736), -(class_Enum_Oenum(tc_Option_Ooption(_1826736)))], (45498 ^ _775212) ^ [_1678457, _1678459, _1678461] : [-(c_List_Olist_Olist__size(_1678457, _1678459, _1678461) = 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(_1678457, tc_Nat_Onat), _1678459), _1678461))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678457)), _1678461)))], (46784 ^ _775212) ^ [_1707750, _1707752, _1707754, _1707756, _1707758, _1707760] : [-(hAPP(c_List_Ofoldl(_1707750, _1707752, _1707754, _1707756), hAPP(hAPP(c_List_Olist_OCons(_1707752), _1707758), _1707760)) = hAPP(c_List_Ofoldl(_1707750, _1707752, _1707754, hAPP(hAPP(_1707754, _1707756), _1707758)), _1707760))], (52365 ^ _775212) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (42820 ^ _775212) ^ [_1608995] : [-(c_Relation_Orefl__on(_1608995, c_Orderings_Otop__class_Otop(tc_fun(_1608995, tc_HOL_Obool)), c_Relation_OId(_1608995)))], (51729 ^ _775212) ^ [_1815158, _1815160, _1815162, _1815164, _1815166, _1815168] : [-(c_Partial__Function_Ofun__lub(_1815158, _1815160, _1815162, _1815164, _1815166, _1815168) = hAPP(_1815164, hAPP(c_Set_OCollect(_1815158), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1815162, _1815158), tc_HOL_Obool), tc_HOL_Obool, _1815158), c_HOL_OEx(tc_fun(_1815162, _1815158))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1815162, _1815158), tc_HOL_Obool), tc_fun(tc_fun(_1815162, _1815158), tc_HOL_Obool), _1815158), hAPP(c_COMBS(tc_fun(_1815162, _1815158), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1815162, _1815158)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1815162, _1815158), tc_fun(tc_fun(_1815162, _1815158), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1815162, _1815158))), _1815166)))), hAPP(hAPP(c_COMBC(_1815158, tc_fun(tc_fun(_1815162, _1815158), _1815158), tc_fun(tc_fun(_1815162, _1815158), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1815158, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1815162, _1815158), _1815158), tc_fun(tc_fun(_1815162, _1815158), tc_HOL_Obool)), _1815158), c_COMBB(_1815158, tc_HOL_Obool, tc_fun(_1815162, _1815158))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1815162, _1815158), _1815162, _1815158), c_COMBI(tc_fun(_1815162, _1815158))), _1815168)))))))], (44112 ^ _775212) ^ [_1639801, _1639803] : [-(c_FunDef_Ois__measure(_1639801, _1639803))], (16425 ^ _775212) ^ [_1054360, _1054362] : [class_Int_Onumber__ring(_1054360), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1054360), hAPP(c_Int_Onumber__class_Onumber__of(_1054360), _1054362)) = hAPP(c_Int_Onumber__class_Onumber__of(_1054360), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1054362)))], (34035 ^ _775212) ^ [_1397215, _1397217, _1397219, _1397221, _1397223] : [hBOOL(hAPP(hAPP(c_member(_1397215), _1397217), hAPP(c_Relation_OImage(_1397219, _1397215, _1397221), hAPP(hAPP(c_Set_Oinsert(_1397219), _1397223), c_Orderings_Obot__class_Obot(tc_fun(_1397219, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1397219, _1397215)), hAPP(hAPP(c_Product__Type_OPair(_1397219, _1397215), _1397223), _1397217)), _1397221)))], (40494 ^ _775212) ^ [_1553332, _1553334, _1553336, _1553338, _1553340, _1553342, _1553344, _1553346, _1553348, _1553350] : [-(c_Product__Type_Omap__pair(_1553332, _1553334, _1553336, _1553338, hAPP(c_Fun_Ocomp(_1553340, _1553334, _1553332, _1553342), _1553344), hAPP(c_Fun_Ocomp(_1553346, _1553338, _1553336, _1553348), _1553350)) = hAPP(c_Fun_Ocomp(tc_prod(_1553340, _1553346), tc_prod(_1553334, _1553338), tc_prod(_1553332, _1553336), c_Product__Type_Omap__pair(_1553340, _1553334, _1553346, _1553338, _1553342, _1553348)), c_Product__Type_Omap__pair(_1553332, _1553340, _1553336, _1553346, _1553344, _1553350)))], (18721 ^ _775212) ^ [_1093146, _1093148, _1093150] : [class_Rings_Ocomm__semiring__1(_1093146), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1093146), _1093148), 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)))), _1093150)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093146), hAPP(hAPP(c_Power_Opower__class_Opower(_1093146), _1093148), _1093150)), hAPP(hAPP(c_Power_Opower__class_Opower(_1093146), _1093148), _1093150)))], (28155 ^ _775212) ^ [_1274172, _1274174, _1274176] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1274172), _1274174)), 28158 ^ _775212 : [(28178 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1274172, tc_Nat_Onat), _1274176), _1274174) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 28179 ^ _775212 : [(28180 ^ _775212) ^ [_1274653] : [hBOOL(hAPP(hAPP(c_member(_1274172), _1274653), _1274174)), hAPP(_1274176, _1274653) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 28188 ^ _775212 : [(28193 ^ _775212) ^ [] : [hAPP(_1274176, 28187 ^ [_1274172, _1274174, _1274176, _1274653]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28191 ^ _775212) ^ [] : [_1274653 = 28187 ^ [_1274172, _1274174, _1274176, _1274653]], (28189 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1274172), 28187 ^ [_1274172, _1274174, _1274176, _1274653]), _1274174)))]]]]], (28159 ^ _775212) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1274172, tc_Nat_Onat), _1274176), _1274174) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 28163 ^ _775212 : [(28168 ^ _775212) ^ [_1274492] : [hBOOL(hAPP(hAPP(c_member(_1274172), _1274492), _1274174)), -(28162 ^ [_1274172, _1274174, _1274176] = _1274492), -(hAPP(_1274176, _1274492) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28166 ^ _775212) ^ [] : [-(hAPP(_1274176, 28162 ^ [_1274172, _1274174, _1274176]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28164 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1274172), 28162 ^ [_1274172, _1274174, _1274176]), _1274174)))]]]]], (20115 ^ _775212) ^ [_1118398, _1118400, _1118402, _1118404, _1118406] : [class_Fields_Ofield(_1118398), -(_1118400 = c_Groups_Ozero__class_Ozero(_1118398)), -(_1118402 = c_Groups_Ozero__class_Ozero(_1118398)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118398), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118398), _1118404), _1118400)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118398), _1118406), _1118402)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118398), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118398), _1118404), _1118402)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118398), _1118406), _1118400))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118398), _1118400), _1118402)))], (37511 ^ _775212) ^ [_1474177, _1474179, _1474181, _1474183] : [hBOOL(hAPP(hAPP(c_member(_1474177), _1474179), _1474181)), -(hAPP(c_Set_Ovimage(_1474183, _1474177, hAPP(c_COMBK(_1474177, _1474183), _1474179)), _1474181) = c_Orderings_Otop__class_Otop(tc_fun(_1474183, tc_HOL_Obool)))], (17923 ^ _775212) ^ [_1079363, _1079365] : [class_Groups_Omonoid__mult(_1079363), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079363), _1079365), 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(_1079363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079363), _1079365), _1079365)), _1079365))], (9403 ^ _775212) ^ [_927289, _927291, _927293] : [class_Orderings_Olinorder(_927289), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927289), _927291), _927293))), 9410 ^ _775212 : [(9417 ^ _775212) ^ [] : [_927291 = _927293, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927289), _927291), _927293)))], (9411 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927289), _927291), _927293)), -(_927291 = _927293)]]], (46524 ^ _775212) ^ [_1702124, _1702126, _1702128] : [-(hAPP(hAPP(c_List_Odrop(_1702124), hAPP(c_Nat_OSuc, _1702126)), _1702128) = hAPP(hAPP(c_List_Odrop(_1702124), _1702126), hAPP(c_List_Otl(_1702124), _1702128)))], (1674 ^ _775212) ^ [_798993, _798995] : [-(class_Groups_Ocomm__monoid__add(_798993)), _798995 = _798993, class_Groups_Ocomm__monoid__add(_798995)], (13579 ^ _775212) ^ [_1000410, _1000412] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1000410), _1000412) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13580 ^ _775212 : [(13589 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1000410), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1000412), _1000410))], (13583 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1000410), _1000412))], (13581 ^ _775212) ^ [] : [_1000412 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (15557 ^ _775212) ^ [_1038263, _1038265] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038263, _1038265) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038263, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1038265)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038263, _1038265)), _1038265))], (28626 ^ _775212) ^ [_1283526, _1283528, _1283530, _1283532, _1283534] : [-(hAPP(hAPP(c_Set_Oinsert(_1283526), _1283528), hAPP(hAPP(c_Set_Oinsert(_1283526), _1283530), c_Orderings_Obot__class_Obot(tc_fun(_1283526, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1283526), _1283532), hAPP(hAPP(c_Set_Oinsert(_1283526), _1283534), c_Orderings_Obot__class_Obot(tc_fun(_1283526, tc_HOL_Obool))))), 28627 ^ _775212 : [(28634 ^ _775212) ^ [] : [_1283528 = _1283534, _1283530 = _1283532], (28628 ^ _775212) ^ [] : [_1283528 = _1283532, _1283530 = _1283534]]], (41644 ^ _775212) ^ [_1578178, _1578180, _1578182, _1578184, _1578186] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578178, _1578178)), hAPP(hAPP(c_Product__Type_OPair(_1578178, _1578178), _1578180), _1578182)), _1578184)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578178, _1578178)), hAPP(hAPP(c_Product__Type_OPair(_1578178, _1578178), _1578182), _1578186)), _1578184)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578178, _1578178)), hAPP(hAPP(c_Product__Type_OPair(_1578178, _1578178), _1578180), _1578186)), c_Transitive__Closure_Otrancl(_1578178, _1578184))))], (42824 ^ _775212) ^ [] : [-(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))))], (7401 ^ _775212) ^ [_893004, _893006, _893008, _893010, _893012] : [c_Com_Ocom_OLocal(_893004, _893006, _893008) = c_Com_Ocom_OSemi(_893010, _893012)], (39829 ^ _775212) ^ [_1537340] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1537340)))], (4354 ^ _775212) ^ [_841461, _841463] : [_841463 = _841461, -(c_Orderings_Oord__class_Omax(_841463) = c_Orderings_Oord__class_Omax(_841461))], (26891 ^ _775212) ^ [_1248093, _1248095, _1248097, _1248099] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248093, tc_HOL_Obool)), _1248095), _1248097), _1248099)), -(hBOOL(hAPP(_1248095, _1248099))), -(hBOOL(hAPP(_1248097, _1248099)))], (26479 ^ _775212) ^ [_1240545, _1240547, _1240549] : [class_Orderings_Olinorder(_1240545), 26482 ^ _775212 : [(26489 ^ _775212) ^ [] : [_1240547 = _1240549, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1240545), _1240547) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1240545), _1240549))], (26483 ^ _775212) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1240545), _1240547) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1240545), _1240549), -(_1240547 = _1240549)]]], (18809 ^ _775212) ^ [_1094960, _1094962, _1094964] : [class_Rings_Olinordered__idom(_1094960), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094960), c_Groups_Ozero__class_Ozero(_1094960)), hAPP(hAPP(c_Power_Opower__class_Opower(_1094960), _1094962), 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)))), _1094964)))))], (27193 ^ _775212) ^ [_1254288, _1254290, _1254292] : [class_Lattices_Osemilattice__sup(_1254288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254288), _1254290), _1254292)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254288), _1254290), _1254292) = _1254292)], (27423 ^ _775212) ^ [_1258736, _1258738] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1258736, _1258738)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1258738), hAPP(c_Nat_OSuc, _1258736)))], (28050 ^ _775212) ^ [_1271990, _1271992, _1271994] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1271990), _1271992)), 28053 ^ _775212 : [(28054 ^ _775212) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1271990, tc_Nat_Onat), _1271994), _1271992) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 28057 ^ _775212 : [(28058 ^ _775212) ^ [_1272152] : [hBOOL(hAPP(hAPP(c_member(_1271990), _1272152), _1271992)), -(hAPP(_1271994, _1272152) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (28064 ^ _775212) ^ [] : [28066 ^ _775212 : [(28069 ^ _775212) ^ [] : [hAPP(_1271994, 28065 ^ [_1271990, _1271992, _1271994]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28067 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1271990), 28065 ^ [_1271990, _1271992, _1271994]), _1271992)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1271990, tc_Nat_Onat), _1271994), _1271992) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (23964 ^ _775212) ^ [_1191694, _1191696] : [class_Rings_Ocomm__semiring__1(_1191694), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1191694), c_Groups_Oone__class_Oone(_1191694)), _1191696)))], (26933 ^ _775212) ^ [_1248922, _1248924] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248922, tc_HOL_Obool)), _1248924), _1248924) = _1248924)], (10531 ^ _775212) ^ [_947009, _947011] : [class_Groups_Oordered__ab__group__add(_947009), 10534 ^ _775212 : [(10541 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947009), c_Groups_Ozero__class_Ozero(_947009)), _947011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947009), hAPP(c_Groups_Ouminus__class_Ouminus(_947009), _947011)), c_Groups_Ozero__class_Ozero(_947009))))], (10535 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947009), hAPP(c_Groups_Ouminus__class_Ouminus(_947009), _947011)), c_Groups_Ozero__class_Ozero(_947009))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947009), c_Groups_Ozero__class_Ozero(_947009)), _947011)))]]], (31027 ^ _775212) ^ [_1335750, _1335752] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1335750), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335752))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335750), _1335752)))], (1574 ^ _775212) ^ [_797743, _797745] : [-(class_Rings_Oordered__cancel__semiring(_797743)), _797745 = _797743, class_Rings_Oordered__cancel__semiring(_797745)], (46174 ^ _775212) ^ [_1694331, _1694333] : [-(hAPP(c_List_Orotate1(_1694331), _1694333) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1694331), _1694331, c_List_Olist_ONil(_1694331), hAPP(hAPP(c_COMBB(tc_List_Olist(_1694331), tc_fun(tc_List_Olist(_1694331), tc_List_Olist(_1694331)), _1694331), hAPP(c_COMBC(tc_List_Olist(_1694331), tc_List_Olist(_1694331), tc_List_Olist(_1694331)), c_List_Oappend(_1694331))), hAPP(hAPP(c_COMBC(_1694331, tc_List_Olist(_1694331), tc_List_Olist(_1694331)), c_List_Olist_OCons(_1694331)), c_List_Olist_ONil(_1694331)))), _1694333))], (39540 ^ _775212) ^ [_1529109, _1529111] : [-(hAPP(c_Relation_ORange(_1529109, _1529111), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529109, _1529111), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1529111, tc_HOL_Obool)))], (1554 ^ _775212) ^ [_797493, _797495] : [-(class_Groups_Oordered__comm__monoid__add(_797493)), _797495 = _797493, class_Groups_Oordered__comm__monoid__add(_797495)], (44833 ^ _775212) ^ [_1660958, _1660960, _1660962, _1660964] : [hBOOL(hAPP(hAPP(c_member(_1660958), _1660960), hAPP(c_List_Oset(_1660958), c_List_Osublist(_1660958, _1660962, _1660964)))), -(hBOOL(hAPP(hAPP(c_member(_1660958), _1660960), hAPP(c_List_Oset(_1660958), _1660962))))], (10319 ^ _775212) ^ [_943103, _943105, _943107, _943109] : [class_Rings_Oordered__semiring(_943103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943103), _943105), _943107)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943103), c_Groups_Ozero__class_Ozero(_943103)), _943109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943103), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943103), _943109), _943105)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943103), _943109), _943107))))], (39530 ^ _775212) ^ [_1528836, _1528838, _1528840, _1528842] : [hAPP(hAPP(c_Relation_Orel__comp(_1528836, _1528836, _1528836), _1528838), _1528840) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528836, _1528836), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1528836, _1528836, _1528836), _1528838), _1528842) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528836, _1528836), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1528836, _1528836, _1528836), _1528838), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528836, _1528836), tc_HOL_Obool)), _1528840), _1528842)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528836, _1528836), tc_HOL_Obool)))], (42197 ^ _775212) ^ [_1591140, _1591142] : [c_Wellfounded_Oacyclic(_1591140, hAPP(c_Relation_Oconverse(_1591140, _1591140), _1591142)), -(c_Wellfounded_Oacyclic(_1591140, _1591142))], (45834 ^ _775212) ^ [_1685598, _1685600, _1685602] : [-(c_List_Olist_ONil(_1685598) = hAPP(hAPP(c_List_Oappend(_1685598), _1685600), _1685602)), _1685600 = c_List_Olist_ONil(_1685598), _1685602 = c_List_Olist_ONil(_1685598)], (14353 ^ _775212) ^ [_1014711] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014711), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1014711)], (22822 ^ _775212) ^ [_1169915, _1169917] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1169915)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169917)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1169917))), 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, _1169915))), 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), _1169915)), c_Int_Onat)))))], (52595 ^ _775212) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (35833 ^ _775212) ^ [_1437315, _1437317, _1437319, _1437321, _1437323, _1437325] : [c_Equiv__Relations_Ocongruent(_1437315, _1437317, _1437319, _1437321), hBOOL(hAPP(hAPP(c_member(tc_prod(_1437315, _1437315)), hAPP(hAPP(c_Product__Type_OPair(_1437315, _1437315), _1437323), _1437325)), _1437319)), -(hAPP(_1437321, _1437323) = hAPP(_1437321, _1437325))], (20321 ^ _775212) ^ [_1121841, _1121843] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121841), _1121843), hAPP(c_Int_Onumber__class_Onumber__of(_1121841), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1121841)), class_Fields_Ofield__inverse__zero(_1121841), class_Int_Onumber__ring(_1121841)], (50833 ^ _775212) ^ [_1794524, _1794526, _1794528, _1794530, _1794532] : [hBOOL(hAPP(hAPP(_1794528, _1794532), _1794530)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1794524, _1794526, _1794528), _1794530), _1794532)))], (12526 ^ _775212) ^ [_981653, _981655, _981657, _981659, _981661, _981663] : [class_Divides_Osemiring__div(_981653), c_Divides_Odiv__class_Omod(_981653, _981655, _981657) = c_Divides_Odiv__class_Omod(_981653, _981659, _981657), c_Divides_Odiv__class_Omod(_981653, _981661, _981657) = c_Divides_Odiv__class_Omod(_981653, _981663, _981657), -(c_Divides_Odiv__class_Omod(_981653, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981653), _981655), _981661), _981657) = c_Divides_Odiv__class_Omod(_981653, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981653), _981659), _981663), _981657))], (22430 ^ _775212) ^ [_1162198, _1162200, _1162202] : [class_Orderings_Olinorder(_1162198), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162198), _1162200), _1162202) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162198), _1162202), _1162200))], (37966 ^ _775212) ^ [_1486260, _1486262, _1486264, _1486266, _1486268, _1486270] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486260, _1486262)), hAPP(hAPP(c_Product__Type_OPair(_1486260, _1486262), _1486264), _1486266)), hAPP(hAPP(c_Product__Type_OSigma(_1486260, _1486262), _1486268), _1486270))), -(hBOOL(hAPP(hAPP(c_member(_1486260), _1486264), _1486268)))], (35948 ^ _775212) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (6879 ^ _775212) ^ [_884814, _884816] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884814), _884816)), 6880 ^ _775212 : [(6887 ^ _775212) ^ [] : [_884814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _884816 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6881 ^ _775212) ^ [] : [_884814 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _884816 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (18333 ^ _775212) ^ [_1086575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1086575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1086575))))], (4 ^ _775212) ^ [_775262, _775264] : [_775264 = _775262, -(_775262 = _775264)], (42848 ^ _775212) ^ [_1609734, _1609736, _1609738, _1609740, _1609742, _1609744] : [c_Relation_Osingle__valued(_1609734, _1609736, hAPP(c_Relation_Oconverse(_1609736, _1609734), _1609738)), -(_1609740 = c_Orderings_Obot__class_Obot(tc_fun(_1609742, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1609736, _1609734, _1609738), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609742, tc_fun(_1609736, tc_HOL_Obool)), _1609740), _1609744)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609742, tc_fun(_1609734, tc_HOL_Obool)), _1609740), hAPP(hAPP(c_COMBB(tc_fun(_1609736, tc_HOL_Obool), tc_fun(_1609734, tc_HOL_Obool), _1609742), c_Relation_OImage(_1609736, _1609734, _1609738)), _1609744)))], (27660 ^ _775212) ^ [_1263357, _1263359, _1263361, _1263363] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1263357, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1263359)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1263357, tc_HOL_Obool), tc_Nat_Onat), _1263361), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1263363))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1263357, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1263363, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1263359), _1263363))), _1263361))], (47869 ^ _775212) ^ [_1730831, _1730833] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1730831), tc_fun(_1730831, tc_HOL_Obool), c_List_Oset(_1730831)), hAPP(c_List_Oset(tc_List_Olist(_1730831)), c_Enum_Osublists(_1730831, _1730833))) = hAPP(c_Set_OPow(_1730831), hAPP(c_List_Oset(_1730831), _1730833)))], (40275 ^ _775212) ^ [_1548669, _1548671] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548669, _1548669)), _1548671)), 40278 ^ _775212 : [(40285 ^ _775212) ^ [] : [c_Wellfounded_Oacyclic(_1548669, _1548671), -(c_Wellfounded_Owf(_1548669, _1548671))], (40279 ^ _775212) ^ [] : [c_Wellfounded_Owf(_1548669, _1548671), -(c_Wellfounded_Oacyclic(_1548669, _1548671))]]], (39051 ^ _775212) ^ [_1510127, _1510129, _1510131] : [-(hAPP(hAPP(c_Set_Oinsert(_1510127), _1510129), _1510131) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1510127, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1510127), hAPP(hAPP(c_COMBC(_1510127, _1510127, tc_HOL_Obool), c_fequal), _1510129))), _1510131))], (31687 ^ _775212) ^ [_1348686, _1348688] : [class_Rings_Oring__1(_1348686), -(hBOOL(hAPP(hAPP(c_member(_1348686), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1348686), _1348688)), c_Int_Oring__1__class_OInts(_1348686))))], (15339 ^ _775212) ^ [_1033642, _1033644, _1033646, _1033648] : [class_Rings_Olinordered__semidom(_1033642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1033644), _1033646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033642), c_Groups_Oone__class_Oone(_1033642)), _1033648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033642), hAPP(hAPP(c_Power_Opower__class_Opower(_1033642), _1033648), _1033644)), hAPP(hAPP(c_Power_Opower__class_Opower(_1033642), _1033648), _1033646))))], (33427 ^ _775212) ^ [] : [-(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)))))], (1414 ^ _775212) ^ [_795743, _795745] : [-(class_Lattices_Oboolean__algebra(_795743)), _795745 = _795743, class_Lattices_Oboolean__algebra(_795745)], (47746 ^ _775212) ^ [_1727853, _1727855, _1727857] : [c_List_Olist__all2(_1727857, _1727857, c_fequal, _1727853, _1727855), -(_1727853 = _1727855)], (45361 ^ _775212) ^ [_1674543, _1674545, _1674547] : [-(_1674543 = c_List_Olist_ONil(_1674545)), -(hBOOL(hAPP(hAPP(c_member(_1674545), hAPP(c_Product__Type_Ofst(_1674545, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1674545, _1674543), _1674547))), hAPP(c_List_Oset(_1674545), _1674543))))], (2100 ^ _775212) ^ [_805550, _805552, _805554, _805556] : [-(c_Divides_OnegDivAlg(_805556, _805552) = c_Divides_OnegDivAlg(_805554, _805550)), _805556 = _805554, _805552 = _805550], (17829 ^ _775212) ^ [_1077931] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077931))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1077931)))))], (17743 ^ _775212) ^ [_1076513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076513), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1076513)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21359 ^ _775212) ^ [_1141131, _1141133] : [_1141131 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1141131, _1141133) = _1141133)], (30536 ^ _775212) ^ [_1325373, _1325375, _1325377, _1325379] : [hBOOL(hAPP(hAPP(c_member(_1325373), _1325375), _1325377)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1325373, tc_Nat_Onat), _1325379), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325373, tc_HOL_Obool)), _1325377), hAPP(hAPP(c_Set_Oinsert(_1325373), _1325375), c_Orderings_Obot__class_Obot(tc_fun(_1325373, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1325373, tc_Nat_Onat), _1325379), _1325377)), hAPP(_1325379, _1325375)))], (18907 ^ _775212) ^ [_1097008] : [_1097008 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1097008) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22898 ^ _775212) ^ [_1171511, _1171513, _1171515] : [class_Orderings_Olinorder(_1171511), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171511), _1171513), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171511), _1171513), _1171515)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171511), _1171513), _1171515))], (24848 ^ _775212) ^ [_1206861, _1206863, _1206865] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206861), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206863), _1206865))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206861), _1206865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206865), _1206863)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206861), _1206863)))], (16561 ^ _775212) ^ [_1056969] : [_1056969 = 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), _1056969)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (34047 ^ _775212) ^ [_1397563, _1397565, _1397567] : [class_Rings_Oring__1(_1397563), -(hAPP(c_Int_Oring__1__class_Oof__int(_1397563), 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), _1397565), _1397567)), 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(_1397563), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1397563), _1397565)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1397563), _1397567)))], (52701 ^ _775212) ^ [_1828593] : [hBOOL(hAPP(c_fNot, _1828593)), hBOOL(_1828593)], (34497 ^ _775212) ^ [_1408334, _1408336, _1408338] : [class_Lattices_Olattice(_1408334), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408334), _1408336), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408334), _1408336), _1408338)) = _1408336)], (40140 ^ _775212) ^ [_1544736, _1544738, _1544740] : [c_Wellfounded_OwfP(_1544736, _1544738), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1544736, tc_fun(_1544736, tc_HOL_Obool))), _1544740), _1544738)), -(c_Wellfounded_OwfP(_1544736, _1544740))], (27850 ^ _775212) ^ [_1268441, _1268443] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1268441, tc_HOL_Obool)), _1268443)))], (22120 ^ _775212) ^ [_1155001, _1155003] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1155001, _1155003) = 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), _1155001), _1155003)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1155001, _1155003)))], (37176 ^ _775212) ^ [_1466885, _1466887, _1466889, _1466891] : [class_Groups_Ocomm__monoid__mult(_1466885), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466887), _1466889)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1466887, _1466885), _1466891), _1466889) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1466885, _1466887, c_Groups_Otimes__class_Otimes(_1466885)), _1466891), c_Groups_Oone__class_Oone(_1466885)), _1466889))], (38437 ^ _775212) ^ [_1497715, _1497717, _1497719] : [class_Lattices_Osemilattice__inf(_1497715), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497715), _1497717)), -(_1497717 = c_Orderings_Obot__class_Obot(tc_fun(_1497715, tc_HOL_Obool))), 38448 ^ _775212 : [(38449 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497715), _1497719), hAPP(c_Finite__Set_Ofold1(_1497715, c_Lattices_Osemilattice__inf__class_Oinf(_1497715)), _1497717))), 38452 ^ _775212 : [(38453 ^ _775212) ^ [_1498008] : [hBOOL(hAPP(hAPP(c_member(_1497715), _1498008), _1497717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497715), _1497719), _1498008)))]]], (38459 ^ _775212) ^ [] : [38461 ^ _775212 : [(38464 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497715), _1497719), 38460 ^ [_1497715, _1497717, _1497719]))], (38462 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497715), 38460 ^ [_1497715, _1497717, _1497719]), _1497717)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497715), _1497719), hAPP(c_Finite__Set_Ofold1(_1497715, c_Lattices_Osemilattice__inf__class_Oinf(_1497715)), _1497717))))]]], (5619 ^ _775212) ^ [_863674, _863676, _863678, _863680] : [class_Rings_Osemiring__1(_863674), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_863674, _863676, hAPP(c_Nat_OSuc, _863678), _863680) = c_Nat_Osemiring__1__class_Oof__nat__aux(_863674, _863676, _863678, hAPP(_863676, _863680)))], (9765 ^ _775212) ^ [_933074] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _933074), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34547 ^ _775212) ^ [_1409692, _1409694, _1409696, _1409698] : [-(hBOOL(hAPP(hAPP(c_member(_1409692), _1409694), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409692, tc_HOL_Obool)), _1409696), _1409698)))), hBOOL(hAPP(hAPP(c_member(_1409692), _1409694), _1409696)), hBOOL(hAPP(hAPP(c_member(_1409692), _1409694), _1409698))], (15539 ^ _775212) ^ [_1038009, _1038011] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038009, _1038011) = 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), _1038009), _1038011) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43027 ^ _775212) ^ [_1614052, _1614054] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1614052, _1614052), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1614054) = c_Relation_OId(_1614052))], (32369 ^ _775212) ^ [_1361586, _1361588, _1361590, _1361592] : [-(c_Sum__Type_OPlus(_1361586, _1361588, _1361590, _1361592) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1361586, _1361588), tc_HOL_Obool))), _1361590 = c_Orderings_Obot__class_Obot(tc_fun(_1361586, tc_HOL_Obool)), _1361592 = c_Orderings_Obot__class_Obot(tc_fun(_1361588, tc_HOL_Obool))], (18327 ^ _775212) ^ [_1086492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1086492))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1086492)))], (2256 ^ _775212) ^ [_808066, _808068, _808070, _808072] : [-(c_Groups_Osgn__class_Osgn(_808072, _808068) = c_Groups_Osgn__class_Osgn(_808070, _808066)), _808072 = _808070, _808068 = _808066], (17847 ^ _775212) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (49889 ^ _775212) ^ [_1774461, _1774463, _1774465, _1774467, _1774469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1774461, _1774463)), hAPP(_1774461, _1774465))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774467, _1774467)), hAPP(hAPP(c_Product__Type_OPair(_1774467, _1774467), _1774463), _1774465)), c_List_Omeasures(_1774467, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1774467, tc_Nat_Onat)), _1774461), _1774469)))))], (9461 ^ _775212) ^ [_928184, _928186, _928188] : [class_Orderings_Opreorder(_928184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928184), _928186), _928188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928184), _928186), _928188)))], (52050 ^ _775212) ^ [_1820872, _1820874] : [c_Equiv__Relations_Opart__equivp(_1820872, _1820874), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1820872, tc_HOL_Obool)), 52053 ^ [_1820872, _1820874]), hAPP(hAPP(c_COMBB(tc_fun(_1820872, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1820872, tc_HOL_Obool)), c_HOL_OEx(_1820872)), hAPP(hAPP(c_COMBB(tc_fun(_1820872, tc_HOL_Obool), tc_fun(_1820872, tc_HOL_Obool), tc_fun(_1820872, tc_HOL_Obool)), hAPP(c_COMBS(_1820872, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1820872), c_fconj), hAPP(hAPP(c_COMBS(_1820872, _1820872, tc_HOL_Obool), _1820874), c_COMBI(_1820872))))), hAPP(hAPP(c_COMBC(tc_fun(_1820872, tc_HOL_Obool), tc_fun(_1820872, tc_fun(_1820872, tc_HOL_Obool)), tc_fun(_1820872, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1820872, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1820872, tc_fun(_1820872, tc_HOL_Obool)), tc_fun(_1820872, tc_HOL_Obool)), tc_fun(_1820872, tc_HOL_Obool)), c_COMBB(tc_fun(_1820872, tc_HOL_Obool), tc_HOL_Obool, _1820872)), c_fequal)), _1820874))))))], (18215 ^ _775212) ^ [_1084498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084498), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1084498)), c_Int_OPls)))], (41498 ^ _775212) ^ [_1575357, _1575359, _1575361] : [class_Groups_Oab__semigroup__mult(_1575357), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575357), _1575359)), -(hBOOL(hAPP(hAPP(c_member(_1575357), _1575361), _1575359))), -(hAPP(c_Finite__Set_Ofold1(_1575357, c_Groups_Otimes__class_Otimes(_1575357)), hAPP(hAPP(c_Set_Oinsert(_1575357), _1575361), _1575359)) = hAPP(hAPP(c_Finite__Set_Ofold(_1575357, _1575357, c_Groups_Otimes__class_Otimes(_1575357)), _1575361), _1575359))], (31601 ^ _775212) ^ [_1347165, _1347167] : [class_Lattices_Olattice(_1347165), -(c_Big__Operators_Olattice__class_OSup__fin(_1347165, hAPP(hAPP(c_Set_Oinsert(_1347165), _1347167), c_Orderings_Obot__class_Obot(tc_fun(_1347165, tc_HOL_Obool)))) = _1347167)], (51387 ^ _775212) ^ [_1807154] : [-(c_Relation_Otrans(tc_fun(_1807154, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1807154)))], (4390 ^ _775212) ^ [_841993, _841995, _841997, _841999] : [-(c_List_Obutlast(_841999, _841995) = c_List_Obutlast(_841997, _841993)), _841999 = _841997, _841995 = _841993], (35405 ^ _775212) ^ [_1428408, _1428410, _1428412] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1428408), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428408, tc_HOL_Obool)), _1428410), _1428412))), -(hAPP(c_Finite__Set_Ocard(_1428408), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1428408, tc_HOL_Obool)), _1428410), _1428412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1428408), _1428410)), hAPP(c_Finite__Set_Ocard(_1428408), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428408, tc_HOL_Obool)), _1428410), _1428412))))], (21945 ^ _775212) ^ [_1151719, _1151721, _1151723] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1151719, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1151719, tc_HOL_Obool)), _1151721), _1151723)), _1151723) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1151719, tc_HOL_Obool)), _1151721), _1151723))], (10145 ^ _775212) ^ [_939987, _939989] : [class_Groups_Olinordered__ab__group__add(_939987), 10148 ^ _775212 : [(10155 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939987), c_Groups_Ozero__class_Ozero(_939987)), _939989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939987), c_Groups_Ozero__class_Ozero(_939987)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939987), _939989), _939989))))], (10149 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939987), c_Groups_Ozero__class_Ozero(_939987)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939987), _939989), _939989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939987), c_Groups_Ozero__class_Ozero(_939987)), _939989)))]]], (22776 ^ _775212) ^ [_1168862, _1168864] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1168862), hAPP(c_Nat_OSuc, _1168864)) = 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)), _1168864)), _1168862))], (25779 ^ _775212) ^ [_1225973, _1225975, _1225977, _1225979, _1225981] : [class_Orderings_Olinorder(_1225973), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1225973, _1225975), _1225977) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1225973, _1225979), _1225981), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225973), _1225975), _1225977)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225973), _1225979), _1225981)), -(_1225977 = _1225981)], (36465 ^ _775212) ^ [_1452140, _1452142] : [c_Equiv__Relations_Oequivp(_1452140, _1452142), 36468 ^ _775212 : [(36475 ^ _775212) ^ [_1452333, _1452335] : [hAPP(_1452142, _1452335) = hAPP(_1452142, _1452333), -(hBOOL(hAPP(hAPP(_1452142, _1452335), _1452333)))], (36469 ^ _775212) ^ [_1452234, _1452236] : [hBOOL(hAPP(hAPP(_1452142, _1452236), _1452234)), -(hAPP(_1452142, _1452236) = hAPP(_1452142, _1452234))]]], (39991 ^ _775212) ^ [_1541119, _1541121, _1541123, _1541125] : [c_FunDef_Oreduction__pair(_1541119, _1541121), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541119, _1541119), tc_HOL_Obool)), _1541123), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541119, _1541119), tc_HOL_Obool), tc_fun(tc_prod(_1541119, _1541119), tc_HOL_Obool)), _1541121))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541119, _1541119), tc_HOL_Obool)), _1541125), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1541119, _1541119), tc_HOL_Obool), tc_fun(tc_prod(_1541119, _1541119), tc_HOL_Obool)), _1541121))), c_Wellfounded_Owf(_1541119, _1541125), -(c_Wellfounded_Owf(_1541119, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1541119, _1541119), tc_HOL_Obool)), _1541123), _1541125)))], (49183 ^ _775212) ^ [_1759344, _1759346] : [-(hAPP(c_List_Oset(_1759344), hAPP(c_List_Orev(_1759344), _1759346)) = hAPP(c_List_Oset(_1759344), _1759346))], (19657 ^ _775212) ^ [_1109955, _1109957] : [c_Nat__Transfer_Ois__nat(_1109955), c_Nat__Transfer_Ois__nat(_1109957), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1109955, _1109957)))], (49492 ^ _775212) ^ [_1765754] : [-(c_List_Oembed__list(_1765754) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1765754))], (17375 ^ _775212) ^ [_1070367, _1070369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1070367)), _1070369)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070367), _1070369)))], (52489 ^ _775212) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (21875 ^ _775212) ^ [_1150317, _1150319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150319)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1150317), _1150319) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1150317, _1150319)))], (47557 ^ _775212) ^ [_1723897, _1723899, _1723901] : [hBOOL(hAPP(c_List_Olistsp(_1723897, hAPP(hAPP(c_COMBC(_1723897, tc_fun(_1723897, tc_HOL_Obool), tc_HOL_Obool), c_member(_1723897)), _1723899)), _1723901)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1723897)), _1723901), c_List_Olists(_1723897, _1723899))))], (33636 ^ _775212) ^ [_1388209, _1388211, _1388213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1388209, _1388209)), _1388211), c_Relation_OId__on(_1388209, _1388213))), 33640 ^ _775212 : [(33643 ^ _775212) ^ [] : [-(_1388211 = hAPP(hAPP(c_Product__Type_OPair(_1388209, _1388209), 33639 ^ [_1388209, _1388211, _1388213]), 33639 ^ [_1388209, _1388211, _1388213]))], (33641 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388209), 33639 ^ [_1388209, _1388211, _1388213]), _1388213)))]]], (45542 ^ _775212) ^ [_1679459, _1679461, _1679463, _1679465] : [class_Groups_Ocomm__monoid__add(_1679459), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1679459), _1679461), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1679463, _1679465))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1679459), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1679459), _1679461), c_List_Oupto(_1679463, _1679465))))], (37622 ^ _775212) ^ [_1477213, _1477215, _1477217, _1477219, _1477221, _1477223] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1477213, _1477215, _1477217, _1477219, _1477221), _1477223)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1477213), _1477221)))], (17437 ^ _775212) ^ [_1071338, _1071340] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071338)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071340)))), 17440 ^ _775212 : [(17443 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1071340))], (17441 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071338), _1071340)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071338), _1071340))], (34057 ^ _775212) ^ [_1397865] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1397865)) = _1397865)], (36907 ^ _775212) ^ [_1460889, _1460891, _1460893, _1460895] : [c_Fun_Oinj__on(_1460889, _1460891, _1460893, c_Orderings_Otop__class_Otop(tc_fun(_1460889, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1460891, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1460889, _1460891, _1460893), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1460889, tc_HOL_Obool)), _1460895))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1460891, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1460889, _1460891, _1460893), _1460895)))))], (22110 ^ _775212) ^ [_1154814, _1154816, _1154818, _1154820] : [-(_1154814 = _1154816), hAPP(c_Product__Type_Ofst(_1154818, _1154820), _1154814) = hAPP(c_Product__Type_Ofst(_1154818, _1154820), _1154816), hAPP(c_Product__Type_Osnd(_1154818, _1154820), _1154814) = hAPP(c_Product__Type_Osnd(_1154818, _1154820), _1154816)], (52487 ^ _775212) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (46640 ^ _775212) ^ [_1704670, _1704672, _1704674] : [-(hAPP(c_List_Otl(_1704670), hAPP(hAPP(c_List_Oappend(_1704670), _1704672), _1704674)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1704670), _1704670, hAPP(c_List_Otl(_1704670), _1704674), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1704670), tc_List_Olist(_1704670)), _1704670), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704670), tc_List_Olist(_1704670), tc_List_Olist(_1704670)), c_List_Oappend(_1704670)), _1704674))), _1704672))], (37551 ^ _775212) ^ [_1475195, _1475197, _1475199, _1475201, _1475203, _1475205] : [-(hBOOL(hAPP(hAPP(c_member(_1475195), _1475197), _1475199))), 37554 ^ _775212 : [(37561 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475195), _1475201), _1475199))), -(hAPP(c_Set_Ovimage(_1475203, _1475195, hAPP(hAPP(c_COMBC(_1475203, _1475195, _1475195), hAPP(hAPP(c_COMBC(_1475203, _1475195, tc_fun(_1475195, _1475195)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1475195, tc_fun(_1475195, _1475195)), _1475203), c_If(_1475195)), hAPP(hAPP(c_COMBC(_1475203, tc_fun(_1475203, tc_HOL_Obool), tc_HOL_Obool), c_member(_1475203)), _1475205))), _1475197)), _1475201)), _1475199) = c_Orderings_Obot__class_Obot(tc_fun(_1475203, tc_HOL_Obool)))], (37555 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1475195), _1475201), _1475199)), -(hAPP(c_Set_Ovimage(_1475203, _1475195, hAPP(hAPP(c_COMBC(_1475203, _1475195, _1475195), hAPP(hAPP(c_COMBC(_1475203, _1475195, tc_fun(_1475195, _1475195)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1475195, tc_fun(_1475195, _1475195)), _1475203), c_If(_1475195)), hAPP(hAPP(c_COMBC(_1475203, tc_fun(_1475203, tc_HOL_Obool), tc_HOL_Obool), c_member(_1475203)), _1475205))), _1475197)), _1475201)), _1475199) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1475203, tc_HOL_Obool)), _1475205))]]], (26397 ^ _775212) ^ [_1238780, _1238782, _1238784, _1238786, _1238788] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1238780, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1238780, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1238782, _1238780, _1238784), _1238786)), hAPP(c_Set_Oimage(_1238782, _1238780, _1238784), _1238788))), hAPP(c_Set_Oimage(_1238782, _1238780, _1238784), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1238782, tc_HOL_Obool)), _1238786), _1238788)))))], (12470 ^ _775212) ^ [_980401, _980403, _980405, _980407] : [class_Divides_Osemiring__div(_980401), -(c_Divides_Odiv__class_Omod(_980401, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980401), c_Divides_Odiv__class_Omod(_980401, _980403, _980405)), _980407), _980405) = c_Divides_Odiv__class_Omod(_980401, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980401), _980403), _980407), _980405))], (3630 ^ _775212) ^ [_830055, _830057] : [_830057 = _830055, -(c_Equiv__Relations_Oquotient(_830057) = c_Equiv__Relations_Oquotient(_830055))], (14703 ^ _775212) ^ [_1021422, _1021424, _1021426] : [class_Rings_Olinordered__semidom(_1021422), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021422), c_Groups_Ozero__class_Ozero(_1021422)), _1021424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021422), c_Groups_Ozero__class_Ozero(_1021422)), hAPP(hAPP(c_Power_Opower__class_Opower(_1021422), _1021424), _1021426))))], (27395 ^ _775212) ^ [_1258193, _1258195] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1258193), _1258195) = 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)), _1258193)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1258195))))], (4804 ^ _775212) ^ [_848382, _848384] : [_848384 = _848382, -(c_List_Onth(_848384) = c_List_Onth(_848382))], (41085 ^ _775212) ^ [_1566924, _1566926, _1566928, _1566930, _1566932, _1566934] : [class_Groups_Oab__semigroup__mult(_1566924), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566926), _1566928)), 41095 ^ _775212 : [(41098 ^ _775212) ^ [] : [hAPP(_1566930, 41094 ^ [_1566924, _1566926, _1566928, _1566930, _1566932, _1566934]) = hAPP(_1566932, 41094 ^ [_1566924, _1566926, _1566928, _1566930, _1566932, _1566934])], (41096 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566926), 41094 ^ [_1566924, _1566926, _1566928, _1566930, _1566932, _1566934]), _1566928)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1566924, _1566926, c_Groups_Otimes__class_Otimes(_1566924)), _1566930), _1566934), _1566928) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1566924, _1566926, c_Groups_Otimes__class_Otimes(_1566924)), _1566932), _1566934), _1566928))], (49458 ^ _775212) ^ [_1765034, _1765036, _1765038, _1765040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1765034), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765036)), c_List_OtakeWhile(_1765036, _1765038, _1765040)))), -(hAPP(hAPP(c_List_Onth(_1765036), c_List_OtakeWhile(_1765036, _1765038, _1765040)), _1765034) = hAPP(hAPP(c_List_Onth(_1765036), _1765040), _1765034))], (4380 ^ _775212) ^ [_841844, _841846, _841848, _841850] : [-(c_Product__Type_Ofst(_841850, _841846) = c_Product__Type_Ofst(_841848, _841844)), _841850 = _841848, _841846 = _841844], (46915 ^ _775212) ^ [_1710540, _1710542, _1710544] : [-(hAPP(c_List_Orotate(_1710540, _1710542), _1710544) = hAPP(hAPP(c_List_Oappend(_1710540), hAPP(hAPP(c_List_Odrop(_1710540), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1710542, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710540)), _1710544))), _1710544)), hAPP(hAPP(c_List_Otake(_1710540), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1710542, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710540)), _1710544))), _1710544)))], (50853 ^ _775212) ^ [_1794916] : [-(c_Predicate_Oconversep(_1794916, _1794916, c_fequal) = c_fequal)], (50881 ^ _775212) ^ [_1795371, _1795373, _1795375] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795371)), c_List_Oreplicate(_1795371, _1795373, _1795375)) = _1795373)], (6206 ^ _775212) ^ [_873232, _873234] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873232), _873234))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873232), hAPP(c_Nat_OSuc, _873234))), -(_873234 = _873232)], (45256 ^ _775212) ^ [_1671915, _1671917, _1671919] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671915), tc_List_Olist(_1671915))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671915), tc_List_Olist(_1671915)), _1671917), c_List_Olist_ONil(_1671915))), c_List_Olexord(_1671915, _1671919)))], (40598 ^ _775212) ^ [_1555606, _1555608, _1555610, _1555612] : [-(c_Hilbert__Choice_OEps(tc_prod(_1555606, _1555608), hAPP(c_Product__Type_Oprod_Oprod__case(_1555606, _1555608, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1555606, tc_fun(_1555608, tc_HOL_Obool), tc_fun(_1555608, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1555608, tc_HOL_Obool), tc_fun(_1555608, tc_HOL_Obool)), _1555606), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1555608)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1555606), c_fconj), hAPP(c_fequal, _1555610)))), hAPP(c_fequal, _1555612)))) = hAPP(hAPP(c_Product__Type_OPair(_1555606, _1555608), _1555610), _1555612))], (42285 ^ _775212) ^ [_1593687, _1593689, _1593691] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1593689, _1593687)), _1593691)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1593687, _1593689)), hAPP(c_Relation_Oconverse(_1593689, _1593687), _1593691))))], (45230 ^ _775212) ^ [_1670763, _1670765] : [-(_1670765 = c_List_Olist_ONil(_1670763)), -(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(_1670763)), _1670765))))], (48584 ^ _775212) ^ [_1747826, _1747828, _1747830] : [48585 ^ _775212 : [(48588 ^ _775212) ^ [] : [_1747830 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48586 ^ _775212) ^ [] : [-(_1747826 = c_List_Olist_ONil(tc_List_Olist(_1747828)))]], 48592 ^ _775212 : [(48595 ^ _775212) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747828)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1747828)), _1747826), 48591 ^ [_1747826, _1747828, _1747830])) = _1747830], (48593 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48591 ^ [_1747826, _1747828, _1747830]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1747828))), _1747826))))]], -(c_List_Otranspose(_1747828, _1747826) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1747828)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1747828)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1747828), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1747828)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1747828)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1747828), hAPP(hAPP(c_COMBB(tc_List_Olist(_1747828), tc_fun(tc_Nat_Onat, _1747828), tc_Nat_Onat), c_List_Onth(_1747828)), hAPP(c_List_Onth(tc_List_Olist(_1747828)), _1747826))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1747828))), _1747826)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1747830)))], (51205 ^ _775212) ^ [_1803102, _1803104, _1803106] : [c_List_Oall__interval__int(_1803102, _1803104, _1803106), 51208 ^ _775212 : [(51209 ^ _775212) ^ [_1803180] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1803180), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1803104, _1803106))), -(hBOOL(hAPP(_1803102, _1803180)))]]], (26726 ^ _775212) ^ [_1244837, _1244839] : [class_Orderings_Olinorder(_1244837), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1244837, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1244837), _1244839)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1244837), _1244839))], (39912 ^ _775212) ^ [_1539175, _1539177, _1539179] : [-(hAPP(c_Set_Oimage(tc_prod(_1539175, _1539177), _1539175, c_Product__Type_Ofst(_1539175, _1539177)), _1539179) = hAPP(c_Relation_ODomain(_1539175, _1539177), _1539179))], (13276 ^ _775212) ^ [_995453, _995455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995453), _995455)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _995453, _995455) = _995453)], (52281 ^ _775212) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (1444 ^ _775212) ^ [_796118, _796120] : [-(class_Orderings_Obot(_796118)), _796120 = _796118, class_Orderings_Obot(_796120)], (12300 ^ _775212) ^ [_977613, _977615] : [class_Groups_Osgn__if(_977613), 12303 ^ _775212 : [(12310 ^ _775212) ^ [] : [-(_977615 = c_Groups_Ozero__class_Ozero(_977613)), 12313 ^ _775212 : [(12320 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977613), c_Groups_Ozero__class_Ozero(_977613)), _977615))), -(c_Groups_Osgn__class_Osgn(_977613, _977615) = hAPP(c_Groups_Ouminus__class_Ouminus(_977613), c_Groups_Oone__class_Oone(_977613)))], (12314 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977613), c_Groups_Ozero__class_Ozero(_977613)), _977615)), -(c_Groups_Osgn__class_Osgn(_977613, _977615) = c_Groups_Oone__class_Oone(_977613))]]], (12304 ^ _775212) ^ [] : [_977615 = c_Groups_Ozero__class_Ozero(_977613), -(c_Groups_Osgn__class_Osgn(_977613, _977615) = c_Groups_Ozero__class_Ozero(_977613))]]], (2090 ^ _775212) ^ [_805401, _805403, _805405, _805407] : [-(c_Nat__Transfer_Otsub(_805407, _805403) = c_Nat__Transfer_Otsub(_805405, _805401)), _805407 = _805405, _805403 = _805401], (37846 ^ _775212) ^ [_1482587, _1482589, _1482591, _1482593, _1482595, _1482597] : [hBOOL(hAPP(hAPP(c_member(_1482587), _1482589), _1482591)), hBOOL(hAPP(hAPP(c_member(_1482593), _1482595), hAPP(_1482597, _1482589))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1482587, _1482593)), hAPP(hAPP(c_Product__Type_OPair(_1482587, _1482593), _1482589), _1482595)), hAPP(hAPP(c_Product__Type_OSigma(_1482587, _1482593), _1482591), _1482597))))], (42744 ^ _775212) ^ [_1606915, _1606917, _1606919, _1606921] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606915, _1606915)), hAPP(hAPP(c_Product__Type_OPair(_1606915, _1606915), _1606919), _1606921)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1606915, _1606915), tc_HOL_Obool)), _1606917), c_Relation_OId(_1606915)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606915, tc_fun(_1606915, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1606915, tc_fun(tc_prod(_1606915, _1606915), tc_HOL_Obool), tc_fun(_1606915, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1606915, tc_fun(tc_fun(tc_prod(_1606915, _1606915), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1606915, _1606915), tc_HOL_Obool), tc_fun(_1606915, tc_HOL_Obool)), _1606915), c_COMBC(_1606915, tc_fun(tc_prod(_1606915, _1606915), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1606915, tc_prod(_1606915, _1606915)), tc_fun(_1606915, tc_fun(tc_fun(tc_prod(_1606915, _1606915), tc_HOL_Obool), tc_HOL_Obool)), _1606915), hAPP(c_COMBB(tc_prod(_1606915, _1606915), tc_fun(tc_fun(tc_prod(_1606915, _1606915), tc_HOL_Obool), tc_HOL_Obool), _1606915), c_member(tc_prod(_1606915, _1606915)))), c_Product__Type_OPair(_1606915, _1606915)))), _1606917)), c_fequal), _1606919), _1606921)))], (38331 ^ _775212) ^ [_1495903, _1495905, _1495907] : [-(hAPP(c_Finite__Set_Ofold1(_1495903, _1495905), _1495907) = c_HOL_OThe(_1495903, c_Finite__Set_Ofold1Set(_1495903, _1495905, _1495907)))], (52699 ^ _775212) ^ [] : [-(hBOOL(c_fTrue))], (46730 ^ _775212) ^ [_1706576, _1706578, _1706580] : [hBOOL(hAPP(c_List_Odistinct(_1706576), hAPP(c_List_Orotate(_1706576, _1706578), _1706580))), -(hBOOL(hAPP(c_List_Odistinct(_1706576), _1706580)))], (39180 ^ _775212) ^ [_1515249, _1515251] : [-(hAPP(c_Set_OPow(_1515249), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1515249, tc_HOL_Obool)), _1515251)) = hAPP(c_Set_OCollect(tc_fun(_1515249, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1515249, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1515249, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1515249, tc_HOL_Obool), tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1515249, tc_HOL_Obool)), c_COMBS(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1515249, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1515249, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1515249, tc_HOL_Obool), tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_fun(_1515249, tc_HOL_Obool)), tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_fun(_1515249, tc_HOL_Obool)), tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1515249, tc_HOL_Obool)), c_COMBB(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1515249, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1515249, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1515249, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1515249, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1515249, tc_HOL_Obool)), _1515251)), c_Set_OPow(_1515249))))))], (18275 ^ _775212) ^ [_1085520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085520), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1085520)), c_Int_OPls)))], (42814 ^ _775212) ^ [_1608865] : [-(hAPP(c_Relation_ORange(_1608865, _1608865), c_Relation_OId(_1608865)) = c_Orderings_Otop__class_Otop(tc_fun(_1608865, tc_HOL_Obool)))], (50035 ^ _775212) ^ [_1777898, _1777900] : [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), _1777898), _1777900))), 50038 ^ _775212 : [(50045 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1777898), _1777900))), -(c_Lazy__Sequence_Osmall__lazy_H(_1777898, _1777900) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1777900), c_Lazy__Sequence_Osmall__lazy_H(_1777898, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1777900), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50039 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1777898), _1777900)), -(c_Lazy__Sequence_Osmall__lazy_H(_1777898, _1777900) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (5627 ^ _775212) ^ [_863845, _863847, _863849, _863851] : [-(c_Nat_Onat_Onat__case(_863845, _863847, _863849, hAPP(c_Nat_OSuc, _863851)) = hAPP(_863849, _863851))], (38192 ^ _775212) ^ [_1492487, _1492489, _1492491, _1492493, _1492495, _1492497, _1492499, _1492501] : [c_Fun_Oinj__on(_1492487, _1492489, _1492491, _1492493), c_Fun_Oinj__on(_1492495, _1492497, _1492499, _1492501), -(c_Fun_Oinj__on(tc_prod(_1492487, _1492495), tc_prod(_1492489, _1492497), c_Product__Type_Omap__pair(_1492487, _1492489, _1492495, _1492497, _1492491, _1492499), hAPP(hAPP(c_Product__Type_OSigma(_1492487, _1492495), _1492493), hAPP(c_COMBK(tc_fun(_1492495, tc_HOL_Obool), _1492487), _1492501))))], (43861 ^ _775212) ^ [_1633967, _1633969, _1633971, _1633973] : [class_Lattices_Osemilattice__sup(_1633967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1633967), _1633969)), 43871 ^ _775212 : [(43874 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1633967), 43870 ^ [_1633967, _1633969, _1633971, _1633973]), _1633971))], (43872 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633967), 43870 ^ [_1633967, _1633969, _1633971, _1633973]), _1633969)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1633967), hAPP(hAPP(c_Finite__Set_Ofold(_1633967, _1633967, c_Lattices_Osemilattice__sup__class_Osup(_1633967)), _1633973), _1633969)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1633967), _1633971), _1633973))))], (23530 ^ _775212) ^ [_1183673, _1183675, _1183677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1183673), c_Nitpick_Oplus__frac(_1183673, _1183675, c_Nitpick_Ouminus__frac(_1183673, _1183677)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1183673, _1183675, _1183677))], (25723 ^ _775212) ^ [_1225024, _1225026] : [hAPP(_1225024, 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), _1225024), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225026)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1225024), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1225026)))], (23262 ^ _775212) ^ [_1178519, _1178521, _1178523, _1178525] : [class_Orderings_Olinorder(_1178519), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178519), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178519), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1178519), _1178521), _1178523)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1178519), _1178521), _1178525))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1178519), _1178521), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178519), _1178523), _1178525)))))], (8449 ^ _775212) ^ [_911904, _911906, _911908, _911910] : [class_Rings_Olinordered__semiring__strict(_911904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911904), _911906), _911908)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911904), c_Groups_Ozero__class_Ozero(_911904)), _911910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911904), _911906), _911910)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911904), _911908), _911910))))], (49261 ^ _775212) ^ [_1760998, _1761000] : [-(_1760998 = c_List_Olist_ONil(_1761000)), -(c_List_Olast(_1761000, hAPP(c_List_Orev(_1761000), _1760998)) = hAPP(c_List_Ohd(_1761000), _1760998))], (5837 ^ _775212) ^ [_867511] : [hAPP(c_Nat_OSuc, _867511) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49245 ^ _775212) ^ [_1760557, _1760559, _1760561, _1760563, _1760565] : [-(hAPP(c_List_Ofoldl(_1760557, _1760559, _1760561, _1760563), _1760565) = c_List_Ofoldr(_1760559, _1760557, hAPP(c_COMBC(_1760557, _1760559, _1760557), _1760561), hAPP(c_List_Orev(_1760559), _1760565), _1760563))], (34643 ^ _775212) ^ [_1411471, _1411473, _1411475, _1411477] : [class_Lattices_Osemilattice__inf(_1411471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411471), _1411473), _1411475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411471), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411471), _1411477), _1411473)), _1411475)))], (1614 ^ _775212) ^ [_798243, _798245] : [-(class_Rings_Olinordered__semidom(_798243)), _798245 = _798243, class_Rings_Olinordered__semidom(_798245)], (5821 ^ _775212) ^ [_867197, _867199, _867201, _867203, _867205] : [c_Com_Ocom_OSemi(_867197, _867199) = c_Com_Ocom_OCond(_867201, _867203, _867205)], (2684 ^ _775212) ^ [_814806, _814808] : [_814808 = _814806, -(c_DSequence_Oempty(_814808) = c_DSequence_Oempty(_814806))], (44655 ^ _775212) ^ [_1656202, _1656204, _1656206, _1656208] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656202) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1656204), hAPP(hAPP(c_List_Olist_OCons(_1656204), _1656206), _1656208)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656202)) = hAPP(hAPP(c_List_Onth(_1656204), _1656208), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656202)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (50601 ^ _775212) ^ [_1789914, _1789916, _1789918, _1789920] : [-(c_List_Olist__ex1(_1789914, _1789916, hAPP(hAPP(c_List_Olist_OCons(_1789914), _1789918), _1789920))), 50604 ^ _775212 : [(50607 ^ _775212) ^ [] : [c_List_Olist__all(_1789914, hAPP(hAPP(c_COMBS(_1789914, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1789914), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1789914), c_fNot), _1789916))), hAPP(c_fequal, _1789918)), _1789920)], (50605 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1789916, _1789918)))]], 50608 ^ _775212 : [(50611 ^ _775212) ^ [] : [c_List_Olist__ex1(_1789914, _1789916, _1789920)], (50609 ^ _775212) ^ [] : [hBOOL(hAPP(_1789916, _1789918))]]], (16305 ^ _775212) ^ [_1051819, _1051821, _1051823, _1051825] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051819), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051819), _1051821), _1051823)), hAPP(c_Int_Onumber__class_Onumber__of(_1051819), _1051825)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051819), _1051821), hAPP(c_Int_Onumber__class_Onumber__of(_1051819), _1051825))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051819), _1051823), hAPP(c_Int_Onumber__class_Onumber__of(_1051819), _1051825)))), class_Int_Onumber(_1051819), class_Rings_Osemiring(_1051819)], (686 ^ _775212) ^ [_785817, _785819] : [-(c_Nat__Transfer_Onat__set(_785817)), _785819 = _785817, c_Nat__Transfer_Onat__set(_785819)], (40558 ^ _775212) ^ [_1554753, _1554755, _1554757, _1554759, _1554761, _1554763] : [class_Groups_Ocomm__monoid__add(_1554753), c_Fun_Oinj__on(_1554755, _1554757, _1554759, _1554761), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554757, _1554753), _1554763), hAPP(c_Set_Oimage(_1554755, _1554757, _1554759), _1554761)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554755, _1554753), hAPP(c_Fun_Ocomp(_1554757, _1554753, _1554755, _1554763), _1554759)), _1554761))], (9575 ^ _775212) ^ [_929818, _929820, _929822, _929824] : [class_Orderings_Oorder(_929818), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929818), _929820), _929822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929818), _929824), _929820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929818), _929824), _929822)))], (16195 ^ _775212) ^ [_1049819, _1049821] : [class_Groups_Oordered__ab__group__add__abs(_1049819), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049819), hAPP(c_Groups_Ouminus__class_Ouminus(_1049819), _1049821)), hAPP(c_Groups_Oabs__class_Oabs(_1049819), _1049821))))], (34158 ^ _775212) ^ [_1400641, _1400643, _1400645, _1400647] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1400641, tc_HOL_Obool)), _1400643), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400641), _1400645), _1400647))), 34162 ^ _775212 : [(34165 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1400641), 34161 ^ [_1400641, _1400643, _1400645, _1400647]), _1400645)))], (34163 ^ _775212) ^ [] : [-(_1400643 = hAPP(c_Relation_OImage(_1400641, _1400641, _1400647), hAPP(hAPP(c_Set_Oinsert(_1400641), 34161 ^ [_1400641, _1400643, _1400645, _1400647]), c_Orderings_Obot__class_Obot(tc_fun(_1400641, tc_HOL_Obool)))))]]], (50379 ^ _775212) ^ [_1785298, _1785300, _1785302, _1785304] : [50380 ^ _775212 : [(50383 ^ _775212) ^ [] : [c_List_Olist__ex(_1785298, _1785300, _1785304)], (50381 ^ _775212) ^ [] : [c_List_Olist__ex(_1785298, _1785300, _1785302)]], -(c_List_Olist__ex(_1785298, _1785300, hAPP(hAPP(c_List_Oappend(_1785298), _1785302), _1785304)))], (8113 ^ _775212) ^ [] : [-(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))], (28333 ^ _775212) ^ [_1277627] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1277627)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1277627), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1277627), c_Orderings_Otop__class_Otop(tc_fun(_1277627, tc_HOL_Obool)))))], (26635 ^ _775212) ^ [_1243335] : [c_Nat__Transfer_Onat__set(_1243335), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1243335) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1243335)))], (13851 ^ _775212) ^ [_1005246, _1005248, _1005250] : [class_Divides_Osemiring__div(_1005246), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1005246), c_Divides_Odiv__class_Omod(_1005246, _1005248, _1005250)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005246), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1005246), _1005248), _1005250)), _1005250)) = _1005248)], (35445 ^ _775212) ^ [_1429385, _1429387, _1429389, _1429391, _1429393, _1429395, _1429397, _1429399] : [c_Finite__Set_Ofolding__image__simple(_1429385, _1429387, _1429389, _1429391, _1429393, _1429395), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429387), _1429397)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429387), _1429399)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429387, tc_HOL_Obool)), _1429397), _1429399) = c_Orderings_Obot__class_Obot(tc_fun(_1429387, tc_HOL_Obool)), -(hAPP(_1429395, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1429387, tc_HOL_Obool)), _1429397), _1429399)) = hAPP(hAPP(_1429389, hAPP(_1429395, _1429397)), hAPP(_1429395, _1429399)))], (25068 ^ _775212) ^ [_1211188, _1211190, _1211192] : [class_Rings_Ocomm__semiring__1(_1211188), 25073 ^ _775212 : [(25076 ^ _775212) ^ [] : [_1211192 = c_Groups_Oone__class_Oone(_1211188)], (25074 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211190))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1211188), _1211192), hAPP(hAPP(c_Power_Opower__class_Opower(_1211188), _1211192), _1211190))))], (26425 ^ _775212) ^ [_1239345, _1239347, _1239349, _1239351] : [class_Groups_Ocomm__monoid__add(_1239345), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1239347), _1239349)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1239345), _1239351), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1239347, _1239349)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1239345), hAPP(_1239351, _1239347)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1239345), _1239351), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1239347, _1239349))))], (43204 ^ _775212) ^ [_1618429, _1618431, _1618433, _1618435] : [hBOOL(hAPP(hAPP(c_member(_1618429), _1618431), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1618429, tc_HOL_Obool), _1618433))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1618429, tc_HOL_Obool)), _1618435), _1618433)), -(hBOOL(hAPP(hAPP(c_member(_1618429), _1618431), _1618435)))], (37427 ^ _775212) ^ [_1472147, _1472149] : [-(hAPP(c_Set_Ovimage(_1472147, _1472147, c_COMBI(_1472147)), _1472149) = _1472149)], (43222 ^ _775212) ^ [_1618824, _1618826, _1618828] : [class_Complete__Lattice_Ocomplete__lattice(_1618824), 43225 ^ _775212 : [(43226 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1618824), _1618826), c_Complete__Lattice_OInf__class_OInf(_1618824, _1618828))), 43229 ^ _775212 : [(43230 ^ _775212) ^ [_1618982] : [hBOOL(hAPP(hAPP(c_member(_1618824), _1618982), _1618828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1618824), _1618826), _1618982)))]]], (43236 ^ _775212) ^ [] : [43238 ^ _775212 : [(43241 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1618824), _1618826), 43237 ^ [_1618824, _1618826, _1618828]))], (43239 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618824), 43237 ^ [_1618824, _1618826, _1618828]), _1618828)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1618824), _1618826), c_Complete__Lattice_OInf__class_OInf(_1618824, _1618828))))]]], (32339 ^ _775212) ^ [_1360852, _1360854, _1360856, _1360858] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1360852), _1360854)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360856), _1360858)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1360852, _1360856)), c_Sum__Type_OPlus(_1360852, _1360856, _1360854, _1360858)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1360852), _1360854)), hAPP(c_Finite__Set_Ocard(_1360856), _1360858)))], (14835 ^ _775212) ^ [_1023774, _1023776, _1023778, _1023780] : [class_Groups_Omonoid__mult(_1023774), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1023774), _1023776), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1023778), _1023780)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023774), hAPP(hAPP(c_Power_Opower__class_Opower(_1023774), _1023776), _1023778)), hAPP(hAPP(c_Power_Opower__class_Opower(_1023774), _1023776), _1023780)))], (32695 ^ _775212) ^ [_1367718, _1367720, _1367722] : [class_Orderings_Olinorder(_1367718), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367718), _1367720)), -(hBOOL(hAPP(hAPP(c_member(_1367718), _1367722), _1367720))), -(_1367720 = c_Orderings_Obot__class_Obot(tc_fun(_1367718, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1367718, c_Orderings_Oord__class_Omin(_1367718), hAPP(hAPP(c_Set_Oinsert(_1367718), _1367722), _1367720)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367718), _1367722), c_Big__Operators_Olattice_OInf__fin(_1367718, c_Orderings_Oord__class_Omin(_1367718), _1367720)))], (40686 ^ _775212) ^ [_1557627, _1557629, _1557631, _1557633, _1557635, _1557637, _1557639, _1557641] : [c_Finite__Set_Ofolding(_1557627, _1557629, _1557631, _1557633), -(hAPP(c_Fun_Ocomp(_1557629, _1557629, _1557635, hAPP(_1557631, _1557637)), hAPP(c_Fun_Ocomp(_1557629, _1557629, _1557635, hAPP(_1557631, _1557639)), _1557641)) = hAPP(c_Fun_Ocomp(_1557629, _1557629, _1557635, hAPP(_1557631, _1557639)), hAPP(c_Fun_Ocomp(_1557629, _1557629, _1557635, hAPP(_1557631, _1557637)), _1557641)))], (2550 ^ _775212) ^ [_812585, _812587, _812589, _812591, _812593, _812595, _812597, _812599] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_812599, _812595, _812591, _812587) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_812597, _812593, _812589, _812585)), _812599 = _812597, _812595 = _812593, _812591 = _812589, _812587 = _812585], (24164 ^ _775212) ^ [_1194851, _1194853, _1194855] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194851), _1194853)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194853), _1194855)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194851), _1194855)))], (39219 ^ _775212) ^ [_1516905, _1516907, _1516909, _1516911] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1516905, _1516907), _1516909), _1516911) = hAPP(c_Set_OCollect(tc_prod(_1516907, _1516907)), hAPP(c_Product__Type_Oprod_Oprod__case(_1516907, _1516907, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1516907, tc_fun(tc_prod(_1516905, _1516905), tc_HOL_Obool), tc_fun(_1516907, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516907, tc_fun(tc_fun(tc_prod(_1516905, _1516905), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1516905, _1516905), tc_HOL_Obool), tc_fun(_1516907, tc_HOL_Obool)), _1516907), c_COMBC(_1516907, tc_fun(tc_prod(_1516905, _1516905), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516907, tc_prod(_1516905, _1516905)), tc_fun(_1516907, tc_fun(tc_fun(tc_prod(_1516905, _1516905), tc_HOL_Obool), tc_HOL_Obool)), _1516907), hAPP(c_COMBB(tc_prod(_1516905, _1516905), tc_fun(tc_fun(tc_prod(_1516905, _1516905), tc_HOL_Obool), tc_HOL_Obool), _1516907), c_member(tc_prod(_1516905, _1516905)))), hAPP(hAPP(c_COMBC(_1516907, tc_fun(_1516907, _1516905), tc_fun(_1516907, tc_prod(_1516905, _1516905))), hAPP(hAPP(c_COMBB(tc_fun(_1516905, tc_prod(_1516905, _1516905)), tc_fun(tc_fun(_1516907, _1516905), tc_fun(_1516907, tc_prod(_1516905, _1516905))), _1516907), c_COMBB(_1516905, tc_prod(_1516905, _1516905), _1516907)), hAPP(hAPP(c_COMBB(_1516905, tc_fun(_1516905, tc_prod(_1516905, _1516905)), _1516907), c_Product__Type_OPair(_1516905, _1516905)), _1516911))), _1516911)))), _1516909))))], (26130 ^ _775212) ^ [_1233138, _1233140, _1233142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233138)), 26133 ^ _775212 : [(26134 ^ _775212) ^ [_1233272] : [26136 ^ _775212 : [(26142 ^ _775212) ^ [] : [-(_1233272 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26138 ^ [_1233138, _1233140, _1233142, _1233272]), 26135 ^ [_1233138, _1233140, _1233142, _1233272]))], (26140 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26138 ^ [_1233138, _1233140, _1233142, _1233272]), _1233140)))], (26137 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26135 ^ [_1233138, _1233140, _1233142, _1233272]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1233138))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233272), _1233142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1233272), _1233138)), _1233142)))]]], (16125 ^ _775212) ^ [_1048412, _1048414] : [class_Groups_Oordered__ab__group__add__abs(_1048412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048412), hAPP(c_Groups_Oabs__class_Oabs(_1048412), _1048414)), c_Groups_Ozero__class_Ozero(_1048412)))], (42471 ^ _775212) ^ [_1599361, _1599363, _1599365, _1599367, _1599369, _1599371] : [hBOOL(hAPP(hAPP(c_member(_1599361), _1599363), _1599365)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599361, tc_fun(_1599367, tc_HOL_Obool)), _1599365), hAPP(hAPP(c_COMBB(tc_fun(_1599367, tc_HOL_Obool), tc_fun(_1599367, tc_HOL_Obool), _1599361), hAPP(c_Set_Oinsert(_1599367), _1599369)), _1599371)) = hAPP(hAPP(c_Set_Oinsert(_1599367), _1599369), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599361, tc_fun(_1599367, tc_HOL_Obool)), _1599365), _1599371)))], (49563 ^ _775212) ^ [_1767300, _1767302, _1767304] : [hBOOL(hAPP(c_List_Odistinct(_1767300), _1767302)), -(hBOOL(hAPP(c_List_Odistinct(_1767300), c_List_OdropWhile(_1767300, _1767304, _1767302))))], (52763 ^ _775212) ^ [_1829325, _1829327] : [hBOOL(_1829325), -(hBOOL(hAPP(hAPP(c_fimplies, _1829327), _1829325)))], (17265 ^ _775212) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (46069 ^ _775212) ^ [_1691294, _1691296, _1691298, _1691300, _1691302, _1691304, _1691306] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1691294, _1691294)), hAPP(hAPP(c_Product__Type_OPair(_1691294, _1691294), _1691296), _1691298)), _1691300)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691294), tc_List_Olist(_1691294))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691294), tc_List_Olist(_1691294)), hAPP(hAPP(c_List_Oappend(_1691294), _1691302), hAPP(hAPP(c_List_Olist_OCons(_1691294), _1691296), _1691304))), hAPP(hAPP(c_List_Oappend(_1691294), _1691302), hAPP(hAPP(c_List_Olist_OCons(_1691294), _1691298), _1691306)))), c_List_Olexord(_1691294, _1691300))))], (16573 ^ _775212) ^ [_1057237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1057237), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1057237) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1057237))], (2354 ^ _775212) ^ [_809513, _809515, _809517, _809519, _809521, _809523, _809525, _809527] : [-(c_Random_Oiterate(_809527, _809523, _809519, _809515) = c_Random_Oiterate(_809525, _809521, _809517, _809513)), _809527 = _809525, _809523 = _809521, _809519 = _809517, _809515 = _809513], (30542 ^ _775212) ^ [_1325564, _1325566, _1325568, _1325570] : [-(hBOOL(hAPP(hAPP(c_member(_1325564), _1325566), _1325568))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1325564, tc_Nat_Onat), _1325570), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325564, tc_HOL_Obool)), _1325568), hAPP(hAPP(c_Set_Oinsert(_1325564), _1325566), c_Orderings_Obot__class_Obot(tc_fun(_1325564, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1325564, tc_Nat_Onat), _1325570), _1325568))], (39574 ^ _775212) ^ [_1530014, _1530016, _1530018, _1530020] : [hBOOL(hAPP(hAPP(c_member(_1530014), _1530016), hAPP(c_Relation_ORange(_1530018, _1530014), _1530020))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530018, _1530014)), hAPP(hAPP(c_Product__Type_OPair(_1530018, _1530014), 39577 ^ [_1530014, _1530016, _1530018, _1530020]), _1530016)), _1530020)))], (35225 ^ _775212) ^ [_1424202, _1424204, _1424206, _1424208] : [class_Orderings_Oorder(_1424202), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424202, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1424202, _1424204, _1424206)), c_SetInterval_Oord__class_OatLeastAtMost(_1424202, _1424206, _1424208)) = c_Orderings_Obot__class_Obot(tc_fun(_1424202, tc_HOL_Obool)))], (43006 ^ _775212) ^ [_1613496, _1613498, _1613500] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613496, _1613496), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1613498)), _1613500) = hAPP(hAPP(c_Relation_Orel__comp(_1613496, _1613496, _1613496), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613496, _1613496), tc_HOL_Obool), _1613498), _1613500)), _1613500))], (18431 ^ _775212) ^ [_1088286, _1088288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088286), _1088288)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1088286)), c_Int_OBit1(_1088288))))], (44328 ^ _775212) ^ [_1646828, _1646830, _1646832, _1646834] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646828), tc_List_Olist(_1646828))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646828), tc_List_Olist(_1646828)), _1646830), _1646832)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1646828), tc_List_Olist(_1646828)), c_List_Olistrel1(_1646828, _1646834)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646828), tc_List_Olist(_1646828))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646828), tc_List_Olist(_1646828)), _1646830), _1646832)), c_List_Olistrel1(_1646828, hAPP(c_Relation_Oconverse(_1646828, _1646828), _1646834)))))], (5218 ^ _775212) ^ [_854787, _854789] : [_854789 = _854787, -(c_Groups_Ominus__class_Ominus(_854789) = c_Groups_Ominus__class_Ominus(_854787))], (49516 ^ _775212) ^ [_1766413, _1766415, _1766417, _1766419, _1766421] : [-(c_List_OdropWhile(_1766413, _1766415, hAPP(hAPP(c_List_Omap(_1766417, _1766413), _1766419), _1766421)) = hAPP(hAPP(c_List_Omap(_1766417, _1766413), _1766419), c_List_OdropWhile(_1766417, hAPP(c_Fun_Ocomp(_1766413, tc_HOL_Obool, _1766417, _1766415), _1766419), _1766421)))], (40600 ^ _775212) ^ [_1555712, _1555714, _1555716, _1555718, _1555720] : [class_Groups_Ocomm__monoid__add(_1555712), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555714), _1555716)), c_Fun_Oinj__on(_1555714, _1555714, _1555718, _1555716), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1555714, _1555712), _1555720), hAPP(c_Set_Oimage(_1555714, _1555714, _1555718), _1555716)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1555714, _1555712), hAPP(c_Fun_Ocomp(_1555714, _1555712, _1555714, _1555720), _1555718)), _1555716))], (31039 ^ _775212) ^ [_1335979, _1335981, _1335983, _1335985] : [hBOOL(hAPP(hAPP(c_member(_1335979), _1335981), c_SetInterval_Oord_OatLeast(_1335979, _1335983, _1335985))), -(hBOOL(hAPP(hAPP(_1335983, _1335985), _1335981)))], (52305 ^ _775212) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (16495 ^ _775212) ^ [_1055879, _1055881] : [class_Groups_Oordered__ab__group__add__abs(_1055879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055879), _1055881), c_Groups_Ozero__class_Ozero(_1055879))), -(hAPP(c_Groups_Oabs__class_Oabs(_1055879), _1055881) = hAPP(c_Groups_Ouminus__class_Ouminus(_1055879), _1055881))], (35329 ^ _775212) ^ [_1426576, _1426578, _1426580] : [class_Lattices_Oboolean__algebra(_1426576), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426576), _1426578), _1426580) = c_Orderings_Obot__class_Obot(_1426576), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1426576), _1426578), _1426580) = c_Orderings_Otop__class_Otop(_1426576), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1426576), _1426578) = _1426580)], (46492 ^ _775212) ^ [_1701601, _1701603, _1701605] : [hBOOL(hAPP(c_List_Odistinct(_1701601), _1701603)), -(hBOOL(hAPP(c_List_Odistinct(_1701601), hAPP(hAPP(c_List_Otake(_1701601), _1701605), _1701603))))], (6293 ^ _775212) ^ [_874570] : [_874570 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874570), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (27305 ^ _775212) ^ [_1256229, _1256231, _1256233] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256229, tc_HOL_Obool)), _1256231), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256229, tc_HOL_Obool)), _1256231), _1256233))))], (45860 ^ _775212) ^ [_1686251, _1686253, _1686255, _1686257, _1686259, _1686261] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1686251, _1686253), hAPP(hAPP(c_List_Ozip(_1686251, _1686253), _1686255), _1686257)), _1686259), _1686261) = hAPP(hAPP(c_List_Ozip(_1686251, _1686253), hAPP(hAPP(c_List_Olist__update(_1686251, _1686255), _1686259), hAPP(c_Product__Type_Ofst(_1686251, _1686253), _1686261))), hAPP(hAPP(c_List_Olist__update(_1686253, _1686257), _1686259), hAPP(c_Product__Type_Osnd(_1686251, _1686253), _1686261))))], (16289 ^ _775212) ^ [_1051437, _1051439, _1051441] : [class_Rings_Olinordered__idom(_1051437), -(hAPP(c_Groups_Oabs__class_Oabs(_1051437), hAPP(hAPP(c_Power_Opower__class_Opower(_1051437), hAPP(c_Groups_Ouminus__class_Ouminus(_1051437), _1051439)), _1051441)) = hAPP(c_Groups_Oabs__class_Oabs(_1051437), hAPP(hAPP(c_Power_Opower__class_Opower(_1051437), _1051439), _1051441)))], (14661 ^ _775212) ^ [_1020613, _1020615, _1020617] : [class_Groups_Ogroup__add(_1020613), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1020613), _1020615), hAPP(c_Groups_Ouminus__class_Ouminus(_1020613), _1020617)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020613), _1020615), _1020617))], (48299 ^ _775212) ^ [_1740823, _1740825] : [-(c_List_Otranspose(_1740823, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1740823)), c_List_Olist_ONil(_1740823)), _1740825)) = c_List_Otranspose(_1740823, _1740825))], (5026 ^ _775212) ^ [_851809, _851811] : [_851811 = _851809, -(c_Groups_Ozero__class_Ozero(_851811) = c_Groups_Ozero__class_Ozero(_851809))], (34309 ^ _775212) ^ [_1403971, _1403973, _1403975, _1403977, _1403979] : [c_Equiv__Relations_Oequiv(_1403971, _1403973, _1403975), 34312 ^ _775212 : [(34323 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1403971, _1403971)), hAPP(hAPP(c_Product__Type_OPair(_1403971, _1403971), _1403977), _1403979)), _1403975))), hAPP(c_Relation_OImage(_1403971, _1403971, _1403975), hAPP(hAPP(c_Set_Oinsert(_1403971), _1403977), c_Orderings_Obot__class_Obot(tc_fun(_1403971, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1403971, _1403971, _1403975), hAPP(hAPP(c_Set_Oinsert(_1403971), _1403979), c_Orderings_Obot__class_Obot(tc_fun(_1403971, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1403971), _1403977), _1403973)), hBOOL(hAPP(hAPP(c_member(_1403971), _1403979), _1403973))], (34313 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1403971, _1403971)), hAPP(hAPP(c_Product__Type_OPair(_1403971, _1403971), _1403977), _1403979)), _1403975)), 34316 ^ _775212 : [(34321 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403971), _1403979), _1403973)))], (34319 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403971), _1403977), _1403973)))], (34317 ^ _775212) ^ [] : [-(hAPP(c_Relation_OImage(_1403971, _1403971, _1403975), hAPP(hAPP(c_Set_Oinsert(_1403971), _1403977), c_Orderings_Obot__class_Obot(tc_fun(_1403971, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1403971, _1403971, _1403975), hAPP(hAPP(c_Set_Oinsert(_1403971), _1403979), c_Orderings_Obot__class_Obot(tc_fun(_1403971, tc_HOL_Obool)))))]]]]], (17345 ^ _775212) ^ [_1069954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1069954), 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), _1069954)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20225 ^ _775212) ^ [_1120206, _1120208, _1120210, _1120212] : [class_Fields_Ofield__inverse__zero(_1120206), class_Int_Onumber(_1120206), 20232 ^ _775212 : [(20233 ^ _775212) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120206), _1120208), _1120210) = hAPP(c_Int_Onumber__class_Onumber__of(_1120206), _1120212), 20236 ^ _775212 : [(20243 ^ _775212) ^ [] : [_1120210 = c_Groups_Ozero__class_Ozero(_1120206), -(hAPP(c_Int_Onumber__class_Onumber__of(_1120206), _1120212) = c_Groups_Ozero__class_Ozero(_1120206))], (20237 ^ _775212) ^ [] : [-(_1120210 = c_Groups_Ozero__class_Ozero(_1120206)), -(_1120208 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120206), hAPP(c_Int_Onumber__class_Onumber__of(_1120206), _1120212)), _1120210))]]], (20249 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120206), _1120208), _1120210) = hAPP(c_Int_Onumber__class_Onumber__of(_1120206), _1120212)), 20252 ^ _775212 : [(20255 ^ _775212) ^ [] : [_1120208 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120206), hAPP(c_Int_Onumber__class_Onumber__of(_1120206), _1120212)), _1120210)], (20253 ^ _775212) ^ [] : [_1120210 = c_Groups_Ozero__class_Ozero(_1120206)]], 20256 ^ _775212 : [(20259 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1120206), _1120212) = c_Groups_Ozero__class_Ozero(_1120206)], (20257 ^ _775212) ^ [] : [-(_1120210 = c_Groups_Ozero__class_Ozero(_1120206))]]]]], (46782 ^ _775212) ^ [_1707703, _1707705, _1707707] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707703)), hAPP(c_List_Orotate(_1707703, _1707705), _1707707)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707703)), _1707707))], (41981 ^ _775212) ^ [_1586105, _1586107, _1586109, _1586111, _1586113] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586105, _1586105)), hAPP(hAPP(c_Product__Type_OPair(_1586105, _1586105), _1586107), _1586109)), c_Transitive__Closure_Otrancl(_1586105, _1586111))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586105, _1586105)), hAPP(hAPP(c_Product__Type_OPair(_1586105, _1586105), _1586109), _1586113)), c_Transitive__Closure_Ortrancl(_1586105, _1586111))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586105, _1586105)), hAPP(hAPP(c_Product__Type_OPair(_1586105, _1586105), _1586107), _1586113)), c_Transitive__Closure_Otrancl(_1586105, _1586111))))], (45236 ^ _775212) ^ [_1670812, _1670814, _1670816] : [-(hAPP(hAPP(c_List_Otake(_1670812), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1670812), _1670814), _1670816)) = hAPP(hAPP(c_List_Olist_OCons(_1670812), _1670814), c_List_Olist_ONil(_1670812)))], (34877 ^ _775212) ^ [_1415745, _1415747, _1415749] : [class_Lattices_Osemilattice__inf(_1415745), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415745), _1415747), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415745), _1415747), _1415749)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415745), _1415747), _1415749))], (43400 ^ _775212) ^ [_1622917, _1622919, _1622921, _1622923] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1622917, _1622919), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1622917, tc_HOL_Obool), _1622921)), _1622923) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1622917, tc_HOL_Obool), tc_fun(tc_prod(_1622917, _1622919), tc_HOL_Obool)), _1622921), hAPP(hAPP(c_COMBC(tc_fun(_1622917, tc_HOL_Obool), tc_fun(_1622917, tc_fun(_1622919, tc_HOL_Obool)), tc_fun(tc_prod(_1622917, _1622919), tc_HOL_Obool)), c_Product__Type_OSigma(_1622917, _1622919)), _1622923)))], (4744 ^ _775212) ^ [_847510, _847512] : [_847512 = _847510, -(c_List_Orev(_847512) = c_List_Orev(_847510))], (33602 ^ _775212) ^ [_1387526, _1387528] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1387526, _1387526)), _1387528)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1387526), hAPP(c_Relation_OField(_1387526), _1387528))))], (43902 ^ _775212) ^ [_1635007, _1635009] : [-(c_Wellfounded_Owf(_1635007, _1635009)), 43905 ^ _775212 : [(43908 ^ _775212) ^ [_1635227] : [hBOOL(hAPP(hAPP(c_member(_1635007), _1635227), 43903 ^ [_1635007, _1635009])), 43912 ^ _775212 : [(43915 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1635007), 43911 ^ [_1635007, _1635009, _1635227]), 43903 ^ [_1635007, _1635009])))], (43913 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635007, _1635007)), hAPP(hAPP(c_Product__Type_OPair(_1635007, _1635007), 43911 ^ [_1635007, _1635009, _1635227]), _1635227)), _1635009)))]]], (43906 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1635007), 43904 ^ [_1635007, _1635009]), 43903 ^ [_1635007, _1635009])))]]], (9607 ^ _775212) ^ [_930336, _930338] : [class_Groups_Omonoid__mult(_930336), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930336), c_Groups_Oone__class_Oone(_930336)), _930338) = _930338)], (22144 ^ _775212) ^ [_1155542, _1155544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1155542)), _1155544)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1155542), _1155544)))], (13334 ^ _775212) ^ [_996509, _996511, _996513] : [_996509 = 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), _996509), _996511)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996509), _996513)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50695 ^ _775212) ^ [_1791916, _1791918] : [-(c_List_Oconcat(_1791916, c_List_Oreplicate(tc_List_Olist(_1791916), _1791918, c_List_Olist_ONil(_1791916))) = c_List_Olist_ONil(_1791916))], (52311 ^ _775212) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (31009 ^ _775212) ^ [_1335359, _1335361, _1335363, _1335365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1335365, _1335361)), hAPP(_1335365, _1335363))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1335359, _1335359)), hAPP(hAPP(c_Product__Type_OPair(_1335359, _1335359), _1335361), _1335363)), hAPP(c_Wellfounded_Omeasure(_1335359), _1335365))))], (21419 ^ _775212) ^ [_1142271] : [-(_1142271 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1142271), 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)))))], (1804 ^ _775212) ^ [_800618, _800620] : [-(class_Rings_Omult__zero(_800618)), _800620 = _800618, class_Rings_Omult__zero(_800620)], (41060 ^ _775212) ^ [_1566291, _1566293, _1566295, _1566297] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1566291, tc_HOL_Obool), tc_fun(_1566291, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1566291, tc_HOL_Obool), tc_fun(_1566291, tc_HOL_Obool)), _1566293), _1566295)), c_Wellfounded_Omax__ext(_1566291, _1566297)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566291), _1566293)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566291), _1566295)), -(_1566295 = c_Orderings_Obot__class_Obot(tc_fun(_1566291, tc_HOL_Obool))), 41074 ^ _775212 : [(41077 ^ _775212) ^ [_1566696] : [hBOOL(hAPP(hAPP(c_member(_1566291), _1566696), _1566295)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1566291, _1566291)), hAPP(hAPP(c_Product__Type_OPair(_1566291, _1566291), 41073 ^ [_1566291, _1566293, _1566295, _1566297]), _1566696)), _1566297))], (41075 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566291), 41073 ^ [_1566291, _1566293, _1566295, _1566297]), _1566293)))]]], (23816 ^ _775212) ^ [_1189135] : [-(c_Code__Numeral_OSuc__code__numeral(_1189135) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1189135))))], (4648 ^ _775212) ^ [_846060, _846062] : [_846062 = _846060, -(c_Lazy__Sequence_Osingle(_846062) = c_Lazy__Sequence_Osingle(_846060))], (2322 ^ _775212) ^ [_809045, _809047] : [_809047 = _809045, -(c_Nitpick_Ozero__frac(_809047) = c_Nitpick_Ozero__frac(_809045))], (20149 ^ _775212) ^ [_1119001, _1119003, _1119005, _1119007] : [class_Fields_Ofield__inverse__zero(_1119001), class_Int_Onumber(_1119001), 20156 ^ _775212 : [(20157 ^ _775212) ^ [] : [_1119003 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119001), _1119005), hAPP(c_Int_Onumber__class_Onumber__of(_1119001), _1119007)), 20160 ^ _775212 : [(20167 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1119001), _1119007) = c_Groups_Ozero__class_Ozero(_1119001), -(_1119003 = c_Groups_Ozero__class_Ozero(_1119001))], (20161 ^ _775212) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1119001), _1119007) = c_Groups_Ozero__class_Ozero(_1119001)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119001), _1119003), hAPP(c_Int_Onumber__class_Onumber__of(_1119001), _1119007)) = _1119005)]]], (20173 ^ _775212) ^ [] : [-(_1119003 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119001), _1119005), hAPP(c_Int_Onumber__class_Onumber__of(_1119001), _1119007))), 20176 ^ _775212 : [(20179 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119001), _1119003), hAPP(c_Int_Onumber__class_Onumber__of(_1119001), _1119007)) = _1119005], (20177 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1119001), _1119007) = c_Groups_Ozero__class_Ozero(_1119001)]], 20180 ^ _775212 : [(20183 ^ _775212) ^ [] : [_1119003 = c_Groups_Ozero__class_Ozero(_1119001)], (20181 ^ _775212) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1119001), _1119007) = c_Groups_Ozero__class_Ozero(_1119001))]]]]], (51401 ^ _775212) ^ [_1807364, _1807366] : [c_Relation_Otrans(_1807364, _1807366), 51404 ^ _775212 : [(51405 ^ _775212) ^ [_1807500, _1807502] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1807364, _1807364)), hAPP(hAPP(c_Product__Type_OPair(_1807364, _1807364), _1807502), _1807500)), _1807366)), 51408 ^ _775212 : [(51409 ^ _775212) ^ [_1807643] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1807364, _1807364)), hAPP(hAPP(c_Product__Type_OPair(_1807364, _1807364), _1807500), _1807643)), _1807366)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1807364, _1807364)), hAPP(hAPP(c_Product__Type_OPair(_1807364, _1807364), _1807502), _1807643)), _1807366)))]]]]], (8039 ^ _775212) ^ [_904321, _904323, _904325, _904327, _904329] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_904321), 8042 ^ _775212 : [(8043 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904321), _904323), _904325)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904321), _904327), _904329)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904321), _904323), _904329)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904321), _904327), _904325)), -(_904323 = _904327), -(_904325 = _904329)], (8053 ^ _775212) ^ [] : [8054 ^ _775212 : [(8057 ^ _775212) ^ [] : [_904325 = _904329], (8055 ^ _775212) ^ [] : [_904323 = _904327]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904321), _904323), _904325)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904321), _904327), _904329)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904321), _904323), _904329)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904321), _904327), _904325)))]]], (45190 ^ _775212) ^ [_1669961, _1669963, _1669965] : [-(hAPP(hAPP(c_List_Ozip(_1669961, _1669963), c_List_Olist_ONil(_1669961)), _1669965) = c_List_Olist_ONil(tc_prod(_1669961, _1669963)))], (6216 ^ _775212) ^ [_873379, _873381] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873379), _873381))), 6219 ^ _775212 : [(6226 ^ _775212) ^ [] : [_873379 = _873381, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873379), hAPP(c_Nat_OSuc, _873381))))], (6220 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873379), hAPP(c_Nat_OSuc, _873381))), -(_873379 = _873381)]]], (48135 ^ _775212) ^ [_1736444, _1736446, _1736448] : [-(c_List_Oconcat(_1736444, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1736444)), _1736446), _1736448)) = hAPP(hAPP(c_List_Oappend(_1736444), c_List_Oconcat(_1736444, _1736446)), c_List_Oconcat(_1736444, _1736448)))], (37447 ^ _775212) ^ [_1472612, _1472614, _1472616, _1472618, _1472620] : [-(hAPP(c_Set_Ovimage(_1472612, _1472614, _1472616), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472614, tc_HOL_Obool)), _1472618), _1472620)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472612, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1472612, _1472614, _1472616), _1472618)), hAPP(c_Set_Ovimage(_1472612, _1472614, _1472616), _1472620)))], (26901 ^ _775212) ^ [_1248223, _1248225, _1248227, _1248229] : [26902 ^ _775212 : [(26905 ^ _775212) ^ [] : [hBOOL(hAPP(_1248227, _1248225))], (26903 ^ _775212) ^ [] : [hBOOL(hAPP(_1248223, _1248225))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248229, tc_HOL_Obool)), _1248227), _1248223), _1248225)))], (12129 ^ _775212) ^ [_974612, _974614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974612), _974614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974612)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974614))))], (47248 ^ _775212) ^ [_1717101, _1717103, _1717105, _1717107] : [-(c_List_Oremove1(_1717101, _1717103, c_List_Oremove1(_1717101, _1717105, _1717107)) = c_List_Oremove1(_1717101, _1717105, c_List_Oremove1(_1717101, _1717103, _1717107)))], (45492 ^ _775212) ^ [_1678336, _1678338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678336), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1678338))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1678338), _1678336)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1678338))))], (8033 ^ _775212) ^ [] : [-(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))], (37120 ^ _775212) ^ [_1465868, _1465870, _1465872, _1465874, _1465876, _1465878] : [class_Groups_Oab__semigroup__mult(_1465868), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465870), _1465872)), -(hBOOL(hAPP(hAPP(c_member(_1465870), _1465874), _1465872))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1465868, _1465870, c_Groups_Otimes__class_Otimes(_1465868)), _1465876), _1465878), hAPP(hAPP(c_Set_Oinsert(_1465870), _1465874), _1465872)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1465868), hAPP(_1465876, _1465874)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1465868, _1465870, c_Groups_Otimes__class_Otimes(_1465868)), _1465876), _1465878), _1465872)))], (37924 ^ _775212) ^ [_1485019, _1485021, _1485023, _1485025] : [-(hAPP(c_Set_Oimage(tc_prod(_1485019, _1485021), tc_prod(_1485021, _1485019), hAPP(c_Product__Type_Oprod_Oprod__case(_1485019, _1485021, tc_prod(_1485021, _1485019)), hAPP(c_COMBC(_1485021, _1485019, tc_prod(_1485021, _1485019)), c_Product__Type_OPair(_1485021, _1485019)))), hAPP(hAPP(c_Product__Type_OSigma(_1485019, _1485021), _1485023), hAPP(c_COMBK(tc_fun(_1485021, tc_HOL_Obool), _1485019), _1485025))) = hAPP(hAPP(c_Product__Type_OSigma(_1485021, _1485019), _1485025), hAPP(c_COMBK(tc_fun(_1485019, tc_HOL_Obool), _1485021), _1485023)))], (46512 ^ _775212) ^ [_1701920, _1701922] : [hBOOL(hAPP(c_List_Odistinct(_1701920), hAPP(c_List_Orotate1(_1701920), _1701922))), -(hBOOL(hAPP(c_List_Odistinct(_1701920), _1701922)))], (35463 ^ _775212) ^ [_1429774, _1429776, _1429778, _1429780, _1429782] : [c_Finite__Set_Ofolding__one(_1429774, _1429776, _1429778), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429774), _1429780)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429774), _1429782)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429774, tc_HOL_Obool)), _1429780), _1429782) = c_Orderings_Obot__class_Obot(tc_fun(_1429774, tc_HOL_Obool))), -(hAPP(hAPP(_1429776, hAPP(_1429778, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1429774, tc_HOL_Obool)), _1429780), _1429782))), hAPP(_1429778, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429774, tc_HOL_Obool)), _1429780), _1429782))) = hAPP(hAPP(_1429776, hAPP(_1429778, _1429780)), hAPP(_1429778, _1429782)))], (14667 ^ _775212) ^ [_1020732, _1020734, _1020736] : [class_Groups_Oab__group__add(_1020732), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1020732), _1020734), _1020736) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020732), _1020734), hAPP(c_Groups_Ouminus__class_Ouminus(_1020732), _1020736)))], (5967 ^ _775212) ^ [_869774, _869776] : [class_Groups_Ozero(_869774), 5970 ^ _775212 : [(5977 ^ _775212) ^ [] : [_869776 = c_Groups_Ozero__class_Ozero(_869774), -(c_Groups_Ozero__class_Ozero(_869774) = _869776)], (5971 ^ _775212) ^ [] : [c_Groups_Ozero__class_Ozero(_869774) = _869776, -(_869776 = c_Groups_Ozero__class_Ozero(_869774))]]], (11826 ^ _775212) ^ [_969243, _969245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969243), _969245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969243), _969245)))], (47571 ^ _775212) ^ [_1724313, _1724315, _1724317, _1724319, _1724321] : [class_Orderings_Olinorder(_1724313), -(hBOOL(hAPP(hAPP(c_member(_1724313), hAPP(_1724315, _1724317)), hAPP(c_Set_Oimage(_1724319, _1724313, _1724315), hAPP(c_List_Oset(_1724319), _1724321))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1724319, _1724313, _1724315, _1724317, _1724321) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1724319, _1724313, _1724315), _1724317), _1724321))], (11260 ^ _775212) ^ [_960123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _960123)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_960123 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14917 ^ _775212) ^ [_1025138, _1025140] : [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), _1025138), _1025140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025140), _1025138)))], (47953 ^ _775212) ^ [_1732941, _1732943] : [c_List_Oremdups(_1732941, _1732943) = _1732943, -(hBOOL(hAPP(c_List_Odistinct(_1732941), _1732943)))], (35099 ^ _775212) ^ [_1421330, _1421332, _1421334, _1421336] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421330, tc_HOL_Obool)), _1421332), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421330, tc_HOL_Obool)), _1421334), _1421336)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421330, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421330, tc_HOL_Obool)), _1421332), _1421334)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421330, tc_HOL_Obool)), _1421332), _1421336)))], (46011 ^ _775212) ^ [_1689906, _1689908, _1689910, _1689912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1689906), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689908)), _1689910))), 46014 ^ _775212 : [(46021 ^ _775212) ^ [] : [hAPP(hAPP(c_List_Onth(_1689908), _1689910), _1689906) = _1689912, -(hAPP(hAPP(c_List_Olist__update(_1689908, _1689910), _1689906), _1689912) = _1689910)], (46015 ^ _775212) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1689908, _1689910), _1689906), _1689912) = _1689910, -(hAPP(hAPP(c_List_Onth(_1689908), _1689910), _1689906) = _1689912)]]], (3332 ^ _775212) ^ [_825376, _825378, _825380, _825382, _825384, _825386, _825388, _825390] : [-(c_Product__Type_Oapsnd(_825390, _825386, _825382, _825378) = c_Product__Type_Oapsnd(_825388, _825384, _825380, _825376)), _825390 = _825388, _825386 = _825384, _825382 = _825380, _825378 = _825376], (37417 ^ _775212) ^ [_1471878, _1471880, _1471882] : [-(hAPP(c_Set_Ovimage(_1471878, _1471880, _1471882), c_Orderings_Obot__class_Obot(tc_fun(_1471880, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1471878, tc_HOL_Obool)))], (50338 ^ _775212) ^ [_1784613, _1784615, _1784617] : [c_List_Olist__ex(_1784613, _1784615, hAPP(c_List_Orev(_1784613), _1784617)), -(c_List_Olist__ex(_1784613, _1784615, _1784617))], (51779 ^ _775212) ^ [_1816171] : [-(c_Relation_Osym(_1816171, c_Relation_OId(_1816171)))], (44154 ^ _775212) ^ [_1641420, _1641422, _1641424, _1641426, _1641428] : [hAPP(hAPP(c_List_Olist_OCons(_1641420), _1641422), _1641424) = hAPP(hAPP(c_List_Olist_OCons(_1641420), _1641426), _1641428), 44157 ^ _775212 : [(44160 ^ _775212) ^ [] : [-(_1641424 = _1641428)], (44158 ^ _775212) ^ [] : [-(_1641422 = _1641426)]]], (49151 ^ _775212) ^ [_1758536, _1758538, _1758540] : [_1758540 = hAPP(hAPP(c_List_Olist_OCons(_1758536), _1758538), c_List_Olist_ONil(_1758536)), -(hAPP(hAPP(c_List_Olist_OCons(_1758536), _1758538), c_List_Olist_ONil(_1758536)) = hAPP(c_List_Orev(_1758536), _1758540))], (20263 ^ _775212) ^ [_1120801, _1120803, _1120805, _1120807] : [class_Fields_Ofield__inverse__zero(_1120801), class_Int_Onumber(_1120801), 20270 ^ _775212 : [(20271 ^ _775212) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120801), _1120803), hAPP(c_Int_Onumber__class_Onumber__of(_1120801), _1120805)) = _1120807, 20274 ^ _775212 : [(20281 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1120801), _1120805) = c_Groups_Ozero__class_Ozero(_1120801), -(_1120807 = c_Groups_Ozero__class_Ozero(_1120801))], (20275 ^ _775212) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1120801), _1120805) = c_Groups_Ozero__class_Ozero(_1120801)), -(_1120803 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120801), _1120807), hAPP(c_Int_Onumber__class_Onumber__of(_1120801), _1120805)))]]], (20287 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120801), _1120803), hAPP(c_Int_Onumber__class_Onumber__of(_1120801), _1120805)) = _1120807), 20290 ^ _775212 : [(20293 ^ _775212) ^ [] : [_1120803 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120801), _1120807), hAPP(c_Int_Onumber__class_Onumber__of(_1120801), _1120805))], (20291 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1120801), _1120805) = c_Groups_Ozero__class_Ozero(_1120801)]], 20294 ^ _775212 : [(20297 ^ _775212) ^ [] : [_1120807 = c_Groups_Ozero__class_Ozero(_1120801)], (20295 ^ _775212) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1120801), _1120805) = c_Groups_Ozero__class_Ozero(_1120801))]]]]], (21961 ^ _775212) ^ [_1152005] : [c_Code__Numeral_OSuc__code__numeral(_1152005) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (35297 ^ _775212) ^ [_1425862, _1425864, _1425866] : [class_Orderings_Oorder(_1425862), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425862, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1425862), _1425864)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1425862, _1425864, _1425866)) = c_Orderings_Obot__class_Obot(tc_fun(_1425862, tc_HOL_Obool)))], (23734 ^ _775212) ^ [_1187705, _1187707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1187705), _1187707)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1187705)), hAPP(c_Code__Numeral_Oof__nat, _1187707))))], (33435 ^ _775212) ^ [_1382580, _1382582, _1382584, _1382586, _1382588, _1382590] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1382580, tc_HOL_Obool), tc_fun(_1382580, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1382580, tc_HOL_Obool), tc_fun(_1382580, tc_HOL_Obool)), _1382582), _1382584)), c_Wellfounded_Omax__ext(_1382580, _1382586))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1382580, tc_HOL_Obool), tc_fun(_1382580, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1382580, tc_HOL_Obool), tc_fun(_1382580, tc_HOL_Obool)), _1382588), _1382590)), c_Wellfounded_Omax__ext(_1382580, _1382586))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1382580, tc_HOL_Obool), tc_fun(_1382580, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1382580, tc_HOL_Obool), tc_fun(_1382580, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1382580, tc_HOL_Obool)), _1382582), _1382588)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1382580, tc_HOL_Obool)), _1382584), _1382590))), c_Wellfounded_Omax__ext(_1382580, _1382586))))], (15775 ^ _775212) ^ [_1042268, _1042270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1042268)), 15778 ^ _775212 : [(15785 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042270), _1042268))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1042270), _1042268) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042270), _1042268)), _1042268)))], (15779 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042270), _1042268)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1042270), _1042268) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (37473 ^ _775212) ^ [_1473348, _1473350, _1473352, _1473354] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1473348), hAPP(c_Set_Ovimage(_1473348, _1473350, _1473352), _1473354))), hAPP(c_Set_Oimage(_1473348, _1473350, _1473352), c_Orderings_Otop__class_Otop(tc_fun(_1473348, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1473350, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1473350), _1473354)))], (14317 ^ _775212) ^ [_1013971, _1013973, _1013975, _1013977] : [class_Groups_Ocomm__monoid__mult(_1013971), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1013971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013971), _1013973), _1013975)), _1013977) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013971), hAPP(hAPP(c_Power_Opower__class_Opower(_1013971), _1013973), _1013977)), hAPP(hAPP(c_Power_Opower__class_Opower(_1013971), _1013975), _1013977)))], (44236 ^ _775212) ^ [_1643892, _1643894, _1643896, _1643898, _1643900, _1643902] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643892), tc_List_Olist(_1643892))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643892), tc_List_Olist(_1643892)), hAPP(hAPP(c_List_Olist_OCons(_1643892), _1643894), _1643896)), hAPP(hAPP(c_List_Olist_OCons(_1643892), _1643898), _1643900))), c_List_Olexord(_1643892, _1643902)))), 44237 ^ _775212 : [(44240 ^ _775212) ^ [] : [_1643894 = _1643898, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643892), tc_List_Olist(_1643892))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643892), tc_List_Olist(_1643892)), _1643896), _1643900)), c_List_Olexord(_1643892, _1643902)))], (44238 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1643892, _1643892)), hAPP(hAPP(c_Product__Type_OPair(_1643892, _1643892), _1643894), _1643898)), _1643902))]]], (2880 ^ _775212) ^ [_818148, _818150, _818152, _818154, _818156, _818158, _818160, _818162] : [-(c_New__Random__Sequence_Opos__empty(_818162, _818158, _818154, _818150) = c_New__Random__Sequence_Opos__empty(_818160, _818156, _818152, _818148)), _818162 = _818160, _818158 = _818156, _818154 = _818152, _818150 = _818148], (16867 ^ _775212) ^ [_1062763, _1062765] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062763))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062763), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062765)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11640 ^ _775212) ^ [_966385, _966387, _966389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966385), _966387)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966387), _966389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966385), _966389)))], (32856 ^ _775212) ^ [_1371088, _1371090, _1371092, _1371094, _1371096, _1371098] : [-(_1371088 = _1371090), -(hAPP(c_Fun_Ofun__upd(_1371092, _1371094, _1371096, _1371090, _1371098), _1371088) = hAPP(_1371096, _1371088))], (47332 ^ _775212) ^ [_1718709, _1718711, _1718713, _1718715, _1718717] : [c_List_Opartition(_1718709, _1718711, _1718713) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1718709), tc_List_Olist(_1718709)), _1718715), _1718717), 47335 ^ _775212 : [(47342 ^ _775212) ^ [_1718971] : [hBOOL(hAPP(hAPP(c_member(_1718709), _1718971), hAPP(c_List_Oset(_1718709), _1718717))), hBOOL(hAPP(_1718711, _1718971))], (47336 ^ _775212) ^ [_1718862] : [hBOOL(hAPP(hAPP(c_member(_1718709), _1718862), hAPP(c_List_Oset(_1718709), _1718715))), -(hBOOL(hAPP(_1718711, _1718862)))]]], (49091 ^ _775212) ^ [_1757280, _1757282, _1757284, _1757286] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1757280), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1757280))), _1757282))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757284), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1757280))), c_List_Otranspose(_1757280, _1757282)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757286), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1757280))), hAPP(c_List_Ofilter(tc_List_Olist(_1757280), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1757280)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757284)), c_Nat_Osize__class_Osize(tc_List_Olist(_1757280)))), _1757282)))), -(hAPP(hAPP(c_List_Onth(_1757280), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1757280)), c_List_Otranspose(_1757280, _1757282)), _1757284)), _1757286) = hAPP(hAPP(c_List_Onth(_1757280), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1757280)), _1757282), _1757286)), _1757284))], (34383 ^ _775212) ^ [_1405736, _1405738, _1405740, _1405742, _1405744, _1405746] : [c_Equiv__Relations_Oequiv(_1405736, _1405738, _1405740), hBOOL(hAPP(hAPP(c_member(_1405736), _1405742), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1405736, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1405736, _1405736, _1405740), hAPP(hAPP(c_Set_Oinsert(_1405736), _1405744), c_Orderings_Obot__class_Obot(tc_fun(_1405736, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1405736, _1405736, _1405740), hAPP(hAPP(c_Set_Oinsert(_1405736), _1405746), c_Orderings_Obot__class_Obot(tc_fun(_1405736, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1405736, _1405736)), hAPP(hAPP(c_Product__Type_OPair(_1405736, _1405736), _1405744), _1405746)), _1405740)))], (2 ^ _775212) ^ [_775239] : [-(_775239 = _775239)], (36921 ^ _775212) ^ [_1461307, _1461309, _1461311, _1461313, _1461315] : [-(c_Fun_Oinj__on(_1461307, _1461309, _1461311, hAPP(hAPP(c_Set_Oinsert(_1461307), _1461313), _1461315))), c_Fun_Oinj__on(_1461307, _1461309, _1461311, _1461315), -(hBOOL(hAPP(hAPP(c_member(_1461309), hAPP(_1461311, _1461313)), hAPP(c_Set_Oimage(_1461307, _1461309, _1461311), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1461307, tc_HOL_Obool)), _1461315), hAPP(hAPP(c_Set_Oinsert(_1461307), _1461313), c_Orderings_Obot__class_Obot(tc_fun(_1461307, tc_HOL_Obool))))))))], (14515 ^ _775212) ^ [_1017721, _1017723, _1017725] : [-(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, _1017721, _1017723)), _1017725), _1017723) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1017721), _1017725), _1017723))], (52667 ^ _775212) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (25799 ^ _775212) ^ [_1226309, _1226311, _1226313, _1226315, _1226317] : [class_Orderings_Oorder(_1226309), 25802 ^ _775212 : [(25815 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1226309, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1226309, _1226311, _1226313)), c_SetInterval_Oord__class_OatLeastAtMost(_1226309, _1226315, _1226317)))), 25816 ^ _775212 : [(25819 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226309), _1226315), _1226311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226309), _1226313), _1226317))], (25817 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226309), _1226311), _1226313)))]]], (25803 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1226309, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1226309, _1226311, _1226313)), c_SetInterval_Oord__class_OatLeastAtMost(_1226309, _1226315, _1226317))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226309), _1226311), _1226313)), 25810 ^ _775212 : [(25813 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226309), _1226313), _1226317)))], (25811 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226309), _1226315), _1226311)))]]]]], (30372 ^ _775212) ^ [_1321943, _1321945, _1321947, _1321949, _1321951] : [hBOOL(hAPP(hAPP(c_member(_1321943), _1321945), _1321947)), -(hAPP(c_Set_Oimage(_1321943, _1321949, hAPP(c_COMBK(_1321949, _1321943), _1321951)), _1321947) = hAPP(hAPP(c_Set_Oinsert(_1321949), _1321951), c_Orderings_Obot__class_Obot(tc_fun(_1321949, tc_HOL_Obool))))], (25955 ^ _775212) ^ [_1229541, _1229543, _1229545] : [class_Groups_Ocomm__monoid__add(_1229541), hAPP(_1229543, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1229541), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1229541), _1229543), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1229545)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1229541), _1229543), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1229545)))], (10459 ^ _775212) ^ [_945777, _945779, _945781, _945783, _945785] : [class_Groups_Oordered__cancel__ab__semigroup__add(_945777), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945777), _945779), _945781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945777), _945783), _945785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945777), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945777), _945779), _945783)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945777), _945781), _945785))))], (8559 ^ _775212) ^ [_913977, _913979] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913977)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913979), 8562 ^ _775212 : [(8565 ^ _775212) ^ [] : [-(_913979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8563 ^ _775212) ^ [] : [-(_913977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (50435 ^ _775212) ^ [_1786550, _1786552, _1786554] : [-(hBOOL(hAPP(hAPP(c_member(_1786550), _1786552), hAPP(c_List_Oset(_1786550), _1786554)))), 50436 ^ _775212 : [(50437 ^ _775212) ^ [_1786639, _1786641] : [_1786554 = hAPP(hAPP(c_List_Oappend(_1786550), _1786641), hAPP(hAPP(c_List_Olist_OCons(_1786550), _1786552), _1786639)), -(hBOOL(hAPP(hAPP(c_member(_1786550), _1786552), hAPP(c_List_Oset(_1786550), _1786639))))]]], (18869 ^ _775212) ^ [_1096247, _1096249, _1096251] : [class_Rings_Olinordered__idom(_1096247), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096247), c_Groups_Ozero__class_Ozero(_1096247)), hAPP(hAPP(c_Power_Opower__class_Opower(_1096247), _1096249), 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)))), _1096251))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096247), c_Groups_Ozero__class_Ozero(_1096247)), _1096249)))], (36549 ^ _775212) ^ [_1453899, _1453901, _1453903, _1453905, _1453907, _1453909] : [c_Fun_Oinj__on(_1453899, _1453901, _1453903, _1453905), -(_1453907 = _1453909), hBOOL(hAPP(hAPP(c_member(_1453899), _1453907), _1453905)), hBOOL(hAPP(hAPP(c_member(_1453899), _1453909), _1453905)), hAPP(_1453903, _1453907) = hAPP(_1453903, _1453909)], (44815 ^ _775212) ^ [_1660549, _1660551, _1660553, _1660555, _1660557] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1660549), tc_List_Olist(_1660551), tc_List_Olist(_1660553), hAPP(c_List_Omap(_1660549, _1660551), _1660555)), hAPP(c_List_Omap(_1660553, _1660549), _1660557)) = hAPP(c_List_Omap(_1660553, _1660551), hAPP(c_Fun_Ocomp(_1660549, _1660551, _1660553, _1660555), _1660557)))], (49605 ^ _775212) ^ [_1768151, _1768153, _1768155, _1768157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1768151), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768153)), c_List_OdropWhile(_1768153, _1768155, _1768157)))), -(hAPP(hAPP(c_List_Onth(_1768153), c_List_OdropWhile(_1768153, _1768155, _1768157)), _1768151) = hAPP(hAPP(c_List_Onth(_1768153), _1768157), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1768151), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768153)), c_List_OtakeWhile(_1768153, _1768155, _1768157)))))], (10900 ^ _775212) ^ [_953386, _953388, _953390] : [class_Groups_Oordered__comm__monoid__add(_953386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953386), _953388), c_Groups_Ozero__class_Ozero(_953386))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953386), _953390), c_Groups_Ozero__class_Ozero(_953386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953386), _953388), _953390)), c_Groups_Ozero__class_Ozero(_953386))))], (43406 ^ _775212) ^ [_1623158, _1623160, _1623162, _1623164] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623158, tc_fun(_1623160, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623158, tc_HOL_Obool), _1623162)), _1623164) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1623158, tc_HOL_Obool), tc_fun(_1623160, tc_HOL_Obool)), _1623162), hAPP(hAPP(c_COMBC(tc_fun(_1623158, tc_HOL_Obool), tc_fun(_1623158, tc_fun(_1623160, tc_HOL_Obool)), tc_fun(_1623160, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623158, tc_fun(_1623160, tc_HOL_Obool))), _1623164)))], (4674 ^ _775212) ^ [_846443, _846445] : [_846445 = _846443, -(c_List_Odistinct(_846445) = c_List_Odistinct(_846443))], (17269 ^ _775212) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45467 ^ _775212) ^ [_1677488, _1677490] : [-(c_Random_Oselect__weight(_1677488, _1677490) = 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(_1677488, 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, _1677488), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1677488)), _1677490)))), hAPP(hAPP(c_COMBB(_1677488, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1677488, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1677488, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1677488, _1677490))))], (25140 ^ _775212) ^ [_1212634, _1212636, _1212638] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212634), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212636, _1212638))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212634), _1212638)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212634), _1212636)))], (2120 ^ _775212) ^ [_805848, _805850, _805852, _805854, _805856, _805858, _805860, _805862, _805864, _805866] : [-(c_Product__Type_Oprod_Oprod__size(_805866, _805862, _805858, _805854, _805850) = c_Product__Type_Oprod_Oprod__size(_805864, _805860, _805856, _805852, _805848)), _805866 = _805864, _805862 = _805860, _805858 = _805856, _805854 = _805852, _805850 = _805848], (31595 ^ _775212) ^ [_1347058, _1347060] : [class_Orderings_Olinorder(_1347058), -(c_Big__Operators_Olinorder__class_OMax(_1347058, hAPP(hAPP(c_Set_Oinsert(_1347058), _1347060), c_Orderings_Obot__class_Obot(tc_fun(_1347058, tc_HOL_Obool)))) = _1347060)], (10115 ^ _775212) ^ [_939449, _939451, _939453] : [class_Groups_Oordered__comm__monoid__add(_939449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939449), c_Groups_Ozero__class_Ozero(_939449)), _939451)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939449), c_Groups_Ozero__class_Ozero(_939449)), _939453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939449), c_Groups_Ozero__class_Ozero(_939449)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939449), _939451), _939453))))], (50915 ^ _775212) ^ [_1796093, _1796095, _1796097] : [-(hAPP(hAPP(c_List_Oappend(_1796093), c_List_Oreplicate(_1796093, _1796095, _1796097)), hAPP(hAPP(c_List_Olist_OCons(_1796093), _1796097), c_List_Olist_ONil(_1796093))) = hAPP(hAPP(c_List_Olist_OCons(_1796093), _1796097), c_List_Oreplicate(_1796093, _1796095, _1796097)))], (45901 ^ _775212) ^ [_1687278, _1687280, _1687282, _1687284] : [_1687282 = _1687284, -(hAPP(hAPP(c_List_Oappend(_1687278), _1687280), _1687282) = hAPP(hAPP(c_List_Oappend(_1687278), _1687280), _1687284))], (40969 ^ _775212) ^ [_1564133, _1564135, _1564137] : [-(hAPP(c_New__DSequence_Opos__single(_1564133, _1564135), _1564137) = hAPP(c_Lazy__Sequence_Osingle(_1564133), _1564135))], (22378 ^ _775212) ^ [_1161207, _1161209] : [-(_1161207 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22381 ^ _775212 : [(22388 ^ _775212) ^ [] : [-(_1161209 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1161207, _1161209) = 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, _1161209))), 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)), _1161209)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1161207))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161209), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161207), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1161207, _1161209)), 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), _1161209))))), c_Divides_Opdivmod(_1161207, _1161209)))))], (22382 ^ _775212) ^ [] : [_1161209 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1161207, _1161209) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1161207))]]], (40971 ^ _775212) ^ [_1564171, _1564173] : [40973 ^ _775212 : [(40976 ^ _775212) ^ [] : [40972 ^ [_1564171, _1564173] = c_Orderings_Obot__class_Obot(tc_fun(_1564171, tc_HOL_Obool))], (40974 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564171, tc_HOL_Obool)), 40972 ^ [_1564171, _1564173]), hAPP(c_Relation_OImage(_1564171, _1564171, _1564173), 40972 ^ [_1564171, _1564173]))))]], -(c_Wellfounded_Owf(_1564171, _1564173))], (12566 ^ _775212) ^ [_982442, _982444] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _982442), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _982444)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _982442, _982444)))], (2540 ^ _775212) ^ [_812436, _812438, _812440, _812442] : [-(c_Divides_Odivmod__nat__rel(_812442, _812438) = c_Divides_Odivmod__nat__rel(_812440, _812436)), _812442 = _812440, _812438 = _812436], (17635 ^ _775212) ^ [_1074629, _1074631] : [class_Int_Onumber__ring(_1074629), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074629), c_Groups_Oone__class_Oone(_1074629)), hAPP(c_Int_Onumber__class_Onumber__of(_1074629), _1074631)) = hAPP(c_Int_Onumber__class_Onumber__of(_1074629), 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), _1074631))))], (7615 ^ _775212) ^ [_896943, _896945, _896947] : [class_Rings_Oring(_896943), -(hAPP(c_Groups_Ouminus__class_Ouminus(_896943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896943), _896945), _896947)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896943), hAPP(c_Groups_Ouminus__class_Ouminus(_896943), _896945)), _896947))], (39508 ^ _775212) ^ [_1528262, _1528264, _1528266, _1528268, _1528270, _1528272, _1528274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528262, _1528264), tc_HOL_Obool)), _1528266), _1528268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528264, _1528270), tc_HOL_Obool)), _1528272), _1528274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528262, _1528270), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1528262, _1528264, _1528270), _1528266), _1528272)), hAPP(hAPP(c_Relation_Orel__comp(_1528262, _1528264, _1528270), _1528268), _1528274))))], (52265 ^ _775212) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (32621 ^ _775212) ^ [_1366451, _1366453] : [class_Orderings_Olinorder(_1366451), -(c_Big__Operators_Olattice_OInf__fin(_1366451, c_Orderings_Oord__class_Omin(_1366451), hAPP(hAPP(c_Set_Oinsert(_1366451), _1366453), c_Orderings_Obot__class_Obot(tc_fun(_1366451, tc_HOL_Obool)))) = _1366453)], (24554 ^ _775212) ^ [_1201533, _1201535] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201533), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1201535), _1201533))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201533), _1201535)))], (52343 ^ _775212) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (8621 ^ _775212) ^ [_914927] : [class_Rings_Oring__1(_914927), -(hAPP(c_Int_Oring__1__class_Oof__int(_914927), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_914927))], (33003 ^ _775212) ^ [_1373737, _1373739, _1373741] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1373737), _1373739)), 33006 ^ _775212 : [(33007 ^ _775212) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1373737, tc_Nat_Onat), _1373741), _1373739) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 33010 ^ _775212 : [(33011 ^ _775212) ^ [_1373899] : [hBOOL(hAPP(hAPP(c_member(_1373737), _1373899), _1373739)), -(hAPP(_1373741, _1373899) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (33017 ^ _775212) ^ [] : [33019 ^ _775212 : [(33022 ^ _775212) ^ [] : [hAPP(_1373741, 33018 ^ [_1373737, _1373739, _1373741]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (33020 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373737), 33018 ^ [_1373737, _1373739, _1373741]), _1373739)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1373737, tc_Nat_Onat), _1373741), _1373739) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (35439 ^ _775212) ^ [_1429242, _1429244] : [class_Orderings_Oorder(_1429242), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429242, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1429242), _1429244)), hAPP(c_SetInterval_Oord__class_OatLeast(_1429242), _1429244)) = hAPP(hAPP(c_Set_Oinsert(_1429242), _1429244), c_Orderings_Obot__class_Obot(tc_fun(_1429242, tc_HOL_Obool))))], (1744 ^ _775212) ^ [_799868, _799870] : [-(class_Orderings_Opreorder(_799868)), _799870 = _799868, class_Orderings_Opreorder(_799870)], (37383 ^ _775212) ^ [_1471139, _1471141, _1471143, _1471145, _1471147, _1471149] : [hAPP(_1471139, _1471141) = _1471143, hBOOL(hAPP(hAPP(c_member(_1471145), _1471143), _1471147)), -(hBOOL(hAPP(hAPP(c_member(_1471149), _1471141), hAPP(c_Set_Ovimage(_1471149, _1471145, _1471139), _1471147))))], (34889 ^ _775212) ^ [_1416013, _1416015, _1416017, _1416019] : [class_Lattices_Olattice(_1416013), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416013), _1416015), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416013), _1416017), _1416019)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416013), _1416017), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416013), _1416015), _1416019)))], (52391 ^ _775212) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (11112 ^ _775212) ^ [_957372, _957374, _957376, _957378, _957380] : [class_Rings_Olinordered__semiring__strict(_957372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957372), _957374), _957376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957372), _957378), _957380)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957372), c_Groups_Ozero__class_Ozero(_957372)), _957374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957372), c_Groups_Ozero__class_Ozero(_957372)), _957378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_957372), _957374), _957378)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_957372), _957376), _957380))))], (15563 ^ _775212) ^ [_1038322, _1038324] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1038322), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1038324), _1038322)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1038324), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038324, _1038322)))], (2236 ^ _775212) ^ [_807768, _807770, _807772, _807774] : [-(c_Divides_Odivmod__int__rel(_807774, _807770) = c_Divides_Odivmod__int__rel(_807772, _807768)), _807774 = _807772, _807770 = _807768], (24388 ^ _775212) ^ [_1198620, _1198622, _1198624, _1198626] : [class_Divides_Osemiring__div(_1198620), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1198620), _1198622), c_Divides_Odiv__class_Omod(_1198620, _1198624, _1198626))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1198620), _1198622), _1198626)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1198620), _1198622), _1198624)))], (27279 ^ _775212) ^ [_1255764, _1255766, _1255768] : [class_Lattices_Olattice(_1255764), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255764), _1255766), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255764), _1255766), _1255768))))], (51837 ^ _775212) ^ [_1817352, _1817354, _1817356] : [c_Relation_Osym(_1817352, _1817354), c_Relation_Osym(_1817352, _1817356), -(c_Relation_Osym(_1817352, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1817352, _1817352), tc_HOL_Obool)), _1817354), _1817356)))], (18059 ^ _775212) ^ [_1081714, _1081716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1081714)), -(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)))), _1081716))), 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)))), _1081714)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1081716), _1081714))], (6262 ^ _775212) ^ [_874123, _874125] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874123), _874125))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874125), hAPP(c_Nat_OSuc, _874123))))], (52341 ^ _775212) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (1604 ^ _775212) ^ [_798118, _798120] : [-(class_Rings_Olinordered__semiring(_798118)), _798120 = _798118, class_Rings_Olinordered__semiring(_798120)], (37234 ^ _775212) ^ [_1468255, _1468257, _1468259, _1468261, _1468263] : [c_Typedef_Otype__definition(_1468255, _1468257, _1468259, _1468261, _1468263), -(hAPP(c_Set_Oimage(_1468255, _1468257, _1468259), c_Orderings_Otop__class_Otop(tc_fun(_1468255, tc_HOL_Obool))) = _1468263)], (21235 ^ _775212) ^ [_1138871, _1138873, _1138875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1138871, tc_fun(_1138871, tc_HOL_Obool))), _1138873), _1138875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1138871, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1138871, _1138875)), c_Wellfounded_Oaccp(_1138871, _1138873))))], (18733 ^ _775212) ^ [_1093424, _1093426, _1093428] : [class_Rings_Olinordered__semidom(_1093424), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093424), hAPP(hAPP(c_Power_Opower__class_Opower(_1093424), _1093426), 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(_1093424), _1093428), 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(_1093424), c_Groups_Ozero__class_Ozero(_1093424)), _1093428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093424), _1093426), _1093428)))], (38871 ^ _775212) ^ [_1505991, _1505993, _1505995] : [hBOOL(hAPP(_1505991, _1505993)), -(hBOOL(hAPP(hAPP(c_member(_1505995), _1505993), hAPP(c_Set_OCollect(_1505995), _1505991))))], (38423 ^ _775212) ^ [_1497478, _1497480, _1497482] : [class_Lattices_Osemilattice__inf(_1497478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497478), _1497480)), hBOOL(hAPP(hAPP(c_member(_1497478), _1497482), _1497480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497478), hAPP(c_Finite__Set_Ofold1(_1497478, c_Lattices_Osemilattice__inf__class_Oinf(_1497478)), _1497480)), _1497482)))], (16765 ^ _775212) ^ [_1061106] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1061106) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1061106))], (21169 ^ _775212) ^ [_1137841, _1137843] : [-(c_Divides_OposDivAlg(_1137841, _1137843) = hAPP(c_Divides_Oadjust(_1137843), c_Divides_OposDivAlg(_1137841, 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)))), _1137843)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137841), _1137843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137843), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37678 ^ _775212) ^ [_1478376, _1478378, _1478380] : [37680 ^ _775212 : [(37683 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1478376), 37679 ^ [_1478376, _1478378, _1478380]), c_Wellfounded_Oacc(_1478376, _1478380)))], (37681 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1478376, _1478376)), hAPP(hAPP(c_Product__Type_OPair(_1478376, _1478376), 37679 ^ [_1478376, _1478378, _1478380]), _1478378)), _1478380)))]], -(hBOOL(hAPP(hAPP(c_member(_1478376), _1478378), c_Wellfounded_Oacc(_1478376, _1478380))))], (13781 ^ _775212) ^ [_1003781, _1003783, _1003785] : [-(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), _1003781), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1003783), _1003781))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1003783, _1003781))), _1003785) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1003783), _1003785))], (30384 ^ _775212) ^ [_1322189, _1322191, _1322193, _1322195, _1322197] : [class_Groups_Ocomm__monoid__add(_1322189), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322191), _1322193)), -(hBOOL(hAPP(hAPP(c_member(_1322191), _1322195), _1322193))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1322191, _1322189), _1322197), hAPP(hAPP(c_Set_Oinsert(_1322191), _1322195), _1322193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1322189), hAPP(_1322197, _1322195)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1322191, _1322189), _1322197), _1322193)))], (28787 ^ _775212) ^ [_1286832, _1286834, _1286836, _1286838] : [28789 ^ _775212 : [(28792 ^ _775212) ^ [] : [hAPP(_1286838, 28788 ^ [_1286832, _1286834, _1286836, _1286838]) = c_Orderings_Obot__class_Obot(tc_fun(_1286832, tc_HOL_Obool))], (28790 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1286834), 28788 ^ [_1286832, _1286834, _1286836, _1286838]), _1286836)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1286832, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1286834, tc_fun(_1286832, tc_HOL_Obool)), _1286836), _1286838))], (45455 ^ _775212) ^ [_1677164, _1677166] : [class_Groups_Ocomm__monoid__add(_1677164), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1677164), _1677166) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1677164), hAPP(c_List_Onth(_1677164), _1677166)), 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(_1677164)), _1677166))))], (54 ^ _775212) ^ [_775915, _775917] : [-(class_Fields_Olinordered__field__inverse__zero(_775915)), _775917 = _775915, class_Fields_Olinordered__field__inverse__zero(_775917)], (13665 ^ _775212) ^ [_1001763, _1001765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001763)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001765), 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), _1001763), _1001765)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23720 ^ _775212) ^ [_1187428, _1187430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1187428), _1187430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1187428)), hAPP(c_Code__Numeral_Oof__nat, _1187430))))], (41905 ^ _775212) ^ [_1584294, _1584296, _1584298, _1584300] : [41906 ^ _775212 : [(41909 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584294, _1584294)), _1584296), c_Transitive__Closure_Ortrancl(_1584294, _1584300)))], (41907 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584294, _1584294)), _1584296), c_Transitive__Closure_Ortrancl(_1584294, _1584298)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584294, _1584294)), _1584296), c_Transitive__Closure_Ortrancl(_1584294, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584294, _1584294), tc_HOL_Obool)), _1584298), _1584300)))))], (48845 ^ _775212) ^ [_1752367, _1752369, _1752371, _1752373, _1752375] : [class_Orderings_Olinorder(_1752367), c_List_Olinorder__class_Osorted(_1752367, hAPP(hAPP(c_List_Omap(_1752369, _1752367), _1752371), _1752373)), -(c_List_Olinorder__class_Osorted(_1752367, hAPP(hAPP(c_List_Omap(_1752369, _1752367), _1752371), hAPP(c_List_Ofilter(_1752369, _1752375), _1752373))))], (5819 ^ _775212) ^ [_867138, _867140, _867142, _867144, _867146] : [c_Com_Ocom_OCond(_867138, _867140, _867142) = c_Com_Ocom_OSemi(_867144, _867146)], (8519 ^ _775212) ^ [_913249, _913251, _913253] : [class_Rings_Olinordered__ring__strict(_913249), 8522 ^ _775212 : [(8531 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913249), _913251), _913251)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913249), _913253), _913253)) = c_Groups_Ozero__class_Ozero(_913249)), _913251 = c_Groups_Ozero__class_Ozero(_913249), _913253 = c_Groups_Ozero__class_Ozero(_913249)], (8523 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913249), _913251), _913251)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913249), _913253), _913253)) = c_Groups_Ozero__class_Ozero(_913249), 8526 ^ _775212 : [(8529 ^ _775212) ^ [] : [-(_913253 = c_Groups_Ozero__class_Ozero(_913249))], (8527 ^ _775212) ^ [] : [-(_913251 = c_Groups_Ozero__class_Ozero(_913249))]]]]], (33741 ^ _775212) ^ [_1390483, _1390485] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1390483, tc_HOL_Obool)), hAPP(c_Set_OPow(_1390483), _1390485))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1390483), _1390485)))], (42408 ^ _775212) ^ [_1597028, _1597030, _1597032, _1597034] : [-(hAPP(c_Relation_Oconverse(_1597028, _1597030), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1597028, _1597030), tc_HOL_Obool)), _1597032), _1597034)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1597030, _1597028), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1597028, _1597030), _1597032)), hAPP(c_Relation_Oconverse(_1597028, _1597030), _1597034)))], (43002 ^ _775212) ^ [_1613388, _1613390] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613388, _1613388), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1613390) = _1613390)], (31661 ^ _775212) ^ [_1348235] : [class_Rings_Oring__1(_1348235), -(hBOOL(hAPP(hAPP(c_member(_1348235), c_Groups_Oone__class_Oone(_1348235)), c_Int_Oring__1__class_OInts(_1348235))))], (12326 ^ _775212) ^ [_978010, _978012] : [class_Rings_Olinordered__idom(_978010), 12329 ^ _775212 : [(12336 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978010), _978012), c_Groups_Ozero__class_Ozero(_978010))), -(c_Groups_Osgn__class_Osgn(_978010, _978012) = hAPP(c_Groups_Ouminus__class_Ouminus(_978010), c_Groups_Oone__class_Oone(_978010)))], (12330 ^ _775212) ^ [] : [c_Groups_Osgn__class_Osgn(_978010, _978012) = hAPP(c_Groups_Ouminus__class_Ouminus(_978010), c_Groups_Oone__class_Oone(_978010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978010), _978012), c_Groups_Ozero__class_Ozero(_978010))))]]], (29246 ^ _775212) ^ [_1295043] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1295043)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1295043)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1295043), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (45989 ^ _775212) ^ [_1689375, _1689377, _1689379, _1689381, _1689383] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1689375), tc_List_Olist(_1689375))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689375), tc_List_Olist(_1689375)), _1689377), _1689379)), c_List_Olexord(_1689375, _1689381))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1689375), tc_List_Olist(_1689375))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689375), tc_List_Olist(_1689375)), hAPP(hAPP(c_List_Oappend(_1689375), _1689383), _1689377)), hAPP(hAPP(c_List_Oappend(_1689375), _1689383), _1689379))), c_List_Olexord(_1689375, _1689381))))], (23234 ^ _775212) ^ [_1177903, _1177905, _1177907, _1177909, _1177911] : [-(hAPP(c_Product__Type_Osnd(_1177903, _1177905), hAPP(c_Product__Type_Oapfst(_1177907, _1177903, _1177905, _1177909), _1177911)) = hAPP(c_Product__Type_Osnd(_1177907, _1177905), _1177911))], (47252 ^ _775212) ^ [_1717193, _1717195, _1717197] : [-(hBOOL(hAPP(hAPP(c_member(_1717193), _1717195), hAPP(c_List_Oset(_1717193), _1717197)))), -(c_List_Oremove1(_1717193, _1717195, _1717197) = _1717197)], (43515 ^ _775212) ^ [_1625554, _1625556, _1625558, _1625560] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625554, tc_HOL_Obool), hAPP(c_Set_Oimage(_1625556, tc_fun(_1625554, tc_HOL_Obool), _1625558), _1625560)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1625556, tc_fun(_1625554, tc_HOL_Obool)), _1625560), _1625558))], (6699 ^ _775212) ^ [_881651, _881653] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _881651)), _881653) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881651), _881653)))], (27411 ^ _775212) ^ [_1258504, _1258506, _1258508] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1258504, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1258504, tc_HOL_Obool)), _1258506), _1258508)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258504, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1258504, tc_HOL_Obool)), _1258506)), _1258508))], (19267 ^ _775212) ^ [_1103511, _1103513, _1103515] : [class_Fields_Olinordered__field__inverse__zero(_1103511), 19270 ^ _775212 : [(19285 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103511), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1103511), _1103513), _1103515)), c_Groups_Ozero__class_Ozero(_1103511)))), 19286 ^ _775212 : [(19293 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103511), _1103513), c_Groups_Ozero__class_Ozero(_1103511))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103511), c_Groups_Ozero__class_Ozero(_1103511)), _1103515))], (19287 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103511), c_Groups_Ozero__class_Ozero(_1103511)), _1103513)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103511), _1103515), c_Groups_Ozero__class_Ozero(_1103511)))]]], (19271 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103511), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1103511), _1103513), _1103515)), c_Groups_Ozero__class_Ozero(_1103511))), 19276 ^ _775212 : [(19279 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103511), _1103515), c_Groups_Ozero__class_Ozero(_1103511))))], (19277 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103511), c_Groups_Ozero__class_Ozero(_1103511)), _1103513)))]], 19280 ^ _775212 : [(19283 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103511), c_Groups_Ozero__class_Ozero(_1103511)), _1103515)))], (19281 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103511), _1103513), c_Groups_Ozero__class_Ozero(_1103511))))]]]]], (31655 ^ _775212) ^ [_1348132, _1348134] : [class_Int_Onumber__ring(_1348132), -(hBOOL(hAPP(hAPP(c_member(_1348132), hAPP(c_Int_Onumber__class_Onumber__of(_1348132), _1348134)), c_Int_Oring__1__class_OInts(_1348132))))], (8858 ^ _775212) ^ [_918847, _918849] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918847), _918849) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918849), _918847))], (45818 ^ _775212) ^ [_1685315, _1685317, _1685319] : [_1685319 = c_List_Olist_ONil(_1685317), -(_1685315 = hAPP(hAPP(c_List_Oappend(_1685317), _1685315), _1685319))], (42367 ^ _775212) ^ [_1596019, _1596021, _1596023, _1596025, _1596027] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596021, _1596019)), hAPP(hAPP(c_Product__Type_OPair(_1596021, _1596019), _1596025), _1596023)), _1596027)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596019, _1596021)), hAPP(hAPP(c_Product__Type_OPair(_1596019, _1596021), _1596023), _1596025)), hAPP(c_Relation_Oconverse(_1596021, _1596019), _1596027))))], (33729 ^ _775212) ^ [_1390212, _1390214] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1390212), _1390214)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1390212, tc_HOL_Obool)), hAPP(c_Set_OPow(_1390212), _1390214)) = 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(_1390212), _1390214)))], (27141 ^ _775212) ^ [_1253358, _1253360, _1253362, _1253364, _1253366] : [class_Lattices_Osemilattice__sup(_1253358), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253358), _1253360), _1253362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253358), _1253364), _1253366)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253358), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1253358), _1253360), _1253364)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1253358), _1253362), _1253366))))], (45192 ^ _775212) ^ [_1670004, _1670006, _1670008] : [-(hAPP(hAPP(c_List_Ozip(_1670004, _1670006), _1670008), c_List_Olist_ONil(_1670006)) = c_List_Olist_ONil(tc_prod(_1670004, _1670006)))], (7941 ^ _775212) ^ [_902779, _902781, _902783] : [class_Groups_Ogroup__add(_902779), -(hAPP(c_Groups_Ouminus__class_Ouminus(_902779), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902779), _902781), _902783)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902779), hAPP(c_Groups_Ouminus__class_Ouminus(_902779), _902783)), hAPP(c_Groups_Ouminus__class_Ouminus(_902779), _902781)))], (50851 ^ _775212) ^ [_1794881, _1794883, _1794885] : [-(c_Predicate_Oconversep(_1794881, _1794883, c_Predicate_Oconversep(_1794883, _1794881, _1794885)) = _1794885)], (49127 ^ _775212) ^ [_1758093, _1758095] : [_1758095 = c_List_Olist_ONil(_1758093), -(c_List_Olist_ONil(_1758093) = hAPP(c_List_Orev(_1758093), _1758095))], (40965 ^ _775212) ^ [_1564049, _1564051, _1564053] : [-(hAPP(c_New__DSequence_Oneg__single(_1564049, _1564051), _1564053) = c_Lazy__Sequence_Ohb__single(_1564049, _1564051))], (40872 ^ _775212) ^ [_1561992, _1561994, _1561996, _1561998] : [-(c_Random__Sequence_Omap(_1561992, _1561994, _1561996, _1561998) = c_Random__Sequence_Obind(_1561992, _1561994, _1561998, hAPP(c_Fun_Ocomp(_1561994, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1561994)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1561992, c_Random__Sequence_Osingle(_1561994)), _1561996)))], (42754 ^ _775212) ^ [_1607445, _1607447, _1607449, _1607451, _1607453] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607445, tc_fun(_1607447, tc_HOL_Obool)), _1607449), _1607451), _1607453)), 42757 ^ _775212 : [(42758 ^ _775212) ^ [_1607554] : [hBOOL(hAPP(hAPP(c_member(_1607445), _1607554), _1607449)), -(hBOOL(hAPP(hAPP(_1607451, _1607554), _1607453)))]]], (5807 ^ _775212) ^ [_866834, _866836, _866838, _866840, _866842] : [c_Com_Ocom_OCond(_866834, _866836, _866838) = c_Com_Ocom_OWhile(_866840, _866842)], (8331 ^ _775212) ^ [_909738, _909740, _909742] : [class_Rings_Olinordered__semiring__strict(_909738), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909738), c_Groups_Ozero__class_Ozero(_909738)), _909740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909738), c_Groups_Ozero__class_Ozero(_909738)), _909742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909738), c_Groups_Ozero__class_Ozero(_909738)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909738), _909740), _909742))))], (154 ^ _775212) ^ [_777409, _777411, _777413, _777415, _777417, _777419, _777421, _777423] : [-(c_Orderings_Oorder_Omono(_777421, _777417, _777413, _777409)), c_Orderings_Oorder_Omono(_777423, _777419, _777415, _777411), _777423 = _777421, _777419 = _777417, _777415 = _777413, _777411 = _777409], (47091 ^ _775212) ^ [_1713981, _1713983, _1713985, _1713987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1713981), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713983)), _1713985))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1713981), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713983)), _1713987))), 47101 ^ _775212 : [(47104 ^ _775212) ^ [] : [hAPP(hAPP(c_List_Onth(_1713983), _1713985), 47100 ^ [_1713981, _1713983, _1713985, _1713987]) = hAPP(hAPP(c_List_Onth(_1713983), _1713987), 47100 ^ [_1713981, _1713983, _1713985, _1713987])], (47102 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47100 ^ [_1713981, _1713983, _1713985, _1713987]), _1713981)))]], -(hAPP(hAPP(c_List_Otake(_1713983), _1713981), _1713985) = hAPP(hAPP(c_List_Otake(_1713983), _1713981), _1713987))], (26615 ^ _775212) ^ [_1243033] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1243033)) = hAPP(c_Nat_OSuc, _1243033))], (8197 ^ _775212) ^ [_907390, _907392, _907394] : [class_Groups_Ogroup__add(_907390), 8200 ^ _775212 : [(8207 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907390), _907392), _907394) = c_Groups_Ozero__class_Ozero(_907390), -(_907392 = hAPP(c_Groups_Ouminus__class_Ouminus(_907390), _907394))], (8201 ^ _775212) ^ [] : [_907392 = hAPP(c_Groups_Ouminus__class_Ouminus(_907390), _907394), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907390), _907392), _907394) = c_Groups_Ozero__class_Ozero(_907390))]]], (43589 ^ _775212) ^ [_1627028, _1627030] : [class_Complete__Lattice_Ocomplete__lattice(_1627028), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627028), _1627030)), -(c_Complete__Lattice_OSup__class_OSup(_1627028, _1627030) = hAPP(hAPP(c_Finite__Set_Ofold(_1627028, _1627028, c_Lattices_Osemilattice__sup__class_Osup(_1627028)), c_Orderings_Obot__class_Obot(_1627028)), _1627030))], (34142 ^ _775212) ^ [_1400201, _1400203, _1400205] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400201), hAPP(hAPP(c_Set_Oinsert(_1400201), _1400203), c_Orderings_Obot__class_Obot(tc_fun(_1400201, tc_HOL_Obool)))), _1400205) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1400201, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1400201, _1400201, _1400205), hAPP(hAPP(c_Set_Oinsert(_1400201), _1400203), c_Orderings_Obot__class_Obot(tc_fun(_1400201, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1400201, tc_HOL_Obool), tc_HOL_Obool))))], (44706 ^ _775212) ^ [_1657712, _1657714, _1657716, _1657718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657712), _1657714)), -(hAPP(hAPP(c_List_Onth(_1657716), hAPP(hAPP(c_List_Otake(_1657716), _1657714), _1657718)), _1657712) = hAPP(hAPP(c_List_Onth(_1657716), _1657718), _1657712))], (24206 ^ _775212) ^ [_1195552, _1195554] : [_1195552 = _1195554, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195552), _1195554)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195554), _1195552)))], (4152 ^ _775212) ^ [_838264, _838266, _838268, _838270] : [-(c_Random_Opick(_838270, _838266) = c_Random_Opick(_838268, _838264)), _838270 = _838268, _838266 = _838264], (41356 ^ _775212) ^ [_1572535, _1572537, _1572539, _1572541] : [class_Lattices_Osemilattice__inf(_1572535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572535), _1572537)), hBOOL(hAPP(hAPP(c_member(_1572535), _1572539), _1572537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1572535), hAPP(hAPP(c_Finite__Set_Ofold(_1572535, _1572535, c_Lattices_Osemilattice__inf__class_Oinf(_1572535)), _1572541), _1572537)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1572535), _1572539), _1572541))))], (52335 ^ _775212) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (52531 ^ _775212) ^ [_1826661] : [class_Finite__Set_Ofinite(_1826661), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1826661)))], (1344 ^ _775212) ^ [_794868, _794870] : [-(class_Orderings_Owellorder(_794868)), _794870 = _794868, class_Orderings_Owellorder(_794870)], (6737 ^ _775212) ^ [_882440, _882442, _882444, _882446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882440), _882442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882444), _882446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882440), _882444)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882442), _882446))))], (49540 ^ _775212) ^ [_1766885, _1766887, _1766889] : [49542 ^ _775212 : [(49545 ^ _775212) ^ [] : [hBOOL(hAPP(_1766887, 49541 ^ [_1766885, _1766887, _1766889]))], (49543 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766885), 49541 ^ [_1766885, _1766887, _1766889]), hAPP(c_List_Oset(_1766885), _1766889))))]], -(c_List_OdropWhile(_1766885, _1766887, _1766889) = c_List_Olist_ONil(_1766885))], (29708 ^ _775212) ^ [_1304382, _1304384, _1304386, _1304388] : [29709 ^ _775212 : [(29712 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1304382), _1304384), _1304388))], (29710 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1304382), _1304384), _1304386))]], -(hBOOL(hAPP(hAPP(c_member(_1304382), _1304384), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304382, tc_HOL_Obool)), _1304386), _1304388))))], (32351 ^ _775212) ^ [_1361111, _1361113, _1361115, _1361117, _1361119, _1361121, _1361123] : [hBOOL(hAPP(_1361111, _1361113)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1361115, _1361115)), hAPP(hAPP(c_Product__Type_OPair(_1361115, _1361115), _1361117), _1361119)), hAPP(_1361121, _1361113))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1361123, _1361115), tc_prod(_1361123, _1361115))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1361123, _1361115), tc_prod(_1361123, _1361115)), hAPP(hAPP(c_Product__Type_OPair(_1361123, _1361115), _1361113), _1361117)), hAPP(hAPP(c_Product__Type_OPair(_1361123, _1361115), _1361113), _1361119))), c_Recdef_Osame__fst(_1361123, _1361115, _1361111, _1361121))))], (31627 ^ _775212) ^ [_1347622, _1347624, _1347626] : [class_Rings_Oring__1(_1347622), hBOOL(hAPP(hAPP(c_member(_1347622), _1347624), c_Int_Oring__1__class_OInts(_1347622))), hBOOL(hAPP(hAPP(c_member(_1347622), _1347626), c_Int_Oring__1__class_OInts(_1347622))), -(hBOOL(hAPP(hAPP(c_member(_1347622), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347622), _1347624), _1347626)), c_Int_Oring__1__class_OInts(_1347622))))], (41889 ^ _775212) ^ [_1583874, _1583876, _1583878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583874, _1583874), tc_HOL_Obool)), _1583876), _1583878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583874, _1583874), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1583874, _1583876)), c_Transitive__Closure_Ortrancl(_1583874, _1583878))))], (52411 ^ _775212) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (37493 ^ _775212) ^ [_1473792, _1473794, _1473796, _1473798] : [-(hAPP(c_Set_Oimage(_1473792, _1473794, _1473796), hAPP(c_Set_Ovimage(_1473792, _1473794, _1473796), _1473798)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473794, tc_HOL_Obool)), _1473798), hAPP(c_Set_Oimage(_1473792, _1473794, _1473796), c_Orderings_Otop__class_Otop(tc_fun(_1473792, tc_HOL_Obool)))))], (12610 ^ _775212) ^ [_983177, _983179, _983181, _983183] : [class_Divides_Osemiring__div(_983177), -(c_Divides_Odiv__class_Omod(_983177, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983177), _983179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983177), _983181), _983183)), _983181) = c_Divides_Odiv__class_Omod(_983177, _983179, _983181))], (45526 ^ _775212) ^ [_1679002, _1679004, _1679006, _1679008, _1679010] : [-(_1679002 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1679004, _1679006, _1679008), _1679002), _1679010) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1679006), _1679004), tc_prod(_1679006, _1679004), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679006), _1679004), c_List_Olist_ONil(_1679006)), _1679010), hAPP(c_Product__Type_Oprod_Oprod__case(_1679006, _1679004, tc_prod(tc_List_Olist(_1679006), _1679004)), hAPP(hAPP(c_COMBC(_1679006, tc_fun(_1679004, tc_prod(tc_List_Olist(_1679006), _1679004)), tc_fun(_1679004, tc_prod(tc_List_Olist(_1679006), _1679004))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1679006), _1679004), tc_prod(tc_List_Olist(_1679006), _1679004)), tc_fun(tc_fun(_1679004, tc_prod(tc_List_Olist(_1679006), _1679004)), tc_fun(_1679004, tc_prod(tc_List_Olist(_1679006), _1679004))), _1679006), c_COMBB(tc_prod(tc_List_Olist(_1679006), _1679004), tc_prod(tc_List_Olist(_1679006), _1679004), _1679004)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1679006), tc_fun(_1679004, tc_prod(tc_List_Olist(_1679006), _1679004))), tc_fun(tc_prod(tc_List_Olist(_1679006), _1679004), tc_prod(tc_List_Olist(_1679006), _1679004)), _1679006), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1679006), _1679004, tc_prod(tc_List_Olist(_1679006), _1679004))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1679006), tc_List_Olist(_1679006)), tc_fun(tc_List_Olist(_1679006), tc_fun(_1679004, tc_prod(tc_List_Olist(_1679006), _1679004))), _1679006), hAPP(c_COMBB(tc_List_Olist(_1679006), tc_fun(_1679004, tc_prod(tc_List_Olist(_1679006), _1679004)), tc_List_Olist(_1679006)), c_Product__Type_OPair(tc_List_Olist(_1679006), _1679004))), c_List_Olist_OCons(_1679006))))), hAPP(c_Lazy__Sequence_Oanamorph(_1679004, _1679006, _1679008), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1679002), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1679008, _1679010)))], (10845 ^ _775212) ^ [_952409, _952411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952411)), -(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), _952409), _952411))))], (14117 ^ _775212) ^ [_1010314, _1010316, _1010318] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1010314), _1010316)), _1010318) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1010314), _1010318)), _1010316))], (17645 ^ _775212) ^ [_1074854, _1074856] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1074854)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1074856)) = 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)))), _1074854)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1074856)))], (34089 ^ _775212) ^ [_1398838, _1398840, _1398842, _1398844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398838), _1398844)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398842), _1398840))), -(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), _1398838), _1398840)), 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), _1398842), _1398844)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (52467 ^ _775212) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (52357 ^ _775212) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (23616 ^ _775212) ^ [_1185327, _1185329, _1185331, _1185333] : [hBOOL(hAPP(_1185327, _1185329)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1185331, tc_HOL_Obool)), _1185327), _1185333)), -(hBOOL(hAPP(_1185333, _1185329)))], (45305 ^ _775212) ^ [_1673220, _1673222, _1673224, _1673226, _1673228, _1673230] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1673220, _1673222)), hAPP(hAPP(c_Product__Type_OPair(_1673220, _1673222), _1673224), _1673226)), hAPP(c_List_Oset(tc_prod(_1673220, _1673222)), hAPP(hAPP(c_List_Ozip(_1673220, _1673222), _1673228), _1673230)))), -(hBOOL(hAPP(hAPP(c_member(_1673220), _1673224), hAPP(c_List_Oset(_1673220), _1673228))))], (2720 ^ _775212) ^ [_815362, _815364, _815366, _815368] : [-(c_Code__Numeral_Onat__of__aux(_815368, _815364) = c_Code__Numeral_Onat__of__aux(_815366, _815362)), _815368 = _815366, _815364 = _815362], (40050 ^ _775212) ^ [_1542909, _1542911, _1542913, _1542915, _1542917] : [hBOOL(hAPP(hAPP(_1542909, _1542911), _1542913)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1542915, _1542917, _1542909), _1542911)))], (17363 ^ _775212) ^ [_1070200] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1070200), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1070200)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1070200)))], (25224 ^ _775212) ^ [_1213984, _1213986, _1213988] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1213984), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213986), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1213984), _1213988)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1213984), _1213986)))], (51755 ^ _775212) ^ [_1815804, _1815806] : [c_Relation_Osym(_1815804, hAPP(c_Relation_Oconverse(_1815804, _1815804), _1815806)), -(c_Relation_Osym(_1815804, _1815806))], (18677 ^ _775212) ^ [_1092536, _1092538] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1092536), hAPP(c_Int_Onumber__class_Onumber__of(_1092536), _1092538)), 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(_1092536), hAPP(c_Int_Onumber__class_Onumber__of(_1092536), _1092538)), hAPP(c_Int_Onumber__class_Onumber__of(_1092536), _1092538))), class_Groups_Omonoid__mult(_1092536), class_Int_Onumber(_1092536)], (17647 ^ _775212) ^ [_1074924, _1074926] : [c_Int_OBit1(_1074924) = c_Int_OBit1(_1074926), -(_1074924 = _1074926)], (49289 ^ _775212) ^ [_1761579, _1761581, _1761583, _1761585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761579), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761581)), _1761583))), -(hAPP(c_List_Orev(_1761581), hAPP(hAPP(c_List_Olist__update(_1761581, _1761583), _1761579), _1761585)) = hAPP(hAPP(c_List_Olist__update(_1761581, hAPP(c_List_Orev(_1761581), _1761583)), 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(_1761581)), _1761583)), _1761579)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1761585))], (15993 ^ _775212) ^ [_1046055, _1046057, _1046059] : [class_Groups_Oordered__ab__group__add__abs(_1046055), -(hAPP(c_Groups_Oabs__class_Oabs(_1046055), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046055), hAPP(c_Groups_Oabs__class_Oabs(_1046055), _1046057)), hAPP(c_Groups_Oabs__class_Oabs(_1046055), _1046059))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046055), hAPP(c_Groups_Oabs__class_Oabs(_1046055), _1046057)), hAPP(c_Groups_Oabs__class_Oabs(_1046055), _1046059)))], (39646 ^ _775212) ^ [_1533703, _1533705, _1533707, _1533709, _1533711] : [hBOOL(hAPP(hAPP(_1533703, _1533705), _1533707)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1533709, _1533711, _1533703), _1533707)))], (50192 ^ _775212) ^ [_1781684, _1781686, _1781688, _1781690, _1781692] : [-(hAPP(c_List_Ofilter(_1781684, _1781686), _1781688) = hAPP(hAPP(c_List_Olist_OCons(_1781684), _1781690), _1781692)), 50193 ^ _775212 : [(50194 ^ _775212) ^ [_1781812, _1781814] : [_1781688 = hAPP(hAPP(c_List_Oappend(_1781684), _1781814), hAPP(hAPP(c_List_Olist_OCons(_1781684), _1781690), _1781812)), 50200 ^ _775212 : [(50203 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1781686, 50199 ^ [_1781684, _1781686, _1781688, _1781690, _1781692, _1781812, _1781814])))], (50201 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781684), 50199 ^ [_1781684, _1781686, _1781688, _1781690, _1781692, _1781812, _1781814]), hAPP(c_List_Oset(_1781684), _1781814))))]], hBOOL(hAPP(_1781686, _1781690)), _1781692 = hAPP(c_List_Ofilter(_1781684, _1781686), _1781812)]]], (37926 ^ _775212) ^ [_1485120, _1485122, _1485124, _1485126] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1485120), _1485122)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1485124), _1485126)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1485120, _1485124)), hAPP(hAPP(c_Product__Type_OSigma(_1485120, _1485124), _1485122), hAPP(c_COMBK(tc_fun(_1485124, tc_HOL_Obool), _1485120), _1485126)))))], (230 ^ _775212) ^ [_778625, _778627] : [-(class_Fields_Ofield__inverse__zero(_778625)), _778627 = _778625, class_Fields_Ofield__inverse__zero(_778627)], (35861 ^ _775212) ^ [_1437941, _1437943, _1437945, _1437947, _1437949, _1437951, _1437953] : [c_Equiv__Relations_Oequiv(_1437941, _1437943, _1437945), c_Equiv__Relations_Ocongruent(_1437941, tc_fun(_1437947, tc_HOL_Obool), _1437945, _1437949), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1437941, tc_fun(_1437947, tc_HOL_Obool)), _1437951), _1437949) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1437941, tc_fun(_1437947, tc_HOL_Obool)), _1437953), _1437949), hBOOL(hAPP(hAPP(c_member(tc_fun(_1437941, tc_HOL_Obool)), _1437951), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1437941), _1437943), _1437945))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1437941, tc_HOL_Obool)), _1437953), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1437941), _1437943), _1437945))), 35883 ^ _775212 : [(35887 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1437941), 35885 ^ [_1437941, _1437943, _1437945, _1437947, _1437949, _1437951, _1437953]), _1437943)))], (35889 ^ _775212) ^ [] : [-(hAPP(_1437949, 35882 ^ [_1437941, _1437943, _1437945, _1437947, _1437949, _1437951, _1437953]) = hAPP(_1437949, 35885 ^ [_1437941, _1437943, _1437945, _1437947, _1437949, _1437951, _1437953]))], (35891 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1437941, _1437941)), hAPP(hAPP(c_Product__Type_OPair(_1437941, _1437941), 35882 ^ [_1437941, _1437943, _1437945, _1437947, _1437949, _1437951, _1437953]), 35885 ^ [_1437941, _1437943, _1437945, _1437947, _1437949, _1437951, _1437953])), _1437945))], (35884 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1437941), 35882 ^ [_1437941, _1437943, _1437945, _1437947, _1437949, _1437951, _1437953]), _1437943)))]], -(_1437951 = _1437953)], (34865 ^ _775212) ^ [_1415495, _1415497, _1415499] : [class_Lattices_Osemilattice__inf(_1415495), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415495), _1415497), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415495), _1415497), _1415499)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415495), _1415497), _1415499))], (23780 ^ _775212) ^ [_1188488] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1188488)) = _1188488)], (30610 ^ _775212) ^ [_1327100, _1327102, _1327104] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327100), _1327102)), hBOOL(hAPP(hAPP(c_member(_1327100), _1327104), _1327102)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1327100), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327100, tc_HOL_Obool)), _1327102), hAPP(hAPP(c_Set_Oinsert(_1327100), _1327104), c_Orderings_Obot__class_Obot(tc_fun(_1327100, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1327100), _1327102))], (22868 ^ _775212) ^ [_1170814, _1170816, _1170818, _1170820] : [class_Orderings_Olinorder(_1170814), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1170814), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1170814), _1170816), _1170818)), _1170820) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1170814), _1170816), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1170814), _1170818), _1170820)))], (21723 ^ _775212) ^ [_1147450, _1147452, _1147454] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1147450, tc_HOL_Obool)), _1147452), _1147454))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1147450, tc_HOL_Obool)), _1147452), _1147454)), -(_1147452 = _1147454)], (51312 ^ _775212) ^ [_1805585, _1805587] : [-(hBOOL(hAPP(_1805587, 51319 ^ [_1805585, _1805587]))), 51313 ^ _775212 : [(51314 ^ _775212) ^ [_1805646] : [hBOOL(hAPP(hAPP(c_member(_1805585), _1805646), c_Orderings_Otop__class_Otop(tc_fun(_1805585, tc_HOL_Obool)))), hBOOL(hAPP(_1805587, _1805646))]]], (1494 ^ _775212) ^ [_796743, _796745] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_796743)), _796745 = _796743, class_Groups_Oordered__cancel__ab__semigroup__add(_796745)], (8856 ^ _775212) ^ [_918808, _918810] : [-(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), _918808))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918810))))], (7244 ^ _775212) ^ [_890289, _890291, _890293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890289), _890291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890289), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _890293), _890291))))], (27715 ^ _775212) ^ [_1264799, _1264801, _1264803, _1264805, _1264807] : [27717 ^ _775212 : [(27723 ^ _775212) ^ [] : [hBOOL(hAPP(_1264807, 27719 ^ [_1264799, _1264801, _1264803, _1264805, _1264807]))], (27721 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1264799), 27719 ^ [_1264799, _1264801, _1264803, _1264805, _1264807]), hAPP(_1264805, 27716 ^ [_1264799, _1264801, _1264803, _1264805, _1264807]))))], (27718 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1264801), 27716 ^ [_1264799, _1264801, _1264803, _1264805, _1264807]), _1264803)))]], 27724 ^ _775212 : [(27725 ^ _775212) ^ [_1265109] : [hBOOL(hAPP(hAPP(c_member(_1264799), _1265109), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1264801, tc_fun(_1264799, tc_HOL_Obool)), _1264803), _1264805))), -(hBOOL(hAPP(_1264807, _1265109)))]]], (23406 ^ _775212) ^ [_1181120] : [-(c_Nitpick_Ozero__frac(_1181120) = c_Nitpick_OAbs__Frac(_1181120, 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))))], (33787 ^ _775212) ^ [_1391497, _1391499] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1391497, tc_HOL_Obool)), _1391499), hAPP(c_Set_OPow(_1391497), _1391499))))], (4086 ^ _775212) ^ [_837215, _837217, _837219, _837221, _837223, _837225] : [-(c_Finite__Set_Ofold(_837225, _837221, _837217) = c_Finite__Set_Ofold(_837223, _837219, _837215)), _837225 = _837223, _837221 = _837219, _837217 = _837215], (32201 ^ _775212) ^ [_1357653, _1357655, _1357657, _1357659, _1357661, _1357663, _1357665] : [c_Nitpick_Ofold__graph_H(_1357653, _1357655, _1357657, _1357659, _1357661, hAPP(hAPP(_1357657, _1357663), _1357665)), 32206 ^ _775212 : [(32209 ^ _775212) ^ [] : [-(hAPP(hAPP(_1357657, _1357663), _1357665) = _1357659)], (32207 ^ _775212) ^ [] : [-(_1357661 = c_Orderings_Obot__class_Obot(tc_fun(_1357653, tc_HOL_Obool)))]], 32212 ^ _775212 : [(32217 ^ _775212) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1357653, _1357655, _1357657, _1357659, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357653, tc_HOL_Obool)), _1357661), hAPP(hAPP(c_Set_Oinsert(_1357653), 32210 ^ [_1357653, _1357655, _1357657, _1357659, _1357661, _1357663, _1357665]), c_Orderings_Obot__class_Obot(tc_fun(_1357653, tc_HOL_Obool)))), 32211 ^ [_1357653, _1357655, _1357657, _1357659, _1357661, _1357663, _1357665]))], (32215 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1357653), 32210 ^ [_1357653, _1357655, _1357657, _1357659, _1357661, _1357663, _1357665]), _1357661)))], (32213 ^ _775212) ^ [] : [-(hAPP(hAPP(_1357657, _1357663), _1357665) = hAPP(hAPP(_1357657, 32210 ^ [_1357653, _1357655, _1357657, _1357659, _1357661, _1357663, _1357665]), 32211 ^ [_1357653, _1357655, _1357657, _1357659, _1357661, _1357663, _1357665]))]]], (28842 ^ _775212) ^ [_1287797, _1287799, _1287801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287797, tc_HOL_Obool)), _1287799), hAPP(hAPP(c_Set_Oinsert(_1287797), _1287801), c_Orderings_Obot__class_Obot(tc_fun(_1287797, tc_HOL_Obool))))), -(_1287799 = c_Orderings_Obot__class_Obot(tc_fun(_1287797, tc_HOL_Obool))), -(_1287799 = hAPP(hAPP(c_Set_Oinsert(_1287797), _1287801), c_Orderings_Obot__class_Obot(tc_fun(_1287797, tc_HOL_Obool))))], (42543 ^ _775212) ^ [_1601339, _1601341] : [c_Wellfounded_Owf(_1601339, hAPP(c_Relation_Oconverse(_1601339, _1601339), _1601341)), -(c_Wellfounded_Owf(_1601339, hAPP(c_Relation_Oconverse(_1601339, _1601339), c_Transitive__Closure_Otrancl(_1601339, _1601341))))], (37990 ^ _775212) ^ [_1486876, _1486878, _1486880, _1486882] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1486876, _1486878)), hAPP(hAPP(c_Product__Type_OSigma(_1486876, _1486878), hAPP(hAPP(c_Set_Oinsert(_1486876), _1486880), c_Orderings_Obot__class_Obot(tc_fun(_1486876, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1486878, tc_HOL_Obool), _1486876), _1486882))) = hAPP(c_Finite__Set_Ocard(_1486878), _1486882))], (29973 ^ _775212) ^ [_1311503, _1311505, _1311507, _1311509] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1311503, tc_fun(_1311505, tc_HOL_Obool))), _1311507), _1311509)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1311503, _1311505)), hAPP(hAPP(c_Product__Type_OPair(_1311503, _1311505), _1311507), _1311509)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1311503, _1311505), tc_HOL_Obool)))))], (27630 ^ _775212) ^ [_1262811] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1262811)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1262811))], (13777 ^ _775212) ^ [_1003667, _1003669, _1003671] : [-(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), _1003667), _1003669)), _1003671)), _1003669) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1003671), _1003669))], (43509 ^ _775212) ^ [_1625393, _1625395] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1625393, tc_HOL_Obool), tc_HOL_Obool)), _1625395), hAPP(c_Set_OPow(_1625393), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625393, tc_HOL_Obool), _1625395)))))], (43296 ^ _775212) ^ [_1620305, _1620307, _1620309] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620305, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1620305, tc_HOL_Obool), tc_HOL_Obool)), _1620307), _1620309)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620305, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620305, tc_HOL_Obool), _1620307)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620305, tc_HOL_Obool), _1620309)))], (33433 ^ _775212) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (42344 ^ _775212) ^ [_1595248, _1595250, _1595252, _1595254] : [42346 ^ _775212 : [(42349 ^ _775212) ^ [] : [hAPP(_1595254, 42345 ^ [_1595248, _1595250, _1595252, _1595254]) = c_Orderings_Otop__class_Otop(tc_fun(_1595248, tc_HOL_Obool))], (42347 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1595250), 42345 ^ [_1595248, _1595250, _1595252, _1595254]), _1595252)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1595248, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595250, tc_fun(_1595248, tc_HOL_Obool)), _1595252), _1595254))], (45471 ^ _775212) ^ [_1677799, _1677801, _1677803, _1677805, _1677807] : [-(hAPP(hAPP(c_List_Ozip(_1677799, _1677801), hAPP(hAPP(c_List_Olist_OCons(_1677799), _1677803), _1677805)), _1677807) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1677799, _1677801)), _1677801, c_List_Olist_ONil(tc_prod(_1677799, _1677801)), hAPP(hAPP(c_COMBC(_1677801, tc_fun(tc_List_Olist(_1677801), tc_List_Olist(tc_prod(_1677799, _1677801))), tc_fun(tc_List_Olist(_1677801), tc_List_Olist(tc_prod(_1677799, _1677801)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1677799, _1677801)), tc_List_Olist(tc_prod(_1677799, _1677801))), tc_fun(tc_fun(tc_List_Olist(_1677801), tc_List_Olist(tc_prod(_1677799, _1677801))), tc_fun(tc_List_Olist(_1677801), tc_List_Olist(tc_prod(_1677799, _1677801)))), _1677801), c_COMBB(tc_List_Olist(tc_prod(_1677799, _1677801)), tc_List_Olist(tc_prod(_1677799, _1677801)), tc_List_Olist(_1677801))), hAPP(hAPP(c_COMBB(tc_prod(_1677799, _1677801), tc_fun(tc_List_Olist(tc_prod(_1677799, _1677801)), tc_List_Olist(tc_prod(_1677799, _1677801))), _1677801), c_List_Olist_OCons(tc_prod(_1677799, _1677801))), hAPP(c_Product__Type_OPair(_1677799, _1677801), _1677803)))), hAPP(c_List_Ozip(_1677799, _1677801), _1677805))), _1677807))], (52293 ^ _775212) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (18545 ^ _775212) ^ [_1090248] : [-(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)))), _1090248) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1090248)))], (8735 ^ _775212) ^ [_916921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _916921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _916921)))], (44140 ^ _775212) ^ [_1640803, _1640805, _1640807] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640803)), c_List_Osublist(_1640803, _1640805, _1640807)) = 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(_1640803)), _1640805)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1640807)))))], (24274 ^ _775212) ^ [_1196633, _1196635, _1196637] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196633), _1196635)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196635), _1196633))), _1196635 = _1196637, 24285 ^ _775212 : [(24288 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196637), _1196633))], (24286 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196633), _1196637)))]]], (33316 ^ _775212) ^ [_1380397, _1380399, _1380401, _1380403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1380397), _1380399)), -(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), _1380397), _1380401)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1380399), _1380403))), c_FunDef_Opair__less)))], (9066 ^ _775212) ^ [_922083, _922085, _922087, _922089] : [class_Orderings_Oord(_922083), 9069 ^ _775212 : [(9076 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922083), hAPP(_922087, 9077 ^ [_922083, _922085, _922087, _922089])), hAPP(_922089, 9077 ^ [_922083, _922085, _922087, _922089]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922085, _922083)), _922087), _922089)))], (9070 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922085, _922083)), _922087), _922089)), 9073 ^ _775212 : [(9074 ^ _775212) ^ [_922240] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922083), hAPP(_922087, _922240)), hAPP(_922089, _922240))))]]]]], (46768 ^ _775212) ^ [_1707468, _1707470, _1707472] : [hAPP(c_List_Orotate(_1707468, _1707470), _1707472) = c_List_Olist_ONil(_1707468), -(_1707472 = c_List_Olist_ONil(_1707468))], (43000 ^ _775212) ^ [_1613325, _1613327, _1613329, _1613331] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1613325, _1613327), tc_fun(_1613325, _1613327)), _1613329), c_Fun_Ocomp(_1613327, _1613327, _1613325, _1613331)) = c_Fun_Ocomp(_1613327, _1613327, _1613325, hAPP(hAPP(c_Nat_Ocompow(_1613327, _1613327), _1613329), _1613331)))], (42361 ^ _775212) ^ [_1595852, _1595854, _1595856, _1595858, _1595860] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595852, _1595854)), hAPP(hAPP(c_Product__Type_OPair(_1595852, _1595854), _1595856), _1595858)), hAPP(c_Relation_Oconverse(_1595854, _1595852), _1595860))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595854, _1595852)), hAPP(hAPP(c_Product__Type_OPair(_1595854, _1595852), _1595858), _1595856)), _1595860)))], (34981 ^ _775212) ^ [_1418420, _1418422, _1418424, _1418426, _1418428] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418420, tc_fun(_1418422, tc_HOL_Obool)), _1418424), hAPP(hAPP(c_COMBC(_1418420, tc_fun(_1418422, tc_HOL_Obool), tc_fun(_1418422, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1418422, tc_HOL_Obool), tc_fun(tc_fun(_1418422, tc_HOL_Obool), tc_fun(_1418422, tc_HOL_Obool)), _1418420), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418422, tc_HOL_Obool))), _1418426)), _1418428)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418422, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418420, tc_fun(_1418422, tc_HOL_Obool)), _1418424), _1418426)), _1418428))], (38212 ^ _775212) ^ [_1493064, _1493066, _1493068] : [-(hAPP(c_Product__Type_Omap__pair(_1493064, _1493064, _1493066, _1493066, c_COMBI(_1493064), c_COMBI(_1493066)), _1493068) = _1493068)], (28456 ^ _775212) ^ [_1279984, _1279986] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279984), _1279986)), 28459 ^ _775212 : [(28466 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279984), c_Orderings_Otop__class_Otop(tc_fun(_1279984, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279984), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1279984, tc_HOL_Obool)), _1279986))))], (28460 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279984), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1279984, tc_HOL_Obool)), _1279986))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279984), c_Orderings_Otop__class_Otop(tc_fun(_1279984, tc_HOL_Obool)))))]]], (42816 ^ _775212) ^ [_1608901, _1608903] : [-(c_Transitive__Closure_Ortrancl(_1608901, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1608901, _1608901), tc_HOL_Obool)), _1608903), c_Relation_OId(_1608901))) = c_Transitive__Closure_Ortrancl(_1608901, _1608903))], (7671 ^ _775212) ^ [_898052, _898054, _898056] : [class_Rings_Oring(_898052), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898052), hAPP(c_Groups_Ouminus__class_Ouminus(_898052), _898054)), hAPP(c_Groups_Ouminus__class_Ouminus(_898052), _898056)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898052), _898054), _898056))], (32828 ^ _775212) ^ [_1370656, _1370658, _1370660, _1370662, _1370664] : [hAPP(_1370660, _1370662) = _1370664, -(c_Fun_Ofun__upd(_1370656, _1370658, _1370660, _1370662, _1370664) = _1370660)], (29286 ^ _775212) ^ [_1295783, _1295785] : [class_Orderings_Olinorder(_1295783), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295783, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1295783), _1295785), c_Orderings_Obot__class_Obot(tc_fun(_1295783, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1295783), _1295785)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1295783), _1295785))], (27383 ^ _775212) ^ [_1257865, _1257867, _1257869, _1257871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257865, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1257865, tc_HOL_Obool)), _1257867), _1257869)), _1257871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257865, tc_HOL_Obool)), _1257867), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257865, tc_HOL_Obool)), _1257869), _1257871))))], (33060 ^ _775212) ^ [_1374936, _1374938, _1374940, _1374942, _1374944] : [class_Rings_Ocomm__semiring__1(_1374936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374938), _1374940)), hBOOL(hAPP(hAPP(c_member(_1374938), _1374942), _1374940)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1374936), hAPP(_1374944, _1374942)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1374938, _1374936), _1374944), _1374940))))], (35309 ^ _775212) ^ [_1426116, _1426118, _1426120] : [class_Orderings_Oorder(_1426116), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426116, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1426116, _1426118, _1426120)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1426116), _1426120)) = c_Orderings_Obot__class_Obot(tc_fun(_1426116, tc_HOL_Obool)))], (7739 ^ _775212) ^ [_899489, _899491, _899493] : [class_Groups_Ogroup__add(_899489), 7742 ^ _775212 : [(7749 ^ _775212) ^ [] : [_899493 = hAPP(c_Groups_Ouminus__class_Ouminus(_899489), _899491), -(_899491 = hAPP(c_Groups_Ouminus__class_Ouminus(_899489), _899493))], (7743 ^ _775212) ^ [] : [_899491 = hAPP(c_Groups_Ouminus__class_Ouminus(_899489), _899493), -(_899493 = hAPP(c_Groups_Ouminus__class_Ouminus(_899489), _899491))]]], (36385 ^ _775212) ^ [_1450787, _1450789, _1450791] : [-(c_Fun_Oinj__on(_1450787, _1450789, _1450791, c_Orderings_Obot__class_Obot(tc_fun(_1450787, tc_HOL_Obool))))], (43801 ^ _775212) ^ [_1632659, _1632661, _1632663, _1632665] : [class_Orderings_Olinorder(_1632659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1632659), _1632661)), 43811 ^ _775212 : [(43814 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1632659), 43810 ^ [_1632659, _1632661, _1632663, _1632665]), _1632663))], (43812 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1632659), 43810 ^ [_1632659, _1632661, _1632663, _1632665]), _1632661)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1632659), hAPP(hAPP(c_Finite__Set_Ofold(_1632659, _1632659, c_Orderings_Oord__class_Omax(_1632659)), _1632665), _1632661)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1632659), _1632663), _1632665))))], (38889 ^ _775212) ^ [_1506371, _1506373, _1506375, _1506377] : [-(hAPP(c_Set_OCollect(tc_prod(_1506371, _1506373)), hAPP(c_Product__Type_Oprod_Oprod__case(_1506371, _1506373, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1506371, tc_fun(_1506373, tc_HOL_Obool), tc_fun(_1506373, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1506373, tc_HOL_Obool), tc_fun(_1506373, tc_HOL_Obool)), _1506371), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1506373)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506371), c_fconj), _1506375))), _1506377))) = hAPP(hAPP(c_Product__Type_OSigma(_1506371, _1506373), hAPP(c_Set_OCollect(_1506371), _1506375)), hAPP(c_COMBK(tc_fun(_1506373, tc_HOL_Obool), _1506371), hAPP(c_Set_OCollect(_1506373), _1506377))))], (16807 ^ _775212) ^ [_1061828, _1061830] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1061828) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1061830)), _1061828 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1061830)), 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), _1061830)))], (37160 ^ _775212) ^ [_1466613, _1466615, _1466617, _1466619] : [class_Groups_Ocomm__monoid__mult(_1466613), 37163 ^ _775212 : [(37170 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1466615), _1466617))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1466615, _1466613), _1466619), _1466617) = c_Groups_Oone__class_Oone(_1466613))], (37164 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466615), _1466617)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1466615, _1466613), _1466619), _1466617) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1466613, _1466615, c_Groups_Otimes__class_Otimes(_1466613)), _1466619), c_Groups_Oone__class_Oone(_1466613)), _1466617))]]], (26573 ^ _775212) ^ [_1242391, _1242393] : [c_Nat__Transfer_Onat__set(_1242391), c_Nat__Transfer_Onat__set(_1242393), 26580 ^ _775212 : [(26587 ^ _775212) ^ [] : [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), _1242391)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1242393))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1242391), _1242393)))], (26581 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1242391), _1242393)), -(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), _1242391)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1242393))))]]], (35765 ^ _775212) ^ [_1435818, _1435820, _1435822] : [class_Orderings_Olinorder(_1435818), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435818), _1435820)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435818), _1435822)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435818, tc_HOL_Obool)), _1435820), _1435822) = c_Orderings_Obot__class_Obot(tc_fun(_1435818, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1435818), c_Big__Operators_Olattice_OSup__fin(_1435818, c_Orderings_Oord__class_Omax(_1435818), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1435818, tc_HOL_Obool)), _1435820), _1435822))), c_Big__Operators_Olattice_OSup__fin(_1435818, c_Orderings_Oord__class_Omax(_1435818), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435818, tc_HOL_Obool)), _1435820), _1435822))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1435818), c_Big__Operators_Olattice_OSup__fin(_1435818, c_Orderings_Oord__class_Omax(_1435818), _1435820)), c_Big__Operators_Olattice_OSup__fin(_1435818, c_Orderings_Oord__class_Omax(_1435818), _1435822)))], (13274 ^ _775212) ^ [_995402, _995404, _995406] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _995402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995404), _995406)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _995402), _995404)), _995406))], (40301 ^ _775212) ^ [_1549048, _1549050] : [c_Nitpick_Owf_H(_1549048, _1549050), 40304 ^ _775212 : [(40307 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1549048, _1549048)), _1549050))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (40305 ^ _775212) ^ [] : [-(c_Wellfounded_Oacyclic(_1549048, _1549050))]]], (39860 ^ _775212) ^ [_1537911, _1537913, _1537915] : [c_Wellfounded_Owf(_1537911, _1537913), -(hBOOL(hAPP(hAPP(c_member(_1537911), _1537915), c_Wellfounded_Oacc(_1537911, _1537913))))], (7849 ^ _775212) ^ [_901242, _901244] : [class_Groups_Olinordered__ab__group__add(_901242), 7852 ^ _775212 : [(7859 ^ _775212) ^ [] : [_901244 = c_Groups_Ozero__class_Ozero(_901242), -(_901244 = hAPP(c_Groups_Ouminus__class_Ouminus(_901242), _901244))], (7853 ^ _775212) ^ [] : [_901244 = hAPP(c_Groups_Ouminus__class_Ouminus(_901242), _901244), -(_901244 = c_Groups_Ozero__class_Ozero(_901242))]]], (5601 ^ _775212) ^ [_863409, _863411] : [hAPP(c_Nat_OSuc, _863409) = hAPP(c_Nat_OSuc, _863411), -(_863409 = _863411)], (22162 ^ _775212) ^ [_1155868, _1155870, _1155872] : [class_Int_Onumber__ring(_1155868), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1155868), _1155870), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1155872))) = hAPP(hAPP(c_HOL_OLet(_1155868, _1155868), hAPP(hAPP(c_Power_Opower__class_Opower(_1155868), _1155870), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155872))), hAPP(hAPP(c_COMBS(_1155868, _1155868, _1155868), c_Groups_Otimes__class_Otimes(_1155868)), c_COMBI(_1155868))))], (52279 ^ _775212) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (40162 ^ _775212) ^ [_1545304, _1545306] : [c_Wellfounded_Owf(_1545304, _1545306), -(c_Wellfounded_OwfP(_1545304, hAPP(hAPP(c_COMBC(_1545304, tc_fun(tc_prod(_1545304, _1545304), tc_HOL_Obool), tc_fun(_1545304, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545304, tc_fun(tc_fun(tc_prod(_1545304, _1545304), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1545304, _1545304), tc_HOL_Obool), tc_fun(_1545304, tc_HOL_Obool)), _1545304), c_COMBC(_1545304, tc_fun(tc_prod(_1545304, _1545304), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545304, tc_prod(_1545304, _1545304)), tc_fun(_1545304, tc_fun(tc_fun(tc_prod(_1545304, _1545304), tc_HOL_Obool), tc_HOL_Obool)), _1545304), hAPP(c_COMBB(tc_prod(_1545304, _1545304), tc_fun(tc_fun(tc_prod(_1545304, _1545304), tc_HOL_Obool), tc_HOL_Obool), _1545304), c_member(tc_prod(_1545304, _1545304)))), c_Product__Type_OPair(_1545304, _1545304)))), _1545306)))], (15463 ^ _775212) ^ [_1036094, _1036096, _1036098, _1036100, _1036102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036094), _1036096)), 15466 ^ _775212 : [(15473 ^ _775212) ^ [] : [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), _1036096), _1036094)), _1036098)), _1036100)), _1036102)), -(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), _1036096), _1036098)), _1036100)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036094), _1036098)), _1036102))))], (15467 ^ _775212) ^ [] : [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), _1036096), _1036098)), _1036100)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036094), _1036098)), _1036102))), -(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), _1036096), _1036094)), _1036098)), _1036100)), _1036102)))]]], (34765 ^ _775212) ^ [_1413777, _1413779] : [class_Lattices_Obounded__lattice__top(_1413777), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1413777), c_Orderings_Otop__class_Otop(_1413777)), _1413779) = _1413779)], (46460 ^ _775212) ^ [_1700934, _1700936, _1700938] : [-(hAPP(hAPP(c_List_Odrop(_1700934), _1700936), hAPP(c_List_Otl(_1700934), _1700938)) = hAPP(c_List_Otl(_1700934), hAPP(hAPP(c_List_Odrop(_1700934), _1700936), _1700938)))], (42017 ^ _775212) ^ [_1586946, _1586948, _1586950, _1586952] : [hBOOL(hAPP(hAPP(c_member(_1586946), _1586948), c_Wellfounded_Oacc(_1586946, _1586950))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586946, _1586946)), hAPP(hAPP(c_Product__Type_OPair(_1586946, _1586946), _1586952), _1586948)), c_Transitive__Closure_Ortrancl(_1586946, _1586950))), -(hBOOL(hAPP(hAPP(c_member(_1586946), _1586952), c_Wellfounded_Oacc(_1586946, _1586950))))], (45341 ^ _775212) ^ [_1674233, _1674235, _1674237] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1674233))), -(c_List_Osublist(_1674235, hAPP(hAPP(c_List_Olist_OCons(_1674235), _1674237), c_List_Olist_ONil(_1674235)), _1674233) = c_List_Olist_ONil(_1674235))], (27111 ^ _775212) ^ [_1252822, _1252824] : [class_Lattices_Olattice(_1252822), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252822), _1252824), _1252824) = _1252824)], (29698 ^ _775212) ^ [_1304228, _1304230, _1304232, _1304234] : [hBOOL(hAPP(hAPP(c_member(_1304228), _1304230), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304228, tc_HOL_Obool)), _1304232), _1304234))), -(hBOOL(hAPP(hAPP(c_member(_1304228), _1304230), _1304232))), -(hBOOL(hAPP(hAPP(c_member(_1304228), _1304230), _1304234)))], (32321 ^ _775212) ^ [_1360530, _1360532, _1360534, _1360536] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1360530, _1360532)), c_Sum__Type_OPlus(_1360530, _1360532, _1360534, _1360536))), 32324 ^ _775212 : [(32327 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1360532), _1360536)))], (32325 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1360530), _1360534)))]]], (49651 ^ _775212) ^ [_1769221, _1769223, _1769225, _1769227] : [49653 ^ _775212 : [(49658 ^ _775212) ^ [] : [hBOOL(hAPP(_1769227, hAPP(hAPP(c_List_Onth(_1769223), _1769225), 49652 ^ [_1769221, _1769223, _1769225, _1769227])))], (49656 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49652 ^ [_1769221, _1769223, _1769225, _1769227]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769223)), _1769225))))], (49654 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49652 ^ [_1769221, _1769223, _1769225, _1769227]), _1769221)))]], 49661 ^ _775212 : [(49664 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1769227, hAPP(hAPP(c_List_Onth(_1769223), _1769225), _1769221))))], (49662 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1769221), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769223)), _1769225))))]], -(c_List_OtakeWhile(_1769223, _1769227, _1769225) = hAPP(hAPP(c_List_Otake(_1769223), _1769221), _1769225))], (1794 ^ _775212) ^ [_800493, _800495] : [-(class_Rings_Osemiring__0(_800493)), _800495 = _800493, class_Rings_Osemiring__0(_800495)], (14421 ^ _775212) ^ [_1015962, _1015964, _1015966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015962), _1015964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015966), _1015964)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015966), _1015962))))], (38973 ^ _775212) ^ [_1508249, _1508251, _1508253] : [hBOOL(hAPP(hAPP(c_member(_1508249), _1508251), hAPP(c_Set_OCollect(_1508249), _1508253))), -(hBOOL(hAPP(_1508253, _1508251)))], (47194 ^ _775212) ^ [_1716037, _1716039, _1716041, _1716043] : [hAPP(hAPP(c_List_Oappend(_1716037), _1716039), hAPP(hAPP(c_List_Olist_OCons(_1716037), _1716041), c_List_Olist_ONil(_1716037))) = _1716043, 47197 ^ _775212 : [(47202 ^ _775212) ^ [] : [-(c_List_Olast(_1716037, _1716043) = _1716041)], (47200 ^ _775212) ^ [] : [-(c_List_Obutlast(_1716037, _1716043) = _1716039)], (47198 ^ _775212) ^ [] : [_1716043 = c_List_Olist_ONil(_1716037)]]], (13424 ^ _775212) ^ [_997859, _997861] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _997859, _997861) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_997859 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _997861), 13427 ^ [_997859, _997861]))], (42125 ^ _775212) ^ [_1589375, _1589377, _1589379, _1589381, _1589383, _1589385] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589375, tc_fun(_1589377, tc_HOL_Obool)), _1589379), _1589381), _1589383)), -(hBOOL(hAPP(hAPP(_1589381, _1589385), _1589383))), hBOOL(hAPP(hAPP(c_member(_1589375), _1589385), _1589379))], (45758 ^ _775212) ^ [_1684268, _1684270, _1684272] : [hAPP(hAPP(c_List_Oappend(_1684268), _1684270), _1684272) = _1684272, -(_1684270 = c_List_Olist_ONil(_1684268))], (11738 ^ _775212) ^ [_967904, _967906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967904), _967906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967904)), hAPP(c_Nat_OSuc, _967906))))], (12767 ^ _775212) ^ [_985805, _985807] : [class_Lattices_Oab__semigroup__idem__mult(_985805), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985805), _985807), _985807) = _985807)], (37495 ^ _775212) ^ [_1473858, _1473860, _1473862, _1473864] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1473858), _1473860)), c_Fun_Oinj__on(_1473862, _1473858, _1473864, c_Orderings_Otop__class_Otop(tc_fun(_1473862, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1473862), hAPP(c_Set_Ovimage(_1473862, _1473858, _1473864), _1473860))))], (10806 ^ _775212) ^ [_951718] : [10808 ^ _775212 : [(10811 ^ _775212) ^ [] : [hBOOL(hAPP(_951718, hAPP(c_Int_Onat, 10807 ^ [_951718])))], (10809 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10807 ^ [_951718])))]], 10812 ^ _775212 : [(10813 ^ _775212) ^ [_951851] : [-(hBOOL(hAPP(_951718, _951851)))]]], (5474 ^ _775212) ^ [_858749, _858751, _858753, _858755] : [-(tc_sum(_858755, _858751) = tc_sum(_858753, _858749)), _858755 = _858753, _858751 = _858749], (2498 ^ _775212) ^ [_811749, _811751, _811753, _811755] : [-(c_Random_Oinc__shift(_811755, _811751) = c_Random_Oinc__shift(_811753, _811749)), _811755 = _811753, _811751 = _811749], (31162 ^ _775212) ^ [_1338564, _1338566, _1338568, _1338570, _1338572] : [c_Finite__Set_Ofolding__one(_1338564, _1338566, _1338568), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338564), _1338570)), -(hBOOL(hAPP(hAPP(c_member(_1338564), _1338572), _1338570))), -(_1338570 = c_Orderings_Obot__class_Obot(tc_fun(_1338564, tc_HOL_Obool))), -(hAPP(_1338568, hAPP(hAPP(c_Set_Oinsert(_1338564), _1338572), _1338570)) = hAPP(hAPP(_1338566, _1338572), hAPP(_1338568, _1338570)))], (51474 ^ _775212) ^ [_1810185, _1810187, _1810189, _1810191] : [class_Complete__Lattice_Ocomplete__lattice(_1810185), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1810187, _1810185), _1810189), _1810191) = c_Complete__Lattice_OInf__class_OInf(_1810185, hAPP(c_Set_OCollect(_1810185), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1810187, _1810185), tc_HOL_Obool), tc_HOL_Obool, _1810185), c_HOL_OEx(tc_fun(_1810187, _1810185))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1810187, _1810185), tc_HOL_Obool), tc_fun(tc_fun(_1810187, _1810185), tc_HOL_Obool), _1810185), hAPP(c_COMBS(tc_fun(_1810187, _1810185), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1810187, _1810185)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1810187, _1810185), tc_fun(tc_fun(_1810187, _1810185), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1810187, _1810185))), _1810189)))), hAPP(hAPP(c_COMBC(_1810185, tc_fun(tc_fun(_1810187, _1810185), _1810185), tc_fun(tc_fun(_1810187, _1810185), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1810185, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1810187, _1810185), _1810185), tc_fun(tc_fun(_1810187, _1810185), tc_HOL_Obool)), _1810185), c_COMBB(_1810185, tc_HOL_Obool, tc_fun(_1810187, _1810185))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1810187, _1810185), _1810187, _1810185), c_COMBI(tc_fun(_1810187, _1810185))), _1810191)))))))], (34925 ^ _775212) ^ [_1416865, _1416867] : [class_Lattices_Olattice(_1416865), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416865), _1416867), _1416867) = _1416867)], (38363 ^ _775212) ^ [_1496414, _1496416] : [class_Orderings_Olinorder(_1496414), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496414), _1496416)), -(c_Big__Operators_Olinorder__class_OMax(_1496414, _1496416) = hAPP(c_Finite__Set_Ofold1(_1496414, c_Orderings_Oord__class_Omax(_1496414)), _1496416))], (25214 ^ _775212) ^ [_1213828, _1213830, _1213832] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1213828), _1213830)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1213828), _1213832))), -(_1213828 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1213830), _1213832)))], (46220 ^ _775212) ^ [_1695509, _1695511, _1695513] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695509)), hAPP(hAPP(c_List_Odrop(_1695509), _1695511), _1695513)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695509)), _1695513)), _1695511))], (36179 ^ _775212) ^ [_1446507, _1446509, _1446511] : [class_Lattices_Olattice(_1446507), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446507), _1446509)), hBOOL(hAPP(hAPP(c_member(_1446507), _1446511), _1446509)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1446507), _1446511), c_Big__Operators_Olattice__class_OInf__fin(_1446507, _1446509)) = c_Big__Operators_Olattice__class_OInf__fin(_1446507, _1446509))], (35823 ^ _775212) ^ [_1437022, _1437024, _1437026, _1437028] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1437022), _1437024)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1437022), _1437026)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437022, tc_Nat_Onat), _1437028), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437022, tc_HOL_Obool)), _1437024), _1437026)) = 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(_1437022, tc_Nat_Onat), _1437028), _1437024)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437022, tc_Nat_Onat), _1437028), _1437026))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437022, tc_Nat_Onat), _1437028), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437022, tc_HOL_Obool)), _1437024), _1437026))))], (12139 ^ _775212) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (24320 ^ _775212) ^ [_1197405, _1197407, _1197409] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197405), _1197407)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197407), _1197405))), 24335 ^ _775212 : [(24338 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197409), _1197405))], (24336 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197405), _1197409)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197407), _1197409)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197409), _1197407)))], (19233 ^ _775212) ^ [_1102921, _1102923, _1102925] : [class_Fields_Olinordered__field__inverse__zero(_1102921), 19236 ^ _775212 : [(19251 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102921), c_Groups_Ozero__class_Ozero(_1102921)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102921), _1102923), _1102925)))), 19252 ^ _775212 : [(19259 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102921), _1102923), c_Groups_Ozero__class_Ozero(_1102921))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102921), _1102925), c_Groups_Ozero__class_Ozero(_1102921)))], (19253 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102921), c_Groups_Ozero__class_Ozero(_1102921)), _1102923)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102921), c_Groups_Ozero__class_Ozero(_1102921)), _1102925))]]], (19237 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102921), c_Groups_Ozero__class_Ozero(_1102921)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102921), _1102923), _1102925))), 19242 ^ _775212 : [(19245 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102921), c_Groups_Ozero__class_Ozero(_1102921)), _1102925)))], (19243 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102921), c_Groups_Ozero__class_Ozero(_1102921)), _1102923)))]], 19246 ^ _775212 : [(19249 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102921), _1102925), c_Groups_Ozero__class_Ozero(_1102921))))], (19247 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102921), _1102923), c_Groups_Ozero__class_Ozero(_1102921))))]]]]], (12169 ^ _775212) ^ [_975265, _975267, _975269] : [12170 ^ _775212 : [(12173 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975265), _975269))], (12171 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _975267)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975265), _975267)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975269), _975267))))], (766 ^ _775212) ^ [_786923, _786925, _786927, _786929, _786931, _786933, _786935, _786937, _786939, _786941] : [-(c_List_Olist__all2(_786939, _786935, _786931, _786927, _786923)), c_List_Olist__all2(_786941, _786937, _786933, _786929, _786925), _786941 = _786939, _786937 = _786935, _786933 = _786931, _786929 = _786927, _786925 = _786923], (37525 ^ _775212) ^ [_1474460, _1474462, _1474464, _1474466, _1474468] : [c_Fun_Oinj__on(_1474460, _1474462, _1474464, c_Orderings_Otop__class_Otop(tc_fun(_1474460, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474462, tc_HOL_Obool)), _1474466), hAPP(c_Set_Oimage(_1474460, _1474462, _1474464), _1474468))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474460, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1474460, _1474462, _1474464), _1474466)), _1474468)))], (2952 ^ _775212) ^ [_819306, _819308, _819310, _819312] : [-(c_Set_Othe__elem(_819312, _819308) = c_Set_Othe__elem(_819310, _819306)), _819312 = _819310, _819308 = _819306], (21999 ^ _775212) ^ [_1152656, _1152658, _1152660] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1152656, _1152658), _1152660))), _1152656 = 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), _1152660)), _1152658)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1152660)), 22006 ^ _775212 : [(22009 ^ _775212) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1152660) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22007 ^ _775212) ^ [] : [-(_1152658 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 22010 ^ _775212 : [(22013 ^ _775212) ^ [] : [22014 ^ _775212 : [(22017 ^ _775212) ^ [] : [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), _1152660))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1152660)), _1152658))], (22015 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152658)))]], 22022 ^ _775212 : [(22025 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152658), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1152660))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1152660)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22023 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152658))]]], (22011 ^ _775212) ^ [] : [_1152658 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (36279 ^ _775212) ^ [_1448036, _1448038, _1448040] : [class_Lattices_Olattice(_1448036), hBOOL(hAPP(c_Finite__Set_Ofinite(_1448036), _1448038)), 36286 ^ _775212 : [(36293 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1448036, tc_HOL_Obool)), _1448038), hAPP(hAPP(c_Set_Oinsert(_1448036), _1448040), c_Orderings_Obot__class_Obot(tc_fun(_1448036, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1448036, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1448036, hAPP(hAPP(c_Set_Oinsert(_1448036), _1448040), _1448038)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1448036), _1448040), c_Big__Operators_Olattice__class_OInf__fin(_1448036, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1448036, tc_HOL_Obool)), _1448038), hAPP(hAPP(c_Set_Oinsert(_1448036), _1448040), c_Orderings_Obot__class_Obot(tc_fun(_1448036, tc_HOL_Obool)))))))], (36287 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1448036, tc_HOL_Obool)), _1448038), hAPP(hAPP(c_Set_Oinsert(_1448036), _1448040), c_Orderings_Obot__class_Obot(tc_fun(_1448036, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1448036, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1448036, hAPP(hAPP(c_Set_Oinsert(_1448036), _1448040), _1448038)) = _1448040)]]], (3826 ^ _775212) ^ [_833223, _833225, _833227, _833229, _833231, _833233, _833235, _833237] : [-(c_Nat_Onat_Onat__case(_833237, _833233, _833229, _833225) = c_Nat_Onat_Onat__case(_833235, _833231, _833227, _833223)), _833237 = _833235, _833233 = _833231, _833229 = _833227, _833225 = _833223], (28648 ^ _775212) ^ [_1283994, _1283996] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283994, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1283994, tc_HOL_Obool))), _1283996) = _1283996)], (34487 ^ _775212) ^ [_1408002, _1408004, _1408006, _1408008] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408002, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408002, tc_HOL_Obool)), _1408004), _1408006)), _1408008) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408002, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408002, tc_HOL_Obool)), _1408004), _1408008)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408002, tc_HOL_Obool)), _1408006), _1408008)))], (9901 ^ _775212) ^ [_935562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935562)), -(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)), _935562))))], (43138 ^ _775212) ^ [_1616971, _1616973, _1616975, _1616977, _1616979] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616971, _1616971)), hAPP(hAPP(c_Product__Type_OPair(_1616971, _1616971), _1616973), _1616975)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1616971, _1616971), tc_HOL_Obool), _1616977), _1616979))), 43143 ^ _775212 : [(43146 ^ _775212) ^ [] : [-(_1616973 = _1616975)], (43144 ^ _775212) ^ [] : [-(_1616977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 43149 ^ _775212 : [(43154 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616971, _1616971)), hAPP(hAPP(c_Product__Type_OPair(_1616971, _1616971), 43147 ^ [_1616971, _1616973, _1616975, _1616977, _1616979]), _1616975)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1616971, _1616971), tc_HOL_Obool), 43148 ^ [_1616971, _1616973, _1616975, _1616977, _1616979]), _1616979))))], (43152 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616971, _1616971)), hAPP(hAPP(c_Product__Type_OPair(_1616971, _1616971), _1616973), 43147 ^ [_1616971, _1616973, _1616975, _1616977, _1616979])), _1616979)))], (43150 ^ _775212) ^ [] : [-(_1616977 = hAPP(c_Nat_OSuc, 43148 ^ [_1616971, _1616973, _1616975, _1616977, _1616979]))]]], (47883 ^ _775212) ^ [_1731252, _1731254, _1731256] : [-(hAPP(c_List_Oset(tc_List_Olist(_1731252)), c_Enum_On__lists(_1731252, _1731254, _1731256)) = hAPP(c_Set_OCollect(tc_List_Olist(_1731252)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1731252), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1731252)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1731252), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1731252)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1731252)))), _1731254))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1731252), tc_fun(_1731252, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1731252, tc_HOL_Obool), tc_fun(tc_fun(_1731252, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1731252)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1731252, tc_HOL_Obool))), c_List_Oset(_1731252))), hAPP(c_List_Oset(_1731252), _1731256)))))], (29258 ^ _775212) ^ [_1295290, _1295292] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1295290), _1295292)))), -(_1295292 = c_Orderings_Obot__class_Obot(tc_fun(_1295290, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295290), _1295292))], (24642 ^ _775212) ^ [_1202977, _1202979, _1202981] : [class_Divides_Osemiring__div(_1202977), 24645 ^ _775212 : [(24652 ^ _775212) ^ [] : [c_Divides_Odiv__class_Omod(_1202977, _1202981, _1202979) = c_Groups_Ozero__class_Ozero(_1202977), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1202977), _1202979), _1202981)))], (24646 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1202977), _1202979), _1202981)), -(c_Divides_Odiv__class_Omod(_1202977, _1202981, _1202979) = c_Groups_Ozero__class_Ozero(_1202977))]]], (32971 ^ _775212) ^ [_1373271, _1373273, _1373275] : [class_Groups_Ocomm__monoid__mult(_1373271), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1373273, _1373271), _1373275), c_Orderings_Obot__class_Obot(tc_fun(_1373273, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1373271))], (11997 ^ _775212) ^ [_972304, _972306, _972308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _972304)), 12000 ^ _775212 : [(12007 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972306), _972308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972304), _972306)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972304), _972308))))], (12001 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972304), _972306)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972304), _972308))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972306), _972308)))]]], (51379 ^ _775212) ^ [_1807042, _1807044] : [c_Relation_Otrans(_1807042, _1807044), -(c_Relation_Otrans(tc_List_Olist(_1807042), c_List_Olexord(_1807042, _1807044)))], (14747 ^ _775212) ^ [_1022097, _1022099, _1022101] : [class_Rings_Olinordered__semidom(_1022097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022097), c_Groups_Oone__class_Oone(_1022097)), _1022099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022097), c_Groups_Oone__class_Oone(_1022097)), hAPP(hAPP(c_Power_Opower__class_Opower(_1022097), _1022099), _1022101))))], (4500 ^ _775212) ^ [_843672, _843674, _843676, _843678] : [-(c_List_Omeasures(_843678, _843674) = c_List_Omeasures(_843676, _843672)), _843678 = _843676, _843674 = _843672], (33986 ^ _775212) ^ [_1395851, _1395853, _1395855, _1395857, _1395859, _1395861] : [-(hAPP(c_Relation_OImage(_1395851, _1395853, _1395855), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395857, tc_fun(_1395851, tc_HOL_Obool)), _1395859), _1395861)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395857, tc_fun(_1395853, tc_HOL_Obool)), _1395859), hAPP(hAPP(c_COMBB(tc_fun(_1395851, tc_HOL_Obool), tc_fun(_1395853, tc_HOL_Obool), _1395857), c_Relation_OImage(_1395851, _1395853, _1395855)), _1395861)))], (38558 ^ _775212) ^ [_1499928, _1499930, _1499932] : [class_Lattices_Oab__semigroup__idem__mult(_1499928), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499928), _1499930)), -(_1499930 = c_Orderings_Obot__class_Obot(tc_fun(_1499928, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499928), _1499932)), -(_1499932 = c_Orderings_Obot__class_Obot(tc_fun(_1499928, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1499928, c_Groups_Otimes__class_Otimes(_1499928)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1499928, tc_HOL_Obool)), _1499930), _1499932)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1499928), hAPP(c_Finite__Set_Ofold1(_1499928, c_Groups_Otimes__class_Otimes(_1499928)), _1499930)), hAPP(c_Finite__Set_Ofold1(_1499928, c_Groups_Otimes__class_Otimes(_1499928)), _1499932)))], (26361 ^ _775212) ^ [_1238142, _1238144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1238142), _1238144)), -(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)), _1238142)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238144))))], (49861 ^ _775212) ^ [_1773684, _1773686, _1773688] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773684, _1773684)), hAPP(hAPP(c_Product__Type_OPair(_1773684, _1773684), _1773686), _1773688)), c_List_Omeasures(_1773684, c_List_Olist_ONil(tc_fun(_1773684, tc_Nat_Onat)))))], (48975 ^ _775212) ^ [_1754857, _1754859] : [class_Orderings_Olinorder(_1754857), hBOOL(hAPP(c_Finite__Set_Ofinite(_1754857), _1754859)), 48982 ^ _775212 : [(48987 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1754857), c_List_Olinorder__class_Osorted__list__of__set(_1754857, _1754859))))], (48985 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1754857, c_List_Olinorder__class_Osorted__list__of__set(_1754857, _1754859)))], (48983 ^ _775212) ^ [] : [-(hAPP(c_List_Oset(_1754857), c_List_Olinorder__class_Osorted__list__of__set(_1754857, _1754859)) = _1754859)]]], (18569 ^ _775212) ^ [] : [-(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)))))], (37636 ^ _775212) ^ [_1477473, _1477475, _1477477, _1477479] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1477473, _1477475, _1477477, _1477479, c_Orderings_Obot__class_Obot(tc_fun(_1477473, tc_HOL_Obool))), _1477479)))], (5670 ^ _775212) ^ [_864597, _864599] : [c_Com_Ocom_OSemi(_864597, _864599) = c_Com_Ocom_OSKIP], (16011 ^ _775212) ^ [_1046480, _1046482, _1046484] : [class_Groups_Oordered__ab__group__add__abs(_1046480), -(hAPP(c_Groups_Oabs__class_Oabs(_1046480), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1046480), _1046482), _1046484)) = hAPP(c_Groups_Oabs__class_Oabs(_1046480), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1046480), _1046484), _1046482)))], (18687 ^ _775212) ^ [_1092723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1092723), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1092723 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1092723 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50749 ^ _775212) ^ [_1792862, _1792864, _1792866, _1792868] : [50751 ^ _775212 : [(50754 ^ _775212) ^ [] : [hBOOL(hAPP(_1792868, 50750 ^ [_1792862, _1792864, _1792866, _1792868]))], (50752 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1792862), 50750 ^ [_1792862, _1792864, _1792866, _1792868]), hAPP(c_List_Oset(_1792862), c_List_Oreplicate(_1792862, _1792864, _1792866)))))]], -(hBOOL(hAPP(_1792868, _1792866))), -(_1792864 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (878 ^ _775212) ^ [_788637, _788639, _788641, _788643] : [-(c_Predicate_Oreflp(_788641, _788637)), c_Predicate_Oreflp(_788643, _788639), _788643 = _788641, _788639 = _788637], (52547 ^ _775212) ^ [_1826862, _1826864] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1826862, _1826864))), class_Lazy__Sequence_Osmall__lazy(_1826862), class_Lazy__Sequence_Osmall__lazy(_1826864)], (43885 ^ _775212) ^ [_1634488, _1634490] : [c_Wellfounded_Owf(_1634488, _1634490), 43888 ^ _775212 : [(43889 ^ _775212) ^ [_1634620] : [43890 ^ _775212 : [(43891 ^ _775212) ^ [_1634725] : [hBOOL(hAPP(hAPP(c_member(_1634488), _1634725), _1634620))]], 43893 ^ _775212 : [(43896 ^ _775212) ^ [_1634847] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634488, _1634488)), hAPP(hAPP(c_Product__Type_OPair(_1634488, _1634488), _1634847), 43892 ^ [_1634488, _1634490, _1634620])), _1634490)), hBOOL(hAPP(hAPP(c_member(_1634488), _1634847), _1634620))], (43894 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1634488), 43892 ^ [_1634488, _1634490, _1634620]), _1634620)))]]]]], (39674 ^ _775212) ^ [_1534282, _1534284, _1534286, _1534288, _1534290, _1534292, _1534294] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1534282, _1534284, _1534286, _1534288, _1534290), _1534292), _1534294))), 39675 ^ _775212 : [(39676 ^ _775212) ^ [_1534353] : [hBOOL(hAPP(hAPP(_1534288, _1534292), _1534353)), hBOOL(hAPP(hAPP(_1534290, _1534353), _1534294))]]], (47704 ^ _775212) ^ [_1727090, _1727092, _1727094, _1727096, _1727098] : [c_List_Olist__all2(_1727090, _1727092, _1727094, _1727096, _1727098), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727090)), _1727096) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727092)), _1727098))], (26043 ^ _775212) ^ [_1231394, _1231396] : [26051 ^ _775212 : [(26054 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1231396, 26050 ^ [_1231394, _1231396])))], (26052 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26050 ^ [_1231394, _1231396]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1231394))))]], 26044 ^ _775212 : [(26045 ^ _775212) ^ [_1231463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1231463), _1231394)), hBOOL(hAPP(_1231396, _1231463))]]], (17937 ^ _775212) ^ [_1079575, _1079577] : [class_Int_Onumber__ring(_1079575), class_Rings_Olinordered__idom(_1079575), 17944 ^ _775212 : [(17951 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1079577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079575), c_Groups_Oone__class_Oone(_1079575)), hAPP(c_Int_Onumber__class_Onumber__of(_1079575), _1079577))))], (17945 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079575), c_Groups_Oone__class_Oone(_1079575)), hAPP(c_Int_Onumber__class_Onumber__of(_1079575), _1079577))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1079577)))]]], (23824 ^ _775212) ^ [_1189307, _1189309] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1189307), _1189309) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1189307)), hAPP(c_Code__Numeral_Onat__of, _1189309))))], (16147 ^ _775212) ^ [_1048731, _1048733] : [class_Groups_Oordered__ab__group__add__abs(_1048731), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048731), c_Groups_Ozero__class_Ozero(_1048731)), _1048733)), -(hAPP(c_Groups_Oabs__class_Oabs(_1048731), _1048733) = _1048733)], (44819 ^ _775212) ^ [_1660691, _1660693, _1660695, _1660697, _1660699] : [-(hAPP(hAPP(c_List_Omap(_1660691, _1660693), _1660695), hAPP(hAPP(c_List_Olist_OCons(_1660691), _1660697), _1660699)) = hAPP(hAPP(c_List_Olist_OCons(_1660693), hAPP(_1660695, _1660697)), hAPP(hAPP(c_List_Omap(_1660691, _1660693), _1660695), _1660699)))], (29218 ^ _775212) ^ [] : [-(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))))], (39496 ^ _775212) ^ [_1527791, _1527793, _1527795, _1527797, _1527799, _1527801, _1527803] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527791, _1527793, _1527795), _1527797), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527799, tc_fun(tc_prod(_1527793, _1527795), tc_HOL_Obool)), _1527801), _1527803)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527799, tc_fun(tc_prod(_1527791, _1527795), tc_HOL_Obool)), _1527801), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1527793, _1527795), tc_HOL_Obool), tc_fun(tc_prod(_1527791, _1527795), tc_HOL_Obool), _1527799), hAPP(c_Relation_Orel__comp(_1527791, _1527793, _1527795), _1527797)), _1527803)))], (48021 ^ _775212) ^ [_1734134, _1734136, _1734138] : [hBOOL(hAPP(hAPP(c_member(_1734134), _1734136), hAPP(c_List_Oset(_1734134), _1734138))), -(c_List_Oremdups(_1734134, hAPP(hAPP(c_List_Olist_OCons(_1734134), _1734136), _1734138)) = c_List_Oremdups(_1734134, _1734138))], (44839 ^ _775212) ^ [_1661095, _1661097, _1661099, _1661101] : [hBOOL(hAPP(hAPP(c_member(_1661095), _1661097), hAPP(c_List_Oset(_1661095), hAPP(hAPP(c_List_Olist_OCons(_1661095), _1661099), _1661101)))), -(_1661097 = _1661099), -(hBOOL(hAPP(hAPP(c_member(_1661095), _1661097), hAPP(c_List_Oset(_1661095), _1661101))))], (20889 ^ _775212) ^ [_1132453, _1132455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132453)), 20892 ^ _775212 : [(20899 ^ _775212) ^ [] : [-(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), _1132455), _1132453)))), -(c_Divides_OnegDivAlg(_1132455, _1132453) = hAPP(c_Divides_Oadjust(_1132453), c_Divides_OnegDivAlg(_1132455, 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)))), _1132453))))], (20893 ^ _775212) ^ [] : [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), _1132455), _1132453))), -(c_Divides_OnegDivAlg(_1132455, _1132453) = 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), _1132455), _1132453)))]]], (41398 ^ _775212) ^ [_1573336, _1573338, _1573340] : [class_Lattices_Oab__semigroup__idem__mult(_1573336), hBOOL(hAPP(c_Finite__Set_Ofinite(_1573336), _1573338)), -(hAPP(c_Finite__Set_Ofold1(_1573336, c_Groups_Otimes__class_Otimes(_1573336)), hAPP(hAPP(c_Set_Oinsert(_1573336), _1573340), _1573338)) = hAPP(hAPP(c_Finite__Set_Ofold(_1573336, _1573336, c_Groups_Otimes__class_Otimes(_1573336)), _1573340), _1573338))], (15719 ^ _775212) ^ [_1041141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1041141)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041141), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1041141)], (23980 ^ _775212) ^ [_1191936, _1191938] : [class_Rings_Ocomm__semiring__1(_1191936), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1191936), _1191938), _1191938)))], (48246 ^ _775212) ^ [_1739803, _1739805, _1739807, _1739809, _1739811, _1739813] : [class_Orderings_Olinorder(_1739803), -(hBOOL(hAPP(_1739805, _1739807))), -(hAPP(c_List_Ofilter(_1739809, _1739805), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739809, _1739803, _1739811), _1739807), _1739813)) = hAPP(c_List_Ofilter(_1739809, _1739805), _1739813))], (5833 ^ _775212) ^ [_867441] : [hAPP(c_Nat_OSuc, _867441) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50615 ^ _775212) ^ [_1790222, _1790224, _1790226] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790222)), c_List_Osplice(_1790222, _1790224, _1790226)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790222)), _1790224)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790222)), _1790226)))], (1524 ^ _775212) ^ [_797118, _797120] : [-(class_Groups_Olinordered__ab__semigroup__add(_797118)), _797120 = _797118, class_Groups_Olinordered__ab__semigroup__add(_797120)], (52485 ^ _775212) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (5817 ^ _775212) ^ [_867089, _867091] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_867089, _867091)], (7397 ^ _775212) ^ [_892883, _892885, _892887, _892889, _892891, _892893] : [c_Com_Ocom_OLocal(_892883, _892885, _892887) = c_Com_Ocom_OCond(_892889, _892891, _892893)], (11568 ^ _775212) ^ [_965203, _965205, _965207] : [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), _965203), _965205)), _965207)), 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)), _965207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _965203)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _965205), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15199 ^ _775212) ^ [_1031071, _1031073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1031071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031073)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1031073), _1031071)), _1031073) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1031073), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031071), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (15087 ^ _775212) ^ [_1028337, _1028339, _1028341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028337), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028341), _1028339))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028337), _1028339)), _1028341)))], (3844 ^ _775212) ^ [_833524, _833526, _833528, _833530, _833532, _833534, _833536, _833538] : [-(c_Nitpick_Osetsum_H(_833538, _833534, _833530, _833526) = c_Nitpick_Osetsum_H(_833536, _833532, _833528, _833524)), _833538 = _833536, _833534 = _833532, _833530 = _833528, _833526 = _833524], (32922 ^ _775212) ^ [_1372408, _1372410, _1372412, _1372414] : [class_Rings_Ocomm__semiring__1(_1372408), class_Rings_Ono__zero__divisors(_1372408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372410), _1372412)), 32933 ^ _775212 : [(32943 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1372410, _1372408), _1372414), _1372412) = c_Groups_Ozero__class_Ozero(_1372408)), 32944 ^ _775212 : [(32945 ^ _775212) ^ [_1372786] : [hBOOL(hAPP(hAPP(c_member(_1372410), _1372786), _1372412)), hAPP(_1372414, _1372786) = c_Groups_Ozero__class_Ozero(_1372408)]]], (32934 ^ _775212) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1372410, _1372408), _1372414), _1372412) = c_Groups_Ozero__class_Ozero(_1372408), 32938 ^ _775212 : [(32941 ^ _775212) ^ [] : [-(hAPP(_1372414, 32937 ^ [_1372408, _1372410, _1372412, _1372414]) = c_Groups_Ozero__class_Ozero(_1372408))], (32939 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372410), 32937 ^ [_1372408, _1372410, _1372412, _1372414]), _1372412)))]]]]], (24610 ^ _775212) ^ [_1202462, _1202464, _1202466, _1202468] : [class_Rings_Oidom(_1202462), 24613 ^ _775212 : [(24614 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1202462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202462), _1202464), _1202466)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202462), _1202468), _1202466))), -(_1202466 = c_Groups_Ozero__class_Ozero(_1202462)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1202462), _1202464), _1202468)))], (24624 ^ _775212) ^ [] : [24625 ^ _775212 : [(24628 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1202462), _1202464), _1202468))], (24626 ^ _775212) ^ [] : [_1202466 = c_Groups_Ozero__class_Ozero(_1202462)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1202462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202462), _1202464), _1202466)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202462), _1202468), _1202466))))]]], (22406 ^ _775212) ^ [_1161827, _1161829] : [-(c_Divides_Odivmod__nat(_1161829, _1161827) = 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), _1161829), _1161827), _1161827))), -(_1161827 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161829), _1161827)))], (49243 ^ _775212) ^ [_1760500, _1760502, _1760504, _1760506, _1760508] : [-(c_List_Ofoldr(_1760500, _1760502, _1760504, _1760506, _1760508) = hAPP(c_List_Ofoldl(_1760502, _1760500, hAPP(c_COMBC(_1760500, _1760502, _1760502), _1760504), _1760508), hAPP(c_List_Orev(_1760500), _1760506)))], (52647 ^ _775212) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (47032 ^ _775212) ^ [_1712722, _1712724, _1712726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712722), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712724)), _1712726))), -(c_List_Olast(_1712724, hAPP(hAPP(c_List_Odrop(_1712724), _1712722), _1712726)) = c_List_Olast(_1712724, _1712726))], (51918 ^ _775212) ^ [_1818575, _1818577] : [-(c_Equiv__Relations_Opart__equivp(_1818575, _1818577)), 51921 ^ _775212 : [(51922 ^ _775212) ^ [_1818652] : [hBOOL(hAPP(hAPP(_1818577, _1818652), _1818652))]], c_Predicate_Osymp(_1818575, _1818577), c_Predicate_Otransp(_1818575, _1818577)], (39103 ^ _775212) ^ [_1512222, _1512224, _1512226, _1512228] : [-(hAPP(c_Relation_OImage(_1512222, _1512224, _1512226), hAPP(hAPP(c_Set_Oinsert(_1512222), _1512228), c_Orderings_Obot__class_Obot(tc_fun(_1512222, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1512224), hAPP(hAPP(c_COMBC(_1512224, tc_fun(tc_prod(_1512222, _1512224), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1512222, _1512224), tc_fun(tc_fun(tc_prod(_1512222, _1512224), tc_HOL_Obool), tc_HOL_Obool), _1512224), c_member(tc_prod(_1512222, _1512224))), hAPP(c_Product__Type_OPair(_1512222, _1512224), _1512228))), _1512226)))], (49768 ^ _775212) ^ [_1771605, _1771607, _1771609] : [hBOOL(hAPP(c_List_Odistinct(_1771605), _1771607)), -(c_List_Oremove1(_1771605, _1771609, _1771607) = hAPP(c_List_OremoveAll(_1771605, _1771609), _1771607))], (13971 ^ _775212) ^ [_1007599, _1007601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007599)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007601)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007599, _1007601)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1007599), hAPP(c_Int_Onat, _1007601)))], (26760 ^ _775212) ^ [_1245497, _1245499] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1245497), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1245499) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1245497, _1245499))], (1824 ^ _775212) ^ [_800868, _800870] : [-(class_Rings_Osemiring(_800868)), _800870 = _800868, class_Rings_Osemiring(_800870)], (43330 ^ _775212) ^ [_1621106, _1621108, _1621110] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621106, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1621106, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1621106, tc_HOL_Obool), _1621108)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1621106, tc_HOL_Obool), _1621110))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1621106, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1621106, tc_HOL_Obool), tc_HOL_Obool)), _1621108), _1621110)))))], (17913 ^ _775212) ^ [_1079243] : [class_Int_Onumber__ring(_1079243), c_Int_Oiszero(_1079243, hAPP(c_Int_Onumber__class_Onumber__of(_1079243), c_Int_OBit1(c_Int_OPls)))], (15501 ^ _775212) ^ [_1037047, _1037049, _1037051, _1037053, _1037055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037047), _1037049)), 15504 ^ _775212 : [(15511 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037053), 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), _1037049), _1037047)), _1037051)), _1037055))), -(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), _1037047), _1037051)), _1037053)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037049), _1037051)), _1037055))))], (15505 ^ _775212) ^ [] : [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), _1037047), _1037051)), _1037053)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037049), _1037051)), _1037055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037053), 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), _1037049), _1037047)), _1037051)), _1037055))))]]], (40389 ^ _775212) ^ [_1551016, _1551018, _1551020] : [-(c_Hilbert__Choice_OEps(tc_prod(_1551016, _1551018), hAPP(c_Product__Type_Oprod_Oprod__case(_1551016, _1551018, tc_HOL_Obool), _1551020)) = c_Hilbert__Choice_OEps(tc_prod(_1551016, _1551018), hAPP(hAPP(c_COMBS(tc_prod(_1551016, _1551018), _1551018, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1551016, tc_fun(_1551018, tc_HOL_Obool), tc_prod(_1551016, _1551018)), _1551020), c_Product__Type_Ofst(_1551016, _1551018))), c_Product__Type_Osnd(_1551016, _1551018))))], (19413 ^ _775212) ^ [_1106119, _1106121, _1106123, _1106125] : [class_Rings_Odivision__ring(_1106119), -(_1106121 = c_Groups_Ozero__class_Ozero(_1106119)), 19420 ^ _775212 : [(19427 ^ _775212) ^ [] : [_1106123 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106119), _1106125), _1106121), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106119), _1106123), _1106121) = _1106125)], (19421 ^ _775212) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106119), _1106123), _1106121) = _1106125, -(_1106123 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106119), _1106125), _1106121))]]], (3074 ^ _775212) ^ [_821247, _821249, _821251, _821253, _821255, _821257, _821259, _821261, _821263, _821265] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_821265, _821261, _821257, _821253, _821249) = c_SetInterval_Oord_OgreaterThanAtMost(_821263, _821259, _821255, _821251, _821247)), _821265 = _821263, _821261 = _821259, _821257 = _821255, _821253 = _821251, _821249 = _821247], (5378 ^ _775212) ^ [_857267, _857269] : [_857269 = _857267, -(c_member(_857269) = c_member(_857267))], (49814 ^ _775212) ^ [_1772418, _1772420] : [-(c_List_Oinsert(_1772418, _1772420, c_List_Olist_ONil(_1772418)) = hAPP(hAPP(c_List_Olist_OCons(_1772418), _1772420), c_List_Olist_ONil(_1772418)))], (15813 ^ _775212) ^ [_1042824, _1042826, _1042828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1042824)), 15819 ^ _775212 : [(15822 ^ _775212) ^ [] : [hBOOL(hAPP(_1042826, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 15818 ^ [_1042824, _1042826, _1042828]), _1042824)))], (15820 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1042826, 15818 ^ [_1042824, _1042826, _1042828])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1042828)), 15827 ^ _775212 : [(15828 ^ _775212) ^ [_1043113] : [hBOOL(hAPP(_1042826, _1043113)), -(hBOOL(hAPP(_1042826, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1043113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1042828), _1042824)))))]]], (6849 ^ _775212) ^ [_884389, _884391] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884389), _884391) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 6850 ^ _775212 : [(6857 ^ _775212) ^ [] : [_884389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _884391 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6851 ^ _775212) ^ [] : [_884389 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _884391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (28902 ^ _775212) ^ [_1288864, _1288866, _1288868] : [class_Orderings_Oorder(_1288864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288864), _1288866), _1288868)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1288864, _1288868), _1288866) = c_Orderings_Obot__class_Obot(tc_fun(_1288864, tc_HOL_Obool)))], (27075 ^ _775212) ^ [_1251970, _1251972, _1251974, _1251976] : [class_Lattices_Olattice(_1251970), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251970), _1251972), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251970), _1251974), _1251976)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251970), _1251974), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251970), _1251972), _1251976)))], (28199 ^ _775212) ^ [_1275102, _1275104, _1275106] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1275102), _1275104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1275102, tc_HOL_Obool)), _1275106), _1275104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1275102), _1275106)), hAPP(c_Finite__Set_Ocard(_1275102), _1275104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1275102, tc_HOL_Obool)), _1275106), _1275104)))], (51385 ^ _775212) ^ [_1807129] : [-(c_Relation_Otrans(_1807129, c_Relation_OId(_1807129)))], (17251 ^ _775212) ^ [_1068656, _1068658, _1068660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068656), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068656)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068658)), _1068660)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28018 ^ _775212) ^ [] : [-(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)))], (44700 ^ _775212) ^ [_1657593, _1657595, _1657597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657593)), _1657595)), _1657597)), -(hAPP(hAPP(c_List_Otake(_1657593), _1657597), _1657595) = _1657595)], (27862 ^ _775212) ^ [_1268624, _1268626] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1268624), _1268626))))], (16787 ^ _775212) ^ [_1061454, _1061456, _1061458, _1061460] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1061454, _1061456), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1061458), _1061460))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1061454, _1061456) = _1061460)], (10775 ^ _775212) ^ [_951236, _951238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _951236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _951238)), 10782 ^ _775212 : [(10789 ^ _775212) ^ [] : [_951236 = _951238, -(hAPP(c_Int_Onat, _951236) = hAPP(c_Int_Onat, _951238))], (10783 ^ _775212) ^ [] : [hAPP(c_Int_Onat, _951236) = hAPP(c_Int_Onat, _951238), -(_951236 = _951238)]]], (43174 ^ _775212) ^ [_1617855, _1617857] : [class_Complete__Lattice_Ocomplete__lattice(_1617855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617855), _1617857)), -(c_Complete__Lattice_OInf__class_OInf(_1617855, _1617857) = hAPP(hAPP(c_Finite__Set_Ofold(_1617855, _1617855, c_Lattices_Osemilattice__inf__class_Oinf(_1617855)), c_Orderings_Otop__class_Otop(_1617855)), _1617857))], (38921 ^ _775212) ^ [_1507310, _1507312, _1507314] : [-(hAPP(c_Set_OCollect(_1507310), hAPP(hAPP(c_COMBS(_1507310, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507310), c_fdisj), _1507312)), _1507314)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1507310, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1507310), _1507312)), hAPP(c_Set_OCollect(_1507310), _1507314)))], (38893 ^ _775212) ^ [_1506617, _1506619] : [-(hAPP(c_Set_OCollect(_1506617), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1506617), c_fNot), _1506619)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1506617, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1506617), _1506619)))], (17383 ^ _775212) ^ [_1070501] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070501), c_Int_OMin) = c_Int_Opred(_1070501))], (41239 ^ _775212) ^ [_1570082, _1570084, _1570086, _1570088, _1570090] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1570082, _1570084, _1570086), _1570088), _1570090) = c_HOL_OThe(_1570084, c_Finite__Set_Ofold__graph(_1570082, _1570084, _1570086, _1570088, _1570090)))], (41664 ^ _775212) ^ [_1578654, _1578656] : [-(c_Transitive__Closure_Otrancl(_1578654, _1578656) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1578654, _1578654), tc_HOL_Obool)), _1578656), hAPP(hAPP(c_Relation_Orel__comp(_1578654, _1578654, _1578654), c_Transitive__Closure_Otrancl(_1578654, _1578656)), _1578656)))], (15105 ^ _775212) ^ [_1028725] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028725)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1028725)], (20863 ^ _775212) ^ [_1131970, _1131972, _1131974, _1131976] : [class_Fields_Ofield(_1131970), -(_1131972 = c_Groups_Ozero__class_Ozero(_1131970)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1131974), _1131976)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1131970), _1131972), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1131976), _1131974)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131970), hAPP(hAPP(c_Power_Opower__class_Opower(_1131970), _1131972), _1131976)), hAPP(hAPP(c_Power_Opower__class_Opower(_1131970), _1131972), _1131974)))], (23862 ^ _775212) ^ [_1189980, _1189982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1189980)), 23865 ^ _775212 : [(23872 ^ _775212) ^ [] : [_1189982 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1189980), _1189982)), _1189980)))], (23866 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1189980), _1189982)), _1189980)), -(_1189982 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5144 ^ _775212) ^ [_853702, _853704] : [_853704 = _853702, -(c_List_Oset(_853704) = c_List_Oset(_853702))], (27377 ^ _775212) ^ [_1257701, _1257703, _1257705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257701, tc_HOL_Obool)), _1257703), _1257705)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257701, tc_HOL_Obool)), _1257703), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1257701, tc_HOL_Obool)), _1257705), _1257703)) = _1257705)], (43878 ^ _775212) ^ [_1634331, _1634333] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634331, _1634331)), _1634333), c_Relation_OId(_1634331))), -(_1634333 = hAPP(hAPP(c_Product__Type_OPair(_1634331, _1634331), 43881 ^ [_1634331, _1634333]), 43881 ^ [_1634331, _1634333]))], (35201 ^ _775212) ^ [_1423690, _1423692, _1423694] : [class_Orderings_Oorder(_1423690), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423690, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1423690), _1423692)), c_SetInterval_Oord__class_OatLeastAtMost(_1423690, _1423692, _1423694)) = c_Orderings_Obot__class_Obot(tc_fun(_1423690, tc_HOL_Obool)))], (9505 ^ _775212) ^ [_928771, _928773, _928775] : [class_Orderings_Oorder(_928771), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928771), _928773), _928775)), -(_928773 = _928775), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928771), _928773), _928775)))], (45955 ^ _775212) ^ [_1688420, _1688422, _1688424, _1688426] : [-(hAPP(hAPP(c_List_Onth(_1688420), hAPP(hAPP(c_List_Oappend(_1688420), _1688422), hAPP(hAPP(c_List_Olist_OCons(_1688420), _1688424), _1688426))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688420)), _1688422)) = _1688424)], (39416 ^ _775212) ^ [_1525587, _1525589] : [-(c_Product__Type_Oapfst(_1525587, _1525587, _1525589, c_Fun_Oid(_1525587)) = c_Fun_Oid(tc_prod(_1525587, _1525589)))], (42529 ^ _775212) ^ [_1600717, _1600719, _1600721, _1600723, _1600725, _1600727] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600717, tc_fun(_1600719, tc_HOL_Obool)), _1600721), hAPP(hAPP(c_COMBC(_1600717, tc_fun(_1600723, tc_fun(_1600719, tc_HOL_Obool)), tc_fun(_1600719, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1600723, tc_HOL_Obool), tc_fun(tc_fun(_1600723, tc_fun(_1600719, tc_HOL_Obool)), tc_fun(_1600719, tc_HOL_Obool)), _1600717), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600723, tc_fun(_1600719, tc_HOL_Obool))), _1600725)), _1600727)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600723, tc_fun(_1600719, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1600717, tc_fun(_1600723, tc_HOL_Obool)), _1600721), _1600725)), _1600727))], (12993 ^ _775212) ^ [_989848, _989850, _989852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989848)), 12996 ^ _775212 : [(12997 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_989850, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _989852), _989848)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _989852, _989848))), 13000 ^ _775212 : [(13001 ^ _775212) ^ [_990049, _990051] : [-(hBOOL(hAPP(hAPP(_989850, _990051), _990049))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _990049), _989848)), _989852 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _989848), _990051)), _990049)]]], (13015 ^ _775212) ^ [] : [13018 ^ _775212 : [(13021 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 13017 ^ [_989848, _989850, _989852]), _989848)))], (13023 ^ _775212) ^ [] : [-(_989852 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _989848), 13016 ^ [_989848, _989850, _989852])), 13017 ^ [_989848, _989850, _989852]))], (13025 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_989850, 13016 ^ [_989848, _989850, _989852]), 13017 ^ [_989848, _989850, _989852]))], (13019 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13017 ^ [_989848, _989850, _989852])))]], -(hBOOL(hAPP(hAPP(_989850, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _989852), _989848)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _989852, _989848))))]]], (23884 ^ _775212) ^ [_1190349] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1190349), _1190349)))], (27285 ^ _775212) ^ [_1255871, _1255873, _1255875, _1255877] : [class_Lattices_Osemilattice__sup(_1255871), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255871), _1255873), _1255875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255871), _1255873), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255871), _1255877), _1255875))))], (28016 ^ _775212) ^ [] : [-(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)))], (7587 ^ _775212) ^ [_896333, _896335] : [-(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, _896333)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _896335))))], (22102 ^ _775212) ^ [_1154663, _1154665, _1154667, _1154669] : [_1154663 = _1154665, 22105 ^ _775212 : [(22108 ^ _775212) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1154667, _1154669), _1154663) = hAPP(c_Product__Type_Osnd(_1154667, _1154669), _1154665))], (22106 ^ _775212) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1154667, _1154669), _1154663) = hAPP(c_Product__Type_Ofst(_1154667, _1154669), _1154665))]]], (47794 ^ _775212) ^ [_1729069, _1729071, _1729073, _1729075, _1729077, _1729079] : [c_List_Olist__all2(_1729069, _1729071, _1729073, _1729075, _1729077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729079), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729069)), _1729075))), -(hBOOL(hAPP(hAPP(_1729073, hAPP(hAPP(c_List_Onth(_1729069), _1729075), _1729079)), hAPP(hAPP(c_List_Onth(_1729071), _1729077), _1729079))))], (33276 ^ _775212) ^ [_1379567, _1379569, _1379571] : [class_Orderings_Olinorder(_1379567), hAPP(_1379569, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1379567), 33281 ^ [_1379567, _1379569, _1379571]), 33282 ^ [_1379567, _1379569, _1379571])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1379567), hAPP(_1379569, 33281 ^ [_1379567, _1379569, _1379571])), hAPP(_1379569, 33282 ^ [_1379567, _1379569, _1379571])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379567), _1379571)), -(_1379571 = c_Orderings_Obot__class_Obot(tc_fun(_1379567, tc_HOL_Obool))), -(hAPP(_1379569, c_Big__Operators_Olattice_OSup__fin(_1379567, c_Orderings_Oord__class_Omax(_1379567), _1379571)) = c_Big__Operators_Olattice_OSup__fin(_1379567, c_Orderings_Oord__class_Omax(_1379567), hAPP(c_Set_Oimage(_1379567, _1379567, _1379569), _1379571)))], (10263 ^ _775212) ^ [_942069, _942071, _942073] : [class_Rings_Oordered__cancel__semiring(_942069), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942069), c_Groups_Ozero__class_Ozero(_942069)), _942071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942069), _942073), c_Groups_Ozero__class_Ozero(_942069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942069), _942073), _942071)), c_Groups_Ozero__class_Ozero(_942069))))], (5813 ^ _775212) ^ [_867002, _867004, _867006, _867008] : [c_Com_Ocom_OSemi(_867002, _867004) = c_Com_Ocom_OWhile(_867006, _867008)], (35633 ^ _775212) ^ [_1433301, _1433303, _1433305] : [class_Orderings_Olinorder(_1433301), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433301), _1433303)), -(_1433303 = c_Orderings_Obot__class_Obot(tc_fun(_1433301, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433301), _1433305)), -(_1433305 = c_Orderings_Obot__class_Obot(tc_fun(_1433301, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1433301, tc_HOL_Obool)), _1433303), _1433305) = c_Orderings_Obot__class_Obot(tc_fun(_1433301, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1433301, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1433301, tc_HOL_Obool)), _1433303), _1433305)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1433301), c_Big__Operators_Olinorder__class_OMin(_1433301, _1433303)), c_Big__Operators_Olinorder__class_OMin(_1433301, _1433305)))], (48307 ^ _775212) ^ [_1741109, _1741111, _1741113, _1741115] : [-(c_List_Otranspose(_1741109, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1741111), tc_List_Olist(_1741109)), hAPP(c_List_Omap(_1741111, _1741109), _1741113)), _1741115)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1741111), tc_List_Olist(_1741109)), hAPP(c_List_Omap(_1741111, _1741109), _1741113)), c_List_Otranspose(_1741111, _1741115)))], (11662 ^ _775212) ^ [_966677] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966677), _966677)))], (50951 ^ _775212) ^ [_1797282, _1797284] : [-(c_Predicate_Opred__comp(_1797282, _1797282, _1797282, c_fequal, c_Predicate_Opred__comp(_1797282, _1797282, _1797282, _1797284, c_fequal)) = _1797284)], (11945 ^ _775212) ^ [_971518] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971518), _971518))))], (52577 ^ _775212) ^ [_1827249, _1827251] : [-(class_Nat_Osize(tc_prod(_1827249, _1827251)))], (3610 ^ _775212) ^ [_829757, _829759, _829761, _829763] : [-(c_Relation_ODomain(_829763, _829759) = c_Relation_ODomain(_829761, _829757)), _829763 = _829761, _829759 = _829757], (14395 ^ _775212) ^ [_1015370, _1015372, _1015374, _1015376] : [class_Rings_Ocomm__semiring__1(_1015370), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1015370), hAPP(hAPP(c_Power_Opower__class_Opower(_1015370), _1015372), _1015374)), _1015376) = hAPP(hAPP(c_Power_Opower__class_Opower(_1015370), _1015372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015374), _1015376)))], (50459 ^ _775212) ^ [_1787177, _1787179, _1787181] : [c_List_Olist__all(_1787177, _1787179, _1787181), 50462 ^ _775212 : [(50463 ^ _775212) ^ [_1787266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1787266), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1787177)), _1787181))), -(hBOOL(hAPP(_1787179, hAPP(hAPP(c_List_Onth(_1787177), _1787181), _1787266))))]]], (16917 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9141 ^ _775212) ^ [_923237] : [class_Rings_Osemiring__1(_923237), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_923237), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_923237))], (46466 ^ _775212) ^ [_1701096, _1701098, _1701100, _1701102] : [-(hAPP(hAPP(c_List_Omap(_1701096, _1701098), _1701100), hAPP(c_List_Otl(_1701096), _1701102)) = hAPP(c_List_Otl(_1701098), hAPP(hAPP(c_List_Omap(_1701096, _1701098), _1701100), _1701102)))], (50803 ^ _775212) ^ [_1793961, _1793963, _1793965] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1793961, _1793961, hAPP(hAPP(c_COMBB(tc_fun(_1793961, tc_HOL_Obool), tc_fun(_1793961, tc_HOL_Obool), _1793961), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1793961), c_fNot)), c_fequal)), _1793963), _1793965)), _1793963 = _1793965], (45714 ^ _775212) ^ [_1683277, _1683279, _1683281, _1683283, _1683285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1683277), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683279)), _1683281))), -(hAPP(hAPP(c_List_Olist__update(_1683279, hAPP(hAPP(c_List_Oappend(_1683279), _1683281), _1683283)), _1683277), _1683285) = hAPP(hAPP(c_List_Oappend(_1683279), hAPP(hAPP(c_List_Olist__update(_1683279, _1683281), _1683277), _1683285)), _1683283))], (10970 ^ _775212) ^ [_954657, _954659, _954661] : [class_Groups_Oordered__comm__monoid__add(_954657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954657), c_Groups_Ozero__class_Ozero(_954657)), _954659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954657), c_Groups_Ozero__class_Ozero(_954657)), _954661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954657), c_Groups_Ozero__class_Ozero(_954657)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954657), _954659), _954661))))], (48129 ^ _775212) ^ [_1736307, _1736309, _1736311, _1736313, _1736315] : [class_Orderings_Olinorder(_1736307), -(c_List_Olinorder__class_Osort__key(_1736309, _1736307, _1736311, hAPP(hAPP(c_List_Olist_OCons(_1736309), _1736313), _1736315)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1736309, _1736307, _1736311), _1736313), c_List_Olinorder__class_Osort__key(_1736309, _1736307, _1736311, _1736315)))], (15063 ^ _775212) ^ [_1027829, _1027831, _1027833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027829), _1027831)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027833), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027831), _1027829)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027833), _1027831)), _1027829))], (14853 ^ _775212) ^ [_1024068, _1024070] : [14854 ^ _775212 : [(14857 ^ _775212) ^ [] : [_1024068 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14855 ^ _775212) ^ [] : [_1024070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1024068), _1024070) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29456 ^ _775212) ^ [_1299640, _1299642] : [hBOOL(hAPP(hAPP(c_member(_1299640), _1299642), c_Orderings_Obot__class_Obot(tc_fun(_1299640, tc_HOL_Obool))))], (31537 ^ _775212) ^ [_1346045, _1346047, _1346049] : [class_Orderings_Olinorder(_1346045), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346045), _1346047)), hBOOL(hAPP(hAPP(c_member(_1346045), _1346049), _1346047)), 31548 ^ _775212 : [(31555 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346045, tc_HOL_Obool)), _1346047), hAPP(hAPP(c_Set_Oinsert(_1346045), _1346049), c_Orderings_Obot__class_Obot(tc_fun(_1346045, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1346045, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1346045, _1346047) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346045), _1346049), c_Big__Operators_Olinorder__class_OMin(_1346045, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346045, tc_HOL_Obool)), _1346047), hAPP(hAPP(c_Set_Oinsert(_1346045), _1346049), c_Orderings_Obot__class_Obot(tc_fun(_1346045, tc_HOL_Obool)))))))], (31549 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346045, tc_HOL_Obool)), _1346047), hAPP(hAPP(c_Set_Oinsert(_1346045), _1346049), c_Orderings_Obot__class_Obot(tc_fun(_1346045, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1346045, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1346045, _1346047) = _1346049)]]], (49668 ^ _775212) ^ [_1769625, _1769627, _1769629, _1769631] : [49670 ^ _775212 : [(49673 ^ _775212) ^ [] : [hBOOL(hAPP(_1769627, hAPP(hAPP(c_List_Onth(_1769629), _1769631), 49669 ^ [_1769625, _1769627, _1769629, _1769631])))], (49671 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49669 ^ [_1769625, _1769627, _1769629, _1769631]), _1769625)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1769625), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769629)), _1769631))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1769625), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769629)), c_List_OtakeWhile(_1769629, _1769627, _1769631)))))], (42191 ^ _775212) ^ [_1590860, _1590862, _1590864, _1590866] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1590860, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1590862, tc_fun(_1590860, tc_HOL_Obool)), _1590864), _1590866)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590862, tc_fun(_1590860, tc_HOL_Obool)), _1590864), hAPP(hAPP(c_COMBB(tc_fun(_1590860, tc_HOL_Obool), tc_fun(_1590860, tc_HOL_Obool), _1590862), c_Groups_Ouminus__class_Ouminus(tc_fun(_1590860, tc_HOL_Obool))), _1590866)))], (11040 ^ _775212) ^ [_955988, _955990, _955992, _955994] : [class_Rings_Olinordered__semiring__strict(_955988), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955988), _955990), _955992)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955988), _955994), _955992))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955988), c_Groups_Ozero__class_Ozero(_955988)), _955992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955988), _955990), _955994)))], (21921 ^ _775212) ^ [_1151261, _1151263, _1151265] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151261, tc_HOL_Obool)), _1151263) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151261, tc_HOL_Obool)), _1151265), -(_1151263 = _1151265)], (47985 ^ _775212) ^ [_1733493, _1733495] : [c_List_Oremdups(_1733493, _1733495) = _1733495, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733493)), c_List_Oremdups(_1733493, _1733495)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733493)), _1733495))], (14649 ^ _775212) ^ [_1020389, _1020391] : [class_Groups_Ogroup__add(_1020389), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1020389), c_Groups_Ozero__class_Ozero(_1020389)), _1020391) = hAPP(c_Groups_Ouminus__class_Ouminus(_1020389), _1020391))], (49804 ^ _775212) ^ [_1772217, _1772219, _1772221] : [-(c_List_Oinsert(_1772217, _1772219, c_List_Oremdups(_1772217, _1772221)) = c_List_Oremdups(_1772217, c_List_Oinsert(_1772217, _1772219, _1772221)))], (48564 ^ _775212) ^ [_1747328, _1747330] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1747328), hAPP(c_List_Onth(_1747328), _1747330)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747328)), _1747330))) = _1747330)], (18315 ^ _775212) ^ [_1086284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1086284)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086284), c_Int_OMin)))], (20 ^ _775212) ^ [_775472, _775474, _775476, _775478] : [-(c_Int_Oiszero(_775476, _775472)), c_Int_Oiszero(_775478, _775474), _775478 = _775476, _775474 = _775472], (33115 ^ _775212) ^ [_1375962, _1375964, _1375966, _1375968, _1375970] : [class_Groups_Ocomm__monoid__mult(_1375962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375964), _1375966)), 33122 ^ _775212 : [(33129 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1375964), _1375968), _1375966))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1375964, _1375962), hAPP(hAPP(c_COMBC(_1375964, _1375962, _1375962), hAPP(hAPP(c_COMBS(_1375964, _1375962, tc_fun(_1375962, _1375962)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1375962, tc_fun(_1375962, _1375962)), _1375964), c_If(_1375962)), hAPP(c_fequal, _1375968))), _1375970)), c_Groups_Oone__class_Oone(_1375962))), _1375966) = c_Groups_Oone__class_Oone(_1375962))], (33123 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1375964), _1375968), _1375966)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1375964, _1375962), hAPP(hAPP(c_COMBC(_1375964, _1375962, _1375962), hAPP(hAPP(c_COMBS(_1375964, _1375962, tc_fun(_1375962, _1375962)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1375962, tc_fun(_1375962, _1375962)), _1375964), c_If(_1375962)), hAPP(c_fequal, _1375968))), _1375970)), c_Groups_Oone__class_Oone(_1375962))), _1375966) = hAPP(_1375970, _1375968))]]], (43338 ^ _775212) ^ [_1621327, _1621329, _1621331] : [class_Complete__Lattice_Ocomplete__lattice(_1621327), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621327), _1621329)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1621327), _1621331), c_Complete__Lattice_OInf__class_OInf(_1621327, _1621329)) = hAPP(hAPP(c_Finite__Set_Ofold(_1621327, _1621327, c_Lattices_Osemilattice__inf__class_Oinf(_1621327)), _1621331), _1621329))], (17449 ^ _775212) ^ [_1071563, _1071565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071563)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071563), _1071565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071563), c_Int_OPls)))], (44817 ^ _775212) ^ [_1660620, _1660622, _1660624, _1660626, _1660628] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1660620), tc_List_Olist(_1660622), tc_List_Olist(_1660624), hAPP(c_List_Omap(_1660620, _1660622), _1660626)), hAPP(c_List_Omap(_1660624, _1660620), _1660628)) = hAPP(c_List_Omap(_1660624, _1660622), hAPP(c_Fun_Ocomp(_1660620, _1660622, _1660624, _1660626), _1660628)))], (11708 ^ _775212) ^ [_967396, _967398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967398)), _967396)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967396), _967398))], (47182 ^ _775212) ^ [_1715879, _1715881, _1715883, _1715885] : [-(_1715879 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715881)), _1715883)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1715881, hAPP(hAPP(c_List_Olist__update(_1715881, _1715883), _1715879), _1715885)) = hAPP(hAPP(c_List_Olist__update(_1715881, c_List_Obutlast(_1715881, _1715883)), _1715879), _1715885))], (29776 ^ _775212) ^ [_1305791, _1305793, _1305795] : [_1305793 = _1305795, -(hBOOL(hAPP(hAPP(c_member(_1305791), _1305793), hAPP(c_fequal, _1305795))))], (7655 ^ _775212) ^ [_897811, _897813, _897815] : [class_Int_Oring__char__0(_897811), 7658 ^ _775212 : [(7665 ^ _775212) ^ [] : [_897813 = _897815, -(hAPP(c_Int_Oring__1__class_Oof__int(_897811), _897813) = hAPP(c_Int_Oring__1__class_Oof__int(_897811), _897815))], (7659 ^ _775212) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_897811), _897813) = hAPP(c_Int_Oring__1__class_Oof__int(_897811), _897815), -(_897813 = _897815)]]], (51983 ^ _775212) ^ [_1819658, _1819660] : [-(c_Equiv__Relations_Opart__equivp(_1819658, _1819660)), 51986 ^ _775212 : [(51987 ^ _775212) ^ [_1819778] : [hBOOL(hAPP(hAPP(_1819660, _1819778), _1819778))]], 52004 ^ _775212 : [(52007 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1819660, 51989 ^ [_1819658, _1819660]), 51989 ^ [_1819658, _1819660])))], (52009 ^ _775212) ^ [] : [-(hAPP(_1819660, 51988 ^ [_1819658, _1819660]) = hAPP(_1819660, 51989 ^ [_1819658, _1819660]))], (52011 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1819660, 51988 ^ [_1819658, _1819660]), 51989 ^ [_1819658, _1819660]))], (52005 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1819660, 51988 ^ [_1819658, _1819660]), 51988 ^ [_1819658, _1819660])))]], 51992 ^ _775212 : [(51995 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1819660, 51988 ^ [_1819658, _1819660]), 51988 ^ [_1819658, _1819660])), hBOOL(hAPP(hAPP(_1819660, 51989 ^ [_1819658, _1819660]), 51989 ^ [_1819658, _1819660])), hAPP(_1819660, 51988 ^ [_1819658, _1819660]) = hAPP(_1819660, 51989 ^ [_1819658, _1819660])], (51993 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1819660, 51988 ^ [_1819658, _1819660]), 51989 ^ [_1819658, _1819660])))]]], (28490 ^ _775212) ^ [_1280661, _1280663, _1280665] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1280661), _1280663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280661, tc_HOL_Obool)), _1280665), _1280663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1280661), _1280663)), hAPP(c_Finite__Set_Ocard(_1280661), _1280665))), -(_1280665 = _1280663)], (42591 ^ _775212) ^ [_1602588, _1602590, _1602592, _1602594, _1602596] : [-(_1602588 = c_Orderings_Obot__class_Obot(tc_fun(_1602590, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602590, tc_fun(_1602592, tc_HOL_Obool)), _1602588), hAPP(hAPP(c_COMBC(_1602590, tc_fun(_1602592, tc_HOL_Obool), tc_fun(_1602592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602592, tc_HOL_Obool), tc_fun(tc_fun(_1602592, tc_HOL_Obool), tc_fun(_1602592, tc_HOL_Obool)), _1602590), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602592, tc_HOL_Obool))), _1602594)), _1602596)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602592, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602590, tc_fun(_1602592, tc_HOL_Obool)), _1602588), _1602594)), _1602596))], (9307 ^ _775212) ^ [_925940, _925942, _925944] : [class_Orderings_Olinorder(_925940), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925940), _925942), _925944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925940), _925944), _925942)))], (32641 ^ _775212) ^ [_1366784, _1366786, _1366788] : [class_Orderings_Olinorder(_1366784), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366784), _1366786)), -(_1366788 = c_Orderings_Obot__class_Obot(tc_fun(_1366784, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1366784, tc_HOL_Obool)), _1366788), _1366786)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1366784), c_Big__Operators_Olattice_OInf__fin(_1366784, c_Orderings_Oord__class_Omin(_1366784), _1366788)), c_Big__Operators_Olattice_OInf__fin(_1366784, c_Orderings_Oord__class_Omin(_1366784), _1366786)) = c_Big__Operators_Olattice_OInf__fin(_1366784, c_Orderings_Oord__class_Omin(_1366784), _1366786))], (11873 ^ _775212) ^ [_970132, _970134, _970136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970132), _970134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970132), _970136)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970134), _970136))))], (3782 ^ _775212) ^ [_832539, _832541, _832543, _832545] : [-(c_List_Olistset(_832545, _832541) = c_List_Olistset(_832543, _832539)), _832545 = _832543, _832541 = _832539], (52295 ^ _775212) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (39886 ^ _775212) ^ [_1538607, _1538609, _1538611] : [hAPP(c_Relation_ODomain(_1538607, _1538609), _1538611) = c_Orderings_Obot__class_Obot(tc_fun(_1538607, tc_HOL_Obool)), -(_1538611 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1538607, _1538609), tc_HOL_Obool)))], (48187 ^ _775212) ^ [_1738220, _1738222, _1738224, _1738226] : [-(c_List_Otranspose(_1738220, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1738220)), hAPP(hAPP(c_List_Olist_OCons(_1738220), _1738222), _1738224)), _1738226)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1738220)), hAPP(hAPP(c_List_Olist_OCons(_1738220), _1738222), c_List_Oconcat(_1738220, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1738220), tc_List_Olist(_1738220)), c_List_Olist_Olist__case(tc_List_Olist(_1738220), _1738220, c_List_Olist_ONil(_1738220), hAPP(hAPP(c_COMBB(tc_List_Olist(_1738220), tc_fun(tc_List_Olist(_1738220), tc_List_Olist(_1738220)), _1738220), c_COMBK(tc_List_Olist(_1738220), tc_List_Olist(_1738220))), hAPP(hAPP(c_COMBC(_1738220, tc_List_Olist(_1738220), tc_List_Olist(_1738220)), c_List_Olist_OCons(_1738220)), c_List_Olist_ONil(_1738220))))), _1738226)))), c_List_Otranspose(_1738220, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1738220)), _1738224), c_List_Oconcat(tc_List_Olist(_1738220), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1738220), tc_List_Olist(tc_List_Olist(_1738220))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1738220)), _1738220, c_List_Olist_ONil(tc_List_Olist(_1738220)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1738220), tc_List_Olist(tc_List_Olist(_1738220))), _1738220), hAPP(hAPP(c_COMBC(tc_List_Olist(_1738220), tc_List_Olist(tc_List_Olist(_1738220)), tc_List_Olist(tc_List_Olist(_1738220))), c_List_Olist_OCons(tc_List_Olist(_1738220))), c_List_Olist_ONil(tc_List_Olist(_1738220)))))), _1738226))))))], (51367 ^ _775212) ^ [_1806866, _1806868] : [c_Relation_Otrans(_1806866, hAPP(c_Relation_Oconverse(_1806866, _1806866), _1806868)), -(c_Relation_Otrans(_1806866, _1806868))], (28434 ^ _775212) ^ [_1279597, _1279599, _1279601, _1279603] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279597), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279597, tc_HOL_Obool)), _1279599), _1279603))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279597), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279597, tc_HOL_Obool)), _1279599), hAPP(hAPP(c_Set_Oinsert(_1279597), _1279601), _1279603)))))], (22130 ^ _775212) ^ [_1155193, _1155195, _1155197] : [-(hAPP(c_Divides_Oadjust(_1155193), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1155195), _1155197)) = 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), _1155197), _1155193)), 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)))), _1155195)), 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)))), _1155195)), _1155197))))], (49277 ^ _775212) ^ [_1761197, _1761199, _1761201] : [-(hAPP(c_List_Orev(_1761197), hAPP(hAPP(c_List_Odrop(_1761197), _1761199), _1761201)) = hAPP(hAPP(c_List_Otake(_1761197), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761197)), _1761201)), _1761199)), hAPP(c_List_Orev(_1761197), _1761201)))], (49377 ^ _775212) ^ [_1763398, _1763400, _1763402] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763398)), c_List_OtakeWhile(_1763398, _1763400, _1763402))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763398)), _1763402))))], (38482 ^ _775212) ^ [_1498530, _1498532, _1498534] : [class_Lattices_Oab__semigroup__idem__mult(_1498530), -(_1498532 = c_Orderings_Obot__class_Obot(tc_fun(_1498530, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1498530), _1498532)), -(hAPP(c_Finite__Set_Ofold1(_1498530, c_Groups_Otimes__class_Otimes(_1498530)), hAPP(hAPP(c_Set_Oinsert(_1498530), _1498534), _1498532)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1498530), _1498534), hAPP(c_Finite__Set_Ofold1(_1498530, c_Groups_Otimes__class_Otimes(_1498530)), _1498532)))], (17227 ^ _775212) ^ [_1068278] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1068278)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068278) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15251 ^ _775212) ^ [_1032063, _1032065, _1032067] : [class_Rings_Olinordered__semidom(_1032063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032063), c_Groups_Oone__class_Oone(_1032063)), _1032065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032063), hAPP(hAPP(c_Power_Opower__class_Opower(_1032063), _1032065), _1032067)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032063), _1032065), hAPP(hAPP(c_Power_Opower__class_Opower(_1032063), _1032065), _1032067)))))], (33645 ^ _775212) ^ [_1388408, _1388410, _1388412, _1388414, _1388416] : [class_Groups_Ocomm__monoid__mult(_1388408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388410), _1388412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388410, tc_HOL_Obool)), _1388414), _1388412)), 33659 ^ _775212 : [(33662 ^ _775212) ^ [] : [hAPP(_1388416, 33658 ^ [_1388408, _1388410, _1388412, _1388414, _1388416]) = c_Groups_Oone__class_Oone(_1388408)], (33660 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388410), 33658 ^ [_1388408, _1388410, _1388412, _1388414, _1388416]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388410, tc_HOL_Obool)), _1388412), _1388414))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388410, _1388408), _1388416), _1388414) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388410, _1388408), _1388416), _1388412))], (30442 ^ _775212) ^ [_1323406, _1323408, _1323410, _1323412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1323406, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323406, tc_HOL_Obool)), _1323408), hAPP(hAPP(c_Set_Oinsert(_1323406), _1323410), c_Orderings_Obot__class_Obot(tc_fun(_1323406, tc_HOL_Obool))))), _1323412)), hBOOL(hAPP(hAPP(c_member(_1323406), _1323410), _1323408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1323406, tc_HOL_Obool)), _1323408), hAPP(hAPP(c_Set_Oinsert(_1323406), _1323410), _1323412))))], (21965 ^ _775212) ^ [_1152067, _1152069] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1152067, _1152069) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1152067, _1152069)))], (5484 ^ _775212) ^ [_858898, _858900] : [_858900 = _858898, -(tc_Option_Ooption(_858900) = tc_Option_Ooption(_858898))], (30713 ^ _775212) ^ [_1329440, _1329442, _1329444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329440)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1329442), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1329444)), 30720 ^ _775212 : [(30721 ^ _775212) ^ [_1329648] : [30723 ^ _775212 : [(30729 ^ _775212) ^ [] : [-(_1329648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30725 ^ [_1329440, _1329442, _1329444, _1329648]), 30722 ^ [_1329440, _1329442, _1329444, _1329648]))], (30727 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30725 ^ [_1329440, _1329442, _1329444, _1329648]), _1329444)))], (30724 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30722 ^ [_1329440, _1329442, _1329444, _1329648]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1329440))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1329442), _1329648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1329442), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1329648), _1329440))))]]], (14139 ^ _775212) ^ [_1010678, _1010680] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1010678)), _1010680) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1010678), _1010680)))], (38140 ^ _775212) ^ [_1491086, _1491088, _1491090, _1491092, _1491094, _1491096] : [class_Groups_Ocomm__monoid__add(_1491086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491088), _1491090)), 38150 ^ _775212 : [(38153 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491092), hAPP(_1491094, 38149 ^ [_1491086, _1491088, _1491090, _1491092, _1491094, _1491096])))], (38151 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491088), 38149 ^ [_1491086, _1491088, _1491090, _1491092, _1491094, _1491096]), _1491090)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491088, _1491086), hAPP(hAPP(c_COMBS(_1491088, tc_fun(_1491092, tc_HOL_Obool), _1491086), hAPP(hAPP(c_COMBB(tc_fun(_1491092, _1491086), tc_fun(tc_fun(_1491092, tc_HOL_Obool), _1491086), _1491088), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491092, _1491086)), _1491096)), _1491094)), _1491090) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1491088, _1491092), _1491086), hAPP(c_Product__Type_Oprod_Oprod__case(_1491088, _1491092, _1491086), _1491096)), hAPP(hAPP(c_Product__Type_OSigma(_1491088, _1491092), _1491090), _1491094)))], (32868 ^ _775212) ^ [_1371266, _1371268, _1371270, _1371272, _1371274, _1371276] : [_1371266 = _1371268, -(hAPP(c_Fun_Ofun__upd(_1371270, _1371272, _1371274, _1371268, _1371276), _1371266) = _1371276)], (15999 ^ _775212) ^ [_1046214, _1046216, _1046218] : [class_Rings_Olinordered__idom(_1046214), -(hAPP(c_Groups_Oabs__class_Oabs(_1046214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046214), _1046216), _1046218)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046214), hAPP(c_Groups_Oabs__class_Oabs(_1046214), _1046216)), hAPP(c_Groups_Oabs__class_Oabs(_1046214), _1046218)))], (7457 ^ _775212) ^ [_894139] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894139) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_894139 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33366 ^ _775212) ^ [_1381436] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1381436)), -(_1381436 = 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))), _1381436)), c_FunDef_Omax__strict)))], (14673 ^ _775212) ^ [_1020851, _1020853, _1020855] : [class_Groups_Ogroup__add(_1020851), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1020851), _1020853), _1020855) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020851), _1020853), hAPP(c_Groups_Ouminus__class_Ouminus(_1020851), _1020855)))], (29190 ^ _775212) ^ [_1294008, _1294010] : [hAPP(c_Finite__Set_Ocard(_1294008), _1294010) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1294010 = c_Orderings_Obot__class_Obot(tc_fun(_1294008, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294008), _1294010))], (18697 ^ _775212) ^ [] : [-(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))))], (8683 ^ _775212) ^ [_915983, _915985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915983), hAPP(c_Int_Onat, _915985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _915983)), _915985)))], (43519 ^ _775212) ^ [_1625668, _1625670, _1625672] : [class_Complete__Lattice_Ocomplete__lattice(_1625668), hBOOL(hAPP(hAPP(c_member(_1625668), _1625670), _1625672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625668), _1625670), c_Complete__Lattice_OSup__class_OSup(_1625668, _1625672))))], (40961 ^ _775212) ^ [_1563938, _1563940, _1563942, _1563944, _1563946] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1563938), _1563940), _1563942), _1563944), _1563946) = c_New__DSequence_Oneg__single(_1563938, _1563940))], (19079 ^ _775212) ^ [_1100382, _1100384, _1100386] : [class_Fields_Olinordered__field__inverse__zero(_1100382), -(hAPP(c_Groups_Oabs__class_Oabs(_1100382), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100382), _1100384), _1100386)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100382), hAPP(c_Groups_Oabs__class_Oabs(_1100382), _1100384)), hAPP(c_Groups_Oabs__class_Oabs(_1100382), _1100386)))], (23284 ^ _775212) ^ [_1179080, _1179082] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1179080)), _1179082) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1179080), 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), _1179080)), _1179082))], (23518 ^ _775212) ^ [_1183427, _1183429, _1183431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1183427), c_Nitpick_Oplus__frac(_1183427, _1183429, c_Nitpick_Ouminus__frac(_1183427, _1183431)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1183427, _1183429, _1183431))], (43031 ^ _775212) ^ [_1614140, _1614142, _1614144] : [c_Relation_Ototal__on(_1614140, _1614142, hAPP(c_Relation_Oconverse(_1614140, _1614140), _1614144)), -(c_Relation_Ototal__on(_1614140, _1614142, _1614144))], (31853 ^ _775212) ^ [_1351334, _1351336, _1351338] : [class_Lattices_Olattice(_1351334), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351334), _1351336)), -(_1351336 = c_Orderings_Obot__class_Obot(tc_fun(_1351334, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1351334, hAPP(hAPP(c_Set_Oinsert(_1351334), _1351338), _1351336)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1351334), _1351338), c_Big__Operators_Olattice__class_OSup__fin(_1351334, _1351336)))], (6254 ^ _775212) ^ [_873971, _873973] : [6255 ^ _775212 : [(6258 ^ _775212) ^ [] : [_873971 = _873973], (6256 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873971), _873973))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873971), hAPP(c_Nat_OSuc, _873973))))], (46953 ^ _775212) ^ [_1711489, _1711491, _1711493, _1711495, _1711497] : [class_Groups_Omonoid__add(_1711489), class_Groups_Oordered__ab__semigroup__add(_1711489), 46963 ^ _775212 : [(46966 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711489), hAPP(_1711495, 46962 ^ [_1711489, _1711491, _1711493, _1711495, _1711497])), hAPP(_1711497, 46962 ^ [_1711489, _1711491, _1711493, _1711495, _1711497])))], (46964 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1711491), 46962 ^ [_1711489, _1711491, _1711493, _1711495, _1711497]), hAPP(c_List_Oset(_1711491), _1711493))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711489), hAPP(c_List_Omonoid__add__class_Olistsum(_1711489), hAPP(hAPP(c_List_Omap(_1711491, _1711489), _1711495), _1711493))), hAPP(c_List_Omonoid__add__class_Olistsum(_1711489), hAPP(hAPP(c_List_Omap(_1711491, _1711489), _1711497), _1711493)))))], (31461 ^ _775212) ^ [_1344502, _1344504] : [31462 ^ _775212 : [(31465 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344504), _1344502))], (31463 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344502), _1344504)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1344502, _1344504))], (14237 ^ _775212) ^ [_1012424, _1012426, _1012428, _1012430, _1012432] : [class_Groups_Oordered__ab__group__add(_1012424), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1012424), _1012426), _1012428) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1012424), _1012430), _1012432), 14244 ^ _775212 : [(14251 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012424), _1012430), _1012432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012424), _1012426), _1012428)))], (14245 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012424), _1012426), _1012428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012424), _1012430), _1012432)))]]], (17025 ^ _775212) ^ [_1065024, _1065026] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1065024), _1065026) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 17026 ^ _775212 : [(17033 ^ _775212) ^ [] : [_1065024 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1065026 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (17027 ^ _775212) ^ [] : [_1065024 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1065026 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (39055 ^ _775212) ^ [_1510251, _1510253, _1510255, _1510257] : [-(hAPP(c_Set_Ovimage(_1510251, _1510253, _1510255), _1510257) = hAPP(c_Set_OCollect(_1510251), hAPP(hAPP(c_COMBC(_1510251, tc_fun(_1510253, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1510253, tc_fun(tc_fun(_1510253, tc_HOL_Obool), tc_HOL_Obool), _1510251), c_member(_1510253)), _1510255)), _1510257)))], (512 ^ _775212) ^ [_783104, _783106, _783108, _783110, _783112, _783114, _783116, _783118] : [-(c_Finite__Set_Ofolding(_783116, _783112, _783108, _783104)), c_Finite__Set_Ofolding(_783118, _783114, _783110, _783106), _783118 = _783116, _783114 = _783112, _783110 = _783108, _783106 = _783104], (51517 ^ _775212) ^ [_1811366, _1811368, _1811370, _1811372, _1811374] : [c_Predicate_Otransp(_1811366, _1811368), hBOOL(hAPP(hAPP(_1811368, _1811370), _1811372)), hBOOL(hAPP(hAPP(_1811368, _1811372), _1811374)), -(hBOOL(hAPP(hAPP(_1811368, _1811370), _1811374)))], (52635 ^ _775212) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (32834 ^ _775212) ^ [_1370759, _1370761, _1370763, _1370765, _1370767, _1370769] : [-(c_Fun_Ofun__upd(_1370759, _1370761, c_Fun_Ofun__upd(_1370759, _1370761, _1370763, _1370765, _1370767), _1370765, _1370769) = c_Fun_Ofun__upd(_1370759, _1370761, _1370763, _1370765, _1370769))], (7542 ^ _775212) ^ [_895524, _895526, _895528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _895524), _895526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _895528)), -(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), _895528)), _895524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _895528)), _895526))))], (18251 ^ _775212) ^ [_1085122, _1085124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085122), _1085124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085122)), c_Int_OBit1(_1085124))))], (43286 ^ _775212) ^ [_1620140, _1620142, _1620144] : [class_Complete__Lattice_Ocomplete__lattice(_1620140), hBOOL(hAPP(hAPP(c_member(_1620140), _1620142), _1620144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620140), c_Complete__Lattice_OInf__class_OInf(_1620140, _1620144)), _1620142)))], (7499 ^ _775212) ^ [_894843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _894843)), 7503 ^ _775212 : [(7506 ^ _775212) ^ [] : [-(_894843 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 7502 ^ [_894843]))], (7504 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7502 ^ [_894843])))]]], (26915 ^ _775212) ^ [_1248572, _1248574, _1248576, _1248578] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248572, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248572, tc_HOL_Obool)), _1248574), _1248576)), _1248578) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248572, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248572, tc_HOL_Obool)), _1248574), _1248578)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248572, tc_HOL_Obool)), _1248576), _1248578)))], (41028 ^ _775212) ^ [_1565564, _1565566] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1565564), _1565566)), 41034 ^ _775212 : [(41037 ^ _775212) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (41035 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565564), 41033 ^ [_1565564, _1565566]), _1565566)))]], -(hAPP(c_Finite__Set_Ocard(_1565564), _1565566) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32299 ^ _775212) ^ [_1360106, _1360108, _1360110, _1360112] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1360106, _1360108)), c_Sum__Type_OPlus(_1360106, _1360108, _1360110, _1360112))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1360108), _1360112)))], (12111 ^ _775212) ^ [_974276, _974278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974276)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974276), _974278)))], (29096 ^ _775212) ^ [_1292170, _1292172] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292170, _1292172), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292170), _1292172))], (1020 ^ _775212) ^ [_790686, _790688, _790690, _790692] : [-(c_Predicate_Osymp(_790690, _790686)), c_Predicate_Osymp(_790692, _790688), _790692 = _790690, _790688 = _790686], (41205 ^ _775212) ^ [_1569493, _1569495, _1569497] : [class_Orderings_Olinorder(_1569493), hBOOL(hAPP(c_Finite__Set_Ofinite(_1569493), _1569495)), -(hBOOL(hAPP(hAPP(c_member(_1569493), _1569497), _1569495))), -(c_Big__Operators_Olattice_OSup__fin(_1569493, c_Orderings_Oord__class_Omax(_1569493), hAPP(hAPP(c_Set_Oinsert(_1569493), _1569497), _1569495)) = hAPP(hAPP(c_Finite__Set_Ofold(_1569493, _1569493, c_Orderings_Oord__class_Omax(_1569493)), _1569497), _1569495))], (7084 ^ _775212) ^ [_888056, _888058, _888060] : [class_Orderings_Opreorder(_888056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888056), _888058), _888060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888056), _888060), _888058))], (28504 ^ _775212) ^ [_1280906, _1280908, _1280910] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1280906), _1280908)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280906, tc_HOL_Obool)), _1280910), _1280908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1280906), _1280910)), hAPP(c_Finite__Set_Ocard(_1280906), _1280908))))], (18307 ^ _775212) ^ [_1086110, _1086112] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1086110)), c_Int_OBit1(_1086112)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086110), _1086112)))], (52583 ^ _775212) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (16041 ^ _775212) ^ [_1047039] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1047039)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1047039))], (7755 ^ _775212) ^ [_899730, _899732, _899734] : [class_Groups_Ogroup__add(_899730), 7758 ^ _775212 : [(7765 ^ _775212) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_899730), _899734) = _899732, -(hAPP(c_Groups_Ouminus__class_Ouminus(_899730), _899732) = _899734)], (7759 ^ _775212) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_899730), _899732) = _899734, -(hAPP(c_Groups_Ouminus__class_Ouminus(_899730), _899734) = _899732)]]], (440 ^ _775212) ^ [_781988, _781990] : [-(c_Nitpick_Ounknown(_781988)), _781990 = _781988, c_Nitpick_Ounknown(_781990)], (7641 ^ _775212) ^ [_897496, _897498, _897500, _897502] : [class_Rings_Ocomm__semiring__1(_897496), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897496), _897498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897496), _897500), _897502)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897496), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897496), _897498), _897500)), _897502))], (35195 ^ _775212) ^ [_1423519, _1423521, _1423523, _1423525, _1423527] : [class_Orderings_Olinorder(_1423519), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423519, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1423519, _1423521), _1423523)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1423519, _1423525), _1423527)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1423519, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1423519), _1423521), _1423525)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1423519), _1423523), _1423527)))], (17711 ^ _775212) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (40009 ^ _775212) ^ [_1541520, _1541522, _1541524, _1541526] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1541520, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1541520, _1541522), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1541520, _1541522), tc_HOL_Obool)), _1541524), _1541526))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1541520, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1541520, _1541522), _1541524)), hAPP(c_Relation_ODomain(_1541520, _1541522), _1541526)))))], (40496 ^ _775212) ^ [_1553427, _1553429, _1553431, _1553433, _1553435, _1553437, _1553439, _1553441, _1553443, _1553445] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1553427, _1553429), tc_prod(_1553431, _1553433), tc_prod(_1553435, _1553437), c_Product__Type_Omap__pair(_1553427, _1553431, _1553429, _1553433, _1553439, _1553441)), c_Product__Type_Omap__pair(_1553435, _1553427, _1553437, _1553429, _1553443, _1553445)) = c_Product__Type_Omap__pair(_1553435, _1553431, _1553437, _1553433, hAPP(c_Fun_Ocomp(_1553427, _1553431, _1553435, _1553439), _1553443), hAPP(c_Fun_Ocomp(_1553429, _1553433, _1553437, _1553441), _1553445)))], (34727 ^ _775212) ^ [_1412941, _1412943, _1412945] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412941, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412941, tc_HOL_Obool)), _1412943), _1412945)), _1412945)))], (34973 ^ _775212) ^ [_1417928, _1417930, _1417932, _1417934, _1417936, _1417938, _1417940] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417928, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417930, tc_fun(_1417928, tc_HOL_Obool)), _1417932), _1417934)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417936, tc_fun(_1417928, tc_HOL_Obool)), _1417938), _1417940)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417930, tc_fun(_1417928, tc_HOL_Obool)), _1417932), hAPP(hAPP(c_COMBB(tc_fun(_1417936, tc_fun(_1417928, tc_HOL_Obool)), tc_fun(_1417928, tc_HOL_Obool), _1417930), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417936, tc_fun(_1417928, tc_HOL_Obool)), _1417938)), hAPP(hAPP(c_COMBC(_1417930, tc_fun(_1417936, tc_fun(_1417928, tc_HOL_Obool)), tc_fun(_1417936, tc_fun(_1417928, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1417928, tc_HOL_Obool), tc_fun(_1417928, tc_HOL_Obool)), tc_fun(tc_fun(_1417936, tc_fun(_1417928, tc_HOL_Obool)), tc_fun(_1417936, tc_fun(_1417928, tc_HOL_Obool))), _1417930), c_COMBB(tc_fun(_1417928, tc_HOL_Obool), tc_fun(_1417928, tc_HOL_Obool), _1417936)), hAPP(hAPP(c_COMBB(tc_fun(_1417928, tc_HOL_Obool), tc_fun(tc_fun(_1417928, tc_HOL_Obool), tc_fun(_1417928, tc_HOL_Obool)), _1417930), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417928, tc_HOL_Obool))), _1417934))), _1417940))))], (39847 ^ _775212) ^ [_1537676, _1537678] : [c_Wellfounded_Owf(_1537676, _1537678), 39850 ^ _775212 : [(39851 ^ _775212) ^ [_1537745] : [-(hBOOL(hAPP(hAPP(c_member(_1537676), _1537745), c_Wellfounded_Oacc(_1537676, _1537678))))]]], (14841 ^ _775212) ^ [_1023929] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1023929) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26543 ^ _775212) ^ [_1241791, _1241793, _1241795] : [class_Groups_Oordered__ab__group__add(_1241791), -(hAPP(c_Set_Oimage(_1241791, _1241791, c_Groups_Ouminus__class_Ouminus(_1241791)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241791, _1241793), _1241795)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1241791, hAPP(c_Groups_Ouminus__class_Ouminus(_1241791), _1241795), hAPP(c_Groups_Ouminus__class_Ouminus(_1241791), _1241793)))], (38157 ^ _775212) ^ [_1491563, _1491565, _1491567, _1491569] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491563), _1491565)), 38163 ^ _775212 : [(38166 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491567), hAPP(_1491569, 38162 ^ [_1491563, _1491565, _1491567, _1491569])))], (38164 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491563), 38162 ^ [_1491563, _1491565, _1491567, _1491569]), _1491565)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1491563, _1491567)), hAPP(hAPP(c_Product__Type_OSigma(_1491563, _1491567), _1491565), _1491569)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491563, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1491567, tc_HOL_Obool), tc_Nat_Onat, _1491563), c_Finite__Set_Ocard(_1491567)), _1491569)), _1491565))], (6445 ^ _775212) ^ [_877184, _877186, _877188, _877190] : [class_Groups_Ocancel__semigroup__add(_877184), 6448 ^ _775212 : [(6455 ^ _775212) ^ [] : [_877186 = _877190, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877184), _877186), _877188) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877184), _877190), _877188))], (6449 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877184), _877186), _877188) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877184), _877190), _877188), -(_877186 = _877190)]]], (23410 ^ _775212) ^ [_1181176, _1181178] : [-(c_Nitpick_Onumber__of__frac(_1181176, _1181178) = c_Nitpick_OAbs__Frac(_1181176, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1181178), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (37080 ^ _775212) ^ [_1464909, _1464911, _1464913, _1464915, _1464917] : [c_Fun_Oinj__on(_1464909, _1464911, _1464913, _1464915), hBOOL(hAPP(hAPP(c_member(_1464909), _1464917), _1464915)), -(hAPP(c_Fun_Othe__inv__into(_1464909, _1464911, _1464915, _1464913), hAPP(_1464913, _1464917)) = _1464917)], (41744 ^ _775212) ^ [_1580502, _1580504, _1580506, _1580508, _1580510, _1580512] : [c_Finite__Set_Ofun__left__comm(_1580502, _1580504, _1580506), hBOOL(hAPP(c_Finite__Set_Ofinite(_1580502), _1580508)), -(hAPP(hAPP(_1580506, _1580510), hAPP(hAPP(c_Finite__Set_Ofold(_1580502, _1580504, _1580506), _1580512), _1580508)) = hAPP(hAPP(c_Finite__Set_Ofold(_1580502, _1580504, _1580506), hAPP(hAPP(_1580506, _1580510), _1580512)), _1580508))], (806 ^ _775212) ^ [_787561, _787563, _787565, _787567, _787569, _787571] : [-(c_List_Olist__ex1(_787569, _787565, _787561)), c_List_Olist__ex1(_787571, _787567, _787563), _787571 = _787569, _787567 = _787565, _787563 = _787561], (3982 ^ _775212) ^ [_835629, _835631, _835633, _835635, _835637, _835639] : [-(c_List_Olist_Olist__size(_835639, _835635, _835631) = c_List_Olist_Olist__size(_835637, _835633, _835629)), _835639 = _835637, _835635 = _835633, _835631 = _835629], (29716 ^ _775212) ^ [_1304567, _1304569, _1304571, _1304573] : [hBOOL(hAPP(hAPP(c_member(_1304567), _1304569), _1304571)), -(hBOOL(hAPP(hAPP(c_member(_1304567), _1304569), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304567, tc_HOL_Obool)), _1304571), _1304573))))], (25605 ^ _775212) ^ [_1221676, _1221678, _1221680, _1221682, _1221684] : [class_Rings_Osemiring__0(_1221676), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221676), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221678, _1221676), _1221680), _1221682)), _1221684) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221678, _1221676), hAPP(hAPP(c_COMBC(_1221678, _1221676, _1221676), hAPP(hAPP(c_COMBB(_1221676, tc_fun(_1221676, _1221676), _1221678), c_Groups_Otimes__class_Otimes(_1221676)), _1221680)), _1221684)), _1221682))], (17327 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (11240 ^ _775212) ^ [_959793, _959795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _959793)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _959795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _959793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _959793), _959795))))], (52339 ^ _775212) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (36505 ^ _775212) ^ [_1452903, _1452905] : [-(c_Fun_Oinj__on(_1452903, _1452903, c_COMBI(_1452903), _1452905))], (45776 ^ _775212) ^ [_1684577, _1684579, _1684581] : [_1684581 = c_List_Olist_ONil(_1684577), -(hAPP(hAPP(c_List_Oappend(_1684577), _1684579), _1684581) = _1684579)], (42045 ^ _775212) ^ [_1587604, _1587606, _1587608, _1587610] : [-(c_Wellfounded_Owf(_1587604, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1587604, _1587604)), hAPP(hAPP(c_Product__Type_OPair(_1587604, _1587604), _1587606), _1587608)), _1587610))), c_Wellfounded_Owf(_1587604, _1587610), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587604, _1587604)), hAPP(hAPP(c_Product__Type_OPair(_1587604, _1587604), _1587608), _1587606)), c_Transitive__Closure_Ortrancl(_1587604, _1587610))))], (52405 ^ _775212) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (13651 ^ _775212) ^ [_1001524, _1001526, _1001528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1001526), _1001528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1001524), _1001528)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1001524), _1001526))))], (23936 ^ _775212) ^ [_1191196, _1191198, _1191200, _1191202] : [class_Rings_Ocomm__semiring__1(_1191196), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1191196), _1191198), _1191200)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1191196), _1191198), _1191202)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1191196), _1191198), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191196), _1191200), _1191202))))], (15747 ^ _775212) ^ [_1041726, _1041728, _1041730, _1041732, _1041734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041726), _1041728)), 15750 ^ _775212 : [(15757 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041732), 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), _1041728), _1041726)), _1041730)), _1041734))), -(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), _1041726), _1041730)), _1041732)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1041728), _1041730)), _1041734))))], (15751 ^ _775212) ^ [] : [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), _1041726), _1041730)), _1041732)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1041728), _1041730)), _1041734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041732), 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), _1041728), _1041726)), _1041730)), _1041734))))]]], (28670 ^ _775212) ^ [_1284434, _1284436] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1284434, tc_HOL_Obool)), _1284436), _1284436) = c_Orderings_Obot__class_Obot(tc_fun(_1284434, tc_HOL_Obool)))], (8127 ^ _775212) ^ [_906201, _906203] : [class_Groups_Oordered__ab__group__add(_906201), 8130 ^ _775212 : [(8137 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906201), _906203), c_Groups_Ozero__class_Ozero(_906201))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906201), c_Groups_Ozero__class_Ozero(_906201)), hAPP(c_Groups_Ouminus__class_Ouminus(_906201), _906203))))], (8131 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906201), c_Groups_Ozero__class_Ozero(_906201)), hAPP(c_Groups_Ouminus__class_Ouminus(_906201), _906203))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906201), _906203), c_Groups_Ozero__class_Ozero(_906201))))]]], (35255 ^ _775212) ^ [_1424921, _1424923, _1424925, _1424927] : [class_Orderings_Olinorder(_1424921), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424921, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1424921, _1424923, _1424925)), hAPP(c_SetInterval_Oord__class_OatMost(_1424921), _1424927)) = c_SetInterval_Oord__class_OatLeastAtMost(_1424921, _1424923, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424921), _1424925), _1424927)))], (34515 ^ _775212) ^ [_1408761, _1408763, _1408765, _1408767] : [class_Lattices_Odistrib__lattice(_1408761), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408761), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408761), _1408763), _1408765)), _1408767) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408761), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408761), _1408763), _1408767)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408761), _1408765), _1408767)))], (33763 ^ _775212) ^ [_1390949, _1390951, _1390953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1390949, tc_HOL_Obool)), _1390951), _1390953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1390949, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1390949), _1390951)), hAPP(c_Set_OPow(_1390949), _1390953))))], (45166 ^ _775212) ^ [_1669492, _1669494] : [-(c_List_Osublist(_1669492, _1669494, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1669492))], (18491 ^ _775212) ^ [_1089383, _1089385] : [class_Int_Onumber__ring(_1089383), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089383), hAPP(c_Int_Onumber__class_Onumber__of(_1089383), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1089385) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089383), _1089385), _1089385))], (19067 ^ _775212) ^ [_1100094, _1100096, _1100098] : [class_Fields_Ofield__inverse__zero(_1100094), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1100094), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100094), _1100096), _1100098)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100094), _1100096), hAPP(c_Groups_Ouminus__class_Ouminus(_1100094), _1100098)))], (48260 ^ _775212) ^ [_1740052, _1740054] : [-(hAPP(c_List_Ofilter(_1740052, _1740054), c_List_Olist_ONil(_1740052)) = c_List_Olist_ONil(_1740052))], (44945 ^ _775212) ^ [_1663476, _1663478, _1663480, _1663482, _1663484] : [-(c_List_Olist_Olist__size(_1663476, _1663478, hAPP(hAPP(c_List_Omap(_1663480, _1663476), _1663482), _1663484)) = c_List_Olist_Olist__size(_1663480, hAPP(c_Fun_Ocomp(_1663476, tc_Nat_Onat, _1663480, _1663478), _1663482), _1663484))], (34907 ^ _775212) ^ [_1416442, _1416444, _1416446, _1416448] : [class_Lattices_Olattice(_1416442), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416442), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416442), _1416444), _1416446)), _1416448) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416442), _1416444), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416442), _1416446), _1416448)))], (6719 ^ _775212) ^ [_882095, _882097, _882099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882095), _882097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882095), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882097), _882099))))], (47044 ^ _775212) ^ [_1712929, _1712931, _1712933] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712929)), _1712931), c_List_Olists(_1712929, _1712933))), -(_1712931 = c_List_Olist_ONil(_1712929)), 47053 ^ _775212 : [(47058 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712929)), 47052 ^ [_1712929, _1712931, _1712933]), c_List_Olists(_1712929, _1712933))))], (47056 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1712929), 47051 ^ [_1712929, _1712931, _1712933]), _1712933)))], (47054 ^ _775212) ^ [] : [-(_1712931 = hAPP(hAPP(c_List_Olist_OCons(_1712929), 47051 ^ [_1712929, _1712931, _1712933]), 47052 ^ [_1712929, _1712931, _1712933]))]]], (16223 ^ _775212) ^ [_1050306, _1050308, _1050310] : [class_Groups_Oordered__ab__group__add__abs(_1050306), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050306), _1050308), _1050310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050306), hAPP(c_Groups_Ouminus__class_Ouminus(_1050306), _1050308)), _1050310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050306), hAPP(c_Groups_Oabs__class_Oabs(_1050306), _1050308)), _1050310)))], (7284 ^ _775212) ^ [_890940, _890942, _890944] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_890940), 7287 ^ _775212 : [(7294 ^ _775212) ^ [] : [_890944 = c_Groups_Ozero__class_Ozero(_890940), -(_890942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_890940), _890942), _890944))], (7288 ^ _775212) ^ [] : [_890942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_890940), _890942), _890944), -(_890944 = c_Groups_Ozero__class_Ozero(_890940))]]], (11550 ^ _775212) ^ [_964854, _964856, _964858, _964860, _964862] : [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), _964854), _964856)), _964858)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _964854), _964860)), _964862))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _964858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _964858), _964854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _964862), _964854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _964856), _964860)))], (30234 ^ _775212) ^ [_1316949, _1316951, _1316953, _1316955, _1316957] : [class_Complete__Lattice_Ocomplete__lattice(_1316949), hBOOL(hAPP(hAPP(c_member(_1316951), _1316953), _1316955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316949), hAPP(_1316957, _1316953)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1316951, _1316949), _1316955), _1316957))))], (27389 ^ _775212) ^ [_1258026, _1258028, _1258030, _1258032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1258026, tc_HOL_Obool)), _1258028), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258026, tc_HOL_Obool)), _1258030), _1258032))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1258026, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1258026, tc_HOL_Obool)), _1258028), _1258030)), _1258032)))], (29919 ^ _775212) ^ [_1308422, _1308424] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1308422, tc_HOL_Obool)), _1308424)), -(hBOOL(hAPP(hAPP(c_member(_1308422), _1308424), c_Orderings_Obot__class_Obot(tc_fun(_1308422, tc_HOL_Obool)))))], (37972 ^ _775212) ^ [_1486442, _1486444, _1486446, _1486448, _1486450, _1486452] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486442, _1486444)), hAPP(hAPP(c_Product__Type_OPair(_1486442, _1486444), _1486446), _1486448)), hAPP(hAPP(c_Product__Type_OSigma(_1486442, _1486444), _1486450), _1486452))), 37975 ^ _775212 : [(37978 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486444), _1486448), hAPP(_1486452, _1486446))))], (37976 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486442), _1486446), _1486450)))]]], (23708 ^ _775212) ^ [_1187246] : [-(c_Quickcheck_Obeyond(_1187246, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (30745 ^ _775212) ^ [_1330107, _1330109, _1330111, _1330113, _1330115, _1330117] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330107, tc_fun(_1330109, tc_HOL_Obool))), _1330111), _1330113), _1330115), _1330117)), -(hBOOL(hAPP(hAPP(_1330111, _1330115), _1330117))), -(hBOOL(hAPP(hAPP(_1330113, _1330115), _1330117)))], (32713 ^ _775212) ^ [_1367967, _1367969, _1367971] : [class_Orderings_Olinorder(_1367967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367967), _1367969)), 32720 ^ _775212 : [(32727 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1367967, tc_HOL_Obool)), _1367969), hAPP(hAPP(c_Set_Oinsert(_1367967), _1367971), c_Orderings_Obot__class_Obot(tc_fun(_1367967, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1367967, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1367967, c_Orderings_Oord__class_Omin(_1367967), hAPP(hAPP(c_Set_Oinsert(_1367967), _1367971), _1367969)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367967), _1367971), c_Big__Operators_Olattice_OInf__fin(_1367967, c_Orderings_Oord__class_Omin(_1367967), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1367967, tc_HOL_Obool)), _1367969), hAPP(hAPP(c_Set_Oinsert(_1367967), _1367971), c_Orderings_Obot__class_Obot(tc_fun(_1367967, tc_HOL_Obool)))))))], (32721 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1367967, tc_HOL_Obool)), _1367969), hAPP(hAPP(c_Set_Oinsert(_1367967), _1367971), c_Orderings_Obot__class_Obot(tc_fun(_1367967, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1367967, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1367967, c_Orderings_Oord__class_Omin(_1367967), hAPP(hAPP(c_Set_Oinsert(_1367967), _1367971), _1367969)) = _1367971)]]], (17399 ^ _775212) ^ [_1070730] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1070730), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070730), c_Int_OPls)))], (41144 ^ _775212) ^ [_1568197, _1568199, _1568201] : [class_Orderings_Olinorder(_1568197), hBOOL(hAPP(c_Finite__Set_Ofinite(_1568197), _1568199)), 41154 ^ _775212 : [(41157 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1568197), _1568201), 41153 ^ [_1568197, _1568199, _1568201]))], (41155 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568197), 41153 ^ [_1568197, _1568199, _1568201]), _1568199)))]], hBOOL(hAPP(hAPP(c_member(_1568197), _1568201), _1568199)), -(c_Big__Operators_Olinorder__class_OMin(_1568197, _1568199) = _1568201)], (35021 ^ _775212) ^ [_1419433, _1419435, _1419437] : [class_Lattices_Oboolean__algebra(_1419433), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1419433), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1419433), _1419435), _1419437)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419433), hAPP(c_Groups_Ouminus__class_Ouminus(_1419433), _1419435)), hAPP(c_Groups_Ouminus__class_Ouminus(_1419433), _1419437)))], (28900 ^ _775212) ^ [_1288781, _1288783, _1288785, _1288787] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288781, tc_HOL_Obool)), _1288783), hAPP(hAPP(c_Set_Oinsert(_1288781), _1288785), _1288787)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288781, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288781, tc_HOL_Obool)), _1288783), _1288787)), hAPP(hAPP(c_Set_Oinsert(_1288781), _1288785), c_Orderings_Obot__class_Obot(tc_fun(_1288781, tc_HOL_Obool)))))], (892 ^ _775212) ^ [_788830, _788832, _788834, _788836, _788838, _788840, _788842, _788844] : [-(c_Wellfounded_Omax__extp(_788842, _788838, _788834, _788830)), c_Wellfounded_Omax__extp(_788844, _788840, _788836, _788832), _788844 = _788842, _788840 = _788838, _788836 = _788834, _788832 = _788830], (3262 ^ _775212) ^ [_824263, _824265, _824267, _824269, _824271, _824273] : [-(c_FunDef_Oin__rel(_824273, _824269, _824265) = c_FunDef_Oin__rel(_824271, _824267, _824263)), _824273 = _824271, _824269 = _824267, _824265 = _824263], (28612 ^ _775212) ^ [_1283264, _1283266, _1283268, _1283270, _1283272] : [hAPP(hAPP(c_Set_Oinsert(_1283264), _1283266), hAPP(hAPP(c_Set_Oinsert(_1283264), _1283268), c_Orderings_Obot__class_Obot(tc_fun(_1283264, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1283264), _1283270), hAPP(hAPP(c_Set_Oinsert(_1283264), _1283272), c_Orderings_Obot__class_Obot(tc_fun(_1283264, tc_HOL_Obool)))), 28617 ^ _775212 : [(28620 ^ _775212) ^ [] : [-(_1283268 = _1283272)], (28618 ^ _775212) ^ [] : [-(_1283266 = _1283270)]], 28621 ^ _775212 : [(28624 ^ _775212) ^ [] : [-(_1283268 = _1283270)], (28622 ^ _775212) ^ [] : [-(_1283266 = _1283272)]]], (39379 ^ _775212) ^ [_1523456, _1523458, _1523460, _1523462, _1523464, _1523466, _1523468] : [class_Rings_Osemiring__0(_1523456), c_Fun_Oinj__on(tc_prod(_1523458, _1523460), _1523456, hAPP(c_Product__Type_Oprod_Oprod__case(_1523458, _1523460, _1523456), hAPP(hAPP(c_COMBC(_1523458, tc_fun(_1523460, _1523456), tc_fun(_1523460, _1523456)), hAPP(hAPP(c_COMBB(tc_fun(_1523456, _1523456), tc_fun(tc_fun(_1523460, _1523456), tc_fun(_1523460, _1523456)), _1523458), c_COMBB(_1523456, _1523456, _1523460)), hAPP(hAPP(c_COMBB(_1523456, tc_fun(_1523456, _1523456), _1523458), c_Groups_Otimes__class_Otimes(_1523456)), _1523462))), _1523464)), hAPP(hAPP(c_Product__Type_OSigma(_1523458, _1523460), _1523466), hAPP(c_COMBK(tc_fun(_1523460, tc_HOL_Obool), _1523458), _1523468))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1523456), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1523458, _1523456), _1523462), _1523466)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1523460, _1523456), _1523464), _1523468)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1523456, _1523456), c_Fun_Oid(_1523456)), hAPP(c_Set_OCollect(_1523456), hAPP(hAPP(c_COMBB(tc_fun(_1523458, tc_HOL_Obool), tc_HOL_Obool, _1523456), c_HOL_OEx(_1523458)), hAPP(hAPP(c_COMBB(tc_fun(_1523458, tc_fun(_1523460, tc_HOL_Obool)), tc_fun(_1523458, tc_HOL_Obool), _1523456), hAPP(c_COMBB(tc_fun(_1523460, tc_HOL_Obool), tc_HOL_Obool, _1523458), c_HOL_OEx(_1523460))), hAPP(hAPP(c_COMBC(_1523456, tc_fun(_1523458, tc_fun(_1523460, tc_HOL_Obool)), tc_fun(_1523458, tc_fun(_1523460, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523458, tc_fun(tc_fun(_1523460, tc_HOL_Obool), tc_fun(_1523460, tc_HOL_Obool))), tc_fun(tc_fun(_1523458, tc_fun(_1523460, tc_HOL_Obool)), tc_fun(_1523458, tc_fun(_1523460, tc_HOL_Obool))), _1523456), c_COMBS(_1523458, tc_fun(_1523460, tc_HOL_Obool), tc_fun(_1523460, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523458, tc_fun(_1523460, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1523458, tc_fun(tc_fun(_1523460, tc_HOL_Obool), tc_fun(_1523460, tc_HOL_Obool))), _1523456), hAPP(c_COMBB(tc_fun(_1523460, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1523460, tc_HOL_Obool), tc_fun(_1523460, tc_HOL_Obool)), _1523458), c_COMBS(_1523460, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523458, tc_fun(_1523460, tc_HOL_Obool)), tc_fun(_1523458, tc_fun(_1523460, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1523456), hAPP(c_COMBB(tc_fun(_1523460, tc_HOL_Obool), tc_fun(_1523460, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1523458), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523460), c_fconj))), hAPP(hAPP(c_COMBC(_1523456, tc_fun(_1523458, tc_fun(_1523460, _1523456)), tc_fun(_1523458, tc_fun(_1523460, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1523460, _1523456), tc_fun(_1523460, tc_HOL_Obool)), tc_fun(tc_fun(_1523458, tc_fun(_1523460, _1523456)), tc_fun(_1523458, tc_fun(_1523460, tc_HOL_Obool))), _1523456), c_COMBB(tc_fun(_1523460, _1523456), tc_fun(_1523460, tc_HOL_Obool), _1523458)), hAPP(hAPP(c_COMBB(tc_fun(_1523456, tc_HOL_Obool), tc_fun(tc_fun(_1523460, _1523456), tc_fun(_1523460, tc_HOL_Obool)), _1523456), c_COMBB(_1523456, tc_HOL_Obool, _1523460)), c_fequal))), hAPP(hAPP(c_COMBC(_1523458, tc_fun(_1523460, _1523456), tc_fun(_1523460, _1523456)), hAPP(hAPP(c_COMBB(tc_fun(_1523456, _1523456), tc_fun(tc_fun(_1523460, _1523456), tc_fun(_1523460, _1523456)), _1523458), c_COMBB(_1523456, _1523456, _1523460)), hAPP(hAPP(c_COMBB(_1523456, tc_fun(_1523456, _1523456), _1523458), c_Groups_Otimes__class_Otimes(_1523456)), _1523462))), _1523464)))))), hAPP(hAPP(c_COMBC(_1523458, tc_fun(_1523460, tc_HOL_Obool), tc_fun(_1523460, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1523460, tc_HOL_Obool), tc_fun(_1523460, tc_HOL_Obool)), _1523458), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1523460)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523458), c_fconj), hAPP(hAPP(c_COMBC(_1523458, tc_fun(_1523458, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523458)), _1523466)))), hAPP(hAPP(c_COMBC(_1523460, tc_fun(_1523460, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523460)), _1523468))))))))], (5230 ^ _775212) ^ [_854957, _854959, _854961, _854963, _854965, _854967, _854969, _854971, _854973, _854975, _854977, _854979] : [-(c_Partial__Function_Ofun__lub(_854979, _854975, _854971, _854967, _854963, _854959) = c_Partial__Function_Ofun__lub(_854977, _854973, _854969, _854965, _854961, _854957)), _854979 = _854977, _854975 = _854973, _854971 = _854969, _854967 = _854965, _854963 = _854961, _854959 = _854957], (23832 ^ _775212) ^ [_1189468, _1189470, _1189472, _1189474, _1189476] : [-(_1189468 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1189470, _1189472, _1189474, _1189476), _1189468) = c_Lazy__Sequence_Ohb__bind(_1189470, _1189472, hAPP(_1189474, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1189468), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1189470, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1189472))), _1189476), _1189468)))], (23638 ^ _775212) ^ [_1185738, _1185740] : [-(c_HOL_OThe(_1185738, hAPP(c_fequal, _1185740)) = _1185740)], (3054 ^ _775212) ^ [_820941, _820943, _820945, _820947, _820949, _820951] : [-(c_Partial__Function_Oflat__lub(_820951, _820947, _820943) = c_Partial__Function_Oflat__lub(_820949, _820945, _820941)), _820951 = _820949, _820947 = _820945, _820943 = _820941], (30003 ^ _775212) ^ [_1312417, _1312419, _1312421, _1312423] : [hBOOL(hAPP(hAPP(c_member(_1312417), _1312423), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312417, tc_HOL_Obool)), _1312419), _1312421))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312417, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1312417, tc_fun(_1312417, tc_HOL_Obool), tc_HOL_Obool), c_member(_1312417)), _1312419)), hAPP(hAPP(c_COMBC(_1312417, tc_fun(_1312417, tc_HOL_Obool), tc_HOL_Obool), c_member(_1312417)), _1312421)), _1312423)))], (5961 ^ _775212) ^ [_869706, _869708, _869710] : [-(c_Nat_Onat_Onat__case(_869706, _869708, _869710, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _869708)], (29268 ^ _775212) ^ [_1295456, _1295458] : [class_Orderings_Olinorder(_1295456), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295456, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1295456), _1295458)), hAPP(hAPP(c_Set_Oinsert(_1295456), _1295458), c_Orderings_Obot__class_Obot(tc_fun(_1295456, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1295456), _1295458))], (30352 ^ _775212) ^ [_1321405, _1321407, _1321409, _1321411, _1321413] : [class_Groups_Ocomm__monoid__add(_1321405), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321407), _1321409)), 30359 ^ _775212 : [(30366 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1321407), _1321411), _1321409))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1321407, _1321405), hAPP(hAPP(c_COMBC(_1321407, _1321405, _1321405), hAPP(hAPP(c_COMBS(_1321407, _1321405, tc_fun(_1321405, _1321405)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1321405, tc_fun(_1321405, _1321405)), _1321407), c_If(_1321405)), hAPP(hAPP(c_COMBC(_1321407, _1321407, tc_HOL_Obool), c_fequal), _1321411))), _1321413)), c_Groups_Ozero__class_Ozero(_1321405))), _1321409) = c_Groups_Ozero__class_Ozero(_1321405))], (30360 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1321407), _1321411), _1321409)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1321407, _1321405), hAPP(hAPP(c_COMBC(_1321407, _1321405, _1321405), hAPP(hAPP(c_COMBS(_1321407, _1321405, tc_fun(_1321405, _1321405)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1321405, tc_fun(_1321405, _1321405)), _1321407), c_If(_1321405)), hAPP(hAPP(c_COMBC(_1321407, _1321407, tc_HOL_Obool), c_fequal), _1321411))), _1321413)), c_Groups_Ozero__class_Ozero(_1321405))), _1321409) = hAPP(_1321413, _1321411))]]], (46786 ^ _775212) ^ [_1707813, _1707815, _1707817, _1707819, _1707821, _1707823] : [-(hAPP(c_List_Ofoldl(_1707813, _1707815, _1707817, _1707819), hAPP(hAPP(c_List_Oappend(_1707815), _1707821), _1707823)) = hAPP(c_List_Ofoldl(_1707813, _1707815, _1707817, hAPP(c_List_Ofoldl(_1707813, _1707815, _1707817, _1707819), _1707821)), _1707823))], (4248 ^ _775212) ^ [_839714, _839716, _839718, _839720, _839722, _839724, _839726, _839728] : [-(c_List_Olinorder__class_Osort__key(_839728, _839724, _839720, _839716) = c_List_Olinorder__class_Osort__key(_839726, _839722, _839718, _839714)), _839728 = _839726, _839724 = _839722, _839720 = _839718, _839716 = _839714], (43045 ^ _775212) ^ [_1614386, _1614388, _1614390, _1614392] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614386, _1614386)), hAPP(hAPP(c_Product__Type_OPair(_1614386, _1614386), _1614388), _1614390)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1614386, _1614386), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1614392))), -(_1614388 = _1614390)], (40127 ^ _775212) ^ [_1544526, _1544528] : [c_Wellfounded_OwfP(_1544526, _1544528), 40130 ^ _775212 : [(40131 ^ _775212) ^ [_1544590] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1544526, _1544528), _1544590)))]]], (41959 ^ _775212) ^ [_1585576, _1585578, _1585580, _1585582] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585576, _1585576)), hAPP(hAPP(c_Product__Type_OPair(_1585576, _1585576), _1585578), _1585580)), c_Transitive__Closure_Ortrancl(_1585576, _1585582))), -(_1585578 = _1585580), 41966 ^ _775212 : [(41969 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585576, _1585576)), hAPP(hAPP(c_Product__Type_OPair(_1585576, _1585576), _1585578), _1585580)), c_Transitive__Closure_Otrancl(_1585576, _1585582))))], (41967 ^ _775212) ^ [] : [_1585578 = _1585580]]], (18189 ^ _775212) ^ [_1084039, _1084041] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1084039)), c_Int_OBit0(_1084041)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1084039), _1084041)))], (9769 ^ _775212) ^ [_933147, _933149, _933151] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _933147)), _933149) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _933147)), _933151), -(_933149 = _933151)], (25877 ^ _775212) ^ [_1228008, _1228010, _1228012] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1228008, tc_Nat_Onat), _1228010), _1228012)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1228008, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1228008), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1228010)), _1228012))], (48558 ^ _775212) ^ [_1747214, _1747216] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1747214, _1747216) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1747214), hAPP(c_Nat_OSuc, _1747216))))], (34827 ^ _775212) ^ [_1414731, _1414733, _1414735] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414731, tc_HOL_Obool)), _1414733), _1414735) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414731, tc_HOL_Obool)), _1414735), _1414733))], (51149 ^ _775212) ^ [_1802007, _1802009, _1802011, _1802013, _1802015, _1802017, _1802019] : [51151 ^ _775212 : [(51154 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1802011, 51150 ^ [_1802007, _1802009, _1802011, _1802013, _1802015, _1802017, _1802019]), _1802013), _1802015))], (51152 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802007), 51150 ^ [_1802007, _1802009, _1802011, _1802013, _1802015, _1802017, _1802019]), _1802009)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1802007, tc_fun(_1802017, tc_fun(_1802019, tc_HOL_Obool))), _1802009), _1802011), _1802013), _1802015)))], (33588 ^ _775212) ^ [_1387140, _1387142] : [-(c_Relation_OId__on(_1387140, _1387142) = hAPP(c_Product__Type_Oprod_Oprod__case(_1387140, _1387140, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1387140, tc_HOL_Obool, tc_fun(_1387140, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1387140, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1387140, tc_HOL_Obool)), _1387140), c_COMBC(_1387140, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1387140, tc_HOL_Obool), tc_fun(_1387140, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1387140), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1387140), c_fconj)), c_fequal))), _1387142)))], (25843 ^ _775212) ^ [_1227093, _1227095, _1227097, _1227099] : [class_Groups_Ocomm__monoid__add(_1227093), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227093), _1227095), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1227097)), hAPP(c_Nat_OSuc, _1227099))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227093), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1227093, tc_Nat_Onat), _1227095), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1227097), _1227099)))], (9645 ^ _775212) ^ [_931011, _931013, _931015, _931017, _931019] : [class_Groups_Oordered__ab__semigroup__add(_931011), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931011), _931013), _931015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931011), _931017), _931019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931011), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931011), _931013), _931017)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931011), _931015), _931019))))], (12791 ^ _775212) ^ [_986233, _986235, _986237] : [class_Lattices_Oboolean__algebra(_986233), 12794 ^ _775212 : [(12801 ^ _775212) ^ [] : [_986235 = _986237, -(hAPP(c_Groups_Ouminus__class_Ouminus(_986233), _986235) = hAPP(c_Groups_Ouminus__class_Ouminus(_986233), _986237))], (12795 ^ _775212) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_986233), _986235) = hAPP(c_Groups_Ouminus__class_Ouminus(_986233), _986237), -(_986235 = _986237)]]], (47464 ^ _775212) ^ [_1721966, _1721968, _1721970, _1721972] : [-(hBOOL(hAPP(c_List_Olistsp(_1721966, hAPP(hAPP(c_COMBS(_1721966, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1721966), c_fconj), _1721968)), _1721970)), _1721972))), hBOOL(hAPP(c_List_Olistsp(_1721966, _1721968), _1721972)), hBOOL(hAPP(c_List_Olistsp(_1721966, _1721970), _1721972))], (9034 ^ _775212) ^ [_921638, _921640, _921642] : [class_Orderings_Oorder(_921638), 9037 ^ _775212 : [(9046 ^ _775212) ^ [] : [-(_921640 = _921642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921638), _921640), _921642)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921638), _921642), _921640))], (9038 ^ _775212) ^ [] : [_921640 = _921642, 9041 ^ _775212 : [(9044 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921638), _921642), _921640)))], (9042 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921638), _921640), _921642)))]]]]], (39696 ^ _775212) ^ [_1534790, _1534792, _1534794, _1534796] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1534790), _1534792))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534794), hAPP(c_Set_Oimage(_1534790, _1534794, _1534796), _1534792))), 39704 ^ _775212 : [(39707 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534790), hAPP(c_Set_OCollect(_1534790), hAPP(hAPP(c_COMBS(_1534790, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534790), c_fconj), hAPP(hAPP(c_COMBC(_1534790, tc_fun(_1534790, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534790)), _1534792))), hAPP(hAPP(c_COMBC(_1534790, _1534794, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1534794, tc_fun(_1534794, tc_HOL_Obool), _1534790), c_fequal), _1534796)), hAPP(_1534796, 39703 ^ [_1534790, _1534792, _1534794, _1534796]))))))], (39705 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1534790), 39703 ^ [_1534790, _1534792, _1534794, _1534796]), _1534792)))]]], (3816 ^ _775212) ^ [_833074, _833076, _833078, _833080] : [-(c_List_Olistrel1(_833080, _833076) = c_List_Olistrel1(_833078, _833074)), _833080 = _833078, _833076 = _833074], (5126 ^ _775212) ^ [_853401, _853403, _853405, _853407, _853409, _853411, _853413, _853415] : [-(c_Wellfounded_Olex__prod(_853415, _853411, _853407, _853403) = c_Wellfounded_Olex__prod(_853413, _853409, _853405, _853401)), _853415 = _853413, _853411 = _853409, _853407 = _853405, _853403 = _853401], (17393 ^ _775212) ^ [_1070663] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070663), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1070663)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1070663)))], (7649 ^ _775212) ^ [_897682, _897684, _897686] : [class_Rings_Oring(_897682), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897682), hAPP(c_Groups_Ouminus__class_Ouminus(_897682), _897684)), _897686) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897682), _897684), hAPP(c_Groups_Ouminus__class_Ouminus(_897682), _897686)))], (1960 ^ _775212) ^ [_802660, _802662, _802664, _802666] : [-(v_fun2(_802664, _802660)), v_fun2(_802666, _802662), _802666 = _802664, _802662 = _802660], (39221 ^ _775212) ^ [_1517146] : [-(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)))), _1517146)) = 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), _1517146), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (39077 ^ _775212) ^ [_1511287, _1511289, _1511291, _1511293] : [_1511287 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1511289, _1511291), 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)), _1511293))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1511289), _1511287)))], (13392 ^ _775212) ^ [_997387, _997389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _997387), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13395 ^ _775212 : [(13402 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _997389), _997387)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13396 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _997389), _997387)), 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)), _997389)))]]], (46292 ^ _775212) ^ [_1697176, _1697178, _1697180, _1697182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1697176), _1697178)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697180)), _1697182))), -(hAPP(hAPP(c_List_Onth(_1697180), hAPP(hAPP(c_List_Odrop(_1697180), _1697176), _1697182)), _1697178) = hAPP(hAPP(c_List_Onth(_1697180), _1697182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1697176), _1697178)))], (29550 ^ _775212) ^ [_1301334, _1301336, _1301338, _1301340, _1301342, _1301344] : [hBOOL(hAPP(hAPP(c_member(_1301334), _1301336), _1301338)), hBOOL(hAPP(hAPP(c_member(_1301340), _1301342), hAPP(_1301344, _1301336))), -(hBOOL(hAPP(hAPP(c_member(_1301340), _1301342), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1301334, tc_fun(_1301340, tc_HOL_Obool)), _1301338), _1301344))))], (25731 ^ _775212) ^ [_1225185, _1225187, _1225189, _1225191, _1225193] : [class_Orderings_Olinorder(_1225185), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225185), _1225187), _1225189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225185), _1225191), _1225193)), 25742 ^ _775212 : [(25751 ^ _775212) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1225185, _1225187), _1225189) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1225185, _1225191), _1225193)), _1225187 = _1225191, _1225189 = _1225193], (25743 ^ _775212) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1225185, _1225187), _1225189) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1225185, _1225191), _1225193), 25746 ^ _775212 : [(25749 ^ _775212) ^ [] : [-(_1225189 = _1225193)], (25747 ^ _775212) ^ [] : [-(_1225187 = _1225191)]]]]], (43627 ^ _775212) ^ [_1627770, _1627772] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1627770, tc_HOL_Obool)), _1627772)), 43633 ^ _775212 : [(43636 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1627770), 43632 ^ [_1627770, _1627772]))], (43634 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1627770, tc_HOL_Obool)), 43632 ^ [_1627770, _1627772]), _1627772)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1627770), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1627770, tc_HOL_Obool), _1627772))))], (27866 ^ _775212) ^ [_1268688, _1268690] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1268688, _1268690))))], (18571 ^ _775212) ^ [] : [-(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)))))], (41861 ^ _775212) ^ [_1583215, _1583217, _1583219, _1583221, _1583223] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583215, _1583215)), hAPP(hAPP(c_Product__Type_OPair(_1583215, _1583215), _1583217), _1583219)), c_Transitive__Closure_Ortrancl(_1583215, _1583221))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583215, _1583215)), hAPP(hAPP(c_Product__Type_OPair(_1583215, _1583215), _1583219), _1583223)), c_Transitive__Closure_Ortrancl(_1583215, _1583221))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583215, _1583215)), hAPP(hAPP(c_Product__Type_OPair(_1583215, _1583215), _1583217), _1583223)), c_Transitive__Closure_Ortrancl(_1583215, _1583221))))], (39476 ^ _775212) ^ [_1527150, _1527152, _1527154] : [-(hAPP(c_Relation_ORange(_1527150, _1527152), hAPP(c_Set_OCollect(tc_prod(_1527150, _1527152)), hAPP(c_Product__Type_Oprod_Oprod__case(_1527150, _1527152, tc_HOL_Obool), _1527154))) = hAPP(c_Set_OCollect(_1527152), hAPP(hAPP(c_COMBB(tc_fun(_1527150, tc_HOL_Obool), tc_HOL_Obool, _1527152), c_HOL_OEx(_1527150)), hAPP(c_COMBC(_1527150, _1527152, tc_HOL_Obool), _1527154))))], (26754 ^ _775212) ^ [_1245338, _1245340, _1245342] : [class_Groups_Ocomm__monoid__add(_1245338), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245338), _1245340), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1245342))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245338), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245338), _1245340), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1245342))), hAPP(_1245340, hAPP(c_Nat_OSuc, _1245342))))], (27914 ^ _775212) ^ [_1269720, _1269722] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269720, tc_HOL_Obool)), _1269722), c_Orderings_Otop__class_Otop(tc_fun(_1269720, tc_HOL_Obool)))))], (18087 ^ _775212) ^ [_1082306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082306)), -(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), _1082306), 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)))))))], (4980 ^ _775212) ^ [_851120, _851122, _851124, _851126] : [-(c_HOL_OThe(_851126, _851122) = c_HOL_OThe(_851124, _851120)), _851126 = _851124, _851122 = _851120], (48771 ^ _775212) ^ [_1751037, _1751039, _1751041] : [class_Orderings_Olinorder(_1751037), c_List_Olinorder__class_Osorted(_1751037, _1751039), hBOOL(hAPP(c_List_Odistinct(_1751037), _1751039)), c_List_Olinorder__class_Osorted(_1751037, _1751041), hBOOL(hAPP(c_List_Odistinct(_1751037), _1751041)), hAPP(c_List_Oset(_1751037), _1751039) = hAPP(c_List_Oset(_1751037), _1751041), -(_1751039 = _1751041)], (33074 ^ _775212) ^ [_1375193, _1375195, _1375197] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1375193), _1375195)), 33077 ^ _775212 : [(33078 ^ _775212) ^ [] : [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(_1375193, tc_Nat_Onat), _1375197), _1375195))), 33081 ^ _775212 : [(33082 ^ _775212) ^ [_1375361] : [hBOOL(hAPP(hAPP(c_member(_1375193), _1375361), _1375195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1375197, _1375361))))]]], (33088 ^ _775212) ^ [] : [33090 ^ _775212 : [(33093 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1375197, 33089 ^ [_1375193, _1375195, _1375197])))], (33091 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1375193), 33089 ^ [_1375193, _1375195, _1375197]), _1375195)))]], -(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(_1375193, tc_Nat_Onat), _1375197), _1375195))))]]], (15971 ^ _775212) ^ [_1045732, _1045734] : [class_Groups_Oordered__ab__group__add__abs(_1045732), 15974 ^ _775212 : [(15981 ^ _775212) ^ [] : [_1045734 = c_Groups_Ozero__class_Ozero(_1045732), -(hAPP(c_Groups_Oabs__class_Oabs(_1045732), _1045734) = c_Groups_Ozero__class_Ozero(_1045732))], (15975 ^ _775212) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1045732), _1045734) = c_Groups_Ozero__class_Ozero(_1045732), -(_1045734 = c_Groups_Ozero__class_Ozero(_1045732))]]], (28602 ^ _775212) ^ [_1283037, _1283039] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1283037, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1283037, tc_HOL_Obool))), _1283039)))], (45287 ^ _775212) ^ [_1672786, _1672788, _1672790, _1672792] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1672786, _1672786)), hAPP(hAPP(c_Product__Type_OPair(_1672786, _1672786), _1672788), _1672790)), hAPP(c_List_Oset(tc_prod(_1672786, _1672786)), hAPP(hAPP(c_List_Ozip(_1672786, _1672786), _1672792), _1672792)))), 45290 ^ _775212 : [(45293 ^ _775212) ^ [] : [-(_1672788 = _1672790)], (45291 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1672786), _1672788), hAPP(c_List_Oset(_1672786), _1672792))))]]], (26917 ^ _775212) ^ [_1248656] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1248656) = c_Orderings_Oord__class_Omax(_1248656)), class_Lattices_Osemilattice__sup(_1248656), class_Orderings_Olinorder(_1248656)], (27123 ^ _775212) ^ [_1253024, _1253026, _1253028, _1253030] : [hBOOL(hAPP(_1253024, _1253026)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1253028, tc_HOL_Obool)), _1253030), _1253024), _1253026)))], (14811 ^ _775212) ^ [_1023298, _1023300, _1023302] : [class_Groups_Omonoid__mult(_1023298), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1023298), _1023300), hAPP(c_Nat_OSuc, _1023302)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023298), hAPP(hAPP(c_Power_Opower__class_Opower(_1023298), _1023300), _1023302)), _1023300))], (25334 ^ _775212) ^ [_1216112, _1216114] : [-(_1216112 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1216114), _1216112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1216114)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1216112))))], (36375 ^ _775212) ^ [_1450438, _1450440, _1450442] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1450438), _1450440)), c_Fun_Oinj__on(_1450438, tc_fun(tc_fun(_1450438, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1450438, tc_fun(tc_prod(_1450438, _1450438), tc_HOL_Obool), tc_fun(tc_fun(_1450438, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450438, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1450438, _1450438), tc_HOL_Obool), tc_fun(tc_fun(_1450438, tc_HOL_Obool), tc_HOL_Obool)), _1450438), c_Equiv__Relations_Oquotient(_1450438)), hAPP(hAPP(c_COMBC(_1450438, tc_fun(_1450438, tc_HOL_Obool), tc_fun(_1450438, tc_HOL_Obool)), c_Set_Oinsert(_1450438)), c_Orderings_Obot__class_Obot(tc_fun(_1450438, tc_HOL_Obool))))), _1450442), _1450440), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1450438, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1450438), _1450440), _1450442)) = hAPP(c_Finite__Set_Ocard(_1450438), _1450440))], (41289 ^ _775212) ^ [_1571196, _1571198] : [c_Wellfounded_Oacyclic(_1571196, _1571198), 41292 ^ _775212 : [(41293 ^ _775212) ^ [_1571281] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571196, _1571196)), hAPP(hAPP(c_Product__Type_OPair(_1571196, _1571196), _1571281), _1571281)), c_Transitive__Closure_Otrancl(_1571196, _1571198)))]]], (18553 ^ _775212) ^ [_1090377, _1090379] : [class_Rings_Oring__1(_1090377), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1090377), hAPP(c_Groups_Ouminus__class_Ouminus(_1090377), _1090379)), 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(_1090377), _1090379), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (28948 ^ _775212) ^ [_1289560, _1289562] : [class_Orderings_Oorder(_1289560), -(c_SetInterval_Oord__class_OatLeastAtMost(_1289560, _1289562, _1289562) = hAPP(hAPP(c_Set_Oinsert(_1289560), _1289562), c_Orderings_Obot__class_Obot(tc_fun(_1289560, tc_HOL_Obool))))], (46027 ^ _775212) ^ [_1690200, _1690202, _1690204, _1690206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690200), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690202)), _1690204))), -(hAPP(hAPP(c_List_Onth(_1690202), hAPP(hAPP(c_List_Olist__update(_1690202, _1690204), _1690200), _1690206)), _1690200) = _1690206)], (21967 ^ _775212) ^ [_1152120, _1152122, _1152124] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1152120, _1152122), _1152124)), 21970 ^ _775212 : [(21979 ^ _775212) ^ [] : [-(_1152122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21982 ^ _775212 : [(21991 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152122))), 21994 ^ _775212 : [(21997 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1152124)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21995 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152122), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1152124))))]]], (21983 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152122)), 21986 ^ _775212 : [(21989 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1152124)), _1152122)))], (21987 ^ _775212) ^ [] : [-(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), _1152124))))]]]]], (21973 ^ _775212) ^ [] : [_1152122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1152124) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21971 ^ _775212) ^ [] : [-(_1152120 = 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), _1152124)), _1152122)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1152124)))]]], (43014 ^ _775212) ^ [_1613729, _1613731, _1613733] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613729, _1613729)), _1613731), c_Transitive__Closure_Ortrancl(_1613729, _1613733))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613729, _1613729)), _1613731), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613729, _1613729), tc_HOL_Obool), 43017 ^ [_1613729, _1613731, _1613733]), _1613733))))], (50644 ^ _775212) ^ [_1790904, _1790906, _1790908] : [-(c_List_Olist__ex1(_1790904, _1790906, _1790908)), 50645 ^ _775212 : [(50646 ^ _775212) ^ [_1790998] : [hBOOL(hAPP(hAPP(c_member(_1790904), _1790998), hAPP(c_List_Oset(_1790904), _1790908))), hBOOL(hAPP(_1790906, _1790998)), 50654 ^ _775212 : [(50659 ^ _775212) ^ [] : [50653 ^ [_1790904, _1790906, _1790908, _1790998] = _1790998], (50657 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1790906, 50653 ^ [_1790904, _1790906, _1790908, _1790998])))], (50655 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790904), 50653 ^ [_1790904, _1790906, _1790908, _1790998]), hAPP(c_List_Oset(_1790904), _1790908))))]]]]], (19959 ^ _775212) ^ [_1115526, _1115528, _1115530, _1115532] : [class_Fields_Olinordered__field(_1115526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115526), c_Groups_Ozero__class_Ozero(_1115526)), _1115528)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115526), _1115530), _1115528)), _1115532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115526), _1115530), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115526), _1115532), _1115528))))], (44911 ^ _775212) ^ [_1662618, _1662620] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1662618), hAPP(c_List_Oset(_1662618), _1662620))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662618)), _1662620))))], (47654 ^ _775212) ^ [_1726071, _1726073, _1726075, _1726077, _1726079, _1726081, _1726083] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726071)), _1726073) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726075)), _1726077), 47657 ^ _775212 : [(47666 ^ _775212) ^ [] : [-(c_List_Olist__all2(_1726071, _1726075, _1726079, hAPP(hAPP(c_List_Oappend(_1726071), _1726073), _1726081), hAPP(hAPP(c_List_Oappend(_1726075), _1726077), _1726083))), c_List_Olist__all2(_1726071, _1726075, _1726079, _1726073, _1726077), c_List_Olist__all2(_1726071, _1726075, _1726079, _1726081, _1726083)], (47658 ^ _775212) ^ [] : [c_List_Olist__all2(_1726071, _1726075, _1726079, hAPP(hAPP(c_List_Oappend(_1726071), _1726073), _1726081), hAPP(hAPP(c_List_Oappend(_1726075), _1726077), _1726083)), 47661 ^ _775212 : [(47664 ^ _775212) ^ [] : [-(c_List_Olist__all2(_1726071, _1726075, _1726079, _1726081, _1726083))], (47662 ^ _775212) ^ [] : [-(c_List_Olist__all2(_1726071, _1726075, _1726079, _1726073, _1726077))]]]]], (3202 ^ _775212) ^ [_823337, _823339] : [_823339 = _823337, -(c_Wellfounded_Omeasure(_823339) = c_Wellfounded_Omeasure(_823337))], (29370 ^ _775212) ^ [_1297766, _1297768, _1297770, _1297772] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1297766, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29371 ^ [_1297766, _1297768, _1297770, _1297772])), _1297768) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1297766, 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), 29371 ^ [_1297766, _1297768, _1297770, _1297772]), _1297770))), _1297772), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1297766, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1297768) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1297766, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1297772))], (17233 ^ _775212) ^ [_1068369] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068369) = 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(_1068369)))))], (3096 ^ _775212) ^ [_821636, _821638, _821640, _821642, _821644, _821646, _821648, _821650, _821652, _821654] : [-(c_SetInterval_Oord_OatLeastLessThan(_821654, _821650, _821646, _821642, _821638) = c_SetInterval_Oord_OatLeastLessThan(_821652, _821648, _821644, _821640, _821636)), _821654 = _821652, _821650 = _821648, _821646 = _821644, _821642 = _821640, _821638 = _821636], (23556 ^ _775212) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (51881 ^ _775212) ^ [_1817988, _1817990, _1817992] : [-(c_Equiv__Relations_Oequiv(_1817988, _1817990, _1817992)), c_Relation_Orefl__on(_1817988, _1817990, _1817992), c_Relation_Osym(_1817988, _1817992), c_Relation_Otrans(_1817988, _1817992)], (16719 ^ _775212) ^ [_1060349, _1060351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1060349), _1060351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060349)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060351))))], (51177 ^ _775212) ^ [_1802670, _1802672, _1802674] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1802670, _1802672, _1802674) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1802670)], (39737 ^ _775212) ^ [_1535748, _1535750] : [c_Wellfounded_Owf(_1535748, _1535750), -(c_Wellfounded_Owf(_1535748, hAPP(hAPP(c_Relation_Orel__comp(_1535748, _1535748, _1535748), _1535750), _1535750)))], (26712 ^ _775212) ^ [_1244604, _1244606] : [c_Nat__Transfer_Ois__nat(_1244604), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1244604, _1244606)))], (49233 ^ _775212) ^ [_1760316, _1760318] : [-(hAPP(c_List_Orev(_1760316), hAPP(c_List_Orev(_1760316), _1760318)) = _1760318)], (52401 ^ _775212) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (46736 ^ _775212) ^ [_1706679, _1706681, _1706683] : [hBOOL(hAPP(c_List_Odistinct(_1706679), _1706683)), -(hBOOL(hAPP(c_List_Odistinct(_1706679), hAPP(c_List_Orotate(_1706679, _1706681), _1706683))))], (51428 ^ _775212) ^ [_1808226, _1808228, _1808230, _1808232, _1808234] : [c_Relation_Otrans(_1808226, _1808228), hBOOL(hAPP(hAPP(c_member(tc_prod(_1808226, _1808226)), hAPP(hAPP(c_Product__Type_OPair(_1808226, _1808226), _1808230), _1808232)), _1808228)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1808226, _1808226)), hAPP(hAPP(c_Product__Type_OPair(_1808226, _1808226), _1808232), _1808234)), _1808228)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1808226, _1808226)), hAPP(hAPP(c_Product__Type_OPair(_1808226, _1808226), _1808230), _1808234)), _1808228)))], (27363 ^ _775212) ^ [_1257424, _1257426, _1257428, _1257430] : [class_Orderings_Olinorder(_1257424), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257424), _1257426), _1257428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257424), _1257428), _1257430)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257424, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257424, _1257426), _1257428)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257424, _1257428), _1257430)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257424, _1257426), _1257430))], (32099 ^ _775212) ^ [_1355314, _1355316, _1355318] : [class_Orderings_Olinorder(_1355314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355314), _1355316)), 32106 ^ _775212 : [(32113 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355314, tc_HOL_Obool)), _1355316), hAPP(hAPP(c_Set_Oinsert(_1355314), _1355318), c_Orderings_Obot__class_Obot(tc_fun(_1355314, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1355314, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1355314, hAPP(hAPP(c_Set_Oinsert(_1355314), _1355318), _1355316)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355314), _1355318), c_Big__Operators_Olinorder__class_OMin(_1355314, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355314, tc_HOL_Obool)), _1355316), hAPP(hAPP(c_Set_Oinsert(_1355314), _1355318), c_Orderings_Obot__class_Obot(tc_fun(_1355314, tc_HOL_Obool)))))))], (32107 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355314, tc_HOL_Obool)), _1355316), hAPP(hAPP(c_Set_Oinsert(_1355314), _1355318), c_Orderings_Obot__class_Obot(tc_fun(_1355314, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1355314, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1355314, hAPP(hAPP(c_Set_Oinsert(_1355314), _1355318), _1355316)) = _1355318)]]], (48659 ^ _775212) ^ [_1749316, _1749318, _1749320] : [class_Orderings_Olinorder(_1749316), c_List_Olinorder__class_Osorted(_1749316, _1749318), -(c_List_Olinorder__class_Osorted(_1749316, hAPP(hAPP(c_List_Otake(_1749316), _1749320), _1749318)))], (16337 ^ _775212) ^ [_1052584, _1052586, _1052588] : [class_Int_Onumber__ring(_1052584), class_Rings_Olinordered__idom(_1052584), 16344 ^ _775212 : [(16351 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052586), _1052588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052584), hAPP(c_Int_Onumber__class_Onumber__of(_1052584), _1052586)), hAPP(c_Int_Onumber__class_Onumber__of(_1052584), _1052588))))], (16345 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052584), hAPP(c_Int_Onumber__class_Onumber__of(_1052584), _1052586)), hAPP(c_Int_Onumber__class_Onumber__of(_1052584), _1052588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052586), _1052588)))]]], (12540 ^ _775212) ^ [_981936, _981938, _981940] : [class_Divides_Oring__div(_981936), -(c_Divides_Odiv__class_Omod(_981936, hAPP(c_Groups_Ouminus__class_Ouminus(_981936), _981938), _981940) = c_Divides_Odiv__class_Omod(_981936, hAPP(c_Groups_Ouminus__class_Ouminus(_981936), c_Divides_Odiv__class_Omod(_981936, _981938, _981940)), _981940))], (18065 ^ _775212) ^ [_1081837, _1081839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1081837), 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)))), _1081839))), 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)))), _1081837)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1081839), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1081837))], (25623 ^ _775212) ^ [_1222399, _1222401, _1222403, _1222405] : [class_Groups_Oab__group__add(_1222399), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222401, _1222399), hAPP(hAPP(c_COMBB(_1222399, _1222399, _1222401), c_Groups_Ouminus__class_Ouminus(_1222399)), _1222403)), _1222405) = hAPP(c_Groups_Ouminus__class_Ouminus(_1222399), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222401, _1222399), _1222403), _1222405)))], (6929 ^ _775212) ^ [_885583, _885585, _885587] : [class_Rings_Olinordered__semidom(_885583), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885585), _885587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885583), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_885583), _885585)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_885583), _885587))))], (48486 ^ _775212) ^ [_1745859, _1745861, _1745863] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1745859), c_List_Oupt(_1745861, _1745863)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1745861), _1745859), _1745863))], (35219 ^ _775212) ^ [_1424075, _1424077, _1424079, _1424081] : [class_Orderings_Oorder(_1424075), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424075, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1424075, _1424077, _1424079)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1424075, _1424079, _1424081)) = c_Orderings_Obot__class_Obot(tc_fun(_1424075, tc_HOL_Obool)))], (17425 ^ _775212) ^ [_1071135, _1071137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071135)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071137))), 17428 ^ _775212 : [(17429 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071135), _1071137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1071137)))], (17435 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071135), _1071137)))]]], (12067 ^ _775212) ^ [_973488, _973490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973488), _973490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973488), hAPP(c_Nat_OSuc, _973490))))], (8277 ^ _775212) ^ [_908751, _908753, _908755, _908757] : [class_Rings_Olinordered__ring__strict(_908751), 8280 ^ _775212 : [(8295 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908751), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908751), _908753), _908755)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908751), _908753), _908757)))), 8296 ^ _775212 : [(8303 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908751), _908753), c_Groups_Ozero__class_Ozero(_908751))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908751), _908757), _908755))], (8297 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908751), c_Groups_Ozero__class_Ozero(_908751)), _908753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908751), _908755), _908757))]]], (8281 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908751), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908751), _908753), _908755)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908751), _908753), _908757))), 8286 ^ _775212 : [(8289 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908751), _908755), _908757)))], (8287 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908751), c_Groups_Ozero__class_Ozero(_908751)), _908753)))]], 8290 ^ _775212 : [(8293 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908751), _908757), _908755)))], (8291 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908751), _908753), c_Groups_Ozero__class_Ozero(_908751))))]]]]], (27353 ^ _775212) ^ [_1257289, _1257291] : [c_Nat__Transfer_Onat__set(_1257289), c_Nat__Transfer_Onat__set(_1257291), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1257289), _1257291)))], (40772 ^ _775212) ^ [_1559551, _1559553, _1559555, _1559557, _1559559, _1559561] : [c_Finite__Set_Ofolding(_1559551, _1559553, _1559555, _1559557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559551), _1559559)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559551), _1559561)), -(hAPP(c_Fun_Ocomp(_1559553, _1559553, _1559553, hAPP(_1559557, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1559551, tc_HOL_Obool)), _1559559), _1559561))), hAPP(_1559557, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1559551, tc_HOL_Obool)), _1559559), _1559561))) = hAPP(c_Fun_Ocomp(_1559553, _1559553, _1559553, hAPP(_1559557, _1559559)), hAPP(_1559557, _1559561)))], (18803 ^ _775212) ^ [_1094745, _1094747, _1094749] : [class_Int_Onumber__ring(_1094745), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1094745), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094745), _1094747), _1094749)), 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(_1094745), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094745), hAPP(hAPP(c_Power_Opower__class_Opower(_1094745), _1094747), 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(_1094745), _1094749), 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(_1094745), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094745), hAPP(c_Int_Onumber__class_Onumber__of(_1094745), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1094747)), _1094749)))], (46198 ^ _775212) ^ [_1695058, _1695060] : [-(hAPP(hAPP(c_List_Odrop(_1695058), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1695060) = _1695060)], (4360 ^ _775212) ^ [_841546, _841548, _841550, _841552] : [-(c_List_Otranspose(_841552, _841548) = c_List_Otranspose(_841550, _841546)), _841552 = _841550, _841548 = _841546], (26641 ^ _775212) ^ [_1243426, _1243428] : [c_Nat__Transfer_Onat__set(_1243426), c_Nat__Transfer_Onat__set(_1243428), 26648 ^ _775212 : [(26655 ^ _775212) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1243426) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1243428), -(_1243426 = _1243428)], (26649 ^ _775212) ^ [] : [_1243426 = _1243428, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1243426) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1243428))]]], (47298 ^ _775212) ^ [_1718025, _1718027, _1718029] : [hBOOL(hAPP(hAPP(c_member(_1718025), _1718027), hAPP(c_List_Oset(_1718025), _1718029))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718025)), c_List_Oremove1(_1718025, _1718027, _1718029)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718025)), _1718029)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (32043 ^ _775212) ^ [_1354370, _1354372, _1354374] : [class_Orderings_Olinorder(_1354370), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354370), _1354372)), -(hBOOL(hAPP(hAPP(c_member(_1354370), _1354374), _1354372))), -(_1354372 = c_Orderings_Obot__class_Obot(tc_fun(_1354370, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1354370, hAPP(hAPP(c_Set_Oinsert(_1354370), _1354374), _1354372)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1354370), _1354374), c_Big__Operators_Olinorder__class_OMin(_1354370, _1354372)))], (52529 ^ _775212) ^ [_1826634, _1826636] : [-(class_Nat_Osize(tc_sum(_1826634, _1826636)))], (35183 ^ _775212) ^ [_1423229, _1423231, _1423233, _1423235] : [class_Orderings_Oorder(_1423229), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423229, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1423229, _1423231), _1423233)), c_SetInterval_Oord__class_OatLeastAtMost(_1423229, _1423233, _1423235)) = c_Orderings_Obot__class_Obot(tc_fun(_1423229, tc_HOL_Obool)))], (25458 ^ _775212) ^ [_1218365, _1218367, _1218369, _1218371] : [class_Orderings_Oorder(_1218365), c_Orderings_Oorder_Omono(tc_Nat_Onat, _1218365, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218367), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218369), _1218371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218365), hAPP(_1218367, _1218369)), hAPP(_1218367, _1218371))))], (23066 ^ _775212) ^ [_1174489, _1174491, _1174493] : [class_Orderings_Olinorder(_1174489), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174489), _1174491), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174489), _1174491), _1174493))))], (52437 ^ _775212) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (1374 ^ _775212) ^ [_795243, _795245] : [-(class_Lattices_Obounded__lattice__bot(_795243)), _795245 = _795243, class_Lattices_Obounded__lattice__bot(_795245)], (7004 ^ _775212) ^ [_886787, _886789, _886791, _886793] : [class_Orderings_Opreorder(_886787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886787), _886789), _886791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886787), _886791), _886793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886787), _886789), _886793)))], (42185 ^ _775212) ^ [_1590692, _1590694] : [-(c_Transitive__Closure_Ortrancl(_1590692, hAPP(c_Relation_Oconverse(_1590692, _1590692), _1590694)) = hAPP(c_Relation_Oconverse(_1590692, _1590692), c_Transitive__Closure_Ortrancl(_1590692, _1590694)))], (28706 ^ _775212) ^ [_1285135, _1285137, _1285139, _1285141] : [_1285141 = c_Orderings_Obot__class_Obot(tc_fun(_1285137, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_1285135, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1285137, _1285135, _1285139), _1285141))], (45405 ^ _775212) ^ [_1675678, _1675680, _1675682] : [class_Groups_Omonoid__add(_1675678), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1675678), hAPP(hAPP(c_List_Omap(_1675680, _1675678), hAPP(c_COMBK(_1675678, _1675680), c_Groups_Ozero__class_Ozero(_1675678))), _1675682)) = c_Groups_Ozero__class_Ozero(_1675678))], (36857 ^ _775212) ^ [_1459875, _1459877, _1459879, _1459881, _1459883] : [c_Fun_Oinj__on(_1459875, _1459877, _1459879, c_Orderings_Otop__class_Otop(tc_fun(_1459875, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1459875, _1459877, _1459879), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1459875, tc_HOL_Obool)), _1459881), _1459883)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1459877, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1459875, _1459877, _1459879), _1459881)), hAPP(c_Set_Oimage(_1459875, _1459877, _1459879), _1459883)))], (17817 ^ _775212) ^ [_1077735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1077735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1077735))))], (5983 ^ _775212) ^ [_869991, _869993, _869995, _869997, _869999] : [hAPP(_869991, 5984 ^ [_869991, _869993, _869995, _869997, _869999]) = hAPP(c_Nat_Onat_Onat__rec(_869993, _869995, _869997), 5984 ^ [_869991, _869993, _869995, _869997, _869999]), -(hAPP(_869991, hAPP(c_Nat_OSuc, _869999)) = hAPP(hAPP(_869997, _869999), hAPP(_869991, _869999)))], (48329 ^ _775212) ^ [_1741696, _1741698] : [c_List_Otranspose(_1741696, _1741698) = c_List_Olist_ONil(tc_List_Olist(_1741696)), 48332 ^ _775212 : [(48333 ^ _775212) ^ [_1741791] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1741696)), _1741791), hAPP(c_List_Oset(tc_List_Olist(_1741696)), _1741698))), -(_1741791 = c_List_Olist_ONil(_1741696))]]], (31339 ^ _775212) ^ [_1342353] : [class_Rings_Osemiring__1(_1342353), -(hBOOL(hAPP(hAPP(c_member(_1342353), c_Groups_Ozero__class_Ozero(_1342353)), c_Nat_Osemiring__1__class_ONats(_1342353))))], (24084 ^ _775212) ^ [_1193625, _1193627] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193625), _1193627)), 24087 ^ _775212 : [(24094 ^ _775212) ^ [] : [_1193627 = _1193625, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193627), _1193625)))], (24088 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193627), _1193625)), -(_1193627 = _1193625)]]], (7463 ^ _775212) ^ [_894216] : [_894216 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894216) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13445 ^ _775212) ^ [_998211, _998213, _998215] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _998211), _998213)), _998215) = 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), _998211), _998215)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _998213), _998215))), 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, _998211, _998215)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _998213, _998215))), _998215)))], (3674 ^ _775212) ^ [_830763, _830765, _830767, _830769] : [-(c_List_Olenlex(_830769, _830765) = c_List_Olenlex(_830767, _830763)), _830769 = _830767, _830765 = _830763], (6956 ^ _775212) ^ [_886061, _886063] : [6957 ^ _775212 : [(6958 ^ _775212) ^ [_886114] : [_886063 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886061), _886114))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886061), _886063)))], (31359 ^ _775212) ^ [_1342703, _1342705, _1342707] : [class_Rings_Osemiring__1(_1342703), hBOOL(hAPP(hAPP(c_member(_1342703), _1342705), c_Nat_Osemiring__1__class_ONats(_1342703))), hBOOL(hAPP(hAPP(c_member(_1342703), _1342707), c_Nat_Osemiring__1__class_ONats(_1342703))), -(hBOOL(hAPP(hAPP(c_member(_1342703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342703), _1342705), _1342707)), c_Nat_Osemiring__1__class_ONats(_1342703))))], (3118 ^ _775212) ^ [_822025, _822027] : [_822027 = _822025, -(c_Int_Oring__1__class_OInts(_822027) = c_Int_Oring__1__class_OInts(_822025))], (48366 ^ _775212) ^ [_1743168, _1743170] : [-(c_Random_Opick(_1743168, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1743168), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1743168, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1743168, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1743168)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1743170)) = c_Random_Opick(_1743168, _1743170))], (42998 ^ _775212) ^ [_1613263, _1613265, _1613267, _1613269] : [-(hAPP(hAPP(c_Nat_Ocompow(_1613263, _1613263), _1613265), hAPP(hAPP(c_Nat_Ocompow(_1613263, _1613263), _1613267), _1613269)) = hAPP(hAPP(c_Nat_Ocompow(_1613263, _1613263), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1613267), _1613265)), _1613269))], (48410 ^ _775212) ^ [_1744438, _1744440, _1744442, _1744444] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1744438, tc_Nat_Onat), _1744438), c_Product__Type_Ofst(_1744438, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1744438, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1744438, 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(_1744438, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1744438, tc_Nat_Onat))), _1744440)), hAPP(hAPP(c_List_Ozip(_1744438, tc_Nat_Onat), _1744442), c_List_Oupt(_1744444, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1744444), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744438)), _1744442)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1744438, tc_Nat_Onat), _1744438), c_Product__Type_Ofst(_1744438, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1744438, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1744438, 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(_1744438, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1744438, 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(_1744438, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1744438, tc_Nat_Onat))), _1744444))), _1744440)), hAPP(hAPP(c_List_Ozip(_1744438, tc_Nat_Onat), _1744442), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744438)), _1744442))))))], (34527 ^ _775212) ^ [_1409100, _1409102, _1409104, _1409106] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409100, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1409100, tc_fun(_1409100, tc_HOL_Obool), tc_HOL_Obool), c_member(_1409100)), _1409102)), hAPP(hAPP(c_COMBC(_1409100, tc_fun(_1409100, tc_HOL_Obool), tc_HOL_Obool), c_member(_1409100)), _1409104)), _1409106)), -(hBOOL(hAPP(hAPP(c_member(_1409100), _1409106), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409100, tc_HOL_Obool)), _1409102), _1409104))))], (46556 ^ _775212) ^ [_1702807, _1702809] : [hBOOL(hAPP(c_List_Odistinct(_1702807), _1702809)), 46559 ^ _775212 : [(46560 ^ _775212) ^ [_1702939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702939), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702807)), _1702809))), 46563 ^ _775212 : [(46564 ^ _775212) ^ [_1703066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703066), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702807)), _1702809))), -(_1702939 = _1703066), hAPP(hAPP(c_List_Onth(_1702807), _1702809), _1702939) = hAPP(hAPP(c_List_Onth(_1702807), _1702809), _1703066)]]]]], (43980 ^ _775212) ^ [_1636696, _1636698, _1636700, _1636702, _1636704, _1636706, _1636708, _1636710] : [c_Finite__Set_Ofolding__image__simple__idem(_1636696, _1636698, _1636700, _1636702, _1636704, _1636706), hBOOL(hAPP(c_Finite__Set_Ofinite(_1636698), _1636708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1636698, tc_HOL_Obool)), _1636710), _1636708)), -(hAPP(hAPP(_1636700, hAPP(_1636706, _1636710)), hAPP(_1636706, _1636708)) = hAPP(_1636706, _1636708))], (34713 ^ _775212) ^ [_1412679, _1412681, _1412683] : [class_Lattices_Osemilattice__inf(_1412679), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412679), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1412679), _1412681), _1412683)), _1412681)))], (7595 ^ _775212) ^ [_896540, _896542, _896544] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896540), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896542), _896544)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896542), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896540), _896544)))], (52373 ^ _775212) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (47764 ^ _775212) ^ [_1728284, _1728286, _1728288, _1728290, _1728292, _1728294, _1728296] : [c_List_Olist__all2(_1728284, _1728286, _1728288, _1728290, hAPP(hAPP(c_List_Omap(_1728292, _1728286), _1728294), _1728296)), -(c_List_Olist__all2(_1728284, _1728292, hAPP(hAPP(c_COMBC(_1728284, tc_fun(_1728292, _1728286), tc_fun(_1728292, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1728286, tc_HOL_Obool), tc_fun(tc_fun(_1728292, _1728286), tc_fun(_1728292, tc_HOL_Obool)), _1728284), c_COMBB(_1728286, tc_HOL_Obool, _1728292)), _1728288)), _1728294), _1728290, _1728296))], (7987 ^ _775212) ^ [_903548, _903550, _903552] : [class_Rings_Oring__no__zero__divisors(_903548), 7990 ^ _775212 : [(7991 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903548), _903550), _903552) = c_Groups_Ozero__class_Ozero(_903548), -(_903550 = c_Groups_Ozero__class_Ozero(_903548)), -(_903552 = c_Groups_Ozero__class_Ozero(_903548))], (8001 ^ _775212) ^ [] : [8002 ^ _775212 : [(8005 ^ _775212) ^ [] : [_903552 = c_Groups_Ozero__class_Ozero(_903548)], (8003 ^ _775212) ^ [] : [_903550 = c_Groups_Ozero__class_Ozero(_903548)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903548), _903550), _903552) = c_Groups_Ozero__class_Ozero(_903548))]]], (46163 ^ _775212) ^ [_1694012, _1694014, _1694016, _1694018, _1694020] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694012), tc_List_Olist(_1694012))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694012), tc_List_Olist(_1694012)), hAPP(hAPP(c_List_Oappend(_1694012), _1694014), _1694016)), hAPP(hAPP(c_List_Oappend(_1694012), _1694014), _1694018))), c_List_Olexord(_1694012, _1694020))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1694012, _1694012)), hAPP(hAPP(c_Product__Type_OPair(_1694012, _1694012), 46168 ^ [_1694012, _1694014, _1694016, _1694018, _1694020]), 46168 ^ [_1694012, _1694014, _1694016, _1694018, _1694020])), _1694020))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694012), tc_List_Olist(_1694012))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694012), tc_List_Olist(_1694012)), _1694016), _1694018)), c_List_Olexord(_1694012, _1694020))))], (12656 ^ _775212) ^ [_983989, _983991] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _983989, _983991) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_983989 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _983991), 12659 ^ [_983989, _983991]))], (37908 ^ _775212) ^ [_1484282, _1484284, _1484286] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1484282, _1484284), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1484282, _1484284), c_Orderings_Otop__class_Otop(tc_fun(_1484282, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1484284, tc_HOL_Obool), _1484282), _1484286))) = hAPP(hAPP(c_Product__Type_OSigma(_1484282, _1484284), c_Orderings_Otop__class_Otop(tc_fun(_1484282, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1484284, tc_HOL_Obool), _1484282), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1484284, tc_HOL_Obool)), _1484286))))], (16477 ^ _775212) ^ [_1055392, _1055394, _1055396, _1055398, _1055400] : [class_Groups_Oordered__ab__group__add__abs(_1055392), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055392), hAPP(c_Groups_Oabs__class_Oabs(_1055392), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1055392), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055392), _1055394), _1055396)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055392), _1055398), _1055400)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055392), hAPP(c_Groups_Oabs__class_Oabs(_1055392), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1055392), _1055394), _1055398))), hAPP(c_Groups_Oabs__class_Oabs(_1055392), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1055392), _1055396), _1055400))))))], (49895 ^ _775212) ^ [_1774632, _1774634, _1774636, _1774638, _1774640, _1774642, _1774644, _1774646] : [49897 ^ _775212 : [(49900 ^ _775212) ^ [] : [hAPP(c_Fun_Ocomp(_1774636, _1774636, _1774638, hAPP(_1774640, 49896 ^ [_1774632, _1774634, _1774636, _1774638, _1774640, _1774642, _1774644, _1774646])), _1774642) = hAPP(c_Fun_Ocomp(_1774638, _1774636, _1774638, _1774642), hAPP(_1774644, 49896 ^ [_1774632, _1774634, _1774636, _1774638, _1774640, _1774642, _1774644, _1774646]))], (49898 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774632), 49896 ^ [_1774632, _1774634, _1774636, _1774638, _1774640, _1774642, _1774644, _1774646]), hAPP(c_List_Oset(_1774632), _1774634))))]], -(hAPP(c_List_Ofoldl(_1774636, _1774632, hAPP(c_COMBC(_1774632, _1774636, _1774636), _1774640), hAPP(_1774642, _1774646)), _1774634) = hAPP(_1774642, hAPP(c_List_Ofoldl(_1774638, _1774632, hAPP(c_COMBC(_1774632, _1774638, _1774638), _1774644), _1774646), _1774634)))], (13745 ^ _775212) ^ [_1003091, _1003093, _1003095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1003091), _1003093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1003095), 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), _1003093), _1003095)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1003091), _1003095))))], (37483 ^ _775212) ^ [_1473549, _1473551, _1473553, _1473555, _1473557] : [hAPP(c_Set_Oimage(_1473549, _1473551, _1473553), c_Orderings_Otop__class_Otop(tc_fun(_1473549, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1473551, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473549, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1473549, _1473551, _1473553), _1473555)), _1473557)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473551, tc_HOL_Obool)), _1473555), hAPP(c_Set_Oimage(_1473549, _1473551, _1473553), _1473557))))], (14555 ^ _775212) ^ [_1018465, _1018467, _1018469] : [hBOOL(hAPP(_1018465, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1018467), _1018469)))), 14558 ^ _775212 : [(14565 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018467), _1018469)), -(hBOOL(hAPP(_1018465, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14559 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1018469), _1018467)), -(hBOOL(hAPP(_1018465, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1018467)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1018469)))))]]], (44752 ^ _775212) ^ [_1659030, _1659032, _1659034, _1659036] : [c_Fun_Oinj__on(_1659030, _1659032, _1659034, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659030, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1659030), tc_fun(_1659030, tc_HOL_Obool), c_List_Oset(_1659030)), _1659036))), -(c_Fun_Oinj__on(tc_List_Olist(_1659030), tc_List_Olist(_1659032), hAPP(c_List_Omap(_1659030, _1659032), _1659034), _1659036))], (4308 ^ _775212) ^ [_840702, _840704, _840706, _840708, _840710, _840712] : [-(c_Divides_Odiv__class_Omod(_840712, _840708, _840704) = c_Divides_Odiv__class_Omod(_840710, _840706, _840702)), _840712 = _840710, _840708 = _840706, _840704 = _840702], (45447 ^ _775212) ^ [_1676957, _1676959, _1676961, _1676963] : [class_Rings_Osemiring__1(_1676957), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676957), hAPP(hAPP(c_List_Omap(_1676959, _1676957), hAPP(c_COMBK(_1676957, _1676959), _1676961)), _1676963)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1676957), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1676957), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676959)), _1676963))), _1676961))], (24306 ^ _775212) ^ [_1197175, _1197177] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197175), _1197177)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197177), _1197175))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197177), _1197175)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197175), _1197177)))], (22033 ^ _775212) ^ [_1153265, _1153267, _1153269, _1153271, _1153273, _1153275] : [hAPP(hAPP(c_Product__Type_OPair(_1153265, _1153267), _1153269), _1153271) = hAPP(hAPP(c_Product__Type_OPair(_1153265, _1153267), _1153273), _1153275), 22036 ^ _775212 : [(22039 ^ _775212) ^ [] : [-(_1153271 = _1153275)], (22037 ^ _775212) ^ [] : [-(_1153269 = _1153273)]]], (52249 ^ _775212) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (28514 ^ _775212) ^ [_1281097, _1281099, _1281101, _1281103] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1281097), _1281099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1281101), hAPP(c_Set_Oimage(_1281097, _1281101, _1281103), _1281099))), hAPP(c_Finite__Set_Ocard(_1281097), _1281099))))], (47885 ^ _775212) ^ [_1731397, _1731399] : [-(c_Enum_Oenum__the(_1731397, _1731399) = c_HOL_OThe(_1731397, _1731399))], (20129 ^ _775212) ^ [_1118645, _1118647, _1118649, _1118651] : [class_Fields_Ofield(_1118645), -(_1118647 = c_Groups_Ozero__class_Ozero(_1118645)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118645), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118645), _1118649), _1118647)), _1118651) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118645), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118645), _1118649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118645), _1118647), _1118651))), _1118647))], (25893 ^ _775212) ^ [_1228389, _1228391, _1228393, _1228395, _1228397] : [class_Groups_Oab__group__add(_1228389), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1228391), _1228393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1228393), _1228395)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1228389), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228389), _1228397), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1228391), _1228395))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228389), _1228397), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1228391), _1228393))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228389), _1228397), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1228393), _1228395)))], (38034 ^ _775212) ^ [_1487895, _1487897, _1487899, _1487901] : [_1487895 = c_Orderings_Obot__class_Obot(tc_fun(_1487897, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1487899, _1487897), _1487899, c_Product__Type_Ofst(_1487899, _1487897)), hAPP(hAPP(c_Product__Type_OSigma(_1487899, _1487897), _1487901), hAPP(c_COMBK(tc_fun(_1487897, tc_HOL_Obool), _1487899), _1487895))) = c_Orderings_Obot__class_Obot(tc_fun(_1487899, tc_HOL_Obool)))], (40077 ^ _775212) ^ [_1543373, _1543375, _1543377] : [c_Wellfounded_Owf(_1543373, _1543375), -(c_Wellfounded_Owf(tc_List_Olist(_1543373), hAPP(c_List_Olexn(_1543373, _1543375), _1543377)))], (17257 ^ _775212) ^ [_1068775, _1068777, _1068779] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068775), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068775)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068777)), _1068779)) = 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), _1068775), _1068777))), _1068779))], (4728 ^ _775212) ^ [_847276, _847278] : [_847278 = _847276, -(c_List_Otl(_847278) = c_List_Otl(_847276))], (6330 ^ _775212) ^ [_875221, _875223, _875225] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_875221, _875223, _875225)) = 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(_875223)), c_Com_Ocom_Ocom__size(_875225))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43184 ^ _775212) ^ [_1618024, _1618026] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1618024), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1618024, tc_HOL_Obool), _1618026)))), 43185 ^ _775212 : [(43186 ^ _775212) ^ [_1618088] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1618024, tc_HOL_Obool)), _1618088), _1618026)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618024), _1618088))]]], (18305 ^ _775212) ^ [_1086067, _1086069] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1086067)), c_Int_OBit0(_1086069)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086067), _1086069)))], (7697 ^ _775212) ^ [_898695, _898697, _898699, _898701, _898703] : [class_Rings_Ocomm__semiring__1(_898695), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898695), _898697), _898699)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898695), _898701), _898703)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898695), _898701), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898695), _898697), _898699)), _898703)))], (44905 ^ _775212) ^ [_1662487, _1662489, _1662491] : [c_Fun_Oinj__on(tc_List_Olist(_1662487), tc_List_Olist(_1662489), hAPP(c_List_Omap(_1662487, _1662489), _1662491), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1662487), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1662487, _1662489, _1662491, c_Orderings_Otop__class_Otop(tc_fun(_1662487, tc_HOL_Obool))))], (4458 ^ _775212) ^ [_843001, _843003, _843005, _843007, _843009, _843011] : [-(c_List_Oinsert(_843011, _843007, _843003) = c_List_Oinsert(_843009, _843005, _843001)), _843011 = _843009, _843007 = _843005, _843003 = _843001], (52403 ^ _775212) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (43077 ^ _775212) ^ [_1615335, _1615337, _1615339] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615335, _1615335)), _1615337), c_Transitive__Closure_Otrancl(_1615335, _1615339))), 43081 ^ _775212 : [(43084 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615335, _1615335)), _1615337), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1615335, _1615335), tc_HOL_Obool), 43080 ^ [_1615335, _1615337, _1615339]), _1615339))))], (43082 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 43080 ^ [_1615335, _1615337, _1615339])))]]], (5098 ^ _775212) ^ [_852959, _852961, _852963, _852965, _852967, _852969] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_852969, _852965, _852961) = c_SetInterval_Oord__class_OatLeastAtMost(_852967, _852963, _852959)), _852969 = _852967, _852965 = _852963, _852961 = _852959], (51242 ^ _775212) ^ [_1803982, _1803984, _1803986, _1803988] : [c_Relation_Otrans(_1803982, _1803984), c_Relation_Otrans(_1803986, _1803988), -(c_Relation_Otrans(tc_prod(_1803982, _1803986), c_Wellfounded_Olex__prod(_1803982, _1803986, _1803984, _1803988)))], (52603 ^ _775212) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (29955 ^ _775212) ^ [_1309694, _1309696, _1309698, _1309700, _1309702, _1309704] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1309694, _1309696)), hAPP(hAPP(c_Product__Type_OPair(_1309694, _1309696), _1309702), _1309704)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool)), _1309698), _1309700))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309694, tc_fun(_1309696, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1309694, tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_fun(_1309696, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1309696, tc_fun(tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_fun(_1309696, tc_HOL_Obool)), _1309694), c_COMBC(_1309696, tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1309696, tc_prod(_1309694, _1309696)), tc_fun(_1309696, tc_fun(tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_HOL_Obool)), _1309694), hAPP(c_COMBB(tc_prod(_1309694, _1309696), tc_fun(tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_HOL_Obool), _1309696), c_member(tc_prod(_1309694, _1309696)))), c_Product__Type_OPair(_1309694, _1309696)))), _1309698)), hAPP(hAPP(c_COMBC(_1309694, tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_fun(_1309696, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1309696, tc_fun(tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_fun(_1309696, tc_HOL_Obool)), _1309694), c_COMBC(_1309696, tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1309696, tc_prod(_1309694, _1309696)), tc_fun(_1309696, tc_fun(tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_HOL_Obool)), _1309694), hAPP(c_COMBB(tc_prod(_1309694, _1309696), tc_fun(tc_fun(tc_prod(_1309694, _1309696), tc_HOL_Obool), tc_HOL_Obool), _1309696), c_member(tc_prod(_1309694, _1309696)))), c_Product__Type_OPair(_1309694, _1309696)))), _1309700)), _1309702), _1309704)))], (5202 ^ _775212) ^ [_854553, _854555, _854557, _854559] : [-(c_Complete__Lattice_OInf__class_OInf(_854559, _854555) = c_Complete__Lattice_OInf__class_OInf(_854557, _854553)), _854559 = _854557, _854555 = _854553], (50957 ^ _775212) ^ [_1797439, _1797441, _1797443, _1797445, _1797447] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1797439, _1797441, _1797443) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1797439, _1797445, _1797447), 50960 ^ _775212 : [(50963 ^ _775212) ^ [] : [-(_1797443 = _1797447)], (50961 ^ _775212) ^ [] : [-(_1797441 = _1797445)]]], (38611 ^ _775212) ^ [_1500885, _1500887, _1500889] : [class_Orderings_Olinorder(_1500885), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500885), _1500887)), -(_1500887 = c_Orderings_Obot__class_Obot(tc_fun(_1500885, tc_HOL_Obool))), 38622 ^ _775212 : [(38632 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500885), hAPP(c_Finite__Set_Ofold1(_1500885, c_Orderings_Oord__class_Omin(_1500885)), _1500887)), _1500889))), 38633 ^ _775212 : [(38634 ^ _775212) ^ [_1501274] : [hBOOL(hAPP(hAPP(c_member(_1500885), _1501274), _1500887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500885), _1501274), _1500889))]]], (38623 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500885), hAPP(c_Finite__Set_Ofold1(_1500885, c_Orderings_Oord__class_Omin(_1500885)), _1500887)), _1500889)), 38627 ^ _775212 : [(38630 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500885), 38626 ^ [_1500885, _1500887, _1500889]), _1500889)))], (38628 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1500885), 38626 ^ [_1500885, _1500887, _1500889]), _1500887)))]]]]], (40492 ^ _775212) ^ [_1553243, _1553245, _1553247, _1553249, _1553251, _1553253, _1553255, _1553257, _1553259, _1553261, _1553263] : [-(hAPP(c_Product__Type_Omap__pair(_1553243, _1553245, _1553247, _1553249, _1553251, _1553253), hAPP(c_Product__Type_Omap__pair(_1553255, _1553243, _1553257, _1553247, _1553259, _1553261), _1553263)) = hAPP(c_Product__Type_Omap__pair(_1553255, _1553245, _1553257, _1553249, hAPP(c_Fun_Ocomp(_1553243, _1553245, _1553255, _1553251), _1553259), hAPP(c_Fun_Ocomp(_1553247, _1553249, _1553257, _1553253), _1553261)), _1553263))], (17709 ^ _775212) ^ [_1076027] : [c_Int_OBit1(_1076027) = c_Int_OPls], (20409 ^ _775212) ^ [_1123396, _1123398, _1123400, _1123402] : [class_Fields_Olinordered__field(_1123396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123396), _1123398), c_Groups_Ozero__class_Ozero(_1123396))), 20416 ^ _775212 : [(20423 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123396), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123396), _1123402), _1123398)), _1123400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123396), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123396), _1123400), _1123398)), _1123402)))], (20417 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123396), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123396), _1123400), _1123398)), _1123402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123396), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123396), _1123402), _1123398)), _1123400)))]]], (30244 ^ _775212) ^ [_1317140] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1317140)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (10683 ^ _775212) ^ [_949673, _949675, _949677] : [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, _949673)), _949675)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _949673)), _949677))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949675), _949677)))], (19087 ^ _775212) ^ [_1100539, _1100541] : [c_Nat__Transfer_Ois__nat(_1100539), c_Nat__Transfer_Ois__nat(_1100541), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1100539), _1100541)))], (23634 ^ _775212) ^ [_1185650, _1185652, _1185654, _1185656, _1185658, _1185660] : [-(c_Nitpick_Opair__box_Opair__box__case(_1185650, _1185652, _1185654, _1185656, c_Nitpick_Opair__box_OPairBox(_1185650, _1185652, _1185658, _1185660)) = hAPP(hAPP(_1185656, _1185658), _1185660))], (11849 ^ _775212) ^ [_969666, _969668, _969670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969666), _969668)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969666), _969670))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969668), _969670)))], (44395 ^ _775212) ^ [_1648831, _1648833, _1648835, _1648837, _1648839] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648831), tc_List_Olist(_1648831))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648831), tc_List_Olist(_1648831)), _1648833), _1648835)), c_List_Olistrel(_1648831, c_Transitive__Closure_Ortrancl(_1648831, _1648837)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648831), tc_List_Olist(_1648831))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648831), tc_List_Olist(_1648831)), _1648835), _1648839)), c_List_Olistrel(_1648831, c_Transitive__Closure_Ortrancl(_1648831, _1648837)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648831), tc_List_Olist(_1648831))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648831), tc_List_Olist(_1648831)), _1648833), _1648839)), c_List_Olistrel(_1648831, c_Transitive__Closure_Ortrancl(_1648831, _1648837)))))], (45196 ^ _775212) ^ [_1670080, _1670082, _1670084, _1670086, _1670088] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1670080, _1670082)), _1670084), hAPP(hAPP(c_List_Ozip(_1670080, _1670082), _1670086), _1670088)) = hAPP(hAPP(c_List_Ozip(_1670080, _1670082), hAPP(hAPP(c_List_Otake(_1670080), _1670084), _1670086)), hAPP(hAPP(c_List_Otake(_1670082), _1670084), _1670088)))], (21409 ^ _775212) ^ [_1142053, _1142055, _1142057, _1142059, _1142061] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1142053, _1142055), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1142057), _1142059))), -(_1142055 = 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), _1142061), _1142053), _1142055), 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), _1142061), _1142057)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142061), _1142059)), _1142055))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142061), _1142059), _1142055)))))], (27932 ^ _775212) ^ [_1269992, _1269994, _1269996, _1269998] : [27933 ^ _775212 : [(27936 ^ _775212) ^ [] : [hBOOL(hAPP(_1269996, _1269998))], (27934 ^ _775212) ^ [] : [_1269994 = _1269998]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1269992), _1269994), _1269996), _1269998)))], (20877 ^ _775212) ^ [_1132254, _1132256] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132254), hAPP(c_Int_Onumber__class_Onumber__of(_1132254), c_Int_OMin)), _1132256) = hAPP(c_Groups_Ouminus__class_Ouminus(_1132254), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132254), c_Groups_Oone__class_Oone(_1132254)), _1132256))), class_Fields_Ofield__inverse__zero(_1132254), class_Int_Onumber__ring(_1132254)], (2004 ^ _775212) ^ [_804108, _804110, _804112, _804114] : [-(c_Com_Ocom_OSemi(_804114, _804110) = c_Com_Ocom_OSemi(_804112, _804108)), _804114 = _804112, _804110 = _804108], (13286 ^ _775212) ^ [_995635, _995637, _995639] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _995635, _995637)), _995639) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995635), _995639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995637), _995639)))], (31216 ^ _775212) ^ [_1339693, _1339695, _1339697] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1339693, tc_HOL_Obool)), _1339695), hAPP(hAPP(c_Set_Oinsert(_1339693), _1339697), c_Orderings_Obot__class_Obot(tc_fun(_1339693, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1339693, _1339697, _1339695) = c_HOL_OThe(_1339693, hAPP(hAPP(c_COMBC(_1339693, tc_fun(_1339693, tc_HOL_Obool), tc_HOL_Obool), c_member(_1339693)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339693, tc_HOL_Obool)), _1339695), hAPP(hAPP(c_Set_Oinsert(_1339693), _1339697), c_Orderings_Obot__class_Obot(tc_fun(_1339693, tc_HOL_Obool)))))))], (18457 ^ _775212) ^ [_1088743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1088743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1088743))))], (6086 ^ _775212) ^ [_871698, _871700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871698), _871700)), _871698 = _871700], (33165 ^ _775212) ^ [_1377209, _1377211, _1377213, _1377215, _1377217] : [class_Groups_Ocomm__monoid__mult(_1377209), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377211), _1377213)), -(hBOOL(hAPP(hAPP(c_member(_1377211), _1377215), _1377213))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377211, _1377209), _1377217), hAPP(hAPP(c_Set_Oinsert(_1377211), _1377215), _1377213)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377209), hAPP(_1377217, _1377215)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377211, _1377209), _1377217), _1377213)))], (13408 ^ _775212) ^ [_997643, _997645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _997643), 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)), _997645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _997643), _997645)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (4412 ^ _775212) ^ [_842312, _842314] : [_842314 = _842312, -(c_Nat_Osemiring__1__class_Oof__nat(_842314) = c_Nat_Osemiring__1__class_Oof__nat(_842312))], (42145 ^ _775212) ^ [_1589793, _1589795, _1589797, _1589799, _1589801, _1589803] : [hBOOL(hAPP(hAPP(c_member(_1589793), _1589795), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589797, tc_fun(_1589793, tc_HOL_Obool)), _1589799), _1589801))), -(hBOOL(hAPP(hAPP(c_member(_1589793), _1589795), hAPP(_1589801, _1589803)))), hBOOL(hAPP(hAPP(c_member(_1589797), _1589803), _1589799))], (52615 ^ _775212) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (2142 ^ _775212) ^ [_806237, _806239] : [_806239 = _806237, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_806239) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_806237))], (26308 ^ _775212) ^ [_1236864, _1236866, _1236868, _1236870] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236864), _1236866)), 26311 ^ _775212 : [(26312 ^ _775212) ^ [_1237022] : [26314 ^ _775212 : [(26320 ^ _775212) ^ [] : [-(_1237022 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26316 ^ [_1236864, _1236866, _1236868, _1236870, _1237022]), 26313 ^ [_1236864, _1236866, _1236868, _1236870, _1237022]))], (26318 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26316 ^ [_1236864, _1236866, _1236868, _1236870, _1237022]), _1236868)))], (26315 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26313 ^ [_1236864, _1236866, _1236868, _1236870, _1237022]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1236866))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1237022), _1236870)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1237022), _1236866)), _1236870)))]]], (48183 ^ _775212) ^ [_1738013, _1738015, _1738017, _1738019] : [-(c_List_Oconcat(_1738013, hAPP(hAPP(c_List_Omap(_1738015, tc_List_Olist(_1738013)), hAPP(hAPP(c_COMBC(_1738015, tc_List_Olist(_1738013), tc_List_Olist(_1738013)), hAPP(hAPP(c_COMBB(_1738013, tc_fun(tc_List_Olist(_1738013), tc_List_Olist(_1738013)), _1738015), c_List_Olist_OCons(_1738013)), _1738017)), c_List_Olist_ONil(_1738013))), _1738019)) = hAPP(hAPP(c_List_Omap(_1738015, _1738013), _1738017), _1738019))], (43717 ^ _775212) ^ [_1630017, _1630019] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630017, _1630017)), hAPP(hAPP(c_Product__Type_OPair(_1630017, _1630017), 43718 ^ [_1630017, _1630019]), 43718 ^ [_1630017, _1630019])), c_Transitive__Closure_Otrancl(_1630017, _1630019)))), -(c_Wellfounded_Oacyclic(_1630017, _1630019))], (27812 ^ _775212) ^ [_1267367, _1267369, _1267371, _1267373, _1267375, _1267377] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267367, tc_fun(_1267369, tc_HOL_Obool)), _1267371), hAPP(hAPP(c_COMBB(_1267373, tc_fun(_1267369, tc_HOL_Obool), _1267367), _1267375), _1267377)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267373, tc_fun(_1267369, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1267367, _1267373, _1267377), _1267371)), _1267375))], (22222 ^ _775212) ^ [_1157359] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1157359))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1157359)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52655 ^ _775212) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (42798 ^ _775212) ^ [_1608553, _1608555, _1608557] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608553, _1608553)), hAPP(hAPP(c_Product__Type_OPair(_1608553, _1608553), _1608555), _1608557)), c_Relation_OId(_1608553))), -(_1608555 = _1608557)], (18863 ^ _775212) ^ [_1096032, _1096034, _1096036] : [class_Int_Onumber__ring(_1096032), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096032), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1096032), _1096034), _1096036)), 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(_1096032), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096032), hAPP(hAPP(c_Power_Opower__class_Opower(_1096032), _1096034), 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(_1096032), _1096036), 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(_1096032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096032), hAPP(c_Int_Onumber__class_Onumber__of(_1096032), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1096034)), _1096036)))], (46348 ^ _775212) ^ [_1698684, _1698686, _1698688, _1698690] : [-(hAPP(c_List_Orotate1(_1698686), hAPP(hAPP(c_List_Olist_OCons(_1698686), _1698688), _1698690)) = hAPP(hAPP(c_List_Oappend(_1698686), _1698690), hAPP(hAPP(c_List_Olist_OCons(_1698686), _1698688), c_List_Olist_ONil(_1698686))))], (7124 ^ _775212) ^ [_888668, _888670, _888672] : [class_Orderings_Opreorder(_888668), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888668), _888670), _888672)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888668), _888672), _888670))], (50929 ^ _775212) ^ [_1796950, _1796952, _1796954] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1796950), hAPP(c_COMBK(_1796950, tc_Nat_Onat), _1796952)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1796954)) = c_List_Oreplicate(_1796950, _1796954, _1796952))], (7230 ^ _775212) ^ [_890036, _890038, _890040, _890042] : [class_Rings_Olinordered__semidom(_890036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890036), c_Groups_Ozero__class_Ozero(_890036)), _890038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890036), _890040), _890042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_890036), _890040), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_890036), _890038), _890042))))], (32587 ^ _775212) ^ [_1365718, _1365720, _1365722, _1365724] : [c_Finite__Set_Ofolding__one(_1365718, _1365720, _1365722), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365718), _1365724)), -(_1365724 = c_Orderings_Obot__class_Obot(tc_fun(_1365718, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1365718), hAPP(hAPP(_1365720, 32600 ^ [_1365718, _1365720, _1365722, _1365724]), 32601 ^ [_1365718, _1365720, _1365722, _1365724])), hAPP(hAPP(c_Set_Oinsert(_1365718), 32600 ^ [_1365718, _1365720, _1365722, _1365724]), hAPP(hAPP(c_Set_Oinsert(_1365718), 32601 ^ [_1365718, _1365720, _1365722, _1365724]), c_Orderings_Obot__class_Obot(tc_fun(_1365718, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1365718), hAPP(_1365722, _1365724)), _1365724)))], (12953 ^ _775212) ^ [_989170, _989172, _989174, _989176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _989172), _989174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _989174), 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), _989172), _989170)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _989172), c_Divides_Odiv__class_Omod(tc_Int_Oint, _989176, _989170))), _989174))))], (45417 ^ _775212) ^ [_1676034, _1676036, _1676038, _1676040, _1676042] : [class_Rings_Osemiring__0(_1676034), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676034), hAPP(hAPP(c_List_Omap(_1676036, _1676034), hAPP(hAPP(c_COMBB(_1676034, _1676034, _1676036), hAPP(c_Groups_Otimes__class_Otimes(_1676034), _1676038)), _1676040)), _1676042)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1676034), _1676038), hAPP(c_List_Omonoid__add__class_Olistsum(_1676034), hAPP(hAPP(c_List_Omap(_1676036, _1676034), _1676040), _1676042))))], (13533 ^ _775212) ^ [_999664, _999666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _999664)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _999666), _999664)), _999664) = _999666)], (47018 ^ _775212) ^ [_1712569, _1712571, _1712573] : [-(_1712569 = c_List_Olist_ONil(_1712571)), -(c_List_Olast(_1712571, hAPP(hAPP(c_List_Oappend(_1712571), _1712573), _1712569)) = c_List_Olast(_1712571, _1712569))], (7320 ^ _775212) ^ [_891519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _891519)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (46376 ^ _775212) ^ [_1699404, _1699406, _1699408, _1699410, _1699412] : [-(hAPP(hAPP(c_List_Ozip(_1699404, _1699406), hAPP(hAPP(c_List_Oappend(_1699404), _1699408), _1699410)), _1699412) = hAPP(hAPP(c_List_Oappend(tc_prod(_1699404, _1699406)), hAPP(hAPP(c_List_Ozip(_1699404, _1699406), _1699408), hAPP(hAPP(c_List_Otake(_1699406), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699404)), _1699408)), _1699412))), hAPP(hAPP(c_List_Ozip(_1699404, _1699406), _1699410), hAPP(hAPP(c_List_Odrop(_1699406), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699404)), _1699408)), _1699412))))], (9823 ^ _775212) ^ [_934120, _934122, _934124] : [class_Groups_Oordered__ab__group__add(_934120), 9826 ^ _775212 : [(9833 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934120), _934124), hAPP(c_Groups_Ouminus__class_Ouminus(_934120), _934122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934120), _934122), hAPP(c_Groups_Ouminus__class_Ouminus(_934120), _934124))))], (9827 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934120), _934122), hAPP(c_Groups_Ouminus__class_Ouminus(_934120), _934124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934120), _934124), hAPP(c_Groups_Ouminus__class_Ouminus(_934120), _934122))))]]], (15241 ^ _775212) ^ [_1031864, _1031866, _1031868] : [class_Rings_Olinordered__semidom(_1031864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031864), c_Groups_Oone__class_Oone(_1031864)), _1031866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031864), c_Groups_Oone__class_Oone(_1031864)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031864), _1031866), hAPP(hAPP(c_Power_Opower__class_Opower(_1031864), _1031866), _1031868)))))], (21483 ^ _775212) ^ [_1143076, _1143078, _1143080, _1143082] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1143076, _1143078), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1143080), _1143082))), -(_1143078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1143076), _1143078) = _1143080)], (34799 ^ _775212) ^ [_1414294, _1414296] : [c_Nat__Transfer_Onat__set(_1414294), c_Nat__Transfer_Onat__set(_1414296), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1414294), _1414296)))], (41227 ^ _775212) ^ [_1569849, _1569851, _1569853, _1569855] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1569849, _1569851, _1569853), _1569855), c_Orderings_Obot__class_Obot(tc_fun(_1569849, tc_HOL_Obool))) = _1569855)], (8027 ^ _775212) ^ [_904143, _904145] : [class_Rings_Omult__zero(_904143), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904143), c_Groups_Ozero__class_Ozero(_904143)), _904145) = c_Groups_Ozero__class_Ozero(_904143))], (16029 ^ _775212) ^ [_1046805, _1046807] : [class_Rings_Olinordered__idom(_1046805), -(hAPP(c_Groups_Oabs__class_Oabs(_1046805), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1046805), _1046807)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1046805), _1046807))], (42657 ^ _775212) ^ [_1604408, _1604410, _1604412, _1604414, _1604416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1604408, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1604410, _1604408, _1604412), _1604414)), _1604416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1604410, tc_HOL_Obool)), _1604414), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1604410, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1604408, _1604410, hAPP(c_Relation_Oconverse(_1604410, _1604408), _1604412)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1604408, tc_HOL_Obool)), _1604416))))))], (49555 ^ _775212) ^ [_1767203, _1767205, _1767207, _1767209] : [-(hBOOL(hAPP(_1767203, _1767205))), -(c_List_OdropWhile(_1767207, _1767203, hAPP(hAPP(c_List_Olist_OCons(_1767207), _1767205), _1767209)) = hAPP(hAPP(c_List_Olist_OCons(_1767207), _1767205), _1767209))], (13993 ^ _775212) ^ [_1007926, _1007928] : [-(_1007926 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13996 ^ _775212 : [(14003 ^ _775212) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007928, _1007926) = 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), _1007928)), _1007926) = 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), _1007928), _1007926))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (13997 ^ _775212) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007928, _1007926) = 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), _1007928)), _1007926) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1007928), _1007926)))]]], (4772 ^ _775212) ^ [_847914, _847916] : [_847916 = _847914, -(c_List_Odrop(_847916) = c_List_Odrop(_847914))], (4904 ^ _775212) ^ [_849936, _849938, _849940, _849942, _849944, _849946, _849948, _849950, _849952, _849954] : [-(c_Option_Ooption_Ooption__case(_849954, _849950, _849946, _849942, _849938) = c_Option_Ooption_Ooption__case(_849952, _849948, _849944, _849940, _849936)), _849954 = _849952, _849950 = _849948, _849946 = _849944, _849942 = _849940, _849938 = _849936], (4714 ^ _775212) ^ [_847055, _847057, _847059, _847061, _847063, _847065] : [-(c_List_Osplice(_847065, _847061, _847057) = c_List_Osplice(_847063, _847059, _847055)), _847065 = _847063, _847061 = _847059, _847057 = _847055], (2230 ^ _775212) ^ [_807683, _807685] : [_807685 = _807683, -(c_Divides_Oadjust(_807685) = c_Divides_Oadjust(_807683))], (44116 ^ _775212) ^ [_1639851, _1639853] : [-(c_FunDef_Ois__measure(_1639851, _1639853))], (45200 ^ _775212) ^ [_1670211, _1670213, _1670215] : [hAPP(hAPP(c_List_Otake(_1670211), _1670213), _1670215) = c_List_Olist_ONil(_1670211), -(_1670213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1670215 = c_List_Olist_ONil(_1670211))], (28095 ^ _775212) ^ [_1272905, _1272907] : [class_Lattices_Oboolean__algebra(_1272905), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272905), _1272907), hAPP(c_Groups_Ouminus__class_Ouminus(_1272905), _1272907)) = c_Orderings_Otop__class_Otop(_1272905))], (52303 ^ _775212) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (29236 ^ _775212) ^ [_1294886, _1294888, _1294890] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1294886, _1294888) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1294890), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1294886 = _1294888, _1294888 = _1294890], (49003 ^ _775212) ^ [_1755319, _1755321, _1755323, _1755325] : [class_Orderings_Olinorder(_1755319), c_List_Olinorder__class_Osorted(_1755319, _1755321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1755323), _1755325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755325), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755319)), _1755321))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1755319), hAPP(hAPP(c_List_Onth(_1755319), _1755321), _1755323)), hAPP(hAPP(c_List_Onth(_1755319), _1755321), _1755325))))], (35950 ^ _775212) ^ [_1440469, _1440471, _1440473, _1440475, _1440477, _1440479] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440469, tc_fun(_1440471, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1440469, tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_fun(_1440471, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440471, tc_fun(tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_fun(_1440471, tc_HOL_Obool)), _1440469), c_COMBC(_1440471, tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440471, tc_prod(_1440469, _1440471)), tc_fun(_1440471, tc_fun(tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_HOL_Obool)), _1440469), hAPP(c_COMBB(tc_prod(_1440469, _1440471), tc_fun(tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_HOL_Obool), _1440471), c_member(tc_prod(_1440469, _1440471)))), c_Product__Type_OPair(_1440469, _1440471)))), _1440473)), hAPP(hAPP(c_COMBC(_1440469, tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_fun(_1440471, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440471, tc_fun(tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_fun(_1440471, tc_HOL_Obool)), _1440469), c_COMBC(_1440471, tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440471, tc_prod(_1440469, _1440471)), tc_fun(_1440471, tc_fun(tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_HOL_Obool)), _1440469), hAPP(c_COMBB(tc_prod(_1440469, _1440471), tc_fun(tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool), tc_HOL_Obool), _1440471), c_member(tc_prod(_1440469, _1440471)))), c_Product__Type_OPair(_1440469, _1440471)))), _1440475)), _1440477), _1440479)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1440469, _1440471)), hAPP(hAPP(c_Product__Type_OPair(_1440469, _1440471), _1440477), _1440479)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1440469, _1440471), tc_HOL_Obool)), _1440473), _1440475))))], (43640 ^ _775212) ^ [_1628028, _1628030, _1628032] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1628028, tc_HOL_Obool)), _1628030), _1628032))), 43646 ^ _775212 : [(43650 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1628028, tc_HOL_Obool)), 43648 ^ [_1628028, _1628030, _1628032]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1628028, tc_HOL_Obool)), _1628030), _1628032))))], (43652 ^ _775212) ^ [] : [43645 ^ [_1628028, _1628030, _1628032] = 43648 ^ [_1628028, _1628030, _1628032]], (43654 ^ _775212) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628028, tc_HOL_Obool)), 43645 ^ [_1628028, _1628030, _1628032]), 43648 ^ [_1628028, _1628030, _1628032]) = c_Orderings_Obot__class_Obot(tc_fun(_1628028, tc_HOL_Obool))], (43647 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1628028, tc_HOL_Obool)), 43645 ^ [_1628028, _1628030, _1628032]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1628028, tc_HOL_Obool)), _1628030), _1628032))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628028, tc_HOL_Obool)), _1628030), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1628028, tc_HOL_Obool), _1628032)) = c_Orderings_Obot__class_Obot(tc_fun(_1628028, tc_HOL_Obool)))], (34004 ^ _775212) ^ [_1396369, _1396371, _1396373, _1396375, _1396377, _1396379] : [hBOOL(hAPP(hAPP(c_member(_1396369), _1396371), _1396373)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1396369, _1396375)), hAPP(hAPP(c_Product__Type_OPair(_1396369, _1396375), _1396371), _1396377)), _1396379)), -(hBOOL(hAPP(hAPP(c_member(_1396375), _1396377), hAPP(c_Relation_OImage(_1396369, _1396375, _1396379), _1396373))))], (32403 ^ _775212) ^ [_1362295, _1362297, _1362299] : [class_Orderings_Olinorder(_1362295), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362295), _1362297)), hBOOL(hAPP(hAPP(c_member(_1362295), _1362299), _1362297)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362295), _1362299), c_Big__Operators_Olattice_OSup__fin(_1362295, c_Orderings_Oord__class_Omax(_1362295), _1362297)) = c_Big__Operators_Olattice_OSup__fin(_1362295, c_Orderings_Oord__class_Omax(_1362295), _1362297))], (40532 ^ _775212) ^ [_1554274, _1554276, _1554278, _1554280, _1554282, _1554284] : [c_Fun_Oinj__on(_1554274, _1554276, _1554278, _1554280), c_Fun_Oinj__on(_1554276, _1554282, _1554284, hAPP(c_Set_Oimage(_1554274, _1554276, _1554278), _1554280)), -(c_Fun_Oinj__on(_1554274, _1554282, hAPP(c_Fun_Ocomp(_1554276, _1554282, _1554274, _1554284), _1554278), _1554280))], (49964 ^ _775212) ^ [_1776007, _1776009, _1776011] : [class_Enum_Oenum(_1776007), class_Enum_Oenum(_1776009), 49971 ^ _775212 : [(49978 ^ _775212) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1776009), hAPP(hAPP(c_COMBB(tc_fun(_1776007, tc_HOL_Obool), tc_HOL_Obool, _1776009), c_Enum_Oenum__class_Oenum__ex(_1776007)), hAPP(hAPP(c_COMBB(tc_fun(_1776007, tc_prod(_1776009, _1776007)), tc_fun(_1776007, tc_HOL_Obool), _1776009), hAPP(c_COMBB(tc_prod(_1776009, _1776007), tc_HOL_Obool, _1776007), _1776011)), c_Product__Type_OPair(_1776009, _1776007))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1776009, _1776007)), _1776011)))], (49972 ^ _775212) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1776009, _1776007)), _1776011)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1776009), hAPP(hAPP(c_COMBB(tc_fun(_1776007, tc_HOL_Obool), tc_HOL_Obool, _1776009), c_Enum_Oenum__class_Oenum__ex(_1776007)), hAPP(hAPP(c_COMBB(tc_fun(_1776007, tc_prod(_1776009, _1776007)), tc_fun(_1776007, tc_HOL_Obool), _1776009), hAPP(c_COMBB(tc_prod(_1776009, _1776007), tc_HOL_Obool, _1776007), _1776011)), c_Product__Type_OPair(_1776009, _1776007))))))]]], (19787 ^ _775212) ^ [_1112334, _1112336, _1112338] : [class_Fields_Olinordered__field(_1112334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112334), _1112336), c_Groups_Ozero__class_Ozero(_1112334))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112334), _1112338), c_Groups_Ozero__class_Ozero(_1112334))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112334), c_Groups_Ozero__class_Ozero(_1112334)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112334), _1112336), _1112338))))], (1394 ^ _775212) ^ [_795493, _795495] : [-(class_Lattices_Osemilattice__inf(_795493)), _795495 = _795493, class_Lattices_Osemilattice__inf(_795495)], (11630 ^ _775212) ^ [_966236, _966238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966236), _966238)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966238), _966236)), -(_966236 = _966238)], (31379 ^ _775212) ^ [_1343053, _1343055] : [class_Rings_Osemiring__1(_1343053), -(hBOOL(hAPP(hAPP(c_member(_1343053), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1343053), _1343055)), c_Nat_Osemiring__1__class_ONats(_1343053))))], (27741 ^ _775212) ^ [_1265691, _1265693, _1265695, _1265697, _1265699, _1265701] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265691, tc_fun(_1265693, tc_HOL_Obool)), _1265695), hAPP(hAPP(c_COMBC(_1265691, tc_fun(_1265697, tc_fun(_1265693, tc_HOL_Obool)), tc_fun(_1265693, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1265697, tc_HOL_Obool), tc_fun(tc_fun(_1265697, tc_fun(_1265693, tc_HOL_Obool)), tc_fun(_1265693, tc_HOL_Obool)), _1265691), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265697, tc_fun(_1265693, tc_HOL_Obool))), _1265699)), _1265701)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265697, tc_fun(_1265693, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265691, tc_fun(_1265697, tc_HOL_Obool)), _1265695), _1265699)), _1265701))], (14341 ^ _775212) ^ [_1014529, _1014531] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014529), _1014531) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014531), _1014529) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1014529 = _1014531)], (28575 ^ _775212) ^ [_1282461, _1282463, _1282465, _1282467, _1282469] : [class_Groups_Ocomm__monoid__add(_1282461), class_Groups_Oordered__ab__semigroup__add(_1282461), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282463), _1282465)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282463, tc_HOL_Obool)), _1282467), _1282465)), 28593 ^ _775212 : [(28596 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282461), c_Groups_Ozero__class_Ozero(_1282461)), hAPP(_1282469, 28592 ^ [_1282461, _1282463, _1282465, _1282467, _1282469])))], (28594 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1282463), 28592 ^ [_1282461, _1282463, _1282465, _1282467, _1282469]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1282463, tc_HOL_Obool)), _1282465), _1282467))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282461), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1282463, _1282461), _1282469), _1282467)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1282463, _1282461), _1282469), _1282465))))], (10619 ^ _775212) ^ [_948481, _948483, _948485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948481), _948483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _948485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948481), _948485)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948483), _948485))))], (28472 ^ _775212) ^ [_1280262, _1280264, _1280266, _1280268, _1280270] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1280262), hAPP(c_Set_Oimage(_1280264, _1280262, _1280266), c_Orderings_Otop__class_Otop(tc_fun(_1280264, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1280268), hAPP(c_Set_Oimage(_1280264, _1280268, hAPP(hAPP(c_COMBB(_1280262, _1280268, _1280264), _1280270), _1280266)), c_Orderings_Otop__class_Otop(tc_fun(_1280264, tc_HOL_Obool))))))], (42695 ^ _775212) ^ [_1605305, _1605307] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1605305, _1605305)), _1605307)), c_Wellfounded_Oacyclic(_1605305, _1605307), -(c_Wellfounded_Owf(_1605305, hAPP(c_Relation_Oconverse(_1605305, _1605305), _1605307)))], (16923 ^ _775212) ^ [_1063614] : [class_Int_Onumber__ring(_1063614), c_Int_Oiszero(_1063614, hAPP(c_Int_Onumber__class_Onumber__of(_1063614), c_Int_OMin))], (48062 ^ _775212) ^ [_1734982, _1734984] : [c_List_Oconcat(_1734982, _1734984) = c_List_Olist_ONil(_1734982), 48065 ^ _775212 : [(48066 ^ _775212) ^ [_1735073] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1734982)), _1735073), hAPP(c_List_Oset(tc_List_Olist(_1734982)), _1734984))), -(_1735073 = c_List_Olist_ONil(_1734982))]]], (46234 ^ _775212) ^ [_1695845, _1695847, _1695849, _1695851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1695845), _1695847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1695849, tc_HOL_Obool)), hAPP(c_List_Oset(_1695849), hAPP(hAPP(c_List_Odrop(_1695849), _1695847), _1695851))), hAPP(c_List_Oset(_1695849), hAPP(hAPP(c_List_Odrop(_1695849), _1695845), _1695851)))))], (34735 ^ _775212) ^ [_1413110, _1413112, _1413114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413110, tc_HOL_Obool)), _1413112), _1413114)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413110, tc_HOL_Obool)), _1413114), _1413112) = _1413112)], (1514 ^ _775212) ^ [_796993, _796995] : [-(class_Rings_Olinordered__comm__semiring__strict(_796993)), _796995 = _796993, class_Rings_Olinordered__comm__semiring__strict(_796995)], (7350 ^ _775212) ^ [_891940, _891942, _891944, _891946, _891948, _891950] : [c_Com_Ocom_OLocal(_891940, _891942, _891944) = c_Com_Ocom_OLocal(_891946, _891948, _891950), 7353 ^ _775212 : [(7358 ^ _775212) ^ [] : [-(_891944 = _891950)], (7356 ^ _775212) ^ [] : [-(_891942 = _891948)], (7354 ^ _775212) ^ [] : [-(_891940 = _891946)]]], (16131 ^ _775212) ^ [_1048516, _1048518] : [class_Groups_Oordered__ab__group__add__abs(_1048516), 16134 ^ _775212 : [(16141 ^ _775212) ^ [] : [-(_1048518 = c_Groups_Ozero__class_Ozero(_1048516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048516), c_Groups_Ozero__class_Ozero(_1048516)), hAPP(c_Groups_Oabs__class_Oabs(_1048516), _1048518))))], (16135 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048516), c_Groups_Ozero__class_Ozero(_1048516)), hAPP(c_Groups_Oabs__class_Oabs(_1048516), _1048518))), _1048518 = c_Groups_Ozero__class_Ozero(_1048516)]]], (5004 ^ _775212) ^ [_851490, _851492] : [_851492 = _851490, -(c_Orderings_Oord__class_Oless(_851492) = c_Orderings_Oord__class_Oless(_851490))], (17767 ^ _775212) ^ [_1076905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076905), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1076905)), c_Int_OPls)))], (42063 ^ _775212) ^ [_1588046, _1588048, _1588050, _1588052] : [-(c_Wellfounded_Oacyclic(_1588046, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1588046, _1588046)), hAPP(hAPP(c_Product__Type_OPair(_1588046, _1588046), _1588048), _1588050)), _1588052))), c_Wellfounded_Oacyclic(_1588046, _1588052), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588046, _1588046)), hAPP(hAPP(c_Product__Type_OPair(_1588046, _1588046), _1588050), _1588048)), c_Transitive__Closure_Ortrancl(_1588046, _1588052))))], (47258 ^ _775212) ^ [_1717246, _1717248, _1717250, _1717252] : [-(hBOOL(hAPP(hAPP(c_member(_1717246), _1717248), hAPP(c_List_Oset(_1717246), _1717250)))), hBOOL(hAPP(hAPP(c_member(_1717246), _1717248), hAPP(c_List_Oset(_1717246), c_List_Oremove1(_1717246, _1717252, _1717250))))], (11278 ^ _775212) ^ [_960402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _960402), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _960402) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52463 ^ _775212) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (2714 ^ _775212) ^ [_815277, _815279] : [_815279 = _815277, -(c_New__DSequence_Opos__not__seq(_815279) = c_New__DSequence_Opos__not__seq(_815277))], (39542 ^ _775212) ^ [_1529171, _1529173, _1529175] : [hAPP(c_Relation_ORange(_1529171, _1529173), _1529175) = c_Orderings_Obot__class_Obot(tc_fun(_1529173, tc_HOL_Obool)), -(_1529175 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529171, _1529173), tc_HOL_Obool)))], (33974 ^ _775212) ^ [_1395583, _1395585] : [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)), _1395583), 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)), _1395585), 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)), _1395583), _1395585)), c_Int_Ointrel)))], (51127 ^ _775212) ^ [_1801520, _1801522, _1801524] : [-(c_FunDef_OTHE__default(_1801522, _1801524, _1801520) = _1801524), 51129 ^ _775212 : [(51132 ^ _775212) ^ [_1801642] : [hBOOL(hAPP(_1801520, _1801642)), -(_1801642 = 51128 ^ [_1801520, _1801522, _1801524])], (51130 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1801520, 51128 ^ [_1801520, _1801522, _1801524])))]]], (21241 ^ _775212) ^ [_1139008, _1139010, _1139012, _1139014] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1139008, _1139010), _1139012)), hBOOL(hAPP(hAPP(_1139010, _1139014), _1139012)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1139008, _1139010), _1139014)))], (4540 ^ _775212) ^ [_844292, _844294, _844296, _844298, _844300, _844302] : [-(c_Lazy__Sequence_Obind(_844302, _844298, _844294) = c_Lazy__Sequence_Obind(_844300, _844296, _844292)), _844302 = _844300, _844298 = _844296, _844294 = _844292], (26056 ^ _775212) ^ [_1231624, _1231626] : [26064 ^ _775212 : [(26067 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1231626, 26063 ^ [_1231624, _1231626])))], (26065 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26063 ^ [_1231624, _1231626]), _1231624)))]], 26057 ^ _775212 : [(26058 ^ _775212) ^ [_1231693] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1231693), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1231624))), hBOOL(hAPP(_1231626, _1231693))]]], (17245 ^ _775212) ^ [_1068580, _1068582] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068580), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068580)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068582)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068580), _1068582)))], (52495 ^ _775212) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (30794 ^ _775212) ^ [_1331228, _1331230] : [c_Nitpick_Orefl_H(_1331228, _1331230), 30797 ^ _775212 : [(30798 ^ _775212) ^ [_1331306] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1331228, _1331228)), hAPP(hAPP(c_Product__Type_OPair(_1331228, _1331228), _1331306), _1331306)), _1331230)))]]], (29142 ^ _775212) ^ [_1292923, _1292925, _1292927, _1292929, _1292931] : [_1292923 = c_Orderings_Obot__class_Obot(tc_fun(_1292925, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292927, tc_HOL_Obool)), _1292929), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292925, tc_fun(_1292927, tc_HOL_Obool)), _1292923), _1292931)) = _1292929)], (38250 ^ _775212) ^ [_1494257, _1494259, _1494261] : [-(c_Relation_Orefl__on(_1494257, _1494259, _1494261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1494257, _1494257), tc_HOL_Obool)), _1494261), hAPP(hAPP(c_Product__Type_OSigma(_1494257, _1494257), _1494259), hAPP(c_COMBK(tc_fun(_1494257, tc_HOL_Obool), _1494257), _1494259)))), 38256 ^ _775212 : [(38259 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494257, _1494257)), hAPP(hAPP(c_Product__Type_OPair(_1494257, _1494257), 38255 ^ [_1494257, _1494259, _1494261]), 38255 ^ [_1494257, _1494259, _1494261])), _1494261))], (38257 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494257), 38255 ^ [_1494257, _1494259, _1494261]), _1494259)))]]], (1990 ^ _775212) ^ [_803887, _803889, _803891, _803893, _803895, _803897] : [-(c_Com_Ocom_OCond(_803897, _803893, _803889) = c_Com_Ocom_OCond(_803895, _803891, _803887)), _803897 = _803895, _803893 = _803891, _803889 = _803887], (51505 ^ _775212) ^ [_1811154, _1811156] : [c_Predicate_Otransp(_1811154, _1811156), -(c_Relation_Otrans(_1811154, hAPP(c_Set_OCollect(tc_prod(_1811154, _1811154)), hAPP(c_Product__Type_Oprod_Oprod__case(_1811154, _1811154, tc_HOL_Obool), _1811156))))], (1664 ^ _775212) ^ [_798868, _798870] : [-(class_Rings_Ono__zero__divisors(_798868)), _798870 = _798868, class_Rings_Ono__zero__divisors(_798870)], (6531 ^ _775212) ^ [_878705, _878707, _878709] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878705), _878707) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878709), _878707), -(_878705 = _878709)], (52173 ^ _775212) ^ [_1823136, _1823138] : [class_Orderings_Oorder(_1823136), -(class_Orderings_Oorder(tc_fun(_1823138, _1823136)))], (43612 ^ _775212) ^ [_1627457, _1627459, _1627461] : [43614 ^ _775212 : [(43617 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627457, tc_HOL_Obool)), 43613 ^ [_1627457, _1627459, _1627461]), _1627461))], (43615 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1627457, tc_HOL_Obool)), 43613 ^ [_1627457, _1627459, _1627461]), _1627459)))]], -(_1627459 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1627457, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627457, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1627457, tc_HOL_Obool), _1627459)), _1627461)))], (34963 ^ _775212) ^ [_1417536, _1417538, _1417540, _1417542] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417536, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417536, tc_HOL_Obool)), _1417538), _1417540)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417536, tc_HOL_Obool)), _1417542), _1417540)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417536, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417536, tc_HOL_Obool)), _1417538), _1417540)), _1417542))], (1694 ^ _775212) ^ [_799243, _799245] : [-(class_Groups_Osemigroup__add(_799243)), _799245 = _799243, class_Groups_Osemigroup__add(_799245)], (50883 ^ _775212) ^ [_1795409, _1795411, _1795413, _1795415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1795409), _1795411)), -(hAPP(hAPP(c_List_Onth(_1795413), c_List_Oreplicate(_1795413, _1795411, _1795415)), _1795409) = _1795415)], (44413 ^ _775212) ^ [_1649416, _1649418, _1649420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1649416, _1649416), tc_HOL_Obool)), _1649418), _1649420)), c_Relation_Orefl__on(_1649416, c_Orderings_Otop__class_Otop(tc_fun(_1649416, tc_HOL_Obool)), _1649420), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1649416), tc_List_Olist(_1649416)), tc_HOL_Obool)), c_List_Olistrel1(_1649416, _1649418)), c_List_Olistrel(_1649416, _1649420))))], (2312 ^ _775212) ^ [_808896, _808898, _808900, _808902] : [-(c_Nitpick_Onat__lcm(_808902, _808898) = c_Nitpick_Onat__lcm(_808900, _808896)), _808902 = _808900, _808898 = _808896], (30322 ^ _775212) ^ [_1320754, _1320756] : [c_Nat__Transfer_Onat__set(_1320754), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1320756), _1320754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1320756)))], (28046 ^ _775212) ^ [_1271900, _1271902] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1271900, tc_HOL_Obool)), _1271902) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1271900, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1271900, tc_HOL_Obool))), _1271902))], (13735 ^ _775212) ^ [_1002910, _1002912, _1002914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002910), _1002912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1002910), _1002914)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1002912), _1002914))))], (52643 ^ _775212) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (22156 ^ _775212) ^ [_1155754] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1155754) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1155754)))], (42535 ^ _775212) ^ [_1601047] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601047, tc_HOL_Obool) = c_Set_OBall(_1601047))], (46837 ^ _775212) ^ [_1708813, _1708815, _1708817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708813)), _1708815)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1708813, _1708817), _1708815) = _1708815)], (46202 ^ _775212) ^ [_1695158, _1695160, _1695162, _1695164] : [-(hAPP(hAPP(c_List_Otake(_1695158), _1695160), hAPP(hAPP(c_List_Odrop(_1695158), _1695162), _1695164)) = hAPP(hAPP(c_List_Odrop(_1695158), _1695162), hAPP(hAPP(c_List_Otake(_1695158), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1695160), _1695162)), _1695164)))], (4114 ^ _775212) ^ [_837657, _837659, _837661, _837663, _837665, _837667] : [-(c_List_Opartition(_837667, _837663, _837659) = c_List_Opartition(_837665, _837661, _837657)), _837667 = _837665, _837663 = _837661, _837659 = _837657], (37806 ^ _775212) ^ [_1481245, _1481247, _1481249, _1481251, _1481253] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1481245, _1481247, hAPP(hAPP(c_Set_Oinsert(_1481245), _1481249), _1481251)), _1481253)), 37811 ^ _775212 : [(37816 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1481245), 37809 ^ [_1481245, _1481247, _1481249, _1481251, _1481253]), 37810 ^ [_1481245, _1481247, _1481249, _1481251, _1481253]))], (37814 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1481245, _1481245, _1481247, 37809 ^ [_1481245, _1481247, _1481249, _1481251, _1481253], 37810 ^ [_1481245, _1481247, _1481249, _1481251, _1481253]), _1481253)))], (37812 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1481245), _1481249), _1481251) = hAPP(hAPP(c_Set_Oinsert(_1481245), 37809 ^ [_1481245, _1481247, _1481249, _1481251, _1481253]), 37810 ^ [_1481245, _1481247, _1481249, _1481251, _1481253]))]]], (39652 ^ _775212) ^ [_1533829, _1533831, _1533833, _1533835] : [hBOOL(hAPP(c_Predicate_ORangeP(_1533829, _1533831, _1533833), _1533835)), -(hBOOL(hAPP(hAPP(_1533833, 39655 ^ [_1533829, _1533831, _1533833, _1533835]), _1533835)))], (52121 ^ _775212) ^ [_1822454, _1822456] : [class_Lattices_Obounded__lattice(_1822454), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1822456, _1822454)))], (25729 ^ _775212) ^ [_1225147, _1225149] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1225147), hAPP(c_Nat_OSuc, _1225149)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1225147, _1225149))], (19137 ^ _775212) ^ [_1101203, _1101205, _1101207] : [class_Fields_Olinordered__field__inverse__zero(_1101203), 19140 ^ _775212 : [(19155 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101203), c_Groups_Ozero__class_Ozero(_1101203)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101203), _1101205), _1101207)))), 19156 ^ _775212 : [(19163 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101203), _1101205), c_Groups_Ozero__class_Ozero(_1101203))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101203), _1101207), c_Groups_Ozero__class_Ozero(_1101203)))], (19157 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101203), c_Groups_Ozero__class_Ozero(_1101203)), _1101205)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101203), c_Groups_Ozero__class_Ozero(_1101203)), _1101207))]]], (19141 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101203), c_Groups_Ozero__class_Ozero(_1101203)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101203), _1101205), _1101207))), 19146 ^ _775212 : [(19149 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101203), c_Groups_Ozero__class_Ozero(_1101203)), _1101207)))], (19147 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101203), c_Groups_Ozero__class_Ozero(_1101203)), _1101205)))]], 19150 ^ _775212 : [(19153 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101203), _1101207), c_Groups_Ozero__class_Ozero(_1101203))))], (19151 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101203), _1101205), c_Groups_Ozero__class_Ozero(_1101203))))]]]]], (49877 ^ _775212) ^ [_1774138, _1774140, _1774142, _1774144, _1774146] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774138, _1774138)), hAPP(hAPP(c_Product__Type_OPair(_1774138, _1774138), _1774140), _1774142)), c_List_Omeasures(_1774138, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1774138, tc_Nat_Onat)), _1774144), _1774146))))), 49878 ^ _775212 : [(49881 ^ _775212) ^ [] : [hAPP(_1774144, _1774140) = hAPP(_1774144, _1774142), hBOOL(hAPP(hAPP(c_member(tc_prod(_1774138, _1774138)), hAPP(hAPP(c_Product__Type_OPair(_1774138, _1774138), _1774140), _1774142)), c_List_Omeasures(_1774138, _1774146)))], (49879 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1774144, _1774140)), hAPP(_1774144, _1774142)))]]], (12592 ^ _775212) ^ [_982840, _982842, _982844] : [class_Rings_Olinordered__idom(_982840), -(c_Groups_Osgn__class_Osgn(_982840, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982840), _982842), _982844)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982840), c_Groups_Osgn__class_Osgn(_982840, _982842)), c_Groups_Osgn__class_Osgn(_982840, _982844)))], (46356 ^ _775212) ^ [_1698896, _1698898, _1698900, _1698902] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1698896) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1698898), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1698896)), hAPP(hAPP(c_List_Olist_OCons(_1698898), _1698900), _1698902)) = hAPP(hAPP(c_List_Odrop(_1698898), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1698896)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1698902))], (51895 ^ _775212) ^ [_1818196, _1818198] : [c_Predicate_Osymp(_1818196, _1818198), -(c_Relation_Osym(_1818196, hAPP(c_Set_OCollect(tc_prod(_1818196, _1818196)), hAPP(c_Product__Type_Oprod_Oprod__case(_1818196, _1818196, tc_HOL_Obool), _1818198))))], (34853 ^ _775212) ^ [_1415277, _1415279, _1415281] : [class_Lattices_Olattice(_1415277), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415277), _1415279), _1415281) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415277), _1415281), _1415279))], (2028 ^ _775212) ^ [_804478, _804480] : [_804480 = _804478, -(c_Nat_Onat_Onat__size(_804480) = c_Nat_Onat_Onat__size(_804478))], (33753 ^ _775212) ^ [_1390699] : [-(hAPP(c_Set_OPow(_1390699), c_Orderings_Otop__class_Otop(tc_fun(_1390699, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1390699, tc_HOL_Obool), tc_HOL_Obool)))], (46903 ^ _775212) ^ [_1710260, _1710262, _1710264, _1710266] : [class_Complete__Lattice_Ocomplete__lattice(_1710260), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1710262, _1710260), hAPP(c_List_Oset(_1710262), _1710264)), _1710266) = hAPP(c_List_Ofoldl(_1710260, _1710262, hAPP(c_COMBC(_1710262, _1710260, _1710260), hAPP(hAPP(c_COMBB(_1710260, tc_fun(_1710260, _1710260), _1710262), c_Lattices_Osemilattice__inf__class_Oinf(_1710260)), _1710266)), c_Orderings_Otop__class_Otop(_1710260)), _1710264))], (34539 ^ _775212) ^ [_1409525, _1409527, _1409529, _1409531] : [hBOOL(hAPP(hAPP(c_member(_1409525), _1409527), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409525, tc_HOL_Obool)), _1409529), _1409531))), 34542 ^ _775212 : [(34545 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409525), _1409527), _1409531)))], (34543 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409525), _1409527), _1409529)))]]], (824 ^ _775212) ^ [_787830, _787832, _787834, _787836, _787838, _787840] : [-(c_List_Olist__all(_787838, _787834, _787830)), c_List_Olist__all(_787840, _787836, _787832), _787840 = _787838, _787836 = _787834, _787832 = _787830], (12729 ^ _775212) ^ [_985178, _985180] : [class_Rings_Olinordered__idom(_985178), 12732 ^ _775212 : [(12739 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985178), _985180), c_Groups_Ozero__class_Ozero(_985178))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985178), c_Groups_Osgn__class_Osgn(_985178, _985180)), c_Groups_Ozero__class_Ozero(_985178))))], (12733 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985178), c_Groups_Osgn__class_Osgn(_985178, _985180)), c_Groups_Ozero__class_Ozero(_985178))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985178), _985180), c_Groups_Ozero__class_Ozero(_985178))))]]], (17921 ^ _775212) ^ [] : [-(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)))], (35133 ^ _775212) ^ [_1422272, _1422274] : [c_Nat__Transfer_Onat__set(_1422272), c_Nat__Transfer_Onat__set(_1422274), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1422272), _1422274) = 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), _1422272)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1422274))))], (7439 ^ _775212) ^ [_893664, _893666, _893668, _893670] : [class_Rings_Ocomm__semiring__1(_893664), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893664), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893664), _893666), _893668)), _893670) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893664), _893666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893664), _893668), _893670)))], (13901 ^ _775212) ^ [_1006274, _1006276, _1006278] : [hBOOL(hAPP(_1006274, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1006276, _1006278))), 13904 ^ _775212 : [(13911 ^ _775212) ^ [] : [-(_1006278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 13914 ^ _775212 : [(13915 ^ _775212) ^ [_1006522, _1006524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006522), _1006278)), _1006276 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1006278), _1006524)), _1006522), -(hBOOL(hAPP(_1006274, _1006522)))]]], (13905 ^ _775212) ^ [] : [_1006278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1006274, _1006276)))]]], (18827 ^ _775212) ^ [_1095399, _1095401] : [class_Rings_Oring__1(_1095399), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1095399), hAPP(c_Groups_Ouminus__class_Ouminus(_1095399), c_Groups_Oone__class_Oone(_1095399))), 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)))), _1095401)) = c_Groups_Oone__class_Oone(_1095399))], (4172 ^ _775212) ^ [_838562, _838564] : [_838564 = _838562, -(c_List_Otranspose__rel(_838564) = c_List_Otranspose__rel(_838562))], (43625 ^ _775212) ^ [_1627719, _1627721] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1627719, tc_HOL_Obool), _1627721) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1627719, tc_HOL_Obool), tc_fun(_1627719, tc_HOL_Obool)), _1627721), c_COMBI(tc_fun(_1627719, tc_HOL_Obool))))], (52621 ^ _775212) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (12889 ^ _775212) ^ [_987946, _987948, _987950] : [-(hBOOL(hAPP(_987946, c_Divides_Odiv__class_Omod(tc_Int_Oint, _987948, _987950)))), 12892 ^ _775212 : [(12895 ^ _775212) ^ [] : [hBOOL(hAPP(_987946, _987948))], (12893 ^ _775212) ^ [] : [-(_987950 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 12898 ^ _775212 : [(12899 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _987950)))], (12905 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 12901 ^ [_987946, _987948, _987950]), _987950)))], (12909 ^ _775212) ^ [] : [hBOOL(hAPP(_987946, 12901 ^ [_987946, _987948, _987950]))], (12907 ^ _775212) ^ [] : [-(_987948 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _987950), 12900 ^ [_987946, _987948, _987950])), 12901 ^ [_987946, _987948, _987950]))], (12903 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12901 ^ [_987946, _987948, _987950])))]], 12910 ^ _775212 : [(12911 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987950), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12917 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 12913 ^ [_987946, _987948, _987950]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12921 ^ _775212) ^ [] : [hBOOL(hAPP(_987946, 12913 ^ [_987946, _987948, _987950]))], (12919 ^ _775212) ^ [] : [-(_987948 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _987950), 12912 ^ [_987946, _987948, _987950])), 12913 ^ [_987946, _987948, _987950]))], (12915 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987950), 12913 ^ [_987946, _987948, _987950])))]]], (36931 ^ _775212) ^ [_1461583, _1461585, _1461587, _1461589, _1461591] : [c_Fun_Oinj__on(_1461583, _1461585, _1461587, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461583, tc_HOL_Obool)), _1461589), _1461591)), 36934 ^ _775212 : [(36939 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461585, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1461583, _1461585, _1461587), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1461583, tc_HOL_Obool)), _1461589), _1461591))), hAPP(c_Set_Oimage(_1461583, _1461585, _1461587), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1461583, tc_HOL_Obool)), _1461591), _1461589))) = c_Orderings_Obot__class_Obot(tc_fun(_1461585, tc_HOL_Obool)))], (36937 ^ _775212) ^ [] : [-(c_Fun_Oinj__on(_1461583, _1461585, _1461587, _1461591))], (36935 ^ _775212) ^ [] : [-(c_Fun_Oinj__on(_1461583, _1461585, _1461587, _1461589))]]], (46340 ^ _775212) ^ [_1698478, _1698480, _1698482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1698478), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698480)), _1698482))), -(hAPP(hAPP(c_List_Olist_OCons(_1698480), hAPP(hAPP(c_List_Onth(_1698480), _1698482), _1698478)), hAPP(hAPP(c_List_Odrop(_1698480), hAPP(c_Nat_OSuc, _1698478)), _1698482)) = hAPP(hAPP(c_List_Odrop(_1698480), _1698478), _1698482))], (21933 ^ _775212) ^ [_1151481, _1151483] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151481, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151481, tc_HOL_Obool)), _1151483)) = _1151483)], (3380 ^ _775212) ^ [_826148, _826150] : [_826150 = _826148, -(c_Nitpick_ORep__Frac(_826150) = c_Nitpick_ORep__Frac(_826148))], (52399 ^ _775212) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (35481 ^ _775212) ^ [_1430130, _1430132, _1430134, _1430136, _1430138] : [c_Finite__Set_Ofolding__one(_1430130, _1430132, _1430134), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430130), _1430136)), -(_1430136 = c_Orderings_Obot__class_Obot(tc_fun(_1430130, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430130), _1430138)), -(_1430138 = c_Orderings_Obot__class_Obot(tc_fun(_1430130, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430130, tc_HOL_Obool)), _1430136), _1430138) = c_Orderings_Obot__class_Obot(tc_fun(_1430130, tc_HOL_Obool)), -(hAPP(_1430134, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430130, tc_HOL_Obool)), _1430136), _1430138)) = hAPP(hAPP(_1430132, hAPP(_1430134, _1430136)), hAPP(_1430134, _1430138)))], (16749 ^ _775212) ^ [_1060895, _1060897] : [class_Rings_Osemiring__1(_1060895), 16752 ^ _775212 : [(16759 ^ _775212) ^ [] : [_1060897 = c_Groups_Ozero__class_Ozero(_1060895), -(c_Int_Oiszero(_1060895, _1060897))], (16753 ^ _775212) ^ [] : [c_Int_Oiszero(_1060895, _1060897), -(_1060897 = c_Groups_Ozero__class_Ozero(_1060895))]]], (16443 ^ _775212) ^ [_1054689, _1054691] : [class_Rings_Olinordered__idom(_1054689), -(hAPP(c_Groups_Oabs__class_Oabs(_1054689), _1054691) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054689), _1054691), c_Groups_Osgn__class_Osgn(_1054689, _1054691)))], (32906 ^ _775212) ^ [_1372056, _1372058, _1372060, _1372062] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1372056), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1372058, tc_Int_Oint), _1372060), _1372062)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1372058, _1372056), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1372056, _1372058), c_Int_Oring__1__class_Oof__int(_1372056)), _1372060)), _1372062)), class_Groups_Ocomm__monoid__mult(_1372056), class_Rings_Oring__1(_1372056)], (44986 ^ _775212) ^ [_1664395, _1664397, _1664399] : [hBOOL(hAPP(hAPP(c_member(_1664395), _1664397), hAPP(c_List_Oset(_1664395), _1664399))), -(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(_1664395)), _1664399))))], (18359 ^ _775212) ^ [_1087003, _1087005] : [class_Int_Onumber__ring(_1087003), class_Int_Oring__char__0(_1087003), 18366 ^ _775212 : [(18373 ^ _775212) ^ [] : [c_Int_Oiszero(_1087003, hAPP(c_Int_Onumber__class_Onumber__of(_1087003), _1087005)), -(c_Int_Oiszero(_1087003, hAPP(c_Int_Onumber__class_Onumber__of(_1087003), c_Int_OBit0(_1087005))))], (18367 ^ _775212) ^ [] : [c_Int_Oiszero(_1087003, hAPP(c_Int_Onumber__class_Onumber__of(_1087003), c_Int_OBit0(_1087005))), -(c_Int_Oiszero(_1087003, hAPP(c_Int_Onumber__class_Onumber__of(_1087003), _1087005)))]]], (17919 ^ _775212) ^ [] : [-(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)))))], (52665 ^ _775212) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (41774 ^ _775212) ^ [_1581091, _1581093, _1581095, _1581097, _1581099, _1581101] : [c_Finite__Set_Ofun__left__comm(_1581091, _1581093, _1581095), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581091), _1581097)), -(hBOOL(hAPP(hAPP(c_member(_1581091), _1581099), _1581097))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1581091, _1581093, _1581095), _1581101), hAPP(hAPP(c_Set_Oinsert(_1581091), _1581099), _1581097)) = hAPP(hAPP(c_Finite__Set_Ofold(_1581091, _1581093, _1581095), hAPP(hAPP(_1581095, _1581099), _1581101)), _1581097))], (1464 ^ _775212) ^ [_796368, _796370] : [-(class_Lazy__Sequence_Osmall__lazy(_796368)), _796370 = _796368, class_Lazy__Sequence_Osmall__lazy(_796370)], (45453 ^ _775212) ^ [_1677116, _1677118, _1677120] : [-(c_List_Olistset(_1677116, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1677116, tc_HOL_Obool)), _1677118), _1677120)) = c_List_Oset__Cons(_1677116, _1677118, c_List_Olistset(_1677116, _1677120)))], (51697 ^ _775212) ^ [_1814575, _1814577, _1814579, _1814581] : [c_Relation_Oantisym(_1814575, _1814577), hBOOL(hAPP(hAPP(c_member(tc_prod(_1814575, _1814575)), hAPP(hAPP(c_Product__Type_OPair(_1814575, _1814575), _1814579), _1814581)), _1814577)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1814575, _1814575)), hAPP(hAPP(c_Product__Type_OPair(_1814575, _1814575), _1814581), _1814579)), _1814577)), -(_1814579 = _1814581)], (46196 ^ _775212) ^ [_1694999, _1695001, _1695003, _1695005] : [-(hAPP(hAPP(c_List_Odrop(_1694999), _1695001), hAPP(hAPP(c_List_Odrop(_1694999), _1695003), _1695005)) = hAPP(hAPP(c_List_Odrop(_1694999), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1695001), _1695003)), _1695005))], (6637 ^ _775212) ^ [_880581, _880583, _880585, _880587] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_880581), 6640 ^ _775212 : [(6647 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880581), _880585), _880587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880581), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880581), _880583), _880585)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880581), _880583), _880587))))], (6641 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880581), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880581), _880583), _880585)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880581), _880583), _880587))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880581), _880585), _880587)))]]], (12644 ^ _775212) ^ [_983770, _983772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _983770), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _983770), c_Divides_Odiv__class_Omod(tc_Int_Oint, _983772, _983770))))], (7214 ^ _775212) ^ [_889753, _889755] : [class_Rings_Olinordered__idom(_889753), 7217 ^ _775212 : [(7224 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889753), _889755), c_Groups_Ozero__class_Ozero(_889753))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889753), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_889753), _889755), _889755)), c_Groups_Ozero__class_Ozero(_889753))))], (7218 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889753), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_889753), _889755), _889755)), c_Groups_Ozero__class_Ozero(_889753))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889753), _889755), c_Groups_Ozero__class_Ozero(_889753))))]]], (16389 ^ _775212) ^ [_1053550, _1053552, _1053554] : [class_Int_Onumber__ring(_1053550), -(hAPP(c_Int_Onumber__class_Onumber__of(_1053550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1053552), _1053554)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053550), hAPP(c_Int_Onumber__class_Onumber__of(_1053550), _1053552)), hAPP(c_Int_Onumber__class_Onumber__of(_1053550), _1053554)))], (32455 ^ _775212) ^ [_1363207, _1363209, _1363211] : [class_Orderings_Olinorder(_1363207), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363207), _1363209)), hBOOL(hAPP(hAPP(c_member(_1363207), _1363211), _1363209)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1363207), _1363211), c_Big__Operators_Olattice_OSup__fin(_1363207, c_Orderings_Oord__class_Omax(_1363207), _1363209)) = _1363211)], (37900 ^ _775212) ^ [_1484089, _1484091, _1484093, _1484095] : [37901 ^ _775212 : [(37904 ^ _775212) ^ [] : [_1484095 = c_Orderings_Obot__class_Obot(tc_fun(_1484091, tc_HOL_Obool))], (37902 ^ _775212) ^ [] : [_1484093 = c_Orderings_Obot__class_Obot(tc_fun(_1484089, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1484089, _1484091), _1484093), hAPP(c_COMBK(tc_fun(_1484091, tc_HOL_Obool), _1484089), _1484095)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1484089, _1484091), tc_HOL_Obool)))], (28089 ^ _775212) ^ [_1272800, _1272802] : [class_Lattices_Oboolean__algebra(_1272800), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272800), hAPP(c_Groups_Ouminus__class_Ouminus(_1272800), _1272802)), _1272802) = c_Orderings_Otop__class_Otop(_1272800))], (40862 ^ _775212) ^ [_1561791, _1561793, _1561795, _1561797, _1561799, _1561801, _1561803] : [c_Finite__Set_Ofolding__image(_1561791, _1561793, _1561795, _1561797, _1561799), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561793), _1561801)), -(hAPP(hAPP(_1561799, _1561803), _1561801) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1561791, _1561793, _1561795), _1561803), _1561797), _1561801))], (17287 ^ _775212) ^ [] : [c_Int_OMin = c_Int_OPls], (18889 ^ _775212) ^ [_1096637, _1096639] : [class_Rings_Oring__1(_1096637), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096637), hAPP(c_Groups_Ouminus__class_Ouminus(_1096637), c_Groups_Oone__class_Oone(_1096637))), 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)))), _1096639))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1096637), c_Groups_Oone__class_Oone(_1096637)))], (18341 ^ _775212) ^ [_1086729] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1086729)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086729))))], (29178 ^ _775212) ^ [_1293811] : [class_Lattices_Oboolean__algebra(_1293811), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1293811), c_Orderings_Obot__class_Obot(_1293811)) = c_Orderings_Otop__class_Otop(_1293811))], (3584 ^ _775212) ^ [_829366, _829368] : [_829368 = _829366, -(c_Nat_Ofunpow(_829368) = c_Nat_Ofunpow(_829366))], (7703 ^ _775212) ^ [_898872, _898874, _898876, _898878, _898880] : [class_Rings_Ocomm__semiring__1(_898872), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898872), _898874), _898876)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898872), _898878), _898880)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898872), _898874), _898878)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898872), _898876), _898880)))], (37246 ^ _775212) ^ [_1468481, _1468483, _1468485, _1468487, _1468489, _1468491, _1468493] : [c_Big__Operators_Ocomm__monoid__big(_1468481, _1468483, _1468485, _1468487, _1468489), 37249 ^ _775212 : [(37256 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1468483), _1468491))), -(hAPP(hAPP(_1468489, _1468493), _1468491) = _1468487)], (37250 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468483), _1468491)), -(hAPP(hAPP(_1468489, _1468493), _1468491) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1468481, _1468483, _1468485), _1468493), _1468487), _1468491))]]], (36034 ^ _775212) ^ [_1443320, _1443322, _1443324, _1443326, _1443328] : [class_Groups_Ocomm__monoid__mult(_1443320), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443322), _1443324)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443322), _1443326)), 36048 ^ _775212 : [(36051 ^ _775212) ^ [] : [hAPP(_1443328, 36047 ^ [_1443320, _1443322, _1443324, _1443326, _1443328]) = c_Groups_Oone__class_Oone(_1443320)], (36049 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1443322), 36047 ^ [_1443320, _1443322, _1443324, _1443326, _1443328]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443322, tc_HOL_Obool)), _1443324), _1443326))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443322, _1443320), _1443328), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1443322, tc_HOL_Obool)), _1443324), _1443326)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1443320), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443322, _1443320), _1443328), _1443324)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443322, _1443320), _1443328), _1443326)))], (29120 ^ _775212) ^ [_1292465, _1292467] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292467, _1292465) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292465), _1292467)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292467), _1292465)))], (4070 ^ _775212) ^ [_836981, _836983, _836985, _836987] : [-(c_Enum_Oenum__the(_836987, _836983) = c_Enum_Oenum__the(_836985, _836981)), _836987 = _836985, _836983 = _836981], (23436 ^ _775212) ^ [_1181749, _1181751, _1181753, _1181755, _1181757, _1181759, _1181761, _1181763, _1181765] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1181749, _1181751, _1181753, _1181755), hAPP(hAPP(c_Product__Type_Oscomp(_1181749, _1181757, _1181759, tc_prod(_1181751, _1181753)), _1181761), _1181763)), _1181765) = hAPP(hAPP(c_Product__Type_Oscomp(_1181749, _1181757, _1181759, _1181755), _1181761), hAPP(hAPP(c_COMBC(_1181757, tc_fun(_1181751, tc_fun(_1181753, _1181755)), tc_fun(_1181759, _1181755)), hAPP(hAPP(c_COMBB(tc_fun(_1181759, tc_prod(_1181751, _1181753)), tc_fun(tc_fun(_1181751, tc_fun(_1181753, _1181755)), tc_fun(_1181759, _1181755)), _1181757), c_Product__Type_Oscomp(_1181759, _1181751, _1181753, _1181755)), _1181763)), _1181765)))], (42792 ^ _775212) ^ [_1608423, _1608425, _1608427] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1608423, _1608425, _1608425), _1608427), c_Relation_OId(_1608425)) = _1608427)], (29848 ^ _775212) ^ [_1306995, _1306997] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1306995), _1306997)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306995)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1306997))))], (17357 ^ _775212) ^ [_1070103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1070103), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1070103)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9757 ^ _775212) ^ [_932945, _932947] : [9758 ^ _775212 : [(9761 ^ _775212) ^ [] : [_932947 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9759 ^ _775212) ^ [] : [_932945 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932945), _932947) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34563 ^ _775212) ^ [_1410026, _1410028, _1410030, _1410032] : [hBOOL(hAPP(hAPP(c_member(_1410026), _1410028), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410026, tc_HOL_Obool)), _1410030), _1410032))), -(hBOOL(hAPP(hAPP(c_member(_1410026), _1410028), _1410032)))], (52657 ^ _775212) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (17905 ^ _775212) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (24972 ^ _775212) ^ [_1209498, _1209500, _1209502, _1209504, _1209506] : [class_Divides_Osemiring__div(_1209498), -(_1209500 = c_Groups_Ozero__class_Ozero(_1209498)), -(_1209502 = c_Groups_Ozero__class_Ozero(_1209498)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1209498), _1209500), _1209504)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1209498), _1209502), _1209506)), 24991 ^ _775212 : [(24998 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209498), _1209504), _1209502) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209498), _1209500), _1209506), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209498), _1209504), _1209500) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209498), _1209506), _1209502))], (24992 ^ _775212) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209498), _1209504), _1209500) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209498), _1209506), _1209502), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209498), _1209504), _1209502) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209498), _1209500), _1209506))]]], (12089 ^ _775212) ^ [_973873, _973875] : [_973873 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973873), _973875), -(_973875 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_973873 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32886 ^ _775212) ^ [_1371622, _1371624, _1371626] : [class_Groups_Ocomm__monoid__mult(_1371622), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371624, _1371622), hAPP(c_COMBK(_1371622, _1371624), c_Groups_Oone__class_Oone(_1371622))), _1371626) = c_Groups_Oone__class_Oone(_1371622))], (17331 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (52415 ^ _775212) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (26963 ^ _775212) ^ [_1249633, _1249635, _1249637, _1249639] : [26977 ^ _775212 : [(26980 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1249639, 26976 ^ [_1249633, _1249635, _1249637, _1249639])))], (26978 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1249633), 26976 ^ [_1249633, _1249635, _1249637, _1249639]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249633, tc_HOL_Obool)), _1249635), _1249637))))]], 26964 ^ _775212 : [(26971 ^ _775212) ^ [_1249842] : [hBOOL(hAPP(hAPP(c_member(_1249633), _1249842), _1249637)), hBOOL(hAPP(_1249639, _1249842))], (26965 ^ _775212) ^ [_1249746] : [hBOOL(hAPP(hAPP(c_member(_1249633), _1249746), _1249635)), hBOOL(hAPP(_1249639, _1249746))]]], (6577 ^ _775212) ^ [_879435, _879437] : [class_Groups_Omonoid__add(_879435), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879435), c_Groups_Ozero__class_Ozero(_879435)), _879437) = _879437)], (23920 ^ _775212) ^ [_1190928, _1190930, _1190932] : [class_Rings_Olinordered__idom(_1190928), 23923 ^ _775212 : [(23930 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1190928), _1190930), _1190932)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1190928), _1190930), hAPP(c_Groups_Oabs__class_Oabs(_1190928), _1190932))))], (23924 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1190928), _1190930), hAPP(c_Groups_Oabs__class_Oabs(_1190928), _1190932))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1190928), _1190930), _1190932)))]]], (19357 ^ _775212) ^ [_1105121, _1105123, _1105125, _1105127] : [class_Fields_Olinordered__field(_1105121), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105121), _1105123), _1105125)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105121), c_Groups_Ozero__class_Ozero(_1105121)), _1105127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105121), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105121), _1105123), _1105127)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105121), _1105125), _1105127))))], (20301 ^ _775212) ^ [_1121411, _1121413, _1121415] : [class_Fields_Olinordered__field(_1121411), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121411), _1121413), _1121415)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121411), _1121413), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121411), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121411), _1121413), _1121415)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121411), c_Groups_Oone__class_Oone(_1121411)), c_Groups_Oone__class_Oone(_1121411))))))], (45246 ^ _775212) ^ [_1671365, _1671367, _1671369] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671365), tc_List_Olist(_1671365))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671365), tc_List_Olist(_1671365)), c_List_Olist_ONil(_1671365)), _1671367)), c_List_Olistrel1(_1671365, _1671369)))], (45824 ^ _775212) ^ [_1685416, _1685418] : [-(hAPP(hAPP(c_List_Oappend(_1685416), _1685418), c_List_Olist_ONil(_1685416)) = _1685418)], (27942 ^ _775212) ^ [_1270198, _1270200, _1270202] : [-(hAPP(hAPP(c_Set_Oinsert(_1270198), _1270200), hAPP(hAPP(c_Set_Oinsert(_1270198), _1270200), _1270202)) = hAPP(hAPP(c_Set_Oinsert(_1270198), _1270200), _1270202))], (49818 ^ _775212) ^ [_1772507, _1772509, _1772511, _1772513] : [-(c_List_Oconcat(_1772507, hAPP(hAPP(c_List_Omap(_1772509, tc_List_Olist(_1772507)), _1772511), _1772513)) = c_List_Omaps(_1772509, _1772507, _1772511, _1772513))], (52623 ^ _775212) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (4214 ^ _775212) ^ [_839187, _839189, _839191, _839193, _839195, _839197] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_839197, _839193, _839189) = c_SetInterval_Oord__class_OgreaterThanAtMost(_839195, _839191, _839187)), _839197 = _839195, _839193 = _839191, _839189 = _839187], (12967 ^ _775212) ^ [_989441, _989443, _989445, _989447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989441)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _989443), _989445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _989445), 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), _989443), c_Divides_Odiv__class_Omod(tc_Int_Oint, _989447, _989441))), _989445)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14679 ^ _775212) ^ [_1020970, _1020972, _1020974, _1020976] : [class_Rings_Olinordered__semidom(_1020970), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020970), _1020972), _1020974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020970), c_Groups_Ozero__class_Ozero(_1020970)), _1020972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020970), hAPP(hAPP(c_Power_Opower__class_Opower(_1020970), _1020972), _1020976)), hAPP(hAPP(c_Power_Opower__class_Opower(_1020970), _1020974), _1020976))))], (22228 ^ _775212) ^ [_1157448] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1157448)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1157448)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157448)), 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)))))], (3026 ^ _775212) ^ [_820499, _820501, _820503, _820505, _820507, _820509] : [-(c_SetInterval_Oord_OatLeast(_820509, _820505, _820501) = c_SetInterval_Oord_OatLeast(_820507, _820503, _820499)), _820509 = _820507, _820505 = _820503, _820501 = _820499], (23280 ^ _775212) ^ [_1178970, _1178972] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1178970), _1178972)), _1178972) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1178970), _1178972))], (17689 ^ _775212) ^ [_1075654, _1075656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075654), _1075656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1075654)), c_Int_OBit1(_1075656))))], (41624 ^ _775212) ^ [_1577644, _1577646, _1577648, _1577650, _1577652] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577644, _1577644)), hAPP(hAPP(c_Product__Type_OPair(_1577644, _1577644), _1577646), _1577648)), c_Transitive__Closure_Otrancl(_1577644, _1577650))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1577644, _1577644)), hAPP(hAPP(c_Product__Type_OPair(_1577644, _1577644), _1577648), _1577652)), _1577650)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577644, _1577644)), hAPP(hAPP(c_Product__Type_OPair(_1577644, _1577644), _1577646), _1577652)), c_Transitive__Closure_Otrancl(_1577644, _1577650))))], (18857 ^ _775212) ^ [_1095937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1095937)), -(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), _1095937), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (11012 ^ _775212) ^ [_955450, _955452, _955454, _955456] : [class_Rings_Olinordered__semiring__strict(_955450), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955450), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955450), _955452), _955454)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955450), _955452), _955456))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955450), c_Groups_Ozero__class_Ozero(_955450)), _955452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955450), _955454), _955456)))], (42685 ^ _775212) ^ [_1605126, _1605128, _1605130] : [hAPP(hAPP(c_Relation_Orel__comp(_1605126, _1605126, _1605126), hAPP(c_Relation_Oconverse(_1605126, _1605126), _1605128)), _1605128) = _1605128, hAPP(c_Relation_ODomain(_1605126, _1605126), _1605128) = _1605130, -(c_Equiv__Relations_Oequiv(_1605126, _1605130, _1605128))], (7060 ^ _775212) ^ [_887677, _887679, _887681, _887683] : [class_Orderings_Oord(_887677), _887679 = _887681, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887677), _887681), _887683)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887677), _887679), _887683)))], (51847 ^ _775212) ^ [_1817513, _1817515, _1817517] : [c_Equiv__Relations_Oequiv(_1817513, _1817515, _1817517), 51850 ^ _775212 : [(51855 ^ _775212) ^ [] : [-(c_Relation_Otrans(_1817513, _1817517))], (51853 ^ _775212) ^ [] : [-(c_Relation_Osym(_1817513, _1817517))], (51851 ^ _775212) ^ [] : [-(c_Relation_Orefl__on(_1817513, _1817515, _1817517))]]], (39506 ^ _775212) ^ [_1528171, _1528173, _1528175, _1528177, _1528179, _1528181] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1528171, _1528173, _1528175), _1528177), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528173, _1528175), tc_HOL_Obool)), _1528179), _1528181)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528171, _1528175), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1528171, _1528173, _1528175), _1528177), _1528179)), hAPP(hAPP(c_Relation_Orel__comp(_1528171, _1528173, _1528175), _1528177), _1528181)))], (49139 ^ _775212) ^ [_1758296, _1758298] : [_1758298 = c_List_Olist_ONil(_1758296), -(hAPP(c_List_Orev(_1758296), _1758298) = c_List_Olist_ONil(_1758296))], (37419 ^ _775212) ^ [_1471922, _1471924, _1471926, _1471928, _1471930] : [-(hAPP(c_Set_Ovimage(_1471922, _1471924, _1471926), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1471924, tc_HOL_Obool)), _1471928), _1471930)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1471922, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1471922, _1471924, _1471926), _1471928)), hAPP(c_Set_Ovimage(_1471922, _1471924, _1471926), _1471930)))], (13755 ^ _775212) ^ [_1003278, _1003280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1003278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1003280, _1003278)), _1003278)))], (36781 ^ _775212) ^ [_1458214, _1458216, _1458218, _1458220, _1458222] : [c_Fun_Oinj__on(_1458214, _1458216, _1458218, c_Orderings_Otop__class_Otop(tc_fun(_1458214, tc_HOL_Obool))), 36784 ^ _775212 : [(36791 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458214, tc_HOL_Obool)), _1458220), _1458222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458216, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1458214, _1458216, _1458218), _1458220)), hAPP(c_Set_Oimage(_1458214, _1458216, _1458218), _1458222))))], (36785 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458216, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1458214, _1458216, _1458218), _1458220)), hAPP(c_Set_Oimage(_1458214, _1458216, _1458218), _1458222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458214, tc_HOL_Obool)), _1458220), _1458222)))]]], (5613 ^ _775212) ^ [_863585, _863587] : [hAPP(c_Nat_OSuc, _863585) = hAPP(c_Nat_OSuc, _863587), -(_863585 = _863587)], (33813 ^ _775212) ^ [_1392306, _1392308, _1392310] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1392306, tc_HOL_Obool)), _1392310), hAPP(c_Set_OPow(_1392306), _1392308))), -(hBOOL(hAPP(c_Predicate_OPowp(_1392306, hAPP(hAPP(c_COMBC(_1392306, tc_fun(_1392306, tc_HOL_Obool), tc_HOL_Obool), c_member(_1392306)), _1392308)), _1392310)))], (15353 ^ _775212) ^ [_1033907, _1033909, _1033911] : [class_Rings_Oring__1(_1033907), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1033907), hAPP(c_Groups_Ouminus__class_Ouminus(_1033907), _1033909)), _1033911) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033907), hAPP(hAPP(c_Power_Opower__class_Opower(_1033907), hAPP(c_Groups_Ouminus__class_Ouminus(_1033907), c_Groups_Oone__class_Oone(_1033907))), _1033911)), hAPP(hAPP(c_Power_Opower__class_Opower(_1033907), _1033909), _1033911)))], (45156 ^ _775212) ^ [_1669273, _1669275, _1669277, _1669279] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669273)), _1669275) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669277)), _1669279), -(hAPP(hAPP(c_List_Omap(tc_prod(_1669273, _1669277), _1669273), c_Product__Type_Ofst(_1669273, _1669277)), hAPP(hAPP(c_List_Ozip(_1669273, _1669277), _1669275), _1669279)) = _1669275)], (23322 ^ _775212) ^ [_1179686] : [class_Orderings_Olinorder(_1179686), -(c_Orderings_Oord_Omin(_1179686, hAPP(c_COMBC(_1179686, _1179686, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1179686))) = c_Orderings_Oord__class_Omax(_1179686))], (33795 ^ _775212) ^ [_1391712] : [-(hAPP(c_Set_OPow(_1391712), c_Orderings_Obot__class_Obot(tc_fun(_1391712, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1391712, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1391712, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1391712, tc_HOL_Obool), tc_HOL_Obool))))], (16585 ^ _775212) ^ [_1057372, _1057374, _1057376] : [class_Int_Onumber__ring(_1057372), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057372), hAPP(c_Groups_Ouminus__class_Ouminus(_1057372), hAPP(c_Int_Onumber__class_Onumber__of(_1057372), _1057374))), _1057376) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057372), hAPP(c_Int_Onumber__class_Onumber__of(_1057372), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1057374))), _1057376))], (23746 ^ _775212) ^ [_1187968] : [-(_1187968 = 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, _1187968)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1187968))))], (32874 ^ _775212) ^ [_1371363, _1371365, _1371367, _1371369, _1371371, _1371373] : [-(_1371363 = _1371365), -(hAPP(c_Fun_Ofun__upd(_1371367, _1371369, _1371371, _1371365, _1371373), _1371363) = hAPP(_1371371, _1371363))], (34041 ^ _775212) ^ [_1397386, _1397388, _1397390, _1397392, _1397394] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1397390, _1397386)), hAPP(hAPP(c_Product__Type_OPair(_1397390, _1397386), _1397394), _1397388)), _1397392)), -(hBOOL(hAPP(hAPP(c_member(_1397386), _1397388), hAPP(c_Relation_OImage(_1397390, _1397386, _1397392), hAPP(hAPP(c_Set_Oinsert(_1397390), _1397394), c_Orderings_Obot__class_Obot(tc_fun(_1397390, tc_HOL_Obool)))))))], (11901 ^ _775212) ^ [_970668, _970670, _970672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970668), _970670)), _970672)), 11904 ^ _775212 : [(11907 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970670), _970672)))], (11905 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970668), _970672)))]]], (45570 ^ _775212) ^ [_1680010, _1680012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1680010)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1680012))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1680010), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1680012)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1680010)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1680010)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1680012))))], (47264 ^ _775212) ^ [_1717369, _1717371, _1717373, _1717375] : [-(_1717369 = _1717371), 47267 ^ _775212 : [(47274 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1717373), _1717369), hAPP(c_List_Oset(_1717373), _1717375))), -(hBOOL(hAPP(hAPP(c_member(_1717373), _1717369), hAPP(c_List_Oset(_1717373), c_List_Oremove1(_1717373, _1717371, _1717375)))))], (47268 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1717373), _1717369), hAPP(c_List_Oset(_1717373), c_List_Oremove1(_1717373, _1717371, _1717375)))), -(hBOOL(hAPP(hAPP(c_member(_1717373), _1717369), hAPP(c_List_Oset(_1717373), _1717375))))]]], (44998 ^ _775212) ^ [_1664677, _1664679, _1664681] : [hBOOL(hAPP(hAPP(c_member(_1664677), _1664679), hAPP(c_List_Oset(_1664677), _1664681))), 45002 ^ _775212 : [(45005 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1664677), _1664681), 45001 ^ [_1664677, _1664679, _1664681]) = _1664679)], (45003 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45001 ^ [_1664677, _1664679, _1664681]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664677)), _1664681))))]]], (38024 ^ _775212) ^ [_1487716, _1487718, _1487720, _1487722] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1487716, _1487718)), hAPP(hAPP(c_Product__Type_OSigma(_1487716, _1487718), _1487720), hAPP(c_COMBK(tc_fun(_1487718, tc_HOL_Obool), _1487716), _1487722)))), -(_1487722 = c_Orderings_Obot__class_Obot(tc_fun(_1487718, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1487716), _1487720)))], (37453 ^ _775212) ^ [_1472813, _1472815, _1472817, _1472819] : [hAPP(c_Set_Oimage(_1472813, _1472815, _1472817), c_Orderings_Otop__class_Otop(tc_fun(_1472813, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1472815, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1472813, _1472815, _1472817), hAPP(c_Set_Ovimage(_1472813, _1472815, _1472817), _1472819)) = _1472819)], (18195 ^ _775212) ^ [_1084158] : [c_Int_OMin = c_Int_OBit0(_1084158)], (14389 ^ _775212) ^ [_1015313, _1015315] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015313), _1015315))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1015313, _1015315) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015313), _1015315), _1015315))], (48761 ^ _775212) ^ [_1750904, _1750906] : [class_Orderings_Olinorder(_1750904), c_List_Olinorder__class_Osorted(_1750904, _1750906), -(c_List_Olinorder__class_Osorted(_1750904, c_List_Oremdups(_1750904, _1750906)))], (46518 ^ _775212) ^ [_1702019, _1702021] : [hBOOL(hAPP(c_List_Odistinct(_1702019), _1702021)), -(hBOOL(hAPP(c_List_Odistinct(_1702019), hAPP(c_List_Orotate1(_1702019), _1702021))))], (40696 ^ _775212) ^ [_1557950, _1557952, _1557954, _1557956, _1557958, _1557960] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557950, tc_fun(_1557952, tc_HOL_Obool)), _1557954), hAPP(c_Fun_Ocomp(_1557956, tc_fun(_1557952, tc_HOL_Obool), _1557950, _1557958), _1557960)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557956, tc_fun(_1557952, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1557950, _1557956, _1557960), _1557954)), _1557958))], (6232 ^ _775212) ^ [_873628, _873630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _873628)), hAPP(c_Nat_OSuc, _873630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873628), _873630)))], (41229 ^ _775212) ^ [_1569893, _1569895, _1569897, _1569899, _1569901, _1569903] : [c_Finite__Set_Ofolding(_1569893, _1569895, _1569897, _1569899), hBOOL(hAPP(c_Finite__Set_Ofinite(_1569893), _1569901)), -(hAPP(hAPP(_1569899, _1569901), _1569903) = hAPP(hAPP(c_Finite__Set_Ofold(_1569893, _1569895, _1569897), _1569903), _1569901))], (45041 ^ _775212) ^ [_1666502, _1666504, _1666506, _1666508] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1666502), tc_List_Olist(_1666502))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1666502), tc_List_Olist(_1666502)), _1666504), _1666506)), c_List_Olistrel(_1666502, _1666508)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666502)), _1666504) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666502)), _1666506), 45047 ^ _775212 : [(45050 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1666502, _1666502, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1666502, tc_fun(tc_prod(_1666502, _1666502), tc_HOL_Obool), tc_fun(_1666502, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1666502, tc_fun(tc_fun(tc_prod(_1666502, _1666502), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1666502, _1666502), tc_HOL_Obool), tc_fun(_1666502, tc_HOL_Obool)), _1666502), c_COMBC(_1666502, tc_fun(tc_prod(_1666502, _1666502), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1666502, tc_prod(_1666502, _1666502)), tc_fun(_1666502, tc_fun(tc_fun(tc_prod(_1666502, _1666502), tc_HOL_Obool), tc_HOL_Obool)), _1666502), hAPP(c_COMBB(tc_prod(_1666502, _1666502), tc_fun(tc_fun(tc_prod(_1666502, _1666502), tc_HOL_Obool), tc_HOL_Obool), _1666502), c_member(tc_prod(_1666502, _1666502)))), c_Product__Type_OPair(_1666502, _1666502)))), _1666508)), 45046 ^ [_1666502, _1666504, _1666506, _1666508]))], (45048 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1666502, _1666502)), 45046 ^ [_1666502, _1666504, _1666506, _1666508]), hAPP(c_List_Oset(tc_prod(_1666502, _1666502)), hAPP(hAPP(c_List_Ozip(_1666502, _1666502), _1666504), _1666506)))))]]], (13256 ^ _775212) ^ [_994992, _994994] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994992)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994994)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _994992), _994994)))], (40011 ^ _775212) ^ [_1541602, _1541604, _1541606, _1541608] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1541602, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1541602, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1541602, _1541604), _1541606)), hAPP(c_Relation_ODomain(_1541602, _1541604), _1541608))), hAPP(c_Relation_ODomain(_1541602, _1541604), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1541602, _1541604), tc_HOL_Obool)), _1541606), _1541608)))))], (742 ^ _775212) ^ [_786605, _786607] : [-(c_List_Onat__list(_786605)), _786607 = _786605, c_List_Onat__list(_786607)], (39428 ^ _775212) ^ [_1525788, _1525790] : [-(c_Product__Type_Omap__pair(_1525788, _1525788, _1525790, _1525790, c_COMBI(_1525788), c_COMBI(_1525790)) = c_Fun_Oid(tc_prod(_1525788, _1525790)))], (23706 ^ _775212) ^ [_1187200, _1187202] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1187200)), hAPP(c_Code__Numeral_Oof__nat, _1187202)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1187200), _1187202)))], (38293 ^ _775212) ^ [_1495188, _1495190, _1495192, _1495194] : [_1495188 = c_Finite__Set_Ofold1(_1495190, _1495192), -(hAPP(_1495188, hAPP(hAPP(c_Set_Oinsert(_1495190), _1495194), c_Orderings_Obot__class_Obot(tc_fun(_1495190, tc_HOL_Obool)))) = _1495194)], (49992 ^ _775212) ^ [_1776858, _1776860] : [class_Lazy__Sequence_Osmall__lazy(_1776858), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1776858), _1776860) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1776858), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1776858)), c_List_Olist_ONil(_1776858)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1776858))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1776860)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1776858, tc_List_Olist(_1776858)), tc_List_Olist(_1776858), c_Lazy__Sequence_Oproduct(_1776858, tc_List_Olist(_1776858), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1776858, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1776860), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1776858), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1776860), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1776858, tc_List_Olist(_1776858), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1776858))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1776858), tc_List_Olist(_1776858)), tc_fun(tc_List_Olist(_1776858), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1776858))), _1776858), hAPP(c_COMBB(tc_List_Olist(_1776858), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1776858)), tc_List_Olist(_1776858)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1776858)))), c_List_Olist_OCons(_1776858))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1776858)))))], (21625 ^ _775212) ^ [_1145485, _1145487] : [-(c_Divides_Odivmod__int(_1145485, _1145487) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1145485), _1145487)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1145485, _1145487)))], (23498 ^ _775212) ^ [_1183078, _1183080, _1183082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1183078), _1183080)), -(c_Random_Ominus__shift(_1183082, _1183078, _1183080) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1183082), _1183078)), _1183080))], (16999 ^ _775212) ^ [_1064696] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1064696, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18117 ^ _775212) ^ [_1082834, _1082836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1082834)), c_Int_OBit0(_1082836))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1082834), _1082836)))], (6056 ^ _775212) ^ [_871184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871184), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (42899 ^ _775212) ^ [_1610838, _1610840, _1610842, _1610844, _1610846, _1610848] : [c_Relation_Osingle__valued(_1610838, _1610840, _1610842), hBOOL(hAPP(hAPP(c_member(tc_prod(_1610838, _1610840)), hAPP(hAPP(c_Product__Type_OPair(_1610838, _1610840), _1610844), _1610846)), _1610842)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1610838, _1610840)), hAPP(hAPP(c_Product__Type_OPair(_1610838, _1610840), _1610844), _1610848)), _1610842)), -(_1610846 = _1610848)], (30246 ^ _775212) ^ [_1317171, _1317173] : [c_Nat__Transfer_Onat__set(_1317171), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1317173), _1317171)), -(c_Nat__Transfer_Ois__nat(_1317173))], (12037 ^ _775212) ^ [_972949, _972951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972949), _972951)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _972949)), _972951)))], (50801 ^ _775212) ^ [_1793888, _1793890, _1793892, _1793894, _1793896] : [-(c_Predicate_Oconversep(_1793888, _1793890, c_Predicate_Opred__comp(_1793888, _1793892, _1793890, _1793894, _1793896)) = c_Predicate_Opred__comp(_1793890, _1793892, _1793888, c_Predicate_Oconversep(_1793892, _1793890, _1793896), c_Predicate_Oconversep(_1793888, _1793892, _1793894)))], (11818 ^ _775212) ^ [_969108, _969110] : [11819 ^ _775212 : [(11822 ^ _775212) ^ [] : [_969108 = _969110], (11820 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969108), _969110))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969108), _969110)))], (10942 ^ _775212) ^ [_954149, _954151, _954153, _954155] : [class_Groups_Oordered__comm__monoid__add(_954149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954149), c_Groups_Ozero__class_Ozero(_954149)), _954151)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954149), _954153), _954155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954149), _954153), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954149), _954151), _954155))))], (40628 ^ _775212) ^ [_1556262, _1556264, _1556266, _1556268, _1556270, _1556272, _1556274] : [c_Fun_Oinj__on(_1556262, _1556264, _1556266, hAPP(c_Set_Oimage(_1556268, _1556262, _1556270), _1556272)), c_Fun_Oinj__on(_1556268, _1556262, _1556270, _1556272), hBOOL(hAPP(hAPP(c_member(_1556264), _1556274), hAPP(c_Set_Oimage(_1556262, _1556264, _1556266), hAPP(c_Set_Oimage(_1556268, _1556262, _1556270), _1556272)))), -(hAPP(c_Fun_Othe__inv__into(_1556268, _1556264, _1556272, hAPP(c_Fun_Ocomp(_1556262, _1556264, _1556268, _1556266), _1556270)), _1556274) = hAPP(hAPP(c_Fun_Ocomp(_1556262, _1556268, _1556264, c_Fun_Othe__inv__into(_1556268, _1556262, _1556272, _1556270)), c_Fun_Othe__inv__into(_1556262, _1556264, hAPP(c_Set_Oimage(_1556268, _1556262, _1556270), _1556272), _1556266)), _1556274))], (18595 ^ _775212) ^ [_1091148, _1091150, _1091152] : [class_Rings_Olinordered__semidom(_1091148), hAPP(hAPP(c_Power_Opower__class_Opower(_1091148), _1091150), 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(_1091148), _1091152), 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(_1091148), c_Groups_Ozero__class_Ozero(_1091148)), _1091150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091148), c_Groups_Ozero__class_Ozero(_1091148)), _1091152)), -(_1091150 = _1091152)], (27922 ^ _775212) ^ [_1269878, _1269880, _1269882, _1269884] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1269878), _1269880), _1269882), _1269884)), -(_1269880 = _1269884), -(hBOOL(hAPP(_1269882, _1269884)))], (45696 ^ _775212) ^ [_1682876, _1682878, _1682880] : [-(hAPP(c_List_Oset(_1682876), hAPP(hAPP(c_List_Oappend(_1682876), _1682878), _1682880)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1682876, tc_HOL_Obool)), hAPP(c_List_Oset(_1682876), _1682878)), hAPP(c_List_Oset(_1682876), _1682880)))], (8123 ^ _775212) ^ [_906151] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _906151)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _906151))], (2838 ^ _775212) ^ [_817461, _817463, _817465, _817467, _817469, _817471, _817473, _817475] : [-(c_New__DSequence_Oneg__decr__bind(_817475, _817471, _817467, _817463) = c_New__DSequence_Oneg__decr__bind(_817473, _817469, _817465, _817461)), _817475 = _817473, _817471 = _817469, _817467 = _817465, _817463 = _817461], (44813 ^ _775212) ^ [_1660481, _1660483, _1660485, _1660487, _1660489, _1660491] : [-(hAPP(hAPP(c_List_Omap(_1660481, _1660483), _1660485), hAPP(hAPP(c_List_Omap(_1660487, _1660481), _1660489), _1660491)) = hAPP(hAPP(c_List_Omap(_1660487, _1660483), hAPP(c_Fun_Ocomp(_1660481, _1660483, _1660487, _1660485), _1660489)), _1660491))], (29250 ^ _775212) ^ [_1295149, _1295151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1295149), _1295151))), 29253 ^ _775212 : [(29256 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1295149), _1295151)))], (29254 ^ _775212) ^ [] : [_1295151 = c_Orderings_Obot__class_Obot(tc_fun(_1295149, tc_HOL_Obool))]]], (3762 ^ _775212) ^ [_832233, _832235] : [_832235 = _832233, -(c_Groups_Oabs__class_Oabs(_832235) = c_Groups_Oabs__class_Oabs(_832233))], (52713 ^ _775212) ^ [_1828704, _1828706] : [hBOOL(_1828704), hBOOL(_1828706), -(hBOOL(hAPP(hAPP(c_fconj, _1828704), _1828706)))], (11386 ^ _775212) ^ [_962032, _962034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _962032)), 11389 ^ _775212 : [(11396 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _962032), _962034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _962032)), hAPP(c_Int_Onat, _962034))))], (11390 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _962032)), hAPP(c_Int_Onat, _962034))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _962032), _962034)))]]], (6066 ^ _775212) ^ [_871352, _871354, _871356] : [6067 ^ _775212 : [(6070 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_871356, _871354), _871352))], (6068 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871352), _871354)))]], 6073 ^ _775212 : [(6076 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_871356, _871354), _871352))], (6074 ^ _775212) ^ [] : [-(_871352 = _871354)]], 6079 ^ _775212 : [(6082 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_871356, _871354), _871352))], (6080 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871354), _871352)))]], -(hBOOL(hAPP(hAPP(_871356, _871354), _871352)))], (18543 ^ _775212) ^ [_1090213] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1090213), 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, _1090213)))], (22276 ^ _775212) ^ [_1158524, _1158526] : [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(_1158526))), 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), _1158524)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158524)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158526))))], (40967 ^ _775212) ^ [_1564085, _1564087, _1564089, _1564091, _1564093] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1564085), _1564087), _1564089), _1564091), _1564093) = c_New__DSequence_Opos__single(_1564085, _1564087))], (17849 ^ _775212) ^ [_1078225, _1078227] : [class_Int_Onumber__ring(_1078225), -(hAPP(c_Int_Onumber__class_Onumber__of(_1078225), c_Int_OBit1(_1078227)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078225), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078225), c_Groups_Oone__class_Oone(_1078225)), hAPP(c_Int_Onumber__class_Onumber__of(_1078225), _1078227))), hAPP(c_Int_Onumber__class_Onumber__of(_1078225), _1078227)))], (17057 ^ _775212) ^ [_1065500, _1065502] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1065500), hAPP(hAPP(c_Power_Opower__class_Opower(_1065500), hAPP(c_Int_Onumber__class_Onumber__of(_1065500), c_Int_OMin)), _1065502)) = c_Groups_Oone__class_Oone(_1065500)), class_Int_Onumber__ring(_1065500), class_Rings_Olinordered__idom(_1065500)], (1974 ^ _775212) ^ [_803653, _803655] : [_803655 = _803653, -(c_Com_Ocom_Ocom__size(_803655) = c_Com_Ocom_Ocom__size(_803653))], (42783 ^ _775212) ^ [_1608163, _1608165, _1608167, _1608169, _1608171, _1608173, _1608175] : [42785 ^ _775212 : [(42788 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1608171, 42784 ^ [_1608163, _1608165, _1608167, _1608169, _1608171, _1608173, _1608175]), _1608173), _1608175))], (42786 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1608163), 42784 ^ [_1608163, _1608165, _1608167, _1608169, _1608171, _1608173, _1608175]), _1608169)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608163, tc_fun(_1608165, tc_fun(_1608167, tc_HOL_Obool))), _1608169), _1608171), _1608173), _1608175)))], (1914 ^ _775212) ^ [_801993, _801995] : [-(hBOOL(_801993)), _801995 = _801993, hBOOL(_801995)], (12049 ^ _775212) ^ [_973170, _973172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973170)), _973172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973170), _973172)))], (48268 ^ _775212) ^ [_1740237, _1740239, _1740241, _1740243] : [-(hBOOL(hAPP(_1740237, _1740239))), -(hAPP(c_List_Ofilter(_1740241, _1740237), hAPP(hAPP(c_List_Olist_OCons(_1740241), _1740239), _1740243)) = hAPP(c_List_Ofilter(_1740241, _1740237), _1740243))], (42603 ^ _775212) ^ [_1602940, _1602942, _1602944, _1602946, _1602948] : [-(_1602940 = c_Orderings_Obot__class_Obot(tc_fun(_1602942, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602942, tc_fun(_1602944, tc_HOL_Obool)), _1602940), hAPP(hAPP(c_COMBC(_1602942, tc_fun(_1602944, tc_HOL_Obool), tc_fun(_1602944, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602944, tc_HOL_Obool), tc_fun(tc_fun(_1602944, tc_HOL_Obool), tc_fun(_1602944, tc_HOL_Obool)), _1602942), c_Groups_Ominus__class_Ominus(tc_fun(_1602944, tc_HOL_Obool))), _1602946)), _1602948)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1602944, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602942, tc_fun(_1602944, tc_HOL_Obool)), _1602940), _1602946)), _1602948))], (15807 ^ _775212) ^ [_1042762, _1042764] : [-(_1042762 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042762), _1042764) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042764), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042762), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1042764)))], (15565 ^ _775212) ^ [_1038369, _1038371] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038369, _1038371) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1038369), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1038369), _1038371)), _1038371)))], (47907 ^ _775212) ^ [_1731752, _1731754, _1731756] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731752))), c_Enum_On__lists(_1731752, _1731754, _1731756)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731752)), _1731756)), _1731754))], (23844 ^ _775212) ^ [_1189663, _1189665, _1189667, _1189669, _1189671] : [-(_1189663 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1189665, _1189667, _1189669, _1189671), _1189663) = hAPP(c_Lazy__Sequence_Obind(_1189665, _1189667, hAPP(_1189669, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1189663), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1189665, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1189667)), _1189671), _1189663)))], (34533 ^ _775212) ^ [_1409299, _1409301, _1409303, _1409305] : [hBOOL(hAPP(hAPP(c_member(_1409299), _1409305), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409299, tc_HOL_Obool)), _1409301), _1409303))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409299, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1409299, tc_fun(_1409299, tc_HOL_Obool), tc_HOL_Obool), c_member(_1409299)), _1409301)), hAPP(hAPP(c_COMBC(_1409299, tc_fun(_1409299, tc_HOL_Obool), tc_HOL_Obool), c_member(_1409299)), _1409303)), _1409305)))], (49484 ^ _775212) ^ [_1765630] : [c_List_Onat__list(_1765630), -(c_List_Oembed__list(c_List_Oreturn__list(_1765630)) = _1765630)], (26108 ^ _775212) ^ [_1232610, _1232612] : [26110 ^ _775212 : [(26113 ^ _775212) ^ [] : [hBOOL(hAPP(_1232612, 26109 ^ [_1232610, _1232612]))], (26111 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26109 ^ [_1232610, _1232612]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232610))))]], 26114 ^ _775212 : [(26115 ^ _775212) ^ [_1232763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232763), _1232610)), -(hBOOL(hAPP(_1232612, _1232763)))]]], (52545 ^ _775212) ^ [_1826835, _1826837] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1826835, _1826837)))], (35677 ^ _775212) ^ [_1434126, _1434128, _1434130] : [class_Orderings_Olinorder(_1434126), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434126), _1434128)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434126), _1434130)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434126, tc_HOL_Obool)), _1434128), _1434130) = c_Orderings_Obot__class_Obot(tc_fun(_1434126, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1434126), c_Big__Operators_Olinorder__class_OMax(_1434126, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1434126, tc_HOL_Obool)), _1434128), _1434130))), c_Big__Operators_Olinorder__class_OMax(_1434126, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434126, tc_HOL_Obool)), _1434128), _1434130))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1434126), c_Big__Operators_Olinorder__class_OMax(_1434126, _1434128)), c_Big__Operators_Olinorder__class_OMax(_1434126, _1434130)))], (5546 ^ _775212) ^ [_859821, _859823, _859825, _859827, _859829, _859831] : [-(c_COMBC(_859831, _859827, _859823) = c_COMBC(_859829, _859825, _859821)), _859831 = _859829, _859827 = _859825, _859823 = _859821], (620 ^ _775212) ^ [_784726, _784728, _784730, _784732, _784734, _784736, _784738, _784740, _784742, _784744, _784746, _784748] : [-(c_Finite__Set_Ofolding__image__simple__idem(_784746, _784742, _784738, _784734, _784730, _784726)), c_Finite__Set_Ofolding__image__simple__idem(_784748, _784744, _784740, _784736, _784732, _784728), _784748 = _784746, _784744 = _784742, _784740 = _784738, _784736 = _784734, _784732 = _784730, _784728 = _784726], (41199 ^ _775212) ^ [_1569382, _1569384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1569382), _1569384)), -(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), _1569382), _1569384)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (5270 ^ _775212) ^ [_855663, _855665, _855667, _855669] : [-(c_Relation_Oinv__image(_855669, _855665) = c_Relation_Oinv__image(_855667, _855663)), _855669 = _855667, _855665 = _855663], (48015 ^ _775212) ^ [_1734029, _1734031] : [_1734031 = c_List_Olist_ONil(_1734029), -(c_List_Oremdups(_1734029, _1734031) = c_List_Olist_ONil(_1734029))], (46194 ^ _775212) ^ [_1694923, _1694925, _1694927, _1694929, _1694931] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1694923, _1694925)), _1694927), hAPP(hAPP(c_List_Ozip(_1694923, _1694925), _1694929), _1694931)) = hAPP(hAPP(c_List_Ozip(_1694923, _1694925), hAPP(hAPP(c_List_Odrop(_1694923), _1694927), _1694929)), hAPP(hAPP(c_List_Odrop(_1694925), _1694927), _1694931)))], (39418 ^ _775212) ^ [_1525624, _1525626, _1525628] : [c_Predicate_Oreflp(_1525624, _1525626), -(hBOOL(hAPP(hAPP(_1525626, _1525628), _1525628)))], (35747 ^ _775212) ^ [_1435446, _1435448, _1435450] : [class_Orderings_Olinorder(_1435446), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435446), _1435448)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435446), _1435450)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435446, tc_HOL_Obool)), _1435448), _1435450) = c_Orderings_Obot__class_Obot(tc_fun(_1435446, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1435446), c_Big__Operators_Olattice_OInf__fin(_1435446, c_Orderings_Oord__class_Omin(_1435446), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1435446, tc_HOL_Obool)), _1435448), _1435450))), c_Big__Operators_Olattice_OInf__fin(_1435446, c_Orderings_Oord__class_Omin(_1435446), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435446, tc_HOL_Obool)), _1435448), _1435450))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1435446), c_Big__Operators_Olattice_OInf__fin(_1435446, c_Orderings_Oord__class_Omin(_1435446), _1435448)), c_Big__Operators_Olattice_OInf__fin(_1435446, c_Orderings_Oord__class_Omin(_1435446), _1435450)))], (27766 ^ _775212) ^ [_1266304, _1266306, _1266308, _1266310, _1266312] : [class_Complete__Lattice_Ocomplete__lattice(_1266304), class_Orderings_Olinorder(_1266304), 27773 ^ _775212 : [(27783 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266304), _1266306), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1266308, _1266304), _1266310), _1266312)))), 27784 ^ _775212 : [(27785 ^ _775212) ^ [_1266652] : [hBOOL(hAPP(hAPP(c_member(_1266308), _1266652), _1266310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266304), _1266306), hAPP(_1266312, _1266652)))]]], (27774 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266304), _1266306), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1266308, _1266304), _1266310), _1266312))), 27778 ^ _775212 : [(27781 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266304), _1266306), hAPP(_1266312, 27777 ^ [_1266304, _1266306, _1266308, _1266310, _1266312]))))], (27779 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1266308), 27777 ^ [_1266304, _1266306, _1266308, _1266310, _1266312]), _1266310)))]]]]], (45387 ^ _775212) ^ [_1675261, _1675263, _1675265] : [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, _1675261), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1675261)), _1675263)))), -(hBOOL(hAPP(hAPP(c_member(_1675261), hAPP(c_Product__Type_Ofst(_1675261, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1675261, _1675263), _1675265))), hAPP(c_List_Oset(_1675261), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1675261), _1675261), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1675261)), _1675263)))))], (10161 ^ _775212) ^ [_940270, _940272] : [class_Rings_Olinordered__ring(_940270), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940270), c_Groups_Ozero__class_Ozero(_940270)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940270), _940272), _940272))))], (51825 ^ _775212) ^ [_1817094, _1817096, _1817098, _1817100] : [c_Relation_Osym(_1817094, _1817096), hBOOL(hAPP(hAPP(c_member(tc_prod(_1817094, _1817094)), hAPP(hAPP(c_Product__Type_OPair(_1817094, _1817094), _1817098), _1817100)), _1817096)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1817094, _1817094)), hAPP(hAPP(c_Product__Type_OPair(_1817094, _1817094), _1817100), _1817098)), _1817096)))], (41682 ^ _775212) ^ [_1579189, _1579191, _1579193, _1579195, _1579197, _1579199] : [c_Finite__Set_Ofun__left__comm(_1579189, _1579191, _1579193), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579189), _1579195)), hBOOL(hAPP(hAPP(c_member(_1579189), _1579197), _1579195)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1579189, _1579191, _1579193), _1579199), _1579195) = hAPP(hAPP(_1579193, _1579197), hAPP(hAPP(c_Finite__Set_Ofold(_1579189, _1579191, _1579193), _1579199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1579189, tc_HOL_Obool)), _1579195), hAPP(hAPP(c_Set_Oinsert(_1579189), _1579197), c_Orderings_Obot__class_Obot(tc_fun(_1579189, tc_HOL_Obool)))))))], (42826 ^ _775212) ^ [_1609091, _1609093] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1609091, _1609091), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1609091, _1609093)), c_Relation_OId(_1609091)) = c_Transitive__Closure_Ortrancl(_1609091, _1609093))], (3558 ^ _775212) ^ [_828975, _828977, _828979, _828981, _828983, _828985] : [-(c_Finite__Set_Ofold__image(_828985, _828981, _828977) = c_Finite__Set_Ofold__image(_828983, _828979, _828975)), _828985 = _828983, _828981 = _828979, _828977 = _828975], (7407 ^ _775212) ^ [_893134, _893136, _893138] : [class_Rings_Olinordered__idom(_893134), -(_893136 = _893138), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893134), _893136), _893138))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893134), _893138), _893136)))], (18471 ^ _775212) ^ [_1088988, _1088990] : [class_Int_Onumber__ring(_1088988), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088988), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088988), c_Groups_Oone__class_Oone(_1088988)), c_Groups_Oone__class_Oone(_1088988))), hAPP(c_Int_Onumber__class_Onumber__of(_1088988), _1088990)) = hAPP(c_Int_Onumber__class_Onumber__of(_1088988), c_Int_OBit0(_1088990)))], (17909 ^ _775212) ^ [_1079192] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1079192)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1079192)))], (13431 ^ _775212) ^ [_997964, _997966] : [13432 ^ _775212 : [(13433 ^ _775212) ^ [_998013] : [_997964 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _997966), _998013)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _997964, _997966) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48093 ^ _775212) ^ [_1735620, _1735622] : [-(c_List_Oconcat(_1735620, _1735622) = hAPP(c_List_Ofoldl(tc_List_Olist(_1735620), tc_List_Olist(_1735620), c_List_Oappend(_1735620), c_List_Olist_ONil(_1735620)), _1735622))], (51907 ^ _775212) ^ [_1818423, _1818425] : [c_Equiv__Relations_Opart__equivp(_1818423, _1818425), 51911 ^ _775212 : [(51916 ^ _775212) ^ [] : [-(c_Predicate_Otransp(_1818423, _1818425))], (51914 ^ _775212) ^ [] : [-(c_Predicate_Osymp(_1818423, _1818425))], (51912 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1818425, 51910 ^ [_1818423, _1818425]), 51910 ^ [_1818423, _1818425])))]]], (46408 ^ _775212) ^ [_1700197, _1700199, _1700201] : [-(_1700197 = c_List_Olist_ONil(_1700199)), -(hAPP(c_List_Ohd(_1700199), hAPP(hAPP(c_List_Oappend(_1700199), _1700197), _1700201)) = hAPP(c_List_Ohd(_1700199), _1700197))], (17563 ^ _775212) ^ [_1073351, _1073353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1073351), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1073351)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1073353)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1073353))], (26017 ^ _775212) ^ [_1230869, _1230871] : [26019 ^ _775212 : [(26022 ^ _775212) ^ [] : [hBOOL(hAPP(_1230871, 26018 ^ [_1230869, _1230871]))], (26020 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26018 ^ [_1230869, _1230871]), _1230869)))]], 26023 ^ _775212 : [(26024 ^ _775212) ^ [_1231020] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1231020), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1230869))), -(hBOOL(hAPP(_1230871, _1231020)))]]], (37431 ^ _775212) ^ [_1472264, _1472266, _1472268, _1472270, _1472272] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1472264, _1472266, _1472268), _1472270), _1472272)), -(hBOOL(hAPP(_1472270, hAPP(_1472268, _1472272))))], (41312 ^ _775212) ^ [_1571621, _1571623, _1571625, _1571627, _1571629, _1571631] : [c_Finite__Set_Ofun__left__comm__idem(_1571621, _1571623, _1571625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571621), _1571627)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1571621, _1571623, _1571625), _1571629), hAPP(hAPP(c_Set_Oinsert(_1571621), _1571631), _1571627)) = hAPP(hAPP(c_Finite__Set_Ofold(_1571621, _1571623, _1571625), hAPP(hAPP(_1571625, _1571631), _1571629)), _1571627))], (3422 ^ _775212) ^ [_826835, _826837] : [_826837 = _826835, -(c_Random__Sequence_Osingle(_826837) = c_Random__Sequence_Osingle(_826835))], (18833 ^ _775212) ^ [_1095523, _1095525] : [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), _1095523))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1095525))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1095523))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1095525)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1095523)))], (38951 ^ _775212) ^ [_1507782, _1507784, _1507786] : [-(hAPP(hAPP(c_Set_Oinsert(_1507782), _1507784), hAPP(c_Set_OCollect(_1507782), _1507786)) = hAPP(c_Set_OCollect(_1507782), hAPP(hAPP(c_COMBS(_1507782, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507782), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1507782), c_fNot), hAPP(hAPP(c_COMBC(_1507782, _1507782, tc_HOL_Obool), c_fequal), _1507784)))), _1507786)))], (41384 ^ _775212) ^ [_1573069, _1573071, _1573073, _1573075] : [class_Orderings_Olinorder(_1573069), hBOOL(hAPP(c_Finite__Set_Ofinite(_1573069), _1573071)), hBOOL(hAPP(hAPP(c_member(_1573069), _1573073), _1573071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1573069), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1573069), _1573073), _1573075)), hAPP(hAPP(c_Finite__Set_Ofold(_1573069, _1573069, c_Orderings_Oord__class_Omax(_1573069)), _1573075), _1573071))))], (17041 ^ _775212) ^ [_1065250] : [class_Int_Onumber__ring(_1065250), -(hAPP(c_Int_Oring__1__class_Oof__int(_1065250), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1065250), c_Int_OMin))], (52307 ^ _775212) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (6401 ^ _775212) ^ [_876522, _876524, _876526] : [class_Orderings_Olinorder(_876522), 6404 ^ _775212 : [(6405 ^ _775212) ^ [] : [-(_876524 = _876526), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876522), _876524), _876526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876522), _876526), _876524)))], (6415 ^ _775212) ^ [] : [6416 ^ _775212 : [(6419 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876522), _876526), _876524))], (6417 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876522), _876524), _876526))]], _876524 = _876526]]], (12358 ^ _775212) ^ [_978519] : [-(_978519 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12361 ^ _775212 : [(12368 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _978519))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _978519) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (12362 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _978519)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _978519) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (27273 ^ _775212) ^ [_1255657, _1255659, _1255661] : [class_Lattices_Osemilattice__sup(_1255657), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255657), _1255659), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255657), _1255659), _1255661))))], (48839 ^ _775212) ^ [_1752204, _1752206, _1752208, _1752210, _1752212] : [class_Orderings_Olinorder(_1752204), -(c_List_Olinorder__class_Osorted(_1752204, hAPP(hAPP(c_List_Omap(_1752206, _1752204), _1752208), hAPP(c_List_Ofilter(_1752206, hAPP(hAPP(c_COMBC(_1752206, _1752204, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1752204, tc_fun(_1752204, tc_HOL_Obool), _1752206), c_fequal), _1752208)), hAPP(_1752210, _1752212))), _1752212))))], (17719 ^ _775212) ^ [_1076157] : [c_Int_OMin = _1076157, -(c_Int_OMin = c_Int_OBit1(_1076157))], (47204 ^ _775212) ^ [_1716226, _1716228, _1716230, _1716232] : [-(hAPP(hAPP(c_List_Oappend(_1716226), _1716228), hAPP(hAPP(c_List_Olist_OCons(_1716226), _1716230), c_List_Olist_ONil(_1716226))) = _1716232), -(_1716232 = c_List_Olist_ONil(_1716226)), c_List_Obutlast(_1716226, _1716232) = _1716228, c_List_Olast(_1716226, _1716232) = _1716230], (24462 ^ _775212) ^ [_1199884, _1199886, _1199888] : [class_Rings_Ocomm__ring__1(_1199884), 24465 ^ _775212 : [(24472 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199884), _1199886), _1199888)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199884), _1199886), hAPP(c_Groups_Ouminus__class_Ouminus(_1199884), _1199888))))], (24466 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199884), _1199886), hAPP(c_Groups_Ouminus__class_Ouminus(_1199884), _1199888))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199884), _1199886), _1199888)))]]], (27876 ^ _775212) ^ [_1268873, _1268875, _1268877, _1268879] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1268873, tc_HOL_Obool)), _1268875), hAPP(hAPP(c_Set_Oinsert(_1268873), _1268877), _1268879)) = hAPP(hAPP(c_Set_Oinsert(_1268873), _1268877), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1268873, tc_HOL_Obool)), _1268875), _1268879)))], (35721 ^ _775212) ^ [_1434951, _1434953, _1434955] : [class_Orderings_Olinorder(_1434951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434951), _1434953)), -(_1434953 = c_Orderings_Obot__class_Obot(tc_fun(_1434951, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434951), _1434955)), -(_1434955 = c_Orderings_Obot__class_Obot(tc_fun(_1434951, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434951, tc_HOL_Obool)), _1434953), _1434955) = c_Orderings_Obot__class_Obot(tc_fun(_1434951, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1434951, c_Orderings_Oord__class_Omin(_1434951), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1434951, tc_HOL_Obool)), _1434953), _1434955)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1434951), c_Big__Operators_Olattice_OInf__fin(_1434951, c_Orderings_Oord__class_Omin(_1434951), _1434953)), c_Big__Operators_Olattice_OInf__fin(_1434951, c_Orderings_Oord__class_Omin(_1434951), _1434955)))], (16315 ^ _775212) ^ [_1052062, _1052064] : [-(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), _1052062)), _1052064))))], (35123 ^ _775212) ^ [_1422040, _1422042, _1422044] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1422040, tc_HOL_Obool)), _1422042), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1422040, tc_HOL_Obool)), _1422044)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422040, tc_HOL_Obool)), _1422042), _1422044))], (51952 ^ _775212) ^ [_1819077, _1819079] : [c_Equiv__Relations_Opart__equivp(_1819077, _1819079), 51956 ^ _775212 : [(51969 ^ _775212) ^ [_1819419, _1819421] : [-(hBOOL(hAPP(hAPP(_1819079, _1819421), _1819419))), hBOOL(hAPP(hAPP(_1819079, _1819421), _1819421)), hBOOL(hAPP(hAPP(_1819079, _1819419), _1819419)), hAPP(_1819079, _1819421) = hAPP(_1819079, _1819419)], (51959 ^ _775212) ^ [_1819250, _1819252] : [hBOOL(hAPP(hAPP(_1819079, _1819252), _1819250)), 51962 ^ _775212 : [(51967 ^ _775212) ^ [] : [-(hAPP(_1819079, _1819252) = hAPP(_1819079, _1819250))], (51965 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1819079, _1819250), _1819250)))], (51963 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1819079, _1819252), _1819252)))]]], (51957 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1819079, 51955 ^ [_1819077, _1819079]), 51955 ^ [_1819077, _1819079])))]]], (34469 ^ _775212) ^ [_1407552, _1407554] : [class_Lattices_Obounded__lattice__bot(_1407552), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1407552), c_Orderings_Obot__class_Obot(_1407552)), _1407554) = c_Orderings_Obot__class_Obot(_1407552))], (52349 ^ _775212) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (35121 ^ _775212) ^ [_1421983, _1421985, _1421987] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421983, tc_HOL_Obool)), _1421985), _1421987) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421983, tc_HOL_Obool)), _1421985), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1421983, tc_HOL_Obool)), _1421987)))], (51061 ^ _775212) ^ [_1799824, _1799826, _1799828] : [-(c_List_Olist__ex1(_1799824, _1799826, _1799828)), 51062 ^ _775212 : [(51063 ^ _775212) ^ [_1799918] : [hBOOL(hAPP(hAPP(c_member(_1799824), _1799918), hAPP(c_List_Oset(_1799824), _1799828))), hBOOL(hAPP(_1799826, _1799918)), 51071 ^ _775212 : [(51076 ^ _775212) ^ [] : [51070 ^ [_1799824, _1799826, _1799828, _1799918] = _1799918], (51074 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1799826, 51070 ^ [_1799824, _1799826, _1799828, _1799918])))], (51072 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1799824), 51070 ^ [_1799824, _1799826, _1799828, _1799918]), hAPP(c_List_Oset(_1799824), _1799828))))]]]]], (23290 ^ _775212) ^ [_1179194, _1179196] : [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), _1179194), _1179196))), 23293 ^ _775212 : [(23300 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179196), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 23303 ^ _775212 : [(23312 ^ _775212) ^ [] : [-(c_Nitpick_Onorm__frac(_1179194, _1179196) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1179194), _1179196)), 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), _1179194))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179196)))), -(_1179194 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1179196 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23304 ^ _775212) ^ [] : [23305 ^ _775212 : [(23308 ^ _775212) ^ [] : [_1179196 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23306 ^ _775212) ^ [] : [_1179194 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1179194, _1179196) = 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)))]]], (23294 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179196), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1179194, _1179196) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179194), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179196)))]]], (27692 ^ _775212) ^ [_1264188, _1264190, _1264192, _1264194, _1264196, _1264198] : [class_Complete__Lattice_Ocomplete__lattice(_1264188), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1264190, tc_fun(_1264192, _1264188)), _1264194), _1264196), _1264198) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1264190, _1264188), _1264194), hAPP(hAPP(c_COMBC(_1264190, _1264192, _1264188), _1264196), _1264198)))], (26495 ^ _775212) ^ [_1240786, _1240788] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1240786), _1240788)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1240786)), hAPP(c_Nat_OSuc, _1240788)))], (46278 ^ _775212) ^ [_1696890, _1696892, _1696894, _1696896] : [-(hAPP(hAPP(c_List_Odrop(_1696890), _1696892), hAPP(hAPP(c_List_Olist_OCons(_1696890), _1696894), _1696896)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1696890), hAPP(hAPP(c_List_Olist_OCons(_1696890), _1696894), _1696896), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1696890), tc_List_Olist(_1696890)), c_List_Odrop(_1696890)), _1696896), _1696892))], (18839 ^ _775212) ^ [_1095660, _1095662] : [-(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), _1095660)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1095662))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1095660))) = 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), _1095662)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1095660)))], (15365 ^ _775212) ^ [_1034169, _1034171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1034169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034169), hAPP(c_Nat_OSuc, _1034171))), _1034169)))], (1334 ^ _775212) ^ [_794743, _794745] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_794743)), _794745 = _794743, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_794745)], (31057 ^ _775212) ^ [_1336333, _1336335, _1336337, _1336339] : [hBOOL(hAPP(hAPP(_1336337, _1336335), _1336339)), -(hBOOL(hAPP(hAPP(c_member(_1336333), _1336335), c_SetInterval_Oord_OatMost(_1336333, _1336337, _1336339))))], (14035 ^ _775212) ^ [_1008658, _1008660, _1008662] : [class_Divides_Osemiring__div(_1008658), -(_1008660 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008658), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008658), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1008658), _1008660), _1008662)), _1008662)), c_Divides_Odiv__class_Omod(_1008658, _1008660, _1008662)))], (2654 ^ _775212) ^ [_814351, _814353] : [_814353 = _814351, -(c_Lazy__Sequence_Ohb__not__seq(_814353) = c_Lazy__Sequence_Ohb__not__seq(_814351))], (19973 ^ _775212) ^ [_1115795, _1115797, _1115799, _1115801] : [class_Fields_Olinordered__field(_1115795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115795), _1115797), c_Groups_Ozero__class_Ozero(_1115795))), 19980 ^ _775212 : [(19987 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115795), _1115801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115795), _1115799), _1115797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115795), _1115799), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115795), _1115801), _1115797))))], (19981 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115795), _1115799), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115795), _1115801), _1115797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115795), _1115801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115795), _1115799), _1115797))))]]], (43118 ^ _775212) ^ [_1616290, _1616292, _1616294] : [43120 ^ _775212 : [(43121 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1616290), 43119 ^ [_1616290, _1616292, _1616294]), _1616292)))], (43126 ^ _775212) ^ [] : [43119 ^ [_1616290, _1616292, _1616294] = 43122 ^ [_1616290, _1616292, _1616294]], (43130 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616290, _1616290)), hAPP(hAPP(c_Product__Type_OPair(_1616290, _1616290), 43122 ^ [_1616290, _1616292, _1616294]), 43119 ^ [_1616290, _1616292, _1616294])), _1616294))], (43128 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616290, _1616290)), hAPP(hAPP(c_Product__Type_OPair(_1616290, _1616290), 43119 ^ [_1616290, _1616292, _1616294]), 43122 ^ [_1616290, _1616292, _1616294])), _1616294))], (43124 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1616290), 43122 ^ [_1616290, _1616292, _1616294]), _1616292)))]], -(c_Relation_Ototal__on(_1616290, _1616292, _1616294))], (40963 ^ _775212) ^ [_1563986, _1563988, _1563990, _1563992] : [-(c_New__Random__Sequence_Opos__map(_1563986, _1563988, _1563990, _1563992) = c_New__Random__Sequence_Opos__bind(_1563986, _1563988, _1563992, hAPP(c_Fun_Ocomp(_1563988, 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(_1563988))))), _1563986, c_New__Random__Sequence_Opos__single(_1563988)), _1563990)))], (1084 ^ _775212) ^ [_791618, _791620] : [-(class_Lattices_Obounded__lattice(_791618)), _791620 = _791618, class_Lattices_Obounded__lattice(_791620)], (36609 ^ _775212) ^ [_1454922, _1454924, _1454926, _1454928] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1454922), hAPP(c_Set_Oimage(_1454924, _1454922, _1454926), _1454928))), c_Fun_Oinj__on(_1454924, _1454922, _1454926, _1454928), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1454924), _1454928)))], (52115 ^ _775212) ^ [_1822375, _1822377] : [class_Lattices_Obounded__lattice(_1822375), -(class_Lattices_Obounded__lattice__top(tc_fun(_1822377, _1822375)))], (22724 ^ _775212) ^ [_1167585, _1167587] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1167585)), hAPP(c_Nat_OSuc, _1167587)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1167585), _1167587)))], (49792 ^ _775212) ^ [_1772050, _1772052, _1772054] : [-(hBOOL(hAPP(hAPP(c_member(_1772050), _1772052), hAPP(c_List_Oset(_1772050), _1772054)))), -(c_List_Oinsert(_1772050, _1772052, _1772054) = hAPP(hAPP(c_List_Olist_OCons(_1772050), _1772052), _1772054))], (45164 ^ _775212) ^ [_1669461, _1669463] : [-(c_List_Olistrelp(_1669461, _1669463, c_List_Olist_ONil(_1669461), c_List_Olist_ONil(_1669461)))], (45186 ^ _775212) ^ [_1669872, _1669874, _1669876] : [c_List_Olist_ONil(_1669872) = hAPP(hAPP(c_List_Olist_OCons(_1669872), _1669874), _1669876)], (27213 ^ _775212) ^ [_1254628, _1254630, _1254632, _1254634] : [class_Lattices_Osemilattice__sup(_1254628), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254628), _1254630), _1254632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254628), _1254630), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254628), _1254632), _1254634))))], (52091 ^ _775212) ^ [_1821982, _1821984, _1821986, _1821988, _1821990, _1821992] : [hAPP(c_Set_Oimage(_1821982, _1821984, _1821986), _1821988) = _1821990, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1821984, tc_HOL_Obool)), _1821992), _1821990)), -(hAPP(c_Set_Oimage(_1821982, _1821984, _1821986), hAPP(c_Set_Oimage(_1821984, _1821982, c_Hilbert__Choice_Oinv__into(_1821982, _1821984, _1821988, _1821986)), _1821992)) = _1821992)], (52277 ^ _775212) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (39684 ^ _775212) ^ [_1534502, _1534504, _1534506] : [c_Wellfounded_Owf(_1534502, _1534504), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534502, _1534502), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1534502, _1534502, _1534502), _1534504), _1534506)), _1534504)), -(c_FunDef_Oreduction__pair(_1534502, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1534502, _1534502), tc_HOL_Obool), tc_fun(tc_prod(_1534502, _1534502), tc_HOL_Obool)), _1534504), _1534506)))], (52417 ^ _775212) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (52317 ^ _775212) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (42270 ^ _775212) ^ [_1593306, _1593308, _1593310, _1593312, _1593314] : [42272 ^ _775212 : [(42275 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1593306), _1593308), hAPP(_1593314, 42271 ^ [_1593306, _1593308, _1593310, _1593312, _1593314])))], (42273 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1593310), 42271 ^ [_1593306, _1593308, _1593310, _1593312, _1593314]), _1593312)))]], -(hBOOL(hAPP(hAPP(c_member(_1593306), _1593308), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593310, tc_fun(_1593306, tc_HOL_Obool)), _1593312), _1593314))))], (35213 ^ _775212) ^ [_1423948, _1423950, _1423952, _1423954] : [class_Orderings_Oorder(_1423948), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423948, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1423948, _1423950, _1423952)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1423948, _1423952, _1423954)) = c_Orderings_Obot__class_Obot(tc_fun(_1423948, tc_HOL_Obool)))], (664 ^ _775212) ^ [_785464, _785466, _785468, _785470, _785472, _785474, _785476, _785478] : [-(c_List_Olistrelp(_785476, _785472, _785468, _785464)), c_List_Olistrelp(_785478, _785474, _785470, _785466), _785478 = _785476, _785474 = _785472, _785470 = _785468, _785466 = _785464], (30488 ^ _775212) ^ [_1324292, _1324294, _1324296, _1324298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1324292, tc_HOL_Obool)), _1324294), hAPP(hAPP(c_Set_Oinsert(_1324292), _1324296), _1324298))), 30491 ^ _775212 : [(30498 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1324292), _1324296), _1324298))), 30501 ^ _775212 : [(30508 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1324292), _1324296), _1324294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1324292, tc_HOL_Obool)), _1324294), _1324298)))], (30502 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324292), _1324296), _1324294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1324292, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324292, tc_HOL_Obool)), _1324294), hAPP(hAPP(c_Set_Oinsert(_1324292), _1324296), c_Orderings_Obot__class_Obot(tc_fun(_1324292, tc_HOL_Obool))))), _1324298)))]]], (30492 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324292), _1324296), _1324298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1324292, tc_HOL_Obool)), _1324294), _1324298)))]]], (8143 ^ _775212) ^ [_906475, _906477] : [class_Groups_Oordered__ab__group__add(_906475), 8146 ^ _775212 : [(8153 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906475), c_Groups_Ozero__class_Ozero(_906475)), _906477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906475), hAPP(c_Groups_Ouminus__class_Ouminus(_906475), _906477)), c_Groups_Ozero__class_Ozero(_906475))))], (8147 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906475), hAPP(c_Groups_Ouminus__class_Ouminus(_906475), _906477)), c_Groups_Ozero__class_Ozero(_906475))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906475), c_Groups_Ozero__class_Ozero(_906475)), _906477)))]]], (9595 ^ _775212) ^ [_930146, _930148] : [class_Groups_Omonoid__mult(_930146), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930146), _930148), c_Groups_Oone__class_Oone(_930146)) = _930148)], (32509 ^ _775212) ^ [_1364058, _1364060, _1364062] : [class_Orderings_Olinorder(_1364058), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364058), _1364060)), 32516 ^ _775212 : [(32523 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364058, tc_HOL_Obool)), _1364060), hAPP(hAPP(c_Set_Oinsert(_1364058), _1364062), c_Orderings_Obot__class_Obot(tc_fun(_1364058, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1364058, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1364058, c_Orderings_Oord__class_Omax(_1364058), hAPP(hAPP(c_Set_Oinsert(_1364058), _1364062), _1364060)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364058), _1364062), c_Big__Operators_Olattice_OSup__fin(_1364058, c_Orderings_Oord__class_Omax(_1364058), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364058, tc_HOL_Obool)), _1364060), hAPP(hAPP(c_Set_Oinsert(_1364058), _1364062), c_Orderings_Obot__class_Obot(tc_fun(_1364058, tc_HOL_Obool)))))))], (32517 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364058, tc_HOL_Obool)), _1364060), hAPP(hAPP(c_Set_Oinsert(_1364058), _1364062), c_Orderings_Obot__class_Obot(tc_fun(_1364058, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1364058, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1364058, c_Orderings_Oord__class_Omax(_1364058), hAPP(hAPP(c_Set_Oinsert(_1364058), _1364062), _1364060)) = _1364062)]]], (3368 ^ _775212) ^ [_825978, _825980] : [_825980 = _825978, -(c_Nitpick_Odenom(_825980) = c_Nitpick_Odenom(_825978))], (31222 ^ _775212) ^ [_1339802, _1339804, _1339806, _1339808, _1339810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1339802, _1339804)), hAPP(_1339802, _1339806))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1339808, _1339808)), hAPP(hAPP(c_Product__Type_OPair(_1339808, _1339808), _1339804), _1339806)), _1339810)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1339808, _1339808)), hAPP(hAPP(c_Product__Type_OPair(_1339808, _1339808), _1339804), _1339806)), c_Wellfounded_Omlex__prod(_1339808, _1339802, _1339810))))], (42679 ^ _775212) ^ [_1604987, _1604989, _1604991] : [c_Relation_Orefl__on(_1604987, _1604989, _1604991), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1604987, _1604987), tc_HOL_Obool)), _1604991), hAPP(hAPP(c_Relation_Orel__comp(_1604987, _1604987, _1604987), hAPP(c_Relation_Oconverse(_1604987, _1604987), _1604991)), _1604991))))], (12043 ^ _775212) ^ [_973052, _973054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973052), _973054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973052), hAPP(c_Nat_OSuc, _973054))))], (31607 ^ _775212) ^ [_1347272] : [class_Rings_Oring__1(_1347272), -(hBOOL(hAPP(hAPP(c_member(_1347272), c_Groups_Ozero__class_Ozero(_1347272)), c_Int_Oring__1__class_OInts(_1347272))))], (43404 ^ _775212) ^ [_1623068, _1623070, _1623072, _1623074] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1623068, tc_HOL_Obool), tc_fun(_1623070, tc_HOL_Obool)), _1623072), hAPP(hAPP(c_COMBC(tc_fun(_1623068, tc_HOL_Obool), tc_fun(_1623068, tc_fun(_1623070, tc_HOL_Obool)), tc_fun(_1623070, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623068, tc_fun(_1623070, tc_HOL_Obool))), _1623074)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623068, tc_fun(_1623070, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623068, tc_HOL_Obool), _1623072)), _1623074))], (38076 ^ _775212) ^ [_1489114, _1489116, _1489118, _1489120] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1489114, _1489116), _1489118), _1489120) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1489114, tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool)), _1489118), hAPP(hAPP(c_COMBS(_1489114, tc_fun(_1489116, tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool)), tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1489116, tc_HOL_Obool), tc_fun(tc_fun(_1489116, tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool)), tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool)), _1489114), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1489116, tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool))), _1489120)), hAPP(hAPP(c_COMBC(_1489114, tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool), tc_fun(_1489116, tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1489116, tc_fun(tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool), tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool), tc_fun(_1489116, tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool))), _1489114), c_COMBC(_1489116, tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool), tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1489116, tc_prod(_1489114, _1489116)), tc_fun(_1489116, tc_fun(tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool), tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool))), _1489114), hAPP(c_COMBB(tc_prod(_1489114, _1489116), tc_fun(tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool), tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool)), _1489116), c_Set_Oinsert(tc_prod(_1489114, _1489116)))), c_Product__Type_OPair(_1489114, _1489116)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489114, _1489116), tc_HOL_Obool))))))], (50897 ^ _775212) ^ [_1795776, _1795778, _1795780, _1795782] : [hBOOL(hAPP(hAPP(c_member(_1795776), _1795778), hAPP(c_List_Oset(_1795776), c_List_Oreplicate(_1795776, _1795780, _1795782)))), 50900 ^ _775212 : [(50903 ^ _775212) ^ [] : [_1795780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50901 ^ _775212) ^ [] : [-(_1795778 = _1795782)]]], (45732 ^ _775212) ^ [_1683724, _1683726, _1683728, _1683730] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683724)), hAPP(hAPP(c_List_Olist__update(_1683724, _1683726), _1683728), _1683730)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683724)), _1683726))], (36539 ^ _775212) ^ [_1453730, _1453732, _1453734, _1453736, _1453738] : [c_Fun_Oinj__on(_1453730, _1453732, _1453734, _1453736), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1453730, tc_HOL_Obool)), _1453738), _1453736)), -(c_Fun_Oinj__on(_1453730, _1453732, _1453734, _1453738))], (48747 ^ _775212) ^ [_1750712, _1750714] : [class_Orderings_Olinorder(_1750712), -(_1750714 = c_List_Olist_ONil(_1750712)), c_List_Olinorder__class_Osorted(_1750712, _1750714), -(c_List_Olinorder__class_Osorted(_1750712, c_List_Obutlast(_1750712, _1750714)))], (38865 ^ _775212) ^ [_1505861, _1505863] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1505861)), 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)), _1505861))), 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, _1505863))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29114 ^ _775212) ^ [_1292417, _1292419] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292417), _1292419))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292417, _1292419) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (1062 ^ _775212) ^ [_791265, _791267, _791269, _791271, _791273, _791275, _791277, _791279] : [-(c_Fun_Oinj__on(_791277, _791273, _791269, _791265)), c_Fun_Oinj__on(_791279, _791275, _791271, _791267), _791279 = _791277, _791275 = _791273, _791271 = _791269, _791267 = _791265], (3232 ^ _775212) ^ [_823792, _823794] : [_823794 = _823792, -(c_Int_Oint__ge__less__than2(_823794) = c_Int_Oint__ge__less__than2(_823792))], (34124 ^ _775212) ^ [_1399790, _1399792, _1399794] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399790), _1399792), _1399794) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399790, tc_HOL_Obool), tc_HOL_Obool)), -(_1399792 = c_Orderings_Obot__class_Obot(tc_fun(_1399790, tc_HOL_Obool)))], (29526 ^ _775212) ^ [_1300902, _1300904, _1300906, _1300908] : [hBOOL(hAPP(hAPP(c_member(_1300902), _1300904), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300902, tc_HOL_Obool)), _1300906), _1300908))), 29529 ^ _775212 : [(29532 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1300902), _1300904), _1300908))], (29530 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1300902), _1300904), _1300906)))]]], (28530 ^ _775212) ^ [_1281421] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1281421), c_Orderings_Otop__class_Otop(tc_fun(_1281421, 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(_1281421), c_Orderings_Otop__class_Otop(tc_fun(_1281421, tc_HOL_Obool))))))], (2044 ^ _775212) ^ [_804712, _804714] : [_804714 = _804712, -(c_HOL_Obool_Obool__size(_804714) = c_HOL_Obool_Obool__size(_804712))], (39872 ^ _775212) ^ [_1538141, _1538143, _1538145] : [c_Wellfounded_Owf(_1538141, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1538141, _1538141), tc_HOL_Obool)), _1538143), _1538145)), -(c_Wellfounded_Owf(_1538141, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1538141, _1538141), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1538141, _1538141), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1538141, _1538141, _1538141), _1538143), _1538143)), hAPP(hAPP(c_Relation_Orel__comp(_1538141, _1538141, _1538141), _1538145), _1538143))), _1538145)))], (8191 ^ _775212) ^ [_907285, _907287] : [class_Groups_Ogroup__add(_907285), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907285), _907287), hAPP(c_Groups_Ouminus__class_Ouminus(_907285), _907287)) = c_Groups_Ozero__class_Ozero(_907285))], (50521 ^ _775212) ^ [_1788427, _1788429, _1788431] : [50523 ^ _775212 : [(50526 ^ _775212) ^ [] : [hBOOL(hAPP(_1788429, 50522 ^ [_1788427, _1788429, _1788431]))], (50524 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1788427), 50522 ^ [_1788427, _1788429, _1788431]), hAPP(c_List_Oset(_1788427), _1788431))))]], -(c_List_Olist__all(_1788427, _1788429, _1788431))], (18945 ^ _775212) ^ [_1097603, _1097605] : [class_Fields_Olinordered__field__inverse__zero(_1097603), class_Int_Onumber__ring(_1097603), 18952 ^ _775212 : [(18959 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097603), c_Groups_Ozero__class_Ozero(_1097603)), _1097605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097603), c_Groups_Ozero__class_Ozero(_1097603)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1097603), _1097605), hAPP(c_Int_Onumber__class_Onumber__of(_1097603), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (18953 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097603), c_Groups_Ozero__class_Ozero(_1097603)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1097603), _1097605), hAPP(c_Int_Onumber__class_Onumber__of(_1097603), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097603), c_Groups_Ozero__class_Ozero(_1097603)), _1097605)))]]], (31867 ^ _775212) ^ [_1351542, _1351544, _1351546] : [class_Orderings_Olinorder(_1351542), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351542), _1351544)), -(_1351544 = c_Orderings_Obot__class_Obot(tc_fun(_1351542, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1351542, hAPP(hAPP(c_Set_Oinsert(_1351542), _1351546), _1351544)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1351542), _1351546), c_Big__Operators_Olinorder__class_OMin(_1351542, _1351544)))], (43687 ^ _775212) ^ [_1629403, _1629405, _1629407, _1629409, _1629411, _1629413] : [-(_1629403 = c_Orderings_Obot__class_Obot(tc_fun(_1629405, tc_HOL_Obool))), 43693 ^ _775212 : [(43696 ^ _775212) ^ [] : [c_Fun_Oinj__on(_1629407, _1629409, _1629411, hAPP(_1629413, 43692 ^ [_1629403, _1629405, _1629407, _1629409, _1629411, _1629413]))], (43694 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1629405), 43692 ^ [_1629403, _1629405, _1629407, _1629409, _1629411, _1629413]), _1629403)))]], -(c_Fun_Oinj__on(_1629407, _1629409, _1629411, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629405, tc_fun(_1629407, tc_HOL_Obool)), _1629403), _1629413)))], (42669 ^ _775212) ^ [_1604796, _1604798, _1604800, _1604802, _1604804] : [class_Complete__Lattice_Ocomplete__lattice(_1604796), hBOOL(hAPP(hAPP(c_member(_1604798), _1604800), _1604802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1604796), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604798, _1604796), _1604802), _1604804)), hAPP(_1604804, _1604800))))], (24290 ^ _775212) ^ [_1196899, _1196901, _1196903] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196899), _1196901)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196901), _1196899))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196901), _1196903)), 24301 ^ _775212 : [(24304 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196903), _1196899))], (24302 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196899), _1196903)))]]], (39636 ^ _775212) ^ [_1533508, _1533510, _1533512, _1533514, _1533516, _1533518, _1533520, _1533522] : [hBOOL(hAPP(hAPP(_1533508, _1533510), _1533512)), hBOOL(hAPP(hAPP(_1533514, _1533512), _1533516)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1533518, _1533520, _1533522, _1533508, _1533514), _1533510), _1533516)))], (35395 ^ _775212) ^ [_1428151, _1428153, _1428155] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1428151), _1428153)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428151), _1428155)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1428151), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1428151, tc_HOL_Obool)), _1428153), _1428155))), hAPP(c_Finite__Set_Ocard(_1428151), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428151, tc_HOL_Obool)), _1428153), _1428155))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1428151), _1428153)), hAPP(c_Finite__Set_Ocard(_1428151), _1428155)))], (31311 ^ _775212) ^ [_1341848, _1341850, _1341852, _1341854, _1341856, _1341858] : [hBOOL(hAPP(hAPP(c_member(_1341848), _1341850), c_SetInterval_Oord_OatLeastLessThan(_1341848, _1341852, _1341854, _1341856, _1341858))), 31314 ^ _775212 : [(31317 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1341854, _1341850), _1341858)))], (31315 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1341852, _1341856), _1341850)))]]], (5458 ^ _775212) ^ [_858515, _858517, _858519, _858521] : [-(tc_fun(_858521, _858517) = tc_fun(_858519, _858515)), _858521 = _858519, _858517 = _858515], (978 ^ _775212) ^ [_790107, _790109, _790111, _790113] : [-(c_Relation_Otrans(_790111, _790107)), c_Relation_Otrans(_790113, _790109), _790113 = _790111, _790109 = _790107], (45168 ^ _775212) ^ [_1669523, _1669525] : [-(c_List_Olist_Olist__size(_1669523, _1669525, c_List_Olist_ONil(_1669523)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1454 ^ _775212) ^ [_796243, _796245] : [-(class_Groups_Ouminus(_796243)), _796245 = _796243, class_Groups_Ouminus(_796245)], (16247 ^ _775212) ^ [_1050732, _1050734, _1050736] : [class_Rings_Olinordered__idom(_1050732), 16250 ^ _775212 : [(16259 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050732), hAPP(c_Groups_Oabs__class_Oabs(_1050732), _1050734)), _1050736))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050732), _1050734), _1050736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050732), hAPP(c_Groups_Ouminus__class_Ouminus(_1050732), _1050734)), _1050736))], (16251 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050732), hAPP(c_Groups_Oabs__class_Oabs(_1050732), _1050734)), _1050736)), 16254 ^ _775212 : [(16257 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050732), hAPP(c_Groups_Ouminus__class_Ouminus(_1050732), _1050734)), _1050736)))], (16255 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050732), _1050734), _1050736)))]]]]], (47776 ^ _775212) ^ [_1728684, _1728686, _1728688, _1728690, _1728692, _1728694] : [c_List_Olist__all2(_1728684, _1728686, _1728688, _1728690, _1728692), -(c_List_Olist__all2(_1728684, _1728686, _1728688, hAPP(hAPP(c_List_Odrop(_1728684), _1728694), _1728690), hAPP(hAPP(c_List_Odrop(_1728686), _1728694), _1728692)))], (50478 ^ _775212) ^ [_1787599, _1787601] : [-(c_List_Olist__all(_1787599, _1787601, c_List_Olist_ONil(_1787599)))], (36635 ^ _775212) ^ [_1455374, _1455376, _1455378, _1455380, _1455382] : [c_Fun_Oinj__on(_1455374, _1455376, _1455378, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1455374, tc_HOL_Obool)), _1455380), _1455382)), 36638 ^ _775212 : [(36645 ^ _775212) ^ [] : [_1455380 = _1455382, -(hAPP(c_Set_Oimage(_1455374, _1455376, _1455378), _1455380) = hAPP(c_Set_Oimage(_1455374, _1455376, _1455378), _1455382))], (36639 ^ _775212) ^ [] : [hAPP(c_Set_Oimage(_1455374, _1455376, _1455378), _1455380) = hAPP(c_Set_Oimage(_1455374, _1455376, _1455378), _1455382), -(_1455380 = _1455382)]]], (41582 ^ _775212) ^ [_1576657, _1576659, _1576661, _1576663] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576657, _1576657)), hAPP(hAPP(c_Product__Type_OPair(_1576657, _1576657), _1576659), _1576661)), _1576663)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576657, _1576657)), hAPP(hAPP(c_Product__Type_OPair(_1576657, _1576657), _1576659), _1576661)), c_Transitive__Closure_Otrancl(_1576657, _1576663))))], (33026 ^ _775212) ^ [_1374157, _1374159, _1374161] : [class_Groups_Ocomm__monoid__add(_1374157), class_Groups_Ocomm__monoid__mult(_1374157), c_Nat__Transfer_Onat__set(_1374159), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1374157), _1374161), _1374159) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1374157), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1374157, tc_Nat_Onat), _1374161), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1374159)))], (32549 ^ _775212) ^ [_1364996, _1364998] : [class_Orderings_Olinorder(_1364996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364996), _1364998)), -(_1364998 = c_Orderings_Obot__class_Obot(tc_fun(_1364996, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364996), c_Big__Operators_Olattice_OInf__fin(_1364996, c_Orderings_Oord__class_Omin(_1364996), _1364998)), c_Big__Operators_Olattice_OSup__fin(_1364996, c_Orderings_Oord__class_Omax(_1364996), _1364998))))], (50821 ^ _775212) ^ [_1794282, _1794284, _1794286, _1794288, _1794290] : [hBOOL(hAPP(hAPP(_1794282, _1794284), _1794286)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1794288, _1794290, _1794282), _1794286), _1794284)))], (29334 ^ _775212) ^ [_1296959, _1296961, _1296963] : [class_Orderings_Olinorder(_1296959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296959), _1296961), _1296963)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296959, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1296959), _1296961), c_Orderings_Obot__class_Obot(tc_fun(_1296959, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1296959, _1296961, _1296963)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1296959, _1296961), _1296963))], (6244 ^ _775212) ^ [_873859, _873861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873859), hAPP(c_Nat_OSuc, _873861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873859), _873861))), -(_873859 = _873861)], (45027 ^ _775212) ^ [_1665608, _1665610, _1665612] : [-(hAPP(c_List_Oset(_1665608), c_List_Osublist(_1665608, _1665610, _1665612)) = hAPP(c_Set_OCollect(_1665608), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1665608), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1665608, 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)), _1665608), 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)), _1665608), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1665608, tc_fun(tc_Nat_Onat, _1665608), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1665608, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1665608), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1665608), c_COMBB(_1665608, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1665608), _1665610))))), 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(_1665608)), _1665610)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1665612))))))], (34213 ^ _775212) ^ [_1401909, _1401911, _1401913, _1401915, _1401917, _1401919, _1401921] : [c_Equiv__Relations_Oequiv(_1401909, _1401911, _1401913), hBOOL(hAPP(hAPP(c_member(tc_fun(_1401909, tc_HOL_Obool)), _1401915), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401909), _1401911), _1401913))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1401909, tc_HOL_Obool)), _1401917), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401909), _1401911), _1401913))), hBOOL(hAPP(hAPP(c_member(_1401909), _1401919), _1401915)), hBOOL(hAPP(hAPP(c_member(_1401909), _1401921), _1401917)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1401909, _1401909)), hAPP(hAPP(c_Product__Type_OPair(_1401909, _1401909), _1401919), _1401921)), _1401913)), -(_1401915 = _1401917)], (46190 ^ _775212) ^ [_1694803, _1694805, _1694807] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1694803, tc_HOL_Obool)), hAPP(c_List_Oset(_1694803), hAPP(hAPP(c_List_Odrop(_1694803), _1694805), _1694807))), hAPP(c_List_Oset(_1694803), _1694807))))], (52587 ^ _775212) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (49530 ^ _775212) ^ [_1766685, _1766687, _1766689] : [c_List_OdropWhile(_1766685, _1766687, _1766689) = c_List_Olist_ONil(_1766685), 49533 ^ _775212 : [(49534 ^ _775212) ^ [_1766776] : [hBOOL(hAPP(hAPP(c_member(_1766685), _1766776), hAPP(c_List_Oset(_1766685), _1766689))), -(hBOOL(hAPP(_1766687, _1766776)))]]], (37592 ^ _775212) ^ [_1476163, _1476165, _1476167, _1476169, _1476171] : [class_Groups_Oab__semigroup__mult(_1476163), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1476163, _1476163, c_Groups_Otimes__class_Otimes(_1476163), _1476165, _1476167), _1476169)), hBOOL(hAPP(hAPP(c_member(_1476163), _1476171), _1476167)), -(hBOOL(hAPP(hAPP(c_member(_1476163), _1476165), _1476167))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1476163, _1476163, c_Groups_Otimes__class_Otimes(_1476163), _1476171, hAPP(hAPP(c_Set_Oinsert(_1476163), _1476165), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1476163, tc_HOL_Obool)), _1476167), hAPP(hAPP(c_Set_Oinsert(_1476163), _1476171), c_Orderings_Obot__class_Obot(tc_fun(_1476163, tc_HOL_Obool)))))), _1476169)))], (39853 ^ _775212) ^ [_1537778, _1537780] : [hBOOL(hAPP(hAPP(c_member(_1537778), 39854 ^ [_1537778, _1537780]), c_Wellfounded_Oacc(_1537778, _1537780))), -(c_Wellfounded_Owf(_1537778, _1537780))], (34077 ^ _775212) ^ [_1398425, _1398427, _1398429, _1398431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398425), _1398431)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398429), _1398427))), -(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), _1398425), _1398427)), 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), _1398429), _1398431)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (11937 ^ _775212) ^ [_971355, _971357, _971359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971355), _971357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971355), _971359)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971357), _971359))))], (11402 ^ _775212) ^ [_962291, _962293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _962291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _962293)), 11409 ^ _775212 : [(11416 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _962291), _962293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _962291)), hAPP(c_Int_Onat, _962293))))], (11410 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _962291)), hAPP(c_Int_Onat, _962293))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _962291), _962293)))]]], (96 ^ _775212) ^ [_776518, _776520, _776522, _776524, _776526, _776528] : [-(c_Nitpick_Oless__frac(_776526, _776522, _776518)), c_Nitpick_Oless__frac(_776528, _776524, _776520), _776528 = _776526, _776524 = _776522, _776520 = _776518], (41788 ^ _775212) ^ [_1581343, _1581345, _1581347, _1581349, _1581351, _1581353] : [c_Finite__Set_Ofun__left__comm(_1581343, _1581345, _1581347), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581343), _1581349)), -(hBOOL(hAPP(hAPP(c_member(_1581343), _1581351), _1581349))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1581343, _1581345, _1581347), _1581353), hAPP(hAPP(c_Set_Oinsert(_1581343), _1581351), _1581349)) = hAPP(hAPP(_1581347, _1581351), hAPP(hAPP(c_Finite__Set_Ofold(_1581343, _1581345, _1581347), _1581353), _1581349)))], (9589 ^ _775212) ^ [_930051, _930053] : [class_Groups_Ocomm__monoid__mult(_930051), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930051), _930053), c_Groups_Oone__class_Oone(_930051)) = _930053)], (20429 ^ _775212) ^ [_1123777, _1123779, _1123781, _1123783] : [class_Fields_Olinordered__field(_1123777), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123777), _1123779), c_Groups_Ozero__class_Ozero(_1123777))), 20436 ^ _775212 : [(20443 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123777), _1123783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123777), _1123781), _1123779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123777), _1123781), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123777), _1123783), _1123779))))], (20437 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123777), _1123781), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123777), _1123783), _1123779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123777), _1123783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123777), _1123781), _1123779))))]]], (43004 ^ _775212) ^ [_1613425, _1613427, _1613429] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1613425, _1613425, _1613425), _1613427), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613425, _1613425), tc_HOL_Obool), _1613429), _1613427)) = hAPP(hAPP(c_Relation_Orel__comp(_1613425, _1613425, _1613425), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613425, _1613425), tc_HOL_Obool), _1613429), _1613427)), _1613427))], (17835 ^ _775212) ^ [_1078032] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1078032)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1078032))))], (41554 ^ _775212) ^ [_1576223, _1576225, _1576227] : [class_Orderings_Olinorder(_1576223), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576223), _1576225)), -(hBOOL(hAPP(hAPP(c_member(_1576223), _1576227), _1576225))), -(c_Big__Operators_Olinorder__class_OMax(_1576223, hAPP(hAPP(c_Set_Oinsert(_1576223), _1576227), _1576225)) = hAPP(hAPP(c_Finite__Set_Ofold(_1576223, _1576223, c_Orderings_Oord__class_Omax(_1576223)), _1576227), _1576225))], (26617 ^ _775212) ^ [_1243065, _1243067, _1243069] : [class_Orderings_Olinorder(_1243065), 26620 ^ _775212 : [(26627 ^ _775212) ^ [] : [_1243067 = _1243069, -(hAPP(c_SetInterval_Oord__class_OatMost(_1243065), _1243067) = hAPP(c_SetInterval_Oord__class_OatMost(_1243065), _1243069))], (26621 ^ _775212) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1243065), _1243067) = hAPP(c_SetInterval_Oord__class_OatMost(_1243065), _1243069), -(_1243067 = _1243069)]]], (44387 ^ _775212) ^ [_1648609, _1648611] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1648609), tc_List_Olist(_1648609)), tc_HOL_Obool)), c_List_Olistrel(_1648609, _1648611)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1648609), c_List_Olistrel1(_1648609, _1648611)))))], (39709 ^ _775212) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (15081 ^ _775212) ^ [_1028218, _1028220, _1028222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028218), _1028220)), _1028222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028218), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028222), _1028220))))], (45712 ^ _775212) ^ [_1683215, _1683217, _1683219] : [-(hAPP(hAPP(c_List_Olist__update(_1683215, _1683217), _1683219), hAPP(hAPP(c_List_Onth(_1683215), _1683217), _1683219)) = _1683217)], (33775 ^ _775212) ^ [_1391237, _1391239, _1391241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1391237, tc_HOL_Obool)), _1391239), _1391241)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1391237, tc_HOL_Obool)), _1391239), hAPP(c_Set_OPow(_1391237), _1391241))))], (49569 ^ _775212) ^ [_1767402, _1767404, _1767406] : [-(c_List_OdropWhile(_1767402, _1767404, _1767406) = c_List_Olist_ONil(_1767402)), hBOOL(hAPP(_1767404, hAPP(c_List_Ohd(_1767402), c_List_OdropWhile(_1767402, _1767404, _1767406))))], (46204 ^ _775212) ^ [_1695225, _1695227] : [-(hAPP(hAPP(c_List_Odrop(_1695225), _1695227), c_List_Olist_ONil(_1695225)) = c_List_Olist_ONil(_1695225))], (44649 ^ _775212) ^ [_1656083, _1656085, _1656087, _1656089] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656083) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1656085), hAPP(hAPP(c_List_Olist_OCons(_1656085), _1656087), _1656089)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1656083)) = _1656087)], (22448 ^ _775212) ^ [_1162557, _1162559, _1162561, _1162563] : [class_Orderings_Olinorder(_1162557), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162557), _1162559), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162557), _1162561), _1162563)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162557), _1162561), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162557), _1162559), _1162563)))], (42537 ^ _775212) ^ [_1601075, _1601077, _1601079, _1601081, _1601083, _1601085] : [-(hAPP(c_Set_Ovimage(_1601075, _1601077, _1601079), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601081, tc_fun(_1601077, tc_HOL_Obool)), _1601083), _1601085)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601081, tc_fun(_1601075, tc_HOL_Obool)), _1601083), hAPP(hAPP(c_COMBB(tc_fun(_1601077, tc_HOL_Obool), tc_fun(_1601075, tc_HOL_Obool), _1601081), c_Set_Ovimage(_1601075, _1601077, _1601079)), _1601085)))], (44807 ^ _775212) ^ [_1660343] : [-(hAPP(c_List_Omap(_1660343, _1660343), c_COMBI(_1660343)) = c_Fun_Oid(tc_List_Olist(_1660343)))], (29468 ^ _775212) ^ [_1299817, _1299819, _1299821, _1299823] : [29469 ^ _775212 : [(29472 ^ _775212) ^ [] : [_1299819 = _1299823], (29470 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1299817), _1299819), _1299821))]], -(hBOOL(hAPP(hAPP(c_member(_1299817), _1299819), hAPP(hAPP(c_Set_Oinsert(_1299817), _1299823), _1299821))))], (48191 ^ _775212) ^ [_1738589, _1738591, _1738593] : [-(hAPP(c_List_Ofilter(_1738589, _1738591), c_List_Oconcat(_1738589, _1738593)) = c_List_Oconcat(_1738589, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1738589), tc_List_Olist(_1738589)), c_List_Ofilter(_1738589, _1738591)), _1738593)))], (17761 ^ _775212) ^ [_1076810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1076810)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076810), c_Int_OPls)))], (50469 ^ _775212) ^ [_1787391, _1787393, _1787395] : [50471 ^ _775212 : [(50474 ^ _775212) ^ [] : [hBOOL(hAPP(_1787393, hAPP(hAPP(c_List_Onth(_1787391), _1787395), 50470 ^ [_1787391, _1787393, _1787395])))], (50472 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50470 ^ [_1787391, _1787393, _1787395]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1787391)), _1787395))))]], -(c_List_Olist__all(_1787391, _1787393, _1787395))], (22049 ^ _775212) ^ [_1153586, _1153588, _1153590, _1153592, _1153594, _1153596] : [-(hAPP(hAPP(c_Product__Type_OPair(_1153586, _1153588), _1153590), _1153592) = hAPP(hAPP(c_Product__Type_OPair(_1153586, _1153588), _1153594), _1153596)), _1153590 = _1153594, _1153592 = _1153596], (35231 ^ _775212) ^ [_1424329, _1424331, _1424333, _1424335, _1424337] : [class_Orderings_Olinorder(_1424329), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424329, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1424329, _1424331, _1424333)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1424329, _1424335, _1424337)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1424329, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1424329), _1424331), _1424335), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424329), _1424333), _1424337)))], (35303 ^ _775212) ^ [_1425989, _1425991, _1425993] : [class_Orderings_Oorder(_1425989), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425989, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1425989, _1425991, _1425993)), hAPP(c_SetInterval_Oord__class_OatLeast(_1425989), _1425993)) = c_Orderings_Obot__class_Obot(tc_fun(_1425989, tc_HOL_Obool)))], (27648 ^ _775212) ^ [_1263135, _1263137] : [class_Orderings_Olinorder(_1263135), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1263135, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1263135), _1263137)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1263135), _1263137))], (11909 ^ _775212) ^ [_970819, _970821, _970823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970819), _970821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970819), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970823), _970821))))], (52679 ^ _775212) ^ [_1828214, _1828216, _1828218, _1828220, _1828222, _1828224] : [-(hAPP(hAPP(hAPP(c_COMBB(_1828214, _1828216, _1828218), _1828220), _1828222), _1828224) = hAPP(_1828220, hAPP(_1828222, _1828224)))], (48494 ^ _775212) ^ [_1746003, _1746005, _1746007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1746003), _1746005)), _1746007)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1746005), c_List_Oupt(_1746003, _1746007)) = c_List_Oupt(_1746003, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1746003), _1746005)))], (4694 ^ _775212) ^ [_846749, _846751, _846753, _846755, _846757, _846759] : [-(c_List_Olinorder__class_Oinsort__key(_846759, _846755, _846751) = c_List_Olinorder__class_Oinsort__key(_846757, _846753, _846749)), _846759 = _846757, _846755 = _846753, _846751 = _846749], (34337 ^ _775212) ^ [_1404571, _1404573, _1404575, _1404577, _1404579] : [c_Equiv__Relations_Oequiv(_1404571, _1404573, _1404575), hBOOL(hAPP(hAPP(c_member(tc_prod(_1404571, _1404571)), hAPP(hAPP(c_Product__Type_OPair(_1404571, _1404571), _1404577), _1404579)), _1404575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404571, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404571, _1404571, _1404575), hAPP(hAPP(c_Set_Oinsert(_1404571), _1404577), c_Orderings_Obot__class_Obot(tc_fun(_1404571, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1404571, _1404571, _1404575), hAPP(hAPP(c_Set_Oinsert(_1404571), _1404579), c_Orderings_Obot__class_Obot(tc_fun(_1404571, tc_HOL_Obool)))))))], (16093 ^ _775212) ^ [_1047901, _1047903] : [class_Groups_Oordered__ab__group__add__abs(_1047901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047901), c_Groups_Ozero__class_Ozero(_1047901)), _1047903)), -(hAPP(c_Groups_Oabs__class_Oabs(_1047901), _1047903) = _1047903)], (22828 ^ _775212) ^ [_1170152, _1170154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170152), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1170154, _1170152) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1170154), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1170152)))], (30274 ^ _775212) ^ [_1318510, _1318512, _1318514, _1318516, _1318518] : [hBOOL(hAPP(hAPP(c_member(_1318510), _1318512), _1318514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318516, tc_HOL_Obool)), hAPP(_1318518, _1318512)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318510, tc_fun(_1318516, tc_HOL_Obool)), _1318514), _1318518))))], (13352 ^ _775212) ^ [_996790, _996792] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _996790, _996792)) = _996792), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _996790), _996792) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _996790, _996792)))], (51655 ^ _775212) ^ [_1813667] : [-(c_Relation_Oantisym(_1813667, c_Relation_OId(_1813667)))], (49863 ^ _775212) ^ [_1773738, _1773740] : [-(c_List_Omeasures(_1773738, _1773740) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1773738), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1773738, tc_List_Olist(tc_fun(_1773738, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773738, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1773738, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1773738), c_List_Omap(tc_fun(_1773738, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1773738, tc_Nat_Onat), _1773738, tc_Nat_Onat), c_COMBI(tc_fun(_1773738, tc_Nat_Onat))))), _1773740)))], (5733 ^ _775212) ^ [_865658, _865660, _865662, _865664, _865666, _865668] : [-(hBOOL(hAPP(_865658, _865660))), c_Natural_Oevaln(_865662, _865660, _865664, _865666), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_865658, _865668, _865662), _865660, _865664, _865666))], (45945 ^ _775212) ^ [_1688193, _1688195, _1688197, _1688199] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688193)), hAPP(hAPP(c_List_Oappend(_1688193), _1688195), _1688197)), c_List_Olists(_1688193, _1688199)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688193)), _1688195), c_List_Olists(_1688193, _1688199))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688193)), _1688197), c_List_Olists(_1688193, _1688199)))], (29130 ^ _775212) ^ [_1292645, _1292647, _1292649, _1292651, _1292653] : [_1292645 = c_Orderings_Obot__class_Obot(tc_fun(_1292647, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292649, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292647, tc_fun(_1292649, tc_HOL_Obool)), _1292645), _1292651)), _1292653) = _1292653)], (4448 ^ _775212) ^ [_842852, _842854, _842856, _842858] : [-(c_List_Oremdups(_842858, _842854) = c_List_Oremdups(_842856, _842852)), _842858 = _842856, _842854 = _842852], (45252 ^ _775212) ^ [_1671699, _1671701, _1671703, _1671705, _1671707, _1671709] : [-(hAPP(hAPP(c_List_Ozip(_1671699, _1671701), _1671703), hAPP(hAPP(c_List_Omap(_1671705, _1671701), _1671707), _1671709)) = hAPP(hAPP(c_List_Omap(tc_prod(_1671699, _1671705), tc_prod(_1671699, _1671701)), hAPP(c_Product__Type_Oprod_Oprod__case(_1671699, _1671705, tc_prod(_1671699, _1671701)), hAPP(hAPP(c_COMBC(_1671699, tc_fun(_1671705, _1671701), tc_fun(_1671705, tc_prod(_1671699, _1671701))), hAPP(hAPP(c_COMBB(tc_fun(_1671701, tc_prod(_1671699, _1671701)), tc_fun(tc_fun(_1671705, _1671701), tc_fun(_1671705, tc_prod(_1671699, _1671701))), _1671699), c_COMBB(_1671701, tc_prod(_1671699, _1671701), _1671705)), c_Product__Type_OPair(_1671699, _1671701))), _1671707))), hAPP(hAPP(c_List_Ozip(_1671699, _1671705), _1671703), _1671709)))], (31329 ^ _775212) ^ [_1342194, _1342196] : [class_Int_Onumber__ring(_1342194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1342196)), -(hBOOL(hAPP(hAPP(c_member(_1342194), hAPP(c_Int_Onumber__class_Onumber__of(_1342194), _1342196)), c_Nat_Osemiring__1__class_ONats(_1342194))))], (15834 ^ _775212) ^ [_1043236, _1043238, _1043240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1043236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1043238), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1043240), 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), _1043240), _1043238))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1043236)))))], (18797 ^ _775212) ^ [_1094601, _1094603, _1094605] : [class_Rings_Olinordered__idom(_1094601), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094601), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094601), hAPP(hAPP(c_Power_Opower__class_Opower(_1094601), _1094603), 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(_1094601), _1094605), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1094601)))], (16665 ^ _775212) ^ [_1059313, _1059315, _1059317] : [16667 ^ _775212 : [(16670 ^ _775212) ^ [] : [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(_1059315, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 16666 ^ [_1059313, _1059315, _1059317]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1059315, 16666 ^ [_1059313, _1059315, _1059317])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (16668 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16666 ^ [_1059313, _1059315, _1059317]), _1059313)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1059315, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1059317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1059317), hAPP(_1059315, _1059313))), 16680 ^ _775212 : [(16683 ^ _775212) ^ [] : [-(hAPP(_1059315, 16679 ^ [_1059313, _1059315, _1059317]) = _1059317)], (16681 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 16679 ^ [_1059313, _1059315, _1059317]), _1059313)))]]], (39408 ^ _775212) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (12496 ^ _775212) ^ [_980954, _980956, _980958, _980960] : [class_Divides_Osemiring__div(_980954), -(c_Divides_Odiv__class_Omod(_980954, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980954), _980956), _980958), _980960) = c_Divides_Odiv__class_Omod(_980954, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980954), c_Divides_Odiv__class_Omod(_980954, _980956, _980960)), _980958), _980960))], (29642 ^ _775212) ^ [_1303191, _1303193, _1303195, _1303197] : [hBOOL(hAPP(hAPP(c_member(_1303191), _1303193), _1303195)), -(hBOOL(hAPP(hAPP(c_member(_1303191), _1303193), hAPP(hAPP(c_Set_Oinsert(_1303191), _1303197), _1303195))))], (45987 ^ _775212) ^ [_1689309, _1689311, _1689313, _1689315] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1689309, tc_HOL_Obool)), hAPP(c_List_Oset(_1689309), hAPP(hAPP(c_List_Olist__update(_1689309, _1689311), _1689313), _1689315))), hAPP(hAPP(c_Set_Oinsert(_1689309), _1689315), hAPP(c_List_Oset(_1689309), _1689311)))))], (48083 ^ _775212) ^ [_1735430, _1735432, _1735434] : [class_Orderings_Olinorder(_1735430), -(c_List_Olinorder__class_Osort__key(_1735432, _1735430, _1735434, c_List_Olist_ONil(_1735432)) = c_List_Olist_ONil(_1735432))], (34707 ^ _775212) ^ [_1412572, _1412574, _1412576] : [class_Lattices_Olattice(_1412572), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412572), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1412572), _1412574), _1412576)), _1412576)))], (44712 ^ _775212) ^ [_1657851, _1657853, _1657855] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657851)), hAPP(hAPP(c_List_Otake(_1657851), _1657853), _1657855)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657851)), _1657855)), _1657853))], (47995 ^ _775212) ^ [_1733702] : [-(c_List_Oremdups(_1733702, c_List_Olist_ONil(_1733702)) = c_List_Olist_ONil(_1733702))], (13451 ^ _775212) ^ [_998378, _998380, _998382, _998384] : [class_Divides_Osemiring__div(_998378), 13454 ^ _775212 : [(13461 ^ _775212) ^ [] : [-(_998380 = c_Groups_Ozero__class_Ozero(_998378)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_998378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998378), _998380), _998382)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998378), _998380), _998384)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_998378), _998382), _998384))], (13455 ^ _775212) ^ [] : [_998380 = c_Groups_Ozero__class_Ozero(_998378), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_998378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998378), _998380), _998382)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998378), _998380), _998384)) = c_Groups_Ozero__class_Ozero(_998378))]]], (6747 ^ _775212) ^ [_882631, _882633, _882635, _882637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882631), _882633)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882635), _882633) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882631), _882637), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882635), _882637)))], (4654 ^ _775212) ^ [_846145, _846147, _846149, _846151] : [-(c_Lazy__Sequence_Osmall__lazy_H(_846151, _846147) = c_Lazy__Sequence_Osmall__lazy_H(_846149, _846145)), _846151 = _846149, _846147 = _846145], (26503 ^ _775212) ^ [_1240992, _1240994] : [-(hAPP(c_Finite__Set_Ocard(_1240992), _1240994) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1240992, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1240992), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1240994))], (30689 ^ _775212) ^ [_1328956, _1328958, _1328960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1328956)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1328958), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1328960)), 30696 ^ _775212 : [(30697 ^ _775212) ^ [_1329164] : [30699 ^ _775212 : [(30705 ^ _775212) ^ [] : [-(_1329164 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30701 ^ [_1328956, _1328958, _1328960, _1329164]), 30698 ^ [_1328956, _1328958, _1328960, _1329164]))], (30703 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30701 ^ [_1328956, _1328958, _1328960, _1329164]), _1328960)))], (30700 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30698 ^ [_1328956, _1328958, _1328960, _1329164]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1328956))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1329164), _1328958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1329164), _1328956)), _1328958)))]]], (23582 ^ _775212) ^ [_1184610, _1184612, _1184614, _1184616] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1184610, _1184612, _1184614, c_Code__Numeral_OSuc__code__numeral(_1184616)) = hAPP(hAPP(_1184614, _1184616), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1184610, _1184612, _1184614, _1184616)))], (42357 ^ _775212) ^ [_1595674, _1595676, _1595678, _1595680, _1595682, _1595684] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595674, tc_fun(_1595676, tc_HOL_Obool)), _1595678), hAPP(hAPP(c_COMBB(_1595680, tc_fun(_1595676, tc_HOL_Obool), _1595674), _1595682), _1595684)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595680, tc_fun(_1595676, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1595674, _1595680, _1595684), _1595678)), _1595682))], (44439 ^ _775212) ^ [_1650200, _1650202, _1650204, _1650206] : [c_List_Olistrelp(_1650200, hAPP(hAPP(c_COMBC(_1650200, tc_fun(tc_prod(_1650200, _1650200), tc_HOL_Obool), tc_fun(_1650200, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650200, tc_fun(tc_fun(tc_prod(_1650200, _1650200), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1650200, _1650200), tc_HOL_Obool), tc_fun(_1650200, tc_HOL_Obool)), _1650200), c_COMBC(_1650200, tc_fun(tc_prod(_1650200, _1650200), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650200, tc_prod(_1650200, _1650200)), tc_fun(_1650200, tc_fun(tc_fun(tc_prod(_1650200, _1650200), tc_HOL_Obool), tc_HOL_Obool)), _1650200), hAPP(c_COMBB(tc_prod(_1650200, _1650200), tc_fun(tc_fun(tc_prod(_1650200, _1650200), tc_HOL_Obool), tc_HOL_Obool), _1650200), c_member(tc_prod(_1650200, _1650200)))), c_Product__Type_OPair(_1650200, _1650200)))), _1650202), _1650204, _1650206), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650200), tc_List_Olist(_1650200))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650200), tc_List_Olist(_1650200)), _1650204), _1650206)), c_List_Olistrel(_1650200, _1650202))))], (45218 ^ _775212) ^ [_1670466, _1670468] : [-(hAPP(hAPP(c_List_Otake(_1670466), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1670468) = c_List_Olist_ONil(_1670466))], (5490 ^ _775212) ^ [_858983, _858985, _858987, _858989] : [-(tc_Nitpick_Opair__box(_858989, _858985) = tc_Nitpick_Opair__box(_858987, _858983)), _858989 = _858987, _858985 = _858983], (51793 ^ _775212) ^ [_1816385, _1816387] : [c_Relation_Osym(_1816385, _1816387), -(c_Relation_Osym(_1816385, c_Transitive__Closure_Otrancl(_1816385, _1816387)))], (7881 ^ _775212) ^ [_901700] : [class_Groups_Ogroup__add(_901700), -(hAPP(c_Groups_Ouminus__class_Ouminus(_901700), c_Groups_Ozero__class_Ozero(_901700)) = c_Groups_Ozero__class_Ozero(_901700))], (46994 ^ _775212) ^ [_1712186, _1712188, _1712190] : [_1712186 = c_List_Olist_ONil(_1712188), -(c_List_Olast(_1712188, hAPP(hAPP(c_List_Olist_OCons(_1712188), _1712190), _1712186)) = _1712190)], (51224 ^ _775212) ^ [_1803459, _1803461, _1803463, _1803465] : [-(hAPP(c_Relation_OImage(_1803459, _1803461, hAPP(c_Set_OCollect(tc_prod(_1803459, _1803461)), hAPP(c_Product__Type_Oprod_Oprod__case(_1803459, _1803461, tc_HOL_Obool), _1803463))), _1803465) = hAPP(c_Set_OCollect(_1803461), hAPP(hAPP(c_COMBB(tc_fun(_1803459, tc_HOL_Obool), tc_HOL_Obool, _1803461), c_HOL_OEx(_1803459)), hAPP(hAPP(c_COMBB(tc_fun(_1803459, tc_HOL_Obool), tc_fun(_1803459, tc_HOL_Obool), _1803461), hAPP(c_COMBS(_1803459, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1803459), c_fconj), hAPP(hAPP(c_COMBC(_1803459, tc_fun(_1803459, tc_HOL_Obool), tc_HOL_Obool), c_member(_1803459)), _1803465)))), hAPP(c_COMBC(_1803459, _1803461, tc_HOL_Obool), _1803463)))))], (47120 ^ _775212) ^ [_1714597, _1714599, _1714601] : [-(c_List_Obutlast(_1714597, hAPP(hAPP(c_List_Odrop(_1714597), _1714599), _1714601)) = hAPP(hAPP(c_List_Odrop(_1714597), _1714599), c_List_Obutlast(_1714597, _1714601)))], (25328 ^ _775212) ^ [_1215992, _1215994] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1215994), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1215992)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1215992)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1215994))))], (27860 ^ _775212) ^ [_1268596] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1268596))))], (36797 ^ _775212) ^ [_1458555, _1458557, _1458559, _1458561, _1458563, _1458565] : [c_Fun_Oinj__on(_1458555, _1458557, _1458559, _1458561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458555, tc_HOL_Obool)), _1458563), _1458561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458555, tc_HOL_Obool)), _1458565), _1458561)), -(hAPP(c_Set_Oimage(_1458555, _1458557, _1458559), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458555, tc_HOL_Obool)), _1458563), _1458565)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458557, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1458555, _1458557, _1458559), _1458563)), hAPP(c_Set_Oimage(_1458555, _1458557, _1458559), _1458565)))], (39061 ^ _775212) ^ [_1510446, _1510448, _1510450, _1510452, _1510454, _1510456, _1510458] : [class_Groups_Ocomm__monoid__add(_1510446), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510448), _1510450)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510452), _1510454)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510448, _1510446), hAPP(hAPP(c_COMBS(_1510448, tc_fun(_1510452, tc_HOL_Obool), _1510446), hAPP(hAPP(c_COMBB(tc_fun(_1510452, _1510446), tc_fun(tc_fun(_1510452, tc_HOL_Obool), _1510446), _1510448), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510452, _1510446)), _1510456)), hAPP(hAPP(c_COMBB(tc_fun(_1510452, tc_HOL_Obool), tc_fun(_1510452, tc_HOL_Obool), _1510448), c_Set_OCollect(_1510452)), hAPP(hAPP(c_COMBB(tc_fun(_1510452, tc_HOL_Obool), tc_fun(_1510452, tc_HOL_Obool), _1510448), hAPP(c_COMBS(_1510452, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510452), c_fconj), hAPP(hAPP(c_COMBC(_1510452, tc_fun(_1510452, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510452)), _1510454)))), _1510458)))), _1510450) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510452, _1510446), hAPP(hAPP(c_COMBS(_1510452, tc_fun(_1510448, tc_HOL_Obool), _1510446), hAPP(hAPP(c_COMBB(tc_fun(_1510448, _1510446), tc_fun(tc_fun(_1510448, tc_HOL_Obool), _1510446), _1510452), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510448, _1510446)), hAPP(c_COMBC(_1510448, _1510452, _1510446), _1510456))), hAPP(hAPP(c_COMBB(tc_fun(_1510448, tc_HOL_Obool), tc_fun(_1510448, tc_HOL_Obool), _1510452), c_Set_OCollect(_1510448)), hAPP(hAPP(c_COMBB(tc_fun(_1510448, tc_HOL_Obool), tc_fun(_1510448, tc_HOL_Obool), _1510452), hAPP(c_COMBS(_1510448, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510448), c_fconj), hAPP(hAPP(c_COMBC(_1510448, tc_fun(_1510448, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510448)), _1510450)))), hAPP(c_COMBC(_1510448, _1510452, tc_HOL_Obool), _1510458))))), _1510454))], (17653 ^ _775212) ^ [_1075005, _1075007] : [_1075005 = _1075007, -(c_Int_OBit1(_1075005) = c_Int_OBit1(_1075007))], (37449 ^ _775212) ^ [_1472686, _1472688, _1472690, _1472692, _1472694] : [-(hAPP(c_Set_Ovimage(_1472686, _1472688, _1472690), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472688, tc_HOL_Obool)), _1472692), _1472694)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472686, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1472686, _1472688, _1472690), _1472692)), hAPP(c_Set_Ovimage(_1472686, _1472688, _1472690), _1472694)))], (13961 ^ _775212) ^ [_1007428, _1007430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007430)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1007428), hAPP(c_Int_Onat, _1007430)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007428, _1007430)))], (21365 ^ _775212) ^ [_1141208, _1141210] : [-(_1141208 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1141208, _1141210) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1141208), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1141210)))], (29842 ^ _775212) ^ [_1306881, _1306883, _1306885] : [hBOOL(hAPP(_1306885, _1306883)), -(hBOOL(hAPP(hAPP(c_member(_1306881), _1306883), _1306885)))], (28854 ^ _775212) ^ [_1288030, _1288032, _1288034] : [class_Orderings_Oorder(_1288030), 28857 ^ _775212 : [(28864 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288030), _1288032), _1288034))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1288030, _1288032, _1288034) = c_Orderings_Obot__class_Obot(tc_fun(_1288030, tc_HOL_Obool)))], (28858 ^ _775212) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1288030, _1288032, _1288034) = c_Orderings_Obot__class_Obot(tc_fun(_1288030, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288030), _1288032), _1288034))]]], (6120 ^ _775212) ^ [_872018, _872020] : [6121 ^ _775212 : [(6124 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872020), _872018))], (6122 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872018), _872020))]], _872018 = _872020], (16703 ^ _775212) ^ [_1060072, _1060074, _1060076, _1060078] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1060072, _1060074), _1060076)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1060072, _1060074), _1060078)), -(_1060076 = _1060078)], (9533 ^ _775212) ^ [_929119, _929121, _929123, _929125] : [class_Orderings_Opreorder(_929119), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929119), _929121), _929123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929119), _929123), _929125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929119), _929121), _929125)))], (15359 ^ _775212) ^ [_1034072, _1034074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1034072)), -(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), _1034072), _1034074))))], (23784 ^ _775212) ^ [_1188546] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1188546)) = _1188546)], (24726 ^ _775212) ^ [_1204627, _1204629, _1204631] : [class_Divides_Oring__div(_1204627), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204627), _1204629), _1204631)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204627), _1204631), hAPP(c_Groups_Ouminus__class_Ouminus(_1204627), _1204629)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1204627), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204627), _1204631), _1204629)))], (50021 ^ _775212) ^ [_1777717, _1777719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1777717), _1777719)), -(c_Lazy__Sequence_Osmall__lazy_H(_1777717, _1777719) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (16739 ^ _775212) ^ [_1060737, _1060739] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060737)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060739)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1060737), _1060739)))], (18183 ^ _775212) ^ [_1083924] : [-(c_Int_OBit0(_1083924) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1083924), _1083924))], (39749 ^ _775212) ^ [_1535940, _1535942, _1535944] : [c_Wellfounded_Owf(_1535940, _1535942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535940, _1535940), tc_HOL_Obool)), _1535944), _1535942)), -(c_Wellfounded_Owf(_1535940, _1535944))], (20463 ^ _775212) ^ [_1124427, _1124429, _1124431, _1124433] : [class_Fields_Olinordered__field(_1124427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124427), c_Groups_Ozero__class_Ozero(_1124427)), _1124429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124427), _1124431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124427), _1124433), _1124429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124427), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124427), _1124431), _1124429)), _1124433)))], (43037 ^ _775212) ^ [_1614231, _1614233, _1614235] : [c_Relation_Ototal__on(_1614231, _1614233, _1614235), -(c_Relation_Ototal__on(_1614231, _1614233, hAPP(c_Relation_Oconverse(_1614231, _1614231), _1614235)))], (38527 ^ _775212) ^ [_1499378, _1499380, _1499382] : [class_Orderings_Olinorder(_1499378), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499378), _1499380)), -(_1499380 = c_Orderings_Obot__class_Obot(tc_fun(_1499378, tc_HOL_Obool))), 38538 ^ _775212 : [(38548 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499378), hAPP(c_Finite__Set_Ofold1(_1499378, c_Orderings_Oord__class_Omin(_1499378)), _1499380)), _1499382))), 38549 ^ _775212 : [(38550 ^ _775212) ^ [_1499767] : [hBOOL(hAPP(hAPP(c_member(_1499378), _1499767), _1499380)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499378), _1499767), _1499382))]]], (38539 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499378), hAPP(c_Finite__Set_Ofold1(_1499378, c_Orderings_Oord__class_Omin(_1499378)), _1499380)), _1499382)), 38543 ^ _775212 : [(38546 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499378), 38542 ^ [_1499378, _1499380, _1499382]), _1499382)))], (38544 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1499378), 38542 ^ [_1499378, _1499380, _1499382]), _1499380)))]]]]], (27583 ^ _775212) ^ [_1261887, _1261889, _1261891] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1261887, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1261889)), _1261891) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261887, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1261887, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1261889)), _1261891)), hAPP(_1261891, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29383 ^ _775212) ^ [] : [-(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))))], (50300 ^ _775212) ^ [_1783831, _1783833, _1783835] : [class_Orderings_Olinorder(_1783831), 50306 ^ _775212 : [(50309 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1783831), _1783835), 50305 ^ [_1783831, _1783833, _1783835]))], (50307 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1783831), 50305 ^ [_1783831, _1783833, _1783835]), hAPP(c_List_Oset(_1783831), _1783833))))]], c_List_Olinorder__class_Osorted(_1783831, _1783833), -(c_List_Olinorder__class_Osorted(_1783831, hAPP(hAPP(c_List_Olist_OCons(_1783831), _1783835), _1783833)))], (22738 ^ _775212) ^ [_1167980, _1167982, _1167984] : [-(hAPP(c_Product__Type_Osnd(_1167980, _1167982), _1167984) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1167980, _1167982, _1167982), hAPP(c_COMBK(tc_fun(_1167982, _1167982), _1167980), c_COMBI(_1167982))), _1167984))], (6669 ^ _775212) ^ [_881195] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _881195) = _881195)], (1354 ^ _775212) ^ [_794993, _794995] : [-(class_Complete__Lattice_Ocomplete__lattice(_794993)), _794995 = _794993, class_Complete__Lattice_Ocomplete__lattice(_794995)], (26663 ^ _775212) ^ [_1243739, _1243741] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1243739, _1243741)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243741), _1243739))], (1264 ^ _775212) ^ [_793868, _793870] : [-(class_Int_Oring__char__0(_793868)), _793870 = _793868, class_Int_Oring__char__0(_793870)], (30576 ^ _775212) ^ [_1326305, _1326307, _1326309, _1326311, _1326313] : [class_Groups_Oab__group__add(_1326305), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326307), _1326309)), 30583 ^ _775212 : [(30590 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1326307), _1326311), _1326309))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1326307, _1326305), _1326313), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326307, tc_HOL_Obool)), _1326309), hAPP(hAPP(c_Set_Oinsert(_1326307), _1326311), c_Orderings_Obot__class_Obot(tc_fun(_1326307, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1326307, _1326305), _1326313), _1326309))], (30584 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1326307), _1326311), _1326309)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1326307, _1326305), _1326313), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326307, tc_HOL_Obool)), _1326309), hAPP(hAPP(c_Set_Oinsert(_1326307), _1326311), c_Orderings_Obot__class_Obot(tc_fun(_1326307, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1326305), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1326307, _1326305), _1326313), _1326309)), hAPP(_1326313, _1326311)))]]], (11596 ^ _775212) ^ [_965675, _965677, _965679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965675)), 11599 ^ _775212 : [(11606 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965677), _965679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965675), _965677)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965675), _965679))))], (11600 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965675), _965677)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965675), _965679))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965677), _965679)))]]], (24952 ^ _775212) ^ [_1209134, _1209136, _1209138] : [class_Divides_Osemiring__div(_1209134), class_Int_Onumber(_1209134), 24959 ^ _775212 : [(24966 ^ _775212) ^ [] : [c_Divides_Odiv__class_Omod(_1209134, hAPP(c_Int_Onumber__class_Onumber__of(_1209134), _1209138), hAPP(c_Int_Onumber__class_Onumber__of(_1209134), _1209136)) = c_Groups_Ozero__class_Ozero(_1209134), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1209134), hAPP(c_Int_Onumber__class_Onumber__of(_1209134), _1209136)), hAPP(c_Int_Onumber__class_Onumber__of(_1209134), _1209138))))], (24960 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1209134), hAPP(c_Int_Onumber__class_Onumber__of(_1209134), _1209136)), hAPP(c_Int_Onumber__class_Onumber__of(_1209134), _1209138))), -(c_Divides_Odiv__class_Omod(_1209134, hAPP(c_Int_Onumber__class_Onumber__of(_1209134), _1209138), hAPP(c_Int_Onumber__class_Onumber__of(_1209134), _1209136)) = c_Groups_Ozero__class_Ozero(_1209134))]]], (41837 ^ _775212) ^ [_1582608, _1582610] : [-(hAPP(c_Relation_ORange(_1582608, _1582608), c_Transitive__Closure_Ortrancl(_1582608, _1582610)) = c_Orderings_Otop__class_Otop(tc_fun(_1582608, tc_HOL_Obool)))], (36761 ^ _775212) ^ [_1457824, _1457826] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1457824), c_Orderings_Otop__class_Otop(tc_fun(_1457824, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1457824, _1457824, _1457826), c_Orderings_Otop__class_Otop(tc_fun(_1457824, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1457824, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1457824, _1457824, _1457826, c_Orderings_Otop__class_Otop(tc_fun(_1457824, tc_HOL_Obool))))], (37437 ^ _775212) ^ [_1472371, _1472373, _1472375, _1472377, _1472379] : [hBOOL(hAPP(_1472377, hAPP(_1472375, _1472379))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1472371, _1472373, _1472375), _1472377), _1472379)))], (35051 ^ _775212) ^ [_1420086, _1420088, _1420090, _1420092] : [-(hBOOL(hAPP(hAPP(c_member(_1420086), _1420088), _1420090))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420086, tc_HOL_Obool)), _1420090), hAPP(hAPP(c_Set_Oinsert(_1420086), _1420088), _1420092)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420086, tc_HOL_Obool)), _1420090), _1420092))], (26633 ^ _775212) ^ [_1243306] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1243306)) = _1243306)], (3276 ^ _775212) ^ [_824484, _824486, _824488, _824490] : [-(c_Predicate_OPowp(_824490, _824486) = c_Predicate_OPowp(_824488, _824484)), _824490 = _824488, _824486 = _824484], (16407 ^ _775212) ^ [_1053955, _1053957, _1053959, _1053961] : [class_Int_Onumber__ring(_1053955), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053955), hAPP(c_Int_Onumber__class_Onumber__of(_1053955), _1053957)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053955), hAPP(c_Int_Onumber__class_Onumber__of(_1053955), _1053959)), _1053961)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053955), hAPP(c_Int_Onumber__class_Onumber__of(_1053955), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1053957), _1053959))), _1053961))], (14151 ^ _775212) ^ [_1010932, _1010934, _1010936, _1010938, _1010940] : [class_Groups_Ominus(_1010932), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010934, _1010932)), _1010936), _1010938), _1010940) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1010932), hAPP(_1010936, _1010940)), hAPP(_1010938, _1010940)))], (29226 ^ _775212) ^ [_1294711] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1294711, _1294711) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1294711), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (14585 ^ _775212) ^ [_1019029, _1019031, _1019033] : [class_Groups_Oordered__ab__group__add(_1019029), 14588 ^ _775212 : [(14595 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1019029), _1019031), _1019033)), c_Groups_Ozero__class_Ozero(_1019029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019029), _1019031), _1019033)))], (14589 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019029), _1019031), _1019033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1019029), _1019031), _1019033)), c_Groups_Ozero__class_Ozero(_1019029))))]]], (16817 ^ _775212) ^ [_1061993, _1061995] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1061993, _1061995), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1061993), _1061995)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1061993, _1061995)))))], (26069 ^ _775212) ^ [_1231879, _1231881] : [26077 ^ _775212 : [(26080 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1231881, 26076 ^ [_1231879, _1231881])))], (26078 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26076 ^ [_1231879, _1231881]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1231879))))]], 26070 ^ _775212 : [(26071 ^ _775212) ^ [_1231947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1231947), _1231879)), hBOOL(hAPP(_1231881, _1231947))]]], (29362 ^ _775212) ^ [_1297628, _1297630] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297628), _1297630)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1297630, _1297628) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (37950 ^ _775212) ^ [_1485833, _1485835] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1485833, _1485835), c_Orderings_Otop__class_Otop(tc_fun(_1485833, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1485835, tc_HOL_Obool), _1485833), c_Orderings_Otop__class_Otop(tc_fun(_1485835, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1485833, _1485835), tc_HOL_Obool)))], (18311 ^ _775212) ^ [_1086186, _1086188] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1086186)), c_Int_OBit1(_1086188)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1086186), _1086188)))], (27563 ^ _775212) ^ [_1261497, _1261499, _1261501] : [class_Orderings_Olinorder(_1261497), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261497), _1261499), _1261501)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261497, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1261497, _1261499, _1261501)), hAPP(c_SetInterval_Oord__class_OatLeast(_1261497), _1261501)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1261497), _1261499))], (18129 ^ _775212) ^ [_1083057, _1083059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1083057)), c_Int_OBit0(_1083059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083057), _1083059)))], (4424 ^ _775212) ^ [_842482, _842484, _842486, _842488, _842490, _842492] : [-(c_List_Oremove1(_842492, _842488, _842484) = c_List_Oremove1(_842490, _842486, _842482)), _842492 = _842490, _842488 = _842486, _842484 = _842482], (43394 ^ _775212) ^ [_1622654, _1622656, _1622658] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1622654, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1622654, tc_HOL_Obool), _1622656)), _1622658) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1622654, tc_HOL_Obool), tc_fun(_1622654, tc_HOL_Obool)), _1622656), hAPP(hAPP(c_COMBC(tc_fun(_1622654, tc_HOL_Obool), tc_fun(_1622654, tc_HOL_Obool), tc_fun(_1622654, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1622654, tc_HOL_Obool))), _1622658)))], (30562 ^ _775212) ^ [_1325980, _1325982, _1325984, _1325986, _1325988] : [class_Groups_Ocomm__monoid__add(_1325980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325982), _1325984)), hBOOL(hAPP(hAPP(c_member(_1325982), _1325986), _1325984)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1325982, _1325980), _1325988), _1325984) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325980), hAPP(_1325988, _1325986)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1325982, _1325980), _1325988), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325982, tc_HOL_Obool)), _1325984), hAPP(hAPP(c_Set_Oinsert(_1325982), _1325986), c_Orderings_Obot__class_Obot(tc_fun(_1325982, tc_HOL_Obool)))))))], (6525 ^ _775212) ^ [_878582, _878584, _878586] : [_878584 = _878586, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878582), _878584) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878582), _878586))], (34475 ^ _775212) ^ [_1407651, _1407653] : [class_Lattices_Obounded__lattice__bot(_1407651), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1407651), _1407653), c_Orderings_Obot__class_Obot(_1407651)) = c_Orderings_Obot__class_Obot(_1407651))], (48504 ^ _775212) ^ [_1746216, _1746218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1746216)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1746218))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1746216), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1746218)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1746216)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1746216)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1746218))))], (9147 ^ _775212) ^ [_923324, _923326, _923328] : [class_Rings_Olinordered__semidom(_923324), 9150 ^ _775212 : [(9157 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _923326), _923328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923324), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_923324), _923326)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_923324), _923328))))], (9151 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923324), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_923324), _923326)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_923324), _923328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _923326), _923328)))]]], (52407 ^ _775212) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (35279 ^ _775212) ^ [_1425465, _1425467, _1425469, _1425471] : [class_Orderings_Olinorder(_1425465), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425465, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1425465, _1425467, _1425469)), hAPP(c_SetInterval_Oord__class_OatLeast(_1425465), _1425471)) = c_SetInterval_Oord__class_OatLeastAtMost(_1425465, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1425465), _1425467), _1425471), _1425469))], (42441 ^ _775212) ^ [_1598339, _1598341, _1598343, _1598345, _1598347] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598339, tc_fun(_1598341, tc_HOL_Obool)), _1598343), hAPP(hAPP(c_COMBB(tc_fun(_1598341, tc_HOL_Obool), tc_fun(_1598341, tc_HOL_Obool), _1598339), hAPP(c_Set_Oinsert(_1598341), _1598345)), _1598347)) = hAPP(hAPP(c_Set_Oinsert(_1598341), _1598345), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598339, tc_fun(_1598341, tc_HOL_Obool)), _1598343), _1598347)))], (49865 ^ _775212) ^ [_1773859, _1773861, _1773863, _1773865, _1773867] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773859, _1773859)), hAPP(hAPP(c_Product__Type_OPair(_1773859, _1773859), _1773861), _1773863)), c_List_Omeasures(_1773859, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1773859, tc_Nat_Onat)), _1773865), _1773867)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1773865, _1773861)), hAPP(_1773865, _1773863)))), 49872 ^ _775212 : [(49875 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773859, _1773859)), hAPP(hAPP(c_Product__Type_OPair(_1773859, _1773859), _1773861), _1773863)), c_List_Omeasures(_1773859, _1773867))))], (49873 ^ _775212) ^ [] : [-(hAPP(_1773865, _1773861) = hAPP(_1773865, _1773863))]]], (50480 ^ _775212) ^ [_1787645, _1787647, _1787649] : [50482 ^ _775212 : [(50485 ^ _775212) ^ [] : [hBOOL(hAPP(_1787649, 50481 ^ [_1787645, _1787647, _1787649]))], (50483 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1787645), 50481 ^ [_1787645, _1787647, _1787649]), hAPP(c_List_Oset(_1787645), _1787647))))]], -(c_List_Olist__all(_1787645, _1787649, _1787647))], (30763 ^ _775212) ^ [_1330476, _1330478, _1330480, _1330482, _1330484, _1330486, _1330488] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1330476, tc_fun(_1330478, tc_fun(_1330480, tc_HOL_Obool))), _1330482), _1330484), _1330486), _1330488)), 30767 ^ _775212 : [(30770 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1330484, 30766 ^ [_1330476, _1330478, _1330480, _1330482, _1330484, _1330486, _1330488]), _1330486), _1330488)))], (30768 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1330476), 30766 ^ [_1330476, _1330478, _1330480, _1330482, _1330484, _1330486, _1330488]), _1330482)))]]], (28351 ^ _775212) ^ [_1277972, _1277974, _1277976] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1277972), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277972, tc_HOL_Obool)), _1277974), _1277976))), 28354 ^ _775212 : [(28357 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1277972), _1277976)))], (28355 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1277972), _1277974)))]]], (29586 ^ _775212) ^ [_1302184, _1302186] : [-(_1302186 = c_Orderings_Obot__class_Obot(tc_fun(_1302184, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1302184), 29589 ^ [_1302184, _1302186]), _1302186)))], (22282 ^ _775212) ^ [_1158675, _1158677, _1158679, _1158681, _1158683] : [-(c_Nat_Onat_Onat__case(_1158675, _1158677, _1158679, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158681)), _1158683)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1158675), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1158681))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1158675, _1158675), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1158675, tc_fun(_1158675, _1158675)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1158675, tc_fun(_1158675, _1158675)), tc_Int_Oint), c_If(_1158675)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1158675, _1158677, _1158679, _1158683))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1158675, tc_Int_Oint), _1158679), 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)), _1158683)))))], (34411 ^ _775212) ^ [_1406353, _1406355, _1406357, _1406359] : [hBOOL(hAPP(hAPP(c_member(_1406353), _1406355), _1406357)), hBOOL(hAPP(hAPP(c_member(_1406353), _1406355), _1406359)), -(hBOOL(hAPP(hAPP(c_member(_1406353), _1406355), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406353, tc_HOL_Obool)), _1406357), _1406359))))], (41458 ^ _775212) ^ [_1574462, _1574464, _1574466] : [class_Orderings_Olinorder(_1574462), hBOOL(hAPP(c_Finite__Set_Ofinite(_1574462), _1574464)), -(c_Big__Operators_Olattice_OSup__fin(_1574462, c_Orderings_Oord__class_Omax(_1574462), hAPP(hAPP(c_Set_Oinsert(_1574462), _1574466), _1574464)) = hAPP(hAPP(c_Finite__Set_Ofold(_1574462, _1574462, c_Orderings_Oord__class_Omax(_1574462)), _1574466), _1574464))], (17459 ^ _775212) ^ [_1071693, _1071695] : [17460 ^ _775212 : [(17463 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071693), c_Int_OPls))], (17461 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071693), _1071695))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071693)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071695))))], (15113 ^ _775212) ^ [_1028898, _1028900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028898), _1028900)), -(c_Nat__Transfer_Otsub(_1028900, _1028898) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1028900), _1028898))], (51671 ^ _775212) ^ [_1813929, _1813931] : [c_Relation_Oantisym(_1813929, _1813931), 51674 ^ _775212 : [(51675 ^ _775212) ^ [_1814041, _1814043] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1813929, _1813929)), hAPP(hAPP(c_Product__Type_OPair(_1813929, _1813929), _1814043), _1814041)), _1813931)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1813929, _1813929)), hAPP(hAPP(c_Product__Type_OPair(_1813929, _1813929), _1814041), _1814043)), _1813931)), -(_1814043 = _1814041)]]], (27169 ^ _775212) ^ [_1253878, _1253880, _1253882, _1253884] : [class_Lattices_Osemilattice__sup(_1253878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253878), _1253880), _1253882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253878), _1253884), _1253882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253878), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1253878), _1253880), _1253884)), _1253882)))], (21831 ^ _775212) ^ [_1149562, _1149564, _1149566] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1149562), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1149564)), _1149566)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1149562, _1149564), hAPP(c_Divides_OnegateSnd, _1149566))))], (44742 ^ _775212) ^ [_1658767, _1658769, _1658771, _1658773] : [hBOOL(hAPP(hAPP(c_member(_1658767), _1658769), hAPP(c_List_Oset(_1658767), hAPP(hAPP(c_List_Otake(_1658767), _1658771), _1658773)))), -(hBOOL(hAPP(hAPP(c_member(_1658767), _1658769), hAPP(c_List_Oset(_1658767), _1658773))))], (51579 ^ _775212) ^ [_1812254, _1812256] : [c_Equiv__Relations_Oequivp(_1812254, _1812256), 51582 ^ _775212 : [(51587 ^ _775212) ^ [] : [-(c_Predicate_Otransp(_1812254, _1812256))], (51585 ^ _775212) ^ [] : [-(c_Predicate_Osymp(_1812254, _1812256))], (51583 ^ _775212) ^ [] : [-(c_Predicate_Oreflp(_1812254, _1812256))]]], (14931 ^ _775212) ^ [_1025381, _1025383] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025381), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025381), _1025383)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52671 ^ _775212) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (6905 ^ _775212) ^ [_885165, _885167] : [6906 ^ _775212 : [(6909 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _885167))], (6907 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _885165))]], -(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), _885165), _885167))))], (43374 ^ _775212) ^ [_1622152, _1622154, _1622156, _1622158] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1622152, tc_HOL_Obool)), _1622154), _1622156)), hBOOL(hAPP(hAPP(c_member(_1622152), _1622158), _1622154)), -(hBOOL(hAPP(hAPP(c_member(_1622152), _1622158), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1622152, tc_HOL_Obool), _1622156))))], (13328 ^ _775212) ^ [_996398, _996400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996398), _996400)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _996398), _996400) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23814 ^ _775212) ^ [_1189098, _1189100] : [-(c_Code__Numeral_Onat__of__aux(_1189098, _1189100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1189098)), _1189100))], (33807 ^ _775212) ^ [_1392161, _1392163, _1392165] : [hBOOL(hAPP(c_Predicate_OPowp(_1392161, hAPP(hAPP(c_COMBC(_1392161, tc_fun(_1392161, tc_HOL_Obool), tc_HOL_Obool), c_member(_1392161)), _1392163)), _1392165)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1392161, tc_HOL_Obool)), _1392165), hAPP(c_Set_OPow(_1392161), _1392163))))], (42996 ^ _775212) ^ [_1613204, _1613206, _1613208, _1613210] : [-(hAPP(_1613204, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1613206, _1613206), _1613208), _1613204), _1613210)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1613206, _1613206), _1613208), _1613204), hAPP(_1613204, _1613210)))], (21301 ^ _775212) ^ [_1140103] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1140103) = 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)))], (46849 ^ _775212) ^ [_1709073, _1709075] : [class_Complete__Lattice_Ocomplete__lattice(_1709073), -(c_Complete__Lattice_OSup__class_OSup(_1709073, hAPP(c_List_Oset(_1709073), _1709075)) = hAPP(c_List_Ofoldl(_1709073, _1709073, c_Lattices_Osemilattice__sup__class_Osup(_1709073), c_Orderings_Obot__class_Obot(_1709073)), _1709075))], (40266 ^ _775212) ^ [_1548294, _1548296, _1548298, _1548300] : [40268 ^ _775212 : [(40271 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1548294, _1548294, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1548294, tc_fun(_1548294, _1548296), tc_fun(_1548294, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548296, tc_HOL_Obool), tc_fun(tc_fun(_1548294, _1548296), tc_fun(_1548294, tc_HOL_Obool)), _1548294), c_COMBB(_1548296, tc_HOL_Obool, _1548294)), hAPP(hAPP(c_COMBB(_1548296, tc_fun(_1548296, tc_HOL_Obool), _1548294), c_fequal), _1548300))), _1548300)), 40267 ^ [_1548294, _1548296, _1548298, _1548300]))], (40269 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548294, _1548294)), 40267 ^ [_1548294, _1548296, _1548298, _1548300]), _1548298)))]], -(c_Equiv__Relations_Ocongruent(_1548294, _1548296, _1548298, _1548300))], (9839 ^ _775212) ^ [_934403, _934405, _934407] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _934403), _934405)), _934407) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _934403), _934407)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _934405), _934407)))], (47188 ^ _775212) ^ [_1715954, _1715956] : [-(_1715954 = c_List_Olist_ONil(_1715956)), -(hAPP(hAPP(c_List_Oappend(_1715956), c_List_Obutlast(_1715956, _1715954)), hAPP(hAPP(c_List_Olist_OCons(_1715956), c_List_Olast(_1715956, _1715954)), c_List_Olist_ONil(_1715956))) = _1715954)], (18233 ^ _775212) ^ [_1084798, _1084800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1084798)), c_Int_OBit1(_1084800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084798), _1084800)))], (28650 ^ _775212) ^ [_1284035, _1284037] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284035, tc_HOL_Obool)), _1284037), c_Orderings_Obot__class_Obot(tc_fun(_1284035, tc_HOL_Obool))) = _1284037)], (942 ^ _775212) ^ [_789569, _789571, _789573, _789575, _789577, _789579] : [-(c_Equiv__Relations_Oequiv(_789577, _789573, _789569)), c_Equiv__Relations_Oequiv(_789579, _789575, _789571), _789579 = _789577, _789575 = _789573, _789571 = _789569], (52507 ^ _775212) ^ [_1826352] : [-(class_Nat_Osize(tc_List_Olist(_1826352)))], (40852 ^ _775212) ^ [_1561530, _1561532, _1561534, _1561536, _1561538, _1561540, _1561542, _1561544] : [c_Finite__Set_Ofolding__image(_1561530, _1561532, _1561534, _1561536, _1561538), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561532), _1561540)), -(hAPP(hAPP(_1561538, hAPP(hAPP(c_COMBS(_1561532, _1561530, _1561530), hAPP(hAPP(c_COMBB(_1561530, tc_fun(_1561530, _1561530), _1561532), _1561534), _1561542)), _1561544)), _1561540) = hAPP(hAPP(_1561534, hAPP(hAPP(_1561538, _1561542), _1561540)), hAPP(hAPP(_1561538, _1561544), _1561540)))], (21385 ^ _775212) ^ [_1141567, _1141569, _1141571] : [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), _1141567), _1141569))), -(hBOOL(hAPP(hAPP(_1141571, _1141567), _1141569))), 21392 ^ _775212 : [(21395 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1141571, 21390 ^ [_1141567, _1141569, _1141571]), 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)))), 21391 ^ [_1141567, _1141569, _1141571])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 21390 ^ [_1141567, _1141569, _1141571]), 21391 ^ [_1141567, _1141569, _1141571]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 21391 ^ [_1141567, _1141569, _1141571]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21405 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1141571, 21390 ^ [_1141567, _1141569, _1141571]), 21391 ^ [_1141567, _1141569, _1141571]))], (21393 ^ _775212) ^ [] : [-(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), 21390 ^ [_1141567, _1141569, _1141571]), 21391 ^ [_1141567, _1141569, _1141571]))))]]], (36869 ^ _775212) ^ [_1460188, _1460190, _1460192, _1460194, _1460196, _1460198] : [c_Fun_Oinj__on(_1460188, _1460190, _1460192, _1460194), -(hBOOL(hAPP(hAPP(c_member(_1460190), _1460196), hAPP(c_Set_Oimage(_1460188, _1460190, _1460192), _1460194)))), -(c_Fun_Oinj__on(_1460188, _1460190, c_Fun_Ofun__upd(_1460188, _1460190, _1460192, _1460198, _1460196), _1460194))], (44132 ^ _775212) ^ [_1640170] : [class_Nat_Osize(_1640170), -(c_FunDef_Ois__measure(_1640170, c_Nat_Osize__class_Osize(_1640170)))], (25160 ^ _775212) ^ [_1212976, _1212978] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212976), _1212978)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212978), _1212976)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1212976) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1212978))], (21787 ^ _775212) ^ [_1148667, _1148669, _1148671, _1148673, _1148675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1148667, tc_HOL_Obool)), _1148669), _1148671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1148667, tc_HOL_Obool)), _1148673), _1148675)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1148667, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1148667, tc_HOL_Obool)), _1148669), _1148675)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1148667, tc_HOL_Obool)), _1148671), _1148673))))], (16919 ^ _775212) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (584 ^ _775212) ^ [_784188, _784190, _784192, _784194, _784196, _784198] : [-(c_Relation_Osingle__valued(_784196, _784192, _784188)), c_Relation_Osingle__valued(_784198, _784194, _784190), _784198 = _784196, _784194 = _784192, _784190 = _784188], (19679 ^ _775212) ^ [_1110300, _1110302, _1110304] : [class_Fields_Olinordered__field(_1110300), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110300), c_Groups_Ozero__class_Ozero(_1110300)), _1110302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110300), c_Groups_Ozero__class_Ozero(_1110300)), _1110304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110300), c_Groups_Ozero__class_Ozero(_1110300)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110300), _1110302), _1110304))))], (9519 ^ _775212) ^ [_928945, _928947, _928949] : [class_Orderings_Oorder(_928945), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928945), _928947), _928949)), -(_928949 = _928947), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928945), _928947), _928949)))], (34002 ^ _775212) ^ [_1396292, _1396294, _1396296, _1396298, _1396300] : [-(hAPP(c_Relation_OImage(_1396292, _1396294, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1396292, _1396294), tc_HOL_Obool)), _1396296), _1396298)), _1396300) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1396294, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1396292, _1396294, _1396296), _1396300)), hAPP(c_Relation_OImage(_1396292, _1396294, _1396298), _1396300)))], (48540 ^ _775212) ^ [_1746862, _1746864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746862), _1746864)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1746862, _1746864)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1746864), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (20853 ^ _775212) ^ [_1131898, _1131900] : [-(c_Divides_OnegDivAlg(_1131898, _1131900) = hAPP(c_Divides_Oadjust(_1131900), c_Divides_OnegDivAlg(_1131898, 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)))), _1131900)))), -(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), _1131898), _1131900)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131900), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37717 ^ _775212) ^ [_1479263, _1479265, _1479267, _1479269] : [c_Wellfounded_Omax__extp(_1479263, _1479265, _1479267, _1479269), 37720 ^ _775212 : [(37723 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1479263), _1479269)))], (37725 ^ _775212) ^ [] : [_1479269 = c_Orderings_Obot__class_Obot(tc_fun(_1479263, tc_HOL_Obool))], (37727 ^ _775212) ^ [_1479479] : [hBOOL(hAPP(hAPP(c_member(_1479263), _1479479), _1479267)), 37731 ^ _775212 : [(37734 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1479265, _1479479), 37730 ^ [_1479263, _1479265, _1479267, _1479269, _1479479])))], (37732 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1479263), 37730 ^ [_1479263, _1479265, _1479267, _1479269, _1479479]), _1479269)))]]], (37721 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1479263), _1479267)))]]], (8729 ^ _775212) ^ [_916818, _916820] : [_916818 = _916820, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _916818) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _916820))], (29314 ^ _775212) ^ [_1296537, _1296539, _1296541] : [class_Orderings_Olinorder(_1296537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296537), _1296539), _1296541)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296537, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1296537, _1296539), _1296541)), hAPP(hAPP(c_Set_Oinsert(_1296537), _1296541), c_Orderings_Obot__class_Obot(tc_fun(_1296537, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1296537, _1296539, _1296541))], (6098 ^ _775212) ^ [_871883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871883), _871883))], (6395 ^ _775212) ^ [_876432, _876434] : [class_Orderings_Opreorder(_876432), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876432), _876434), _876434))], (27816 ^ _775212) ^ [_1267528, _1267530, _1267532, _1267534, _1267536, _1267538] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267528, tc_fun(_1267530, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1267532, _1267528, _1267534), _1267536)), _1267538) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267532, tc_fun(_1267530, tc_HOL_Obool)), _1267536), hAPP(hAPP(c_COMBB(_1267528, tc_fun(_1267530, tc_HOL_Obool), _1267532), _1267538), _1267534)))], (39424 ^ _775212) ^ [_1525713, _1525715] : [-(hAPP(c_Set_Ovimage(_1525713, _1525713, c_Fun_Oid(_1525713)), _1525715) = _1525715)], (39478 ^ _775212) ^ [_1527225, _1527227, _1527229, _1527231, _1527233, _1527235, _1527237, _1527239] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1527225, _1527227)), hAPP(hAPP(c_Product__Type_OPair(_1527225, _1527227), _1527229), _1527231)), _1527233)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1527227, _1527235)), hAPP(hAPP(c_Product__Type_OPair(_1527227, _1527235), _1527231), _1527237)), _1527239)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1527225, _1527235)), hAPP(hAPP(c_Product__Type_OPair(_1527225, _1527235), _1527229), _1527237)), hAPP(hAPP(c_Relation_Orel__comp(_1527225, _1527227, _1527235), _1527233), _1527239))))], (24254 ^ _775212) ^ [_1196327, _1196329] : [_1196327 = _1196329, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196327), _1196329)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196329), _1196327)))], (1048 ^ _775212) ^ [_791072, _791074, _791076, _791078] : [-(c_Equiv__Relations_Opart__equivp(_791076, _791072)), c_Equiv__Relations_Opart__equivp(_791078, _791074), _791078 = _791076, _791074 = _791072], (48430 ^ _775212) ^ [_1744935, _1744937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1744935), _1744937)), -(c_List_Oupt(_1744935, hAPP(c_Nat_OSuc, _1744937)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1744935, _1744937)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1744937), c_List_Olist_ONil(tc_Nat_Onat))))], (49177 ^ _775212) ^ [_1759163, _1759165, _1759167, _1759169] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759163)), _1759165) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759167)), _1759169), -(hAPP(hAPP(c_List_Ozip(_1759163, _1759167), hAPP(c_List_Orev(_1759163), _1759165)), hAPP(c_List_Orev(_1759167), _1759169)) = hAPP(c_List_Orev(tc_prod(_1759163, _1759167)), hAPP(hAPP(c_List_Ozip(_1759163, _1759167), _1759165), _1759169)))], (16177 ^ _775212) ^ [_1049350, _1049352, _1049354] : [class_Groups_Oordered__ab__group__add__abs(_1049350), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049350), hAPP(c_Groups_Oabs__class_Oabs(_1049350), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049350), hAPP(c_Groups_Oabs__class_Oabs(_1049350), _1049352)), hAPP(c_Groups_Oabs__class_Oabs(_1049350), _1049354)))), hAPP(c_Groups_Oabs__class_Oabs(_1049350), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049350), _1049352), _1049354)))))], (7489 ^ _775212) ^ [_894668, _894670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894668), _894670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894668)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894670))))], (6627 ^ _775212) ^ [_880386, _880388, _880390, _880392] : [class_Groups_Oordered__cancel__ab__semigroup__add(_880386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880386), _880388), _880390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880386), _880388), _880392)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880386), _880390), _880392))))], (42175 ^ _775212) ^ [_1590464, _1590466, _1590468, _1590470] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1590468), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590464, tc_fun(_1590468, tc_HOL_Obool)), _1590466), _1590470)))), 42176 ^ _775212 : [(42177 ^ _775212) ^ [_1590538] : [hBOOL(hAPP(hAPP(c_member(_1590464), _1590538), _1590466)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590468), hAPP(_1590470, _1590538)))]]], (14907 ^ _775212) ^ [_1024964, _1024966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024964)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1024966), _1024964)), _1024966)))], (10609 ^ _775212) ^ [_948300, _948302, _948304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948300), _948302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _948304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948304), _948300)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948304), _948302))))], (34557 ^ _775212) ^ [_1409895, _1409897, _1409899, _1409901] : [hBOOL(hAPP(hAPP(c_member(_1409895), _1409897), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409895, tc_HOL_Obool)), _1409899), _1409901))), -(hBOOL(hAPP(hAPP(c_member(_1409895), _1409897), _1409899)))], (6190 ^ _775212) ^ [_873006, _873008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _873006), _873008)), -(hAPP(c_Nat_OSuc, _873006) = _873008), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _873006)), _873008)))], (27063 ^ _775212) ^ [_1251702, _1251704, _1251706] : [class_Lattices_Osemilattice__sup(_1251702), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251702), _1251704), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251702), _1251704), _1251706)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251702), _1251704), _1251706))], (24190 ^ _775212) ^ [_1195278, _1195280, _1195282] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195278), _1195280)), 24201 ^ _775212 : [(24204 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195282), _1195278))], (24202 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195278), _1195282)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195280), _1195282)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195282), _1195280)))], (10914 ^ _775212) ^ [_953641, _953643, _953645] : [class_Groups_Oordered__comm__monoid__add(_953641), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953641), _953643), c_Groups_Ozero__class_Ozero(_953641))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953641), _953645), c_Groups_Ozero__class_Ozero(_953641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953641), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953641), _953643), _953645)), c_Groups_Ozero__class_Ozero(_953641))))], (44009 ^ _775212) ^ [_1637379, _1637381, _1637383] : [hBOOL(hAPP(hAPP(c_member(_1637379), _1637381), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1637379, tc_HOL_Obool), _1637383))), 44013 ^ _775212 : [(44016 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1637379, tc_HOL_Obool)), 44012 ^ [_1637379, _1637381, _1637383]), _1637383)))], (44014 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1637379), _1637381), 44012 ^ [_1637379, _1637381, _1637383])))]]], (50729 ^ _775212) ^ [_1792523, _1792525, _1792527] : [-(_1792523 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1792525, c_List_Oreplicate(_1792525, _1792523, _1792527)) = _1792527)], (52457 ^ _775212) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (44 ^ _775212) ^ [_775790, _775792] : [-(class_Rings_Odivision__ring(_775790)), _775792 = _775790, class_Rings_Odivision__ring(_775792)], (13346 ^ _775212) ^ [_996691, _996693] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _996691, _996693)) = _996693, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _996691), _996693) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51685 ^ _775212) ^ [_1814254, _1814256] : [51688 ^ _775212 : [(51693 ^ _775212) ^ [] : [51686 ^ [_1814254, _1814256] = 51687 ^ [_1814254, _1814256]], (51691 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1814254, _1814254)), hAPP(hAPP(c_Product__Type_OPair(_1814254, _1814254), 51687 ^ [_1814254, _1814256]), 51686 ^ [_1814254, _1814256])), _1814256)))], (51689 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1814254, _1814254)), hAPP(hAPP(c_Product__Type_OPair(_1814254, _1814254), 51686 ^ [_1814254, _1814256]), 51687 ^ [_1814254, _1814256])), _1814256)))]], -(c_Relation_Oantisym(_1814254, _1814256))], (23232 ^ _775212) ^ [_1177849, _1177851, _1177853, _1177855, _1177857] : [-(hAPP(c_Product__Type_Ofst(_1177849, _1177851), hAPP(c_Product__Type_Oapfst(_1177853, _1177849, _1177851, _1177855), _1177857)) = hAPP(_1177855, hAPP(c_Product__Type_Ofst(_1177853, _1177851), _1177857)))], (15551 ^ _775212) ^ [_1038170, _1038172] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038170, _1038172) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038170, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1038172)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6036 ^ _775212) ^ [_870917, _870919] : [hBOOL(hAPP(_870917, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 6042 ^ _775212 : [(6045 ^ _775212) ^ [] : [hBOOL(hAPP(_870917, hAPP(c_Nat_OSuc, 6041 ^ [_870917, _870919])))], (6043 ^ _775212) ^ [] : [-(hBOOL(hAPP(_870917, 6041 ^ [_870917, _870919])))]], -(hBOOL(hAPP(_870917, _870919)))], (26497 ^ _775212) ^ [_1240832, _1240834] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1240832, _1240834)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1240832), hAPP(c_Nat_OSuc, _1240834)))], (22512 ^ _775212) ^ [_1163817, _1163819, _1163821] : [class_Orderings_Olinorder(_1163817), 22515 ^ _775212 : [(22522 ^ _775212) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1163817), _1163819), _1163821) = _1163819, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163817), _1163819), _1163821)))], (22516 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163817), _1163819), _1163821)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1163817), _1163819), _1163821) = _1163819)]]], (18529 ^ _775212) ^ [_1089981, _1089983] : [class_Rings_Ocomm__semiring__1(_1089981), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089981), _1089983), _1089983) = hAPP(hAPP(c_Power_Opower__class_Opower(_1089981), _1089983), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (48095 ^ _775212) ^ [_1735664, _1735666, _1735668] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1735664), tc_List_Olist(_1735664), c_List_Oappend(_1735664), _1735666), _1735668) = hAPP(hAPP(c_List_Oappend(_1735664), _1735666), c_List_Oconcat(_1735664, _1735668)))], (7445 ^ _775212) ^ [_893807, _893809, _893811, _893813] : [class_Rings_Ocomm__semiring__1(_893807), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893807), _893809), _893811)), _893813) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893807), _893809), _893813)), _893811))], (51171 ^ _775212) ^ [_1802537, _1802539] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1802537, _1802539), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1802537)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28553 ^ _775212) ^ [_1282040, _1282042, _1282044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1282040), _1282042)), -(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)), _1282040)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1282044), _1282042)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1282044), _1282040)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1282042), _1282040)))], (1844 ^ _775212) ^ [_801118, _801120] : [-(class_Groups_Ominus(_801118)), _801120 = _801118, class_Groups_Ominus(_801120)], (25198 ^ _775212) ^ [_1213551, _1213553, _1213555] : [-(_1213551 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25201 ^ _775212 : [(25208 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1213551), _1213553)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1213551), _1213555))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1213553), _1213555)))], (25202 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1213553), _1213555)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1213551), _1213553)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1213551), _1213555))))]]], (31407 ^ _775212) ^ [_1343530, _1343532] : [31408 ^ _775212 : [(31411 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343532), _1343530))], (31409 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343530), _1343532)))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1343530, _1343532) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (47076 ^ _775212) ^ [_1713578, _1713580, _1713582, _1713584] : [47078 ^ _775212 : [(47081 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1713582, 47077 ^ [_1713578, _1713580, _1713582, _1713584])), hAPP(_1713584, 47077 ^ [_1713578, _1713580, _1713582, _1713584])))], (47079 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1713578), 47077 ^ [_1713578, _1713580, _1713582, _1713584]), hAPP(c_List_Oset(_1713578), _1713580))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1713578, _1713582, _1713580)), c_List_Olist_Olist__size(_1713578, _1713584, _1713580))))], (49822 ^ _775212) ^ [_1772591, _1772593, _1772595, _1772597, _1772599] : [-(c_List_Omaps(_1772591, _1772593, _1772595, hAPP(hAPP(c_List_Olist_OCons(_1772591), _1772597), _1772599)) = hAPP(hAPP(c_List_Oappend(_1772593), hAPP(_1772595, _1772597)), c_List_Omaps(_1772591, _1772593, _1772595, _1772599)))], (32812 ^ _775212) ^ [_1370344, _1370346, _1370348] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1370344), _1370346), _1370348) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1370344), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1370344, tc_Int_Oint), _1370346), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1370348))), class_Groups_Ocomm__monoid__add(_1370344), class_Groups_Ocomm__monoid__mult(_1370344)], (39468 ^ _775212) ^ [_1526566, _1526568] : [39469 ^ _775212 : [(39470 ^ _775212) ^ [_1526630, _1526632] : [_1526568 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1526566, _1526630), 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)), _1526632)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1526566), _1526568)))], (52101 ^ _775212) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (30807 ^ _775212) ^ [_1331530, _1331532] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1331530), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1331532))), 30810 ^ _775212 : [(30813 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1331530), _1331532))], (30811 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1331532), _1331530)))]]], (49930 ^ _775212) ^ [_1775521, _1775523] : [class_Enum_Oenum(_1775521), 49933 ^ _775212 : [(49941 ^ _775212) ^ [] : [49942 ^ _775212 : [(49943 ^ _775212) ^ [_1775701] : [hBOOL(hAPP(_1775523, _1775701))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1775521), _1775523)))], (49934 ^ _775212) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1775521), _1775523)), -(hBOOL(hAPP(_1775523, 49937 ^ [_1775521, _1775523])))]]], (52497 ^ _775212) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (21821 ^ _775212) ^ [_1149375, _1149377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1149375), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1149377), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1149375, _1149377) = 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), _1149375), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1149377)))))], (43134 ^ _775212) ^ [_1616872, _1616874] : [-(c_Transitive__Closure_Ortrancl(_1616872, _1616874) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1616872, _1616872), 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(_1616872, _1616872), tc_HOL_Obool), tc_fun(tc_prod(_1616872, _1616872), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1616872, _1616872), tc_HOL_Obool)), _1616874)))], (45248 ^ _775212) ^ [_1671424, _1671426, _1671428, _1671430, _1671432, _1671434, _1671436, _1671438] : [-(hAPP(hAPP(c_List_Ozip(_1671424, _1671426), hAPP(hAPP(c_List_Omap(_1671428, _1671424), _1671430), _1671432)), hAPP(hAPP(c_List_Omap(_1671434, _1671426), _1671436), _1671438)) = hAPP(hAPP(c_List_Omap(tc_prod(_1671428, _1671434), tc_prod(_1671424, _1671426)), hAPP(c_Product__Type_Oprod_Oprod__case(_1671428, _1671434, tc_prod(_1671424, _1671426)), hAPP(hAPP(c_COMBC(_1671428, tc_fun(_1671434, _1671426), tc_fun(_1671434, tc_prod(_1671424, _1671426))), hAPP(hAPP(c_COMBB(tc_fun(_1671426, tc_prod(_1671424, _1671426)), tc_fun(tc_fun(_1671434, _1671426), tc_fun(_1671434, tc_prod(_1671424, _1671426))), _1671428), c_COMBB(_1671426, tc_prod(_1671424, _1671426), _1671434)), hAPP(hAPP(c_COMBB(_1671424, tc_fun(_1671426, tc_prod(_1671424, _1671426)), _1671428), c_Product__Type_OPair(_1671424, _1671426)), _1671430))), _1671436))), hAPP(hAPP(c_List_Ozip(_1671428, _1671434), _1671432), _1671438)))], (7647 ^ _775212) ^ [_897639, _897641] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _897639)), _897641) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _897639), _897641)))], (51240 ^ _775212) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (37858 ^ _775212) ^ [_1482905, _1482907, _1482909, _1482911, _1482913] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1482905, _1482907), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1482905, tc_HOL_Obool)), _1482909), _1482911)), hAPP(c_COMBK(tc_fun(_1482907, tc_HOL_Obool), _1482905), _1482913)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1482905, _1482907), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1482905, _1482907), _1482909), hAPP(c_COMBK(tc_fun(_1482907, tc_HOL_Obool), _1482905), _1482913))), hAPP(hAPP(c_Product__Type_OSigma(_1482905, _1482907), _1482911), hAPP(c_COMBK(tc_fun(_1482907, tc_HOL_Obool), _1482905), _1482913))))], (26415 ^ _775212) ^ [_1239186, _1239188] : [c_Nat__Transfer_Ois__nat(_1239186), c_Nat__Transfer_Ois__nat(_1239188), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1239186, _1239188) = 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, _1239186), hAPP(c_Int_Onat, _1239188))))], (49786 ^ _775212) ^ [_1771945, _1771947, _1771949] : [hBOOL(hAPP(hAPP(c_member(_1771945), _1771947), hAPP(c_List_Oset(_1771945), _1771949))), -(c_List_Oinsert(_1771945, _1771947, _1771949) = _1771949)], (11867 ^ _775212) ^ [_970021, _970023, _970025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970021), _970023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970021), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970025), _970023))))], (24264 ^ _775212) ^ [_1196480, _1196482] : [_1196482 = _1196480, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196480), _1196482)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196482), _1196480)))], (39414 ^ _775212) ^ [_1525550, _1525552] : [-(c_Product__Type_Oapsnd(_1525550, _1525550, _1525552, c_Fun_Oid(_1525550)) = c_Fun_Oid(tc_prod(_1525552, _1525550)))], (36713 ^ _775212) ^ [_1456940, _1456942, _1456944, _1456946] : [-(_1456940 = c_Orderings_Obot__class_Obot(tc_fun(_1456942, tc_HOL_Obool))), 36716 ^ _775212 : [(36717 ^ _775212) ^ [] : [-(hAPP(c_Set_Oimage(_1456944, _1456942, 36724 ^ [_1456940, _1456942, _1456944, _1456946]), _1456946) = _1456940), 36718 ^ _775212 : [(36719 ^ _775212) ^ [_1457081] : [c_Fun_Oinj__on(_1456942, _1456944, _1457081, _1456940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456944, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1456942, _1456944, _1457081), _1456940)), _1456946))]]], (36728 ^ _775212) ^ [] : [36729 ^ _775212 : [(36730 ^ _775212) ^ [_1457273] : [hAPP(c_Set_Oimage(_1456944, _1456942, _1457273), _1456946) = _1456940]], 36732 ^ _775212 : [(36735 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456944, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1456942, _1456944, 36731 ^ [_1456940, _1456942, _1456944, _1456946]), _1456940)), _1456946)))], (36733 ^ _775212) ^ [] : [-(c_Fun_Oinj__on(_1456942, _1456944, 36731 ^ [_1456940, _1456942, _1456944, _1456946], _1456940))]]]]], (33447 ^ _775212) ^ [] : [-(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)))], (29368 ^ _775212) ^ [_1297725, _1297727] : [-(c_Set_Othe__elem(_1297725, hAPP(hAPP(c_Set_Oinsert(_1297725), _1297727), c_Orderings_Obot__class_Obot(tc_fun(_1297725, tc_HOL_Obool)))) = _1297727)], (42325 ^ _775212) ^ [_1594768, _1594770, _1594772, _1594774] : [42327 ^ _775212 : [(42330 ^ _775212) ^ [] : [hAPP(_1594774, 42326 ^ [_1594768, _1594770, _1594772, _1594774]) = c_Orderings_Otop__class_Otop(tc_fun(_1594770, tc_HOL_Obool))], (42328 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1594768), 42326 ^ [_1594768, _1594770, _1594772, _1594774]), _1594772)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594768, tc_fun(_1594770, tc_HOL_Obool)), _1594772), _1594774) = c_Orderings_Otop__class_Otop(tc_fun(_1594770, tc_HOL_Obool)))], (42913 ^ _775212) ^ [_1611139, _1611141, _1611143] : [c_Relation_Osingle__valued(_1611139, _1611141, _1611143), 42916 ^ _775212 : [(42917 ^ _775212) ^ [_1611260, _1611262] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611139, _1611141)), hAPP(hAPP(c_Product__Type_OPair(_1611139, _1611141), _1611262), _1611260)), _1611143)), 42920 ^ _775212 : [(42921 ^ _775212) ^ [_1611386] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611139, _1611141)), hAPP(hAPP(c_Product__Type_OPair(_1611139, _1611141), _1611262), _1611386)), _1611143)), -(_1611260 = _1611386)]]]]], (14499 ^ _775212) ^ [_1017425, _1017427, _1017429] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017425), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1017427), _1017429)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017425), _1017427)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017425), _1017429)))], (17321 ^ _775212) ^ [_1069606, _1069608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1069606)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1069608)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1069606)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1069608), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1069606))))], (39914 ^ _775212) ^ [_1539236, _1539238] : [c_Wellfounded_Owf(_1539236, _1539238), 39918 ^ _775212 : [(39919 ^ _775212) ^ [_1539372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539236, _1539236)), hAPP(hAPP(c_Product__Type_OPair(_1539236, _1539236), hAPP(_1539372, hAPP(c_Nat_OSuc, 39917 ^ [_1539236, _1539238, _1539372]))), hAPP(_1539372, 39917 ^ [_1539236, _1539238, _1539372]))), _1539238))]]], (45568 ^ _775212) ^ [_1679960, _1679962] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1679960, _1679962) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1679960), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1679962)))], (47611 ^ _775212) ^ [_1724979, _1724981, _1724983] : [class_Orderings_Olinorder(_1724979), -(hAPP(c_List_Oset(_1724979), c_List_Olinorder__class_Oinsort__insert__key(_1724979, _1724979, c_COMBI(_1724979), _1724981, _1724983)) = hAPP(hAPP(c_Set_Oinsert(_1724979), _1724981), hAPP(c_List_Oset(_1724979), _1724983)))], (38911 ^ _775212) ^ [_1507081, _1507083, _1507085] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1507081), hAPP(c_Set_OCollect(_1507081), hAPP(hAPP(c_COMBS(_1507081, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507081), c_fdisj), _1507083)), _1507085))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507081), hAPP(c_Set_OCollect(_1507081), _1507083))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507081), hAPP(c_Set_OCollect(_1507081), _1507085)))], (42988 ^ _775212) ^ [_1613020, _1613022, _1613024, _1613026] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613020, _1613020), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1613022), _1613024)), _1613026) = hAPP(hAPP(c_Relation_Orel__comp(_1613020, _1613020, _1613020), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613020, _1613020), tc_HOL_Obool), _1613022), _1613026)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613020, _1613020), tc_HOL_Obool), _1613024), _1613026)))], (28247 ^ _775212) ^ [] : [-(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))], (52659 ^ _775212) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (35343 ^ _775212) ^ [_1426811, _1426813, _1426815, _1426817, _1426819] : [class_Groups_Ocomm__monoid__add(_1426811), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426813), _1426815)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426813), _1426817)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426811), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426813, _1426811), _1426819), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426813, tc_HOL_Obool)), _1426815), _1426817))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426813, _1426811), _1426819), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426813, tc_HOL_Obool)), _1426815), _1426817))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426811), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426813, _1426811), _1426819), _1426815)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426813, _1426811), _1426819), _1426817)))], (40520 ^ _775212) ^ [_1554042, _1554044, _1554046, _1554048, _1554050, _1554052] : [c_Fun_Oinj__on(_1554042, _1554044, hAPP(c_Fun_Ocomp(_1554046, _1554044, _1554042, _1554048), _1554050), _1554052), -(c_Fun_Oinj__on(_1554042, _1554046, _1554050, _1554052))], (25697 ^ _775212) ^ [_1224330, _1224332] : [class_Rings_Ocomm__semiring__1(_1224330), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224330), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224330), c_Groups_Oone__class_Oone(_1224330)), c_Groups_Oone__class_Oone(_1224330))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1224330), c_Nat_Osemiring__1__class_Oof__nat(_1224330)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1224332))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224330), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1224330), _1224332)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224330), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1224330), _1224332)), c_Groups_Oone__class_Oone(_1224330))))], (19085 ^ _775212) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (43501 ^ _775212) ^ [_1625221, _1625223, _1625225] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625221, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1625221, tc_HOL_Obool)), _1625223), _1625225)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1625221, tc_HOL_Obool)), _1625223), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625221, tc_HOL_Obool), _1625225)))], (52227 ^ _775212) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (8237 ^ _775212) ^ [_908035, _908037] : [class_Rings_Olinordered__ring(_908035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908035), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908035), _908037), _908037)), c_Groups_Ozero__class_Ozero(_908035)))], (21797 ^ _775212) ^ [_1148912, _1148914, _1148916] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1148912, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1148912, tc_HOL_Obool)), _1148914), _1148916)), _1148914)))], (34971 ^ _775212) ^ [_1417861, _1417863, _1417865] : [-(hAPP(c_Set_OPow(_1417861), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417861, tc_HOL_Obool)), _1417863), _1417865)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1417861, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1417861), _1417863)), hAPP(c_Set_OPow(_1417861), _1417865)))], (51292 ^ _775212) ^ [_1805055, _1805057, _1805059, _1805061] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1805055, tc_fun(_1805057, tc_HOL_Obool)), _1805059), _1805061) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1805057, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1805057, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1805055, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1805057, tc_HOL_Obool)), c_HOL_OEx(_1805055)), hAPP(hAPP(c_COMBB(tc_fun(_1805055, tc_HOL_Obool), tc_fun(_1805055, tc_HOL_Obool), tc_fun(_1805057, tc_HOL_Obool)), hAPP(c_COMBS(_1805055, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1805055), c_fconj), hAPP(hAPP(c_COMBC(_1805055, tc_fun(_1805055, tc_HOL_Obool), tc_HOL_Obool), c_member(_1805055)), _1805059)))), hAPP(hAPP(c_COMBC(tc_fun(_1805057, tc_HOL_Obool), tc_fun(_1805055, tc_fun(_1805057, tc_HOL_Obool)), tc_fun(_1805055, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1805057, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1805055, tc_fun(_1805057, tc_HOL_Obool)), tc_fun(_1805055, tc_HOL_Obool)), tc_fun(_1805057, tc_HOL_Obool)), c_COMBB(tc_fun(_1805057, tc_HOL_Obool), tc_HOL_Obool, _1805055)), c_fequal)), _1805061))))))], (22342 ^ _775212) ^ [_1160114, _1160116, _1160118] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1160114, _1160116, _1160118, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1160116)], (6136 ^ _775212) ^ [_872225, _872227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872225), _872227)), _872227 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21767 ^ _775212) ^ [_1148249, _1148251, _1148253, _1148255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1148249, tc_HOL_Obool)), _1148251), _1148253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1148249, tc_HOL_Obool)), _1148253), _1148255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1148249, tc_HOL_Obool)), _1148251), _1148255)))], (342 ^ _775212) ^ [_780435, _780437, _780439, _780441, _780443, _780445] : [-(c_Big__Operators_Osemilattice__big(_780443, _780439, _780435)), c_Big__Operators_Osemilattice__big(_780445, _780441, _780437), _780445 = _780443, _780441 = _780439, _780437 = _780435], (7332 ^ _775212) ^ [_891599, _891601, _891603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _891599), _891601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _891599), _891603)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _891601), _891603))))], (38333 ^ _775212) ^ [_1495943, _1495945] : [class_Lattices_Olattice(_1495943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495943), _1495945)), -(c_Big__Operators_Olattice__class_OSup__fin(_1495943, _1495945) = hAPP(c_Finite__Set_Ofold1(_1495943, c_Lattices_Osemilattice__sup__class_Osup(_1495943)), _1495945))], (38089 ^ _775212) ^ [_1489625, _1489627, _1489629, _1489631] : [-(c_Fun_Oinj__on(_1489625, tc_prod(_1489627, _1489625), 38087 ^ [_1489625, _1489627, _1489629, _1489631], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1489627, tc_fun(_1489625, tc_HOL_Obool)), _1489629), _1489631)))], (29820 ^ _775212) ^ [_1306509, _1306511, _1306513, _1306515] : [_1306509 = _1306511, 29823 ^ _775212 : [(29830 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1306513), _1306515), _1306511)), -(hBOOL(hAPP(hAPP(c_member(_1306513), _1306515), _1306509)))], (29824 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1306513), _1306515), _1306509)), -(hBOOL(hAPP(hAPP(c_member(_1306513), _1306515), _1306511)))]]], (8579 ^ _775212) ^ [_914294, _914296, _914298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _914294), _914296)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _914298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _914298), _914294)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _914298), _914296))))], (14193 ^ _775212) ^ [_1011752, _1011754] : [class_Groups_Ogroup__add(_1011752), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1011752), _1011754), c_Groups_Ozero__class_Ozero(_1011752)) = _1011754)], (18655 ^ _775212) ^ [_1092161, _1092163, _1092165] : [class_Rings_Olinordered__idom(_1092161), 18658 ^ _775212 : [(18667 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092161), hAPP(hAPP(c_Power_Opower__class_Opower(_1092161), _1092163), 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(_1092161), _1092165), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1092161)), _1092163 = c_Groups_Ozero__class_Ozero(_1092161), _1092165 = c_Groups_Ozero__class_Ozero(_1092161)], (18659 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092161), hAPP(hAPP(c_Power_Opower__class_Opower(_1092161), _1092163), 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(_1092161), _1092165), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1092161), 18662 ^ _775212 : [(18665 ^ _775212) ^ [] : [-(_1092165 = c_Groups_Ozero__class_Ozero(_1092161))], (18663 ^ _775212) ^ [] : [-(_1092163 = c_Groups_Ozero__class_Ozero(_1092161))]]]]], (24240 ^ _775212) ^ [_1196097, _1196099] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196097), _1196099)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196099), _1196097))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196099), _1196097)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1196097), _1196099)))], (39781 ^ _775212) ^ [_1536520, _1536522, _1536524, _1536526] : [c_Wellfounded_Owf(_1536520, _1536522), hBOOL(hAPP(hAPP(c_member(tc_prod(_1536520, _1536520)), hAPP(hAPP(c_Product__Type_OPair(_1536520, _1536520), _1536524), _1536526)), _1536522)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1536520, _1536520)), hAPP(hAPP(c_Product__Type_OPair(_1536520, _1536520), _1536526), _1536524)), _1536522))], (2158 ^ _775212) ^ [_806471, _806473, _806475, _806477, _806479, _806481, _806483, _806485, _806487, _806489] : [-(c_Product__Type_Oprod_Oprod__rec(_806489, _806485, _806481, _806477, _806473) = c_Product__Type_Oprod_Oprod__rec(_806487, _806483, _806479, _806475, _806471)), _806489 = _806487, _806485 = _806483, _806481 = _806479, _806477 = _806475, _806473 = _806471], (18185 ^ _775212) ^ [_1083955, _1083957] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1083955)), c_Int_OBit0(_1083957)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1083955), _1083957)))], (45764 ^ _775212) ^ [_1684363, _1684365, _1684367] : [_1684365 = c_List_Olist_ONil(_1684363), -(hAPP(hAPP(c_List_Oappend(_1684363), _1684365), _1684367) = _1684367)], (11760 ^ _775212) ^ [_968242, _968244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _968242)), _968244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968242), _968244)))], (44222 ^ _775212) ^ [_1643485, _1643487, _1643489] : [-(c_Random_Oselect__weight(_1643485, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1643485)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1643485), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1643487)), _1643489)) = c_Random_Oselect__weight(_1643485, _1643489))], (19121 ^ _775212) ^ [_1100983, _1100985] : [c_Nat__Transfer_Ois__nat(_1100983), c_Nat__Transfer_Ois__nat(_1100985), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1100983), _1100985)))], (38060 ^ _775212) ^ [_1488533, _1488535, _1488537, _1488539] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1488533), _1488535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1488533, _1488533), tc_HOL_Obool)), _1488537), hAPP(hAPP(c_Product__Type_OSigma(_1488533, _1488533), _1488535), hAPP(c_COMBK(tc_fun(_1488533, tc_HOL_Obool), _1488533), _1488535)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1488533, tc_HOL_Obool)), _1488539), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1488533), _1488535), _1488537))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1488533), _1488539)))], (52543 ^ _775212) ^ [_1826811] : [-(class_Nat_Osize(tc_Option_Ooption(_1826811)))], (51323 ^ _775212) ^ [_1805785, _1805787] : [51324 ^ _775212 : [(51325 ^ _775212) ^ [_1805851] : [hBOOL(hAPP(_1805787, _1805851))]], 51327 ^ _775212 : [(51330 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1805787, 51326 ^ [_1805785, _1805787])))], (51328 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805785), 51326 ^ [_1805785, _1805787]), c_Orderings_Otop__class_Otop(tc_fun(_1805785, tc_HOL_Obool)))))]]], (40692 ^ _775212) ^ [_1557808, _1557810, _1557812, _1557814, _1557816, _1557818] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1557808, _1557810), _1557810, tc_prod(_1557812, _1557814), c_Product__Type_Osnd(_1557808, _1557810)), c_Product__Type_Omap__pair(_1557812, _1557808, _1557814, _1557810, _1557816, _1557818)) = hAPP(c_Fun_Ocomp(_1557814, _1557810, tc_prod(_1557812, _1557814), _1557818), c_Product__Type_Osnd(_1557812, _1557814)))], (43555 ^ _775212) ^ [_1626321, _1626323, _1626325, _1626327, _1626329] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1626321, tc_fun(_1626323, tc_HOL_Obool)), _1626325), hAPP(hAPP(c_COMBS(_1626321, tc_fun(_1626323, tc_HOL_Obool), tc_fun(_1626323, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1626323, tc_HOL_Obool), tc_fun(tc_fun(_1626323, tc_HOL_Obool), tc_fun(_1626323, tc_HOL_Obool)), _1626321), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1626323, tc_HOL_Obool))), _1626327)), _1626329)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1626323, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1626323, tc_HOL_Obool), hAPP(c_Set_Oimage(_1626321, tc_fun(_1626323, tc_HOL_Obool), _1626327), _1626325))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1626323, tc_HOL_Obool), hAPP(c_Set_Oimage(_1626321, tc_fun(_1626323, tc_HOL_Obool), _1626329), _1626325))))], (17569 ^ _775212) ^ [_1073463, _1073465] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1073463), c_Int_OPls))), 17572 ^ _775212 : [(17579 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1073465), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1073463)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1073465)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1073463), _1073465)))], (17573 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1073465), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1073463)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1073465)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1073463))]]], (39121 ^ _775212) ^ [_1512787, _1512789, _1512791, _1512793, _1512795, _1512797] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512787), _1512789)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512791), _1512793)), 39131 ^ _775212 : [(39134 ^ _775212) ^ [] : [hAPP(c_Finite__Set_Ocard(_1512787), hAPP(c_Set_OCollect(_1512787), hAPP(hAPP(c_COMBS(_1512787, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512787), c_fconj), hAPP(hAPP(c_COMBC(_1512787, tc_fun(_1512787, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512787)), _1512789))), hAPP(hAPP(c_COMBC(_1512787, _1512791, tc_HOL_Obool), _1512795), 39130 ^ [_1512787, _1512789, _1512791, _1512793, _1512795, _1512797])))) = _1512797], (39132 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512791), 39130 ^ [_1512787, _1512789, _1512791, _1512793, _1512795, _1512797]), _1512793)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512787, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1512791, tc_HOL_Obool), tc_Nat_Onat, _1512787), c_Finite__Set_Ocard(_1512791)), hAPP(hAPP(c_COMBB(tc_fun(_1512791, tc_HOL_Obool), tc_fun(_1512791, tc_HOL_Obool), _1512787), c_Set_OCollect(_1512791)), hAPP(hAPP(c_COMBB(tc_fun(_1512791, tc_HOL_Obool), tc_fun(_1512791, tc_HOL_Obool), _1512787), hAPP(c_COMBS(_1512791, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512791), c_fconj), hAPP(hAPP(c_COMBC(_1512791, tc_fun(_1512791, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512791)), _1512793)))), _1512795)))), _1512789) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1512797), hAPP(c_Finite__Set_Ocard(_1512791), _1512793)))], (28674 ^ _775212) ^ [_1284516, _1284518] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1284516, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1284516, tc_HOL_Obool))), _1284518) = c_Orderings_Obot__class_Obot(tc_fun(_1284516, tc_HOL_Obool)))], (45244 ^ _775212) ^ [_1671291, _1671293, _1671295] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671291), tc_List_Olist(_1671291))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671291), tc_List_Olist(_1671291)), _1671293), c_List_Olist_ONil(_1671291))), c_List_Olistrel1(_1671291, _1671295)))], (44992 ^ _775212) ^ [_1664516, _1664518, _1664520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1664516), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664518)), _1664520))), -(hBOOL(hAPP(hAPP(c_member(_1664518), hAPP(hAPP(c_List_Onth(_1664518), _1664520), _1664516)), hAPP(c_List_Oset(_1664518), _1664520))))], (16825 ^ _775212) ^ [_1062138] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062138)))), -(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), _1062138)) = 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), _1062138))))], (6681 ^ _775212) ^ [_881376, _881378] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881376), _881378) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _881376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _881378 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5825 ^ _775212) ^ [_867296, _867298, _867300] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_867296, _867298, _867300)], (28728 ^ _775212) ^ [_1285597, _1285599] : [class_Orderings_Obot(_1285597), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285597), c_Orderings_Obot__class_Obot(_1285597)), _1285599)))], (9125 ^ _775212) ^ [_923000] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _923000), _923000)))], (23206 ^ _775212) ^ [_1177196, _1177198, _1177200] : [class_Orderings_Olinorder(_1177196), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177196), _1177198), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1177196), _1177198), _1177200)) = _1177198)], (17405 ^ _775212) ^ [_1070817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070817), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1070817))], (17707 ^ _775212) ^ [_1075993] : [c_Int_OPls = c_Int_OBit1(_1075993)], (35015 ^ _775212) ^ [_1419294, _1419296, _1419298] : [class_Lattices_Oboolean__algebra(_1419294), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1419294), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419294), _1419296), _1419298)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1419294), hAPP(c_Groups_Ouminus__class_Ouminus(_1419294), _1419296)), hAPP(c_Groups_Ouminus__class_Ouminus(_1419294), _1419298)))], (11802 ^ _775212) ^ [_968899, _968901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968899), _968901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968899), _968901)))], (46879 ^ _775212) ^ [_1709690, _1709692, _1709694] : [class_Orderings_Olinorder(_1709690), -(c_Big__Operators_Olinorder__class_OMax(_1709690, hAPP(c_List_Oset(_1709690), hAPP(hAPP(c_List_Olist_OCons(_1709690), _1709692), _1709694))) = hAPP(c_List_Ofoldl(_1709690, _1709690, c_Orderings_Oord__class_Omax(_1709690), _1709692), _1709694))], (44957 ^ _775212) ^ [_1663731, _1663733, _1663735, _1663737, _1663739] : [hBOOL(hAPP(hAPP(c_member(_1663731), _1663733), hAPP(c_List_Oset(_1663731), _1663735))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1663737), hAPP(_1663739, _1663733))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1663737), c_List_Olist_Olist__size(_1663731, _1663739, _1663735))))], (48500 ^ _775212) ^ [_1746140, _1746142] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1746140), _1746142)) = c_List_Oupt(_1746140, _1746142))], (26288 ^ _775212) ^ [_1236392, _1236394, _1236396, _1236398] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236392), _1236394)), 26291 ^ _775212 : [(26292 ^ _775212) ^ [_1236550] : [26294 ^ _775212 : [(26300 ^ _775212) ^ [] : [-(_1236550 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26296 ^ [_1236392, _1236394, _1236396, _1236398, _1236550]), 26293 ^ [_1236392, _1236394, _1236396, _1236398, _1236550]))], (26298 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26296 ^ [_1236392, _1236394, _1236396, _1236398, _1236550]), _1236396)))], (26295 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26293 ^ [_1236392, _1236394, _1236396, _1236398, _1236550]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1236394))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236392), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236550), _1236398)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236392), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1236550), _1236394)), _1236398)))]]], (29748 ^ _775212) ^ [_1305199, _1305201, _1305203, _1305205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1305199, tc_HOL_Obool)), _1305201), _1305203)), hBOOL(hAPP(hAPP(c_member(_1305199), _1305205), _1305201)), -(hBOOL(hAPP(hAPP(c_member(_1305199), _1305205), _1305203)))], (35027 ^ _775212) ^ [_1419587, _1419589, _1419591, _1419593] : [hBOOL(hAPP(hAPP(c_member(_1419587), _1419589), _1419591)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419587, tc_HOL_Obool)), _1419591), hAPP(hAPP(c_Set_Oinsert(_1419587), _1419589), _1419593)) = hAPP(hAPP(c_Set_Oinsert(_1419587), _1419589), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419587, tc_HOL_Obool)), _1419591), _1419593)))], (11336 ^ _775212) ^ [_961317] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _961317))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _961317)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51815 ^ _775212) ^ [_1816829, _1816831] : [51818 ^ _775212 : [(51821 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1816829, _1816829)), hAPP(hAPP(c_Product__Type_OPair(_1816829, _1816829), 51817 ^ [_1816829, _1816831]), 51816 ^ [_1816829, _1816831])), _1816831))], (51819 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1816829, _1816829)), hAPP(hAPP(c_Product__Type_OPair(_1816829, _1816829), 51816 ^ [_1816829, _1816831]), 51817 ^ [_1816829, _1816831])), _1816831)))]], -(c_Relation_Osym(_1816829, _1816831))], (9133 ^ _775212) ^ [_923124] : [class_Rings_Olinordered__semidom(_923124), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923124), c_Groups_Ozero__class_Ozero(_923124)), c_Groups_Oone__class_Oone(_923124))))], (8073 ^ _775212) ^ [_905085, _905087, _905089, _905091] : [class_Rings_Ocomm__semiring__1(_905085), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905085), _905087), _905089)), _905091) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905085), _905087), _905091)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905085), _905089), _905091)))], (27425 ^ _775212) ^ [_1258777, _1258779] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1258777)), _1258779) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1258777, _1258779))], (30034 ^ _775212) ^ [_1313240, _1313242, _1313244] : [hBOOL(hAPP(hAPP(c_member(_1313240), _1313242), hAPP(hAPP(c_Set_Oinsert(_1313240), _1313244), c_Orderings_Obot__class_Obot(tc_fun(_1313240, tc_HOL_Obool))))), -(_1313242 = _1313244)], (43075 ^ _775212) ^ [_1615281, _1615283] : [-(hAPP(hAPP(c_Nat_Ocompow(_1615281, _1615281), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1615283) = c_Fun_Oid(_1615281))], (5256 ^ _775212) ^ [_855442, _855444, _855446, _855448, _855450, _855452] : [-(c_Relation_Orel__comp(_855452, _855448, _855444) = c_Relation_Orel__comp(_855450, _855446, _855442)), _855452 = _855450, _855448 = _855446, _855444 = _855442], (31613 ^ _775212) ^ [_1347367, _1347369, _1347371] : [class_Rings_Oring__1(_1347367), hBOOL(hAPP(hAPP(c_member(_1347367), _1347369), c_Int_Oring__1__class_OInts(_1347367))), hBOOL(hAPP(hAPP(c_member(_1347367), _1347371), c_Int_Oring__1__class_OInts(_1347367))), -(hBOOL(hAPP(hAPP(c_member(_1347367), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347367), _1347369), _1347371)), c_Int_Oring__1__class_OInts(_1347367))))], (21963 ^ _775212) ^ [_1152030, _1152032] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1152030), _1152032) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1152030, _1152032)))], (2276 ^ _775212) ^ [_808364, _808366] : [_808366 = _808364, -(c_Int_Opred(_808366) = c_Int_Opred(_808364))], (26675 ^ _775212) ^ [_1243946] : [26677 ^ _775212 : [(26680 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26676 ^ [_1243946]))], (26678 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26676 ^ [_1243946]), _1243946)))]], -(c_Nat__Transfer_Onat__set(_1243946))], (47310 ^ _775212) ^ [_1718240, _1718242, _1718244] : [class_Orderings_Olinorder(_1718240), hBOOL(hAPP(c_Finite__Set_Ofinite(_1718240), _1718242)), -(c_List_Olinorder__class_Osorted__list__of__set(_1718240, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1718240, tc_HOL_Obool)), _1718242), hAPP(hAPP(c_Set_Oinsert(_1718240), _1718244), c_Orderings_Obot__class_Obot(tc_fun(_1718240, tc_HOL_Obool))))) = c_List_Oremove1(_1718240, _1718244, c_List_Olinorder__class_Osorted__list__of__set(_1718240, _1718242)))], (41895 ^ _775212) ^ [_1584017, _1584019, _1584021] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584017, _1584017), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584017, _1584017), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1584017, _1584019)), c_Transitive__Closure_Ortrancl(_1584017, _1584021))), c_Transitive__Closure_Ortrancl(_1584017, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584017, _1584017), tc_HOL_Obool)), _1584019), _1584021)))))], (12638 ^ _775212) ^ [_983671, _983673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _983671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _983671, _983673)), _983671)))], (14617 ^ _775212) ^ [_1019595, _1019597, _1019599, _1019601, _1019603, _1019605] : [class_Rings_Oring(_1019595), 14620 ^ _775212 : [(14627 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019595), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1019595), _1019597), _1019603)), _1019599)), _1019601) = _1019605, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019595), _1019597), _1019599)), _1019601) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019595), _1019603), _1019599)), _1019605))], (14621 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019595), _1019597), _1019599)), _1019601) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019595), _1019603), _1019599)), _1019605), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019595), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1019595), _1019597), _1019603)), _1019599)), _1019601) = _1019605)]]], (1814 ^ _775212) ^ [_800743, _800745] : [-(class_Orderings_Oorder(_800743)), _800745 = _800743, class_Orderings_Oorder(_800745)], (44354 ^ _775212) ^ [_1647673, _1647675, _1647677, _1647679, _1647681, _1647683] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647673), tc_List_Olist(_1647673))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647673), tc_List_Olist(_1647673)), hAPP(hAPP(c_List_Olist_OCons(_1647673), _1647675), _1647677)), hAPP(hAPP(c_List_Olist_OCons(_1647673), _1647679), _1647681))), c_List_Olistrel1(_1647673, _1647683)))), 44355 ^ _775212 : [(44362 ^ _775212) ^ [] : [_1647675 = _1647679, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647673), tc_List_Olist(_1647673))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647673), tc_List_Olist(_1647673)), _1647677), _1647681)), c_List_Olistrel1(_1647673, _1647683)))], (44356 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1647673, _1647673)), hAPP(hAPP(c_Product__Type_OPair(_1647673, _1647673), _1647675), _1647679)), _1647683)), _1647677 = _1647681]]], (41614 ^ _775212) ^ [_1577371, _1577373, _1577375, _1577377, _1577379] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577371, _1577371)), hAPP(hAPP(c_Product__Type_OPair(_1577371, _1577371), _1577373), _1577375)), c_Transitive__Closure_Otrancl(_1577371, _1577377))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1577371, _1577371)), hAPP(hAPP(c_Product__Type_OPair(_1577371, _1577371), _1577375), _1577379)), c_Transitive__Closure_Otrancl(_1577371, _1577377))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577371, _1577371)), hAPP(hAPP(c_Product__Type_OPair(_1577371, _1577371), _1577373), _1577379)), c_Transitive__Closure_Otrancl(_1577371, _1577377))))], (21659 ^ _775212) ^ [_1146219, _1146221, _1146223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146219, tc_HOL_Obool)), _1146221), _1146223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146219, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1146219, tc_HOL_Obool)), _1146223)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1146219, tc_HOL_Obool)), _1146221))))], (37882 ^ _775212) ^ [_1483603, _1483605, _1483607, _1483609, _1483611, _1483613] : [class_Groups_Ocomm__monoid__add(_1483603), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1483605, _1483603), hAPP(hAPP(c_COMBC(_1483605, tc_fun(_1483607, tc_HOL_Obool), _1483603), hAPP(hAPP(c_COMBB(tc_fun(_1483607, _1483603), tc_fun(tc_fun(_1483607, tc_HOL_Obool), _1483603), _1483605), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1483607, _1483603)), _1483609)), _1483611)), _1483613) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1483605, _1483607), _1483603), hAPP(c_Product__Type_Oprod_Oprod__case(_1483605, _1483607, _1483603), _1483609)), hAPP(hAPP(c_Product__Type_OSigma(_1483605, _1483607), _1483613), hAPP(c_COMBK(tc_fun(_1483607, tc_HOL_Obool), _1483605), _1483611))))], (44529 ^ _775212) ^ [_1652951, _1652953, _1652955, _1652957] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1652951)), hAPP(hAPP(c_List_Olist_OCons(_1652951), _1652953), _1652955)), c_List_Olists(_1652951, _1652957))), 44532 ^ _775212 : [(44535 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1652951)), _1652955), c_List_Olists(_1652951, _1652957))))], (44533 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652951), _1652953), _1652957)))]]], (10753 ^ _775212) ^ [_950923] : [-(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), _950923))))], (37459 ^ _775212) ^ [_1472980, _1472982, _1472984, _1472986, _1472988] : [hBOOL(hAPP(hAPP(c_member(_1472980), _1472982), hAPP(c_Set_Ovimage(_1472980, _1472984, _1472986), hAPP(hAPP(c_Set_Oinsert(_1472984), _1472988), c_Orderings_Obot__class_Obot(tc_fun(_1472984, tc_HOL_Obool)))))), -(hAPP(_1472986, _1472982) = _1472988)], (33515 ^ _775212) ^ [_1384960, _1384962] : [-(c_FunDef_Orp__inv__image(_1384960, _1384962) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1384960, _1384960), tc_HOL_Obool), tc_fun(tc_prod(_1384960, _1384960), tc_HOL_Obool), tc_fun(tc_fun(_1384962, _1384960), tc_prod(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1384960, _1384960), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1384960, _1384960), tc_HOL_Obool), tc_fun(tc_fun(_1384962, _1384960), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1384960, _1384960), tc_HOL_Obool), tc_fun(tc_fun(_1384962, _1384960), tc_prod(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1384962, _1384960), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool)), tc_fun(tc_fun(_1384962, _1384960), tc_prod(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1384960, _1384960), tc_HOL_Obool), tc_fun(tc_fun(_1384962, _1384960), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1384960, _1384960), tc_HOL_Obool), tc_fun(tc_fun(_1384962, _1384960), tc_prod(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool))))), tc_fun(tc_prod(_1384960, _1384960), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1384962, _1384960), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool)), tc_fun(tc_fun(_1384962, _1384960), tc_prod(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool))), tc_fun(tc_prod(_1384960, _1384960), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1384962, _1384960), tc_fun(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1384962, _1384960), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool)), tc_fun(tc_fun(_1384962, _1384960), tc_prod(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool)))), tc_fun(tc_prod(_1384960, _1384960), tc_HOL_Obool)), c_COMBS(tc_fun(_1384962, _1384960), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1384962, _1384960), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool)), tc_fun(tc_fun(_1384962, _1384960), tc_fun(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool)))), tc_fun(tc_prod(_1384960, _1384960), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool))), tc_fun(_1384962, _1384960)), c_Product__Type_OPair(tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool), tc_fun(tc_prod(_1384962, _1384962), tc_HOL_Obool)))), c_Relation_Oinv__image(_1384960, _1384962))))), c_Relation_Oinv__image(_1384960, _1384962))))], (38942 ^ _775212) ^ [_1507686, _1507688] : [-(hBOOL(hAPP(_1507688, 38943 ^ [_1507686, _1507688]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1507686, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1507686), _1507688))], (25264 ^ _775212) ^ [_1214811, _1214813] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1214811)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1214813))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214811), _1214813)))], (13029 ^ _775212) ^ [_990563, _990565, _990567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _990563), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13032 ^ _775212 : [(13033 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_990565, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _990567), _990563)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _990567, _990563))), 13036 ^ _775212 : [(13037 ^ _775212) ^ [_990773, _990775] : [-(hBOOL(hAPP(hAPP(_990565, _990775), _990773))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _990563), _990773)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _990773), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _990567 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _990563), _990775)), _990773)]]], (13051 ^ _775212) ^ [] : [13054 ^ _775212 : [(13057 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 13053 ^ [_990563, _990565, _990567]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13059 ^ _775212) ^ [] : [-(_990567 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _990563), 13052 ^ [_990563, _990565, _990567])), 13053 ^ [_990563, _990565, _990567]))], (13061 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_990565, 13052 ^ [_990563, _990565, _990567]), 13053 ^ [_990563, _990565, _990567]))], (13055 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _990563), 13053 ^ [_990563, _990565, _990567])))]], -(hBOOL(hAPP(hAPP(_990565, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _990567), _990563)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _990567, _990563))))]]], (40237 ^ _775212) ^ [_1547534, _1547536, _1547538] : [hBOOL(hAPP(c_Predicate_OPowp(_1547534, _1547536), _1547538)), 40240 ^ _775212 : [(40241 ^ _775212) ^ [_1547618] : [hBOOL(hAPP(hAPP(c_member(_1547534), _1547618), _1547538)), -(hBOOL(hAPP(_1547536, _1547618)))]]], (4798 ^ _775212) ^ [_848297, _848299] : [_848299 = _848297, -(c_Orderings_Oord__class_Omin(_848299) = c_Orderings_Oord__class_Omin(_848297))], (34033 ^ _775212) ^ [_1397100, _1397102, _1397104, _1397106] : [-(hAPP(c_Relation_OImage(_1397100, _1397102, _1397104), _1397106) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397100, tc_fun(_1397102, tc_HOL_Obool)), _1397106), hAPP(hAPP(c_COMBB(tc_fun(_1397100, tc_HOL_Obool), tc_fun(_1397102, tc_HOL_Obool), _1397100), c_Relation_OImage(_1397100, _1397102, _1397104)), hAPP(hAPP(c_COMBC(_1397100, tc_fun(_1397100, tc_HOL_Obool), tc_fun(_1397100, tc_HOL_Obool)), c_Set_Oinsert(_1397100)), c_Orderings_Obot__class_Obot(tc_fun(_1397100, tc_HOL_Obool))))))], (28912 ^ _775212) ^ [_1289031] : [-(hAPP(c_Finite__Set_Ocard(_1289031), c_Orderings_Obot__class_Obot(tc_fun(_1289031, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9791 ^ _775212) ^ [_933554, _933556, _933558] : [class_Groups_Oordered__ab__group__add(_933554), 9794 ^ _775212 : [(9801 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933554), _933558), _933556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933554), hAPP(c_Groups_Ouminus__class_Ouminus(_933554), _933556)), hAPP(c_Groups_Ouminus__class_Ouminus(_933554), _933558))))], (9795 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933554), hAPP(c_Groups_Ouminus__class_Ouminus(_933554), _933556)), hAPP(c_Groups_Ouminus__class_Ouminus(_933554), _933558))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933554), _933558), _933556)))]]], (2406 ^ _775212) ^ [_810333, _810335, _810337, _810339, _810341, _810343] : [-(c_Nitpick_Otimes__frac(_810343, _810339, _810335) = c_Nitpick_Otimes__frac(_810341, _810337, _810333)), _810343 = _810341, _810339 = _810337, _810335 = _810333], (21493 ^ _775212) ^ [_1143206, _1143208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1143206), 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)), _1143208)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1143206, _1143208), c_Divides_OnegDivAlg(_1143206, _1143208))))], (25170 ^ _775212) ^ [_1213137, _1213139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213139)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1213137), _1213139)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1213139), _1213137)), -(_1213137 = _1213139)], (21675 ^ _775212) ^ [_1146564, _1146566, _1146568] : [-(_1146564 = _1146566), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146568, tc_HOL_Obool)), _1146564), _1146566)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146568, tc_HOL_Obool)), _1146566), _1146564))], (3446 ^ _775212) ^ [_827221, _827223, _827225, _827227, _827229, _827231, _827233, _827235] : [-(c_New__Random__Sequence_Oneg__bind(_827235, _827231, _827227, _827223) = c_New__Random__Sequence_Oneg__bind(_827233, _827229, _827225, _827221)), _827235 = _827233, _827231 = _827229, _827227 = _827225, _827223 = _827221], (52379 ^ _775212) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (43511 ^ _775212) ^ [_1625442] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625442, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1625442, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1625442, tc_HOL_Obool)))], (4162 ^ _775212) ^ [_838413, _838415, _838417, _838419] : [-(c_Random_Oselect__weight(_838419, _838415) = c_Random_Oselect__weight(_838417, _838413)), _838419 = _838417, _838415 = _838413], (14543 ^ _775212) ^ [_1018302, _1018304] : [_1018302 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1018304), _1018302) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7556 ^ _775212) ^ [_895807, _895809] : [hBOOL(hAPP(_895807, hAPP(c_Int_Onat, _895809))), 7559 ^ _775212 : [(7566 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _895809), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_895807, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7560 ^ _775212) ^ [_895907] : [_895809 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _895907), -(hBOOL(hAPP(_895807, _895907)))]]], (21449 ^ _775212) ^ [_1142630, _1142632, _1142634, _1142636, _1142638, _1142640] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1142630, _1142632), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1142634), _1142636))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1142630, _1142632), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1142638), _1142640))), -(_1142632 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1142636 = _1142640)], (29014 ^ _775212) ^ [_1290711, _1290713, _1290715] : [class_Orderings_Oorder(_1290711), 29017 ^ _775212 : [(29024 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290711), _1290713), _1290715))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1290711, _1290713, _1290715) = c_Orderings_Obot__class_Obot(tc_fun(_1290711, tc_HOL_Obool)))], (29018 ^ _775212) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1290711, _1290713, _1290715) = c_Orderings_Obot__class_Obot(tc_fun(_1290711, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290711), _1290713), _1290715))]]], (45590 ^ _775212) ^ [_1680435, _1680437, _1680439, _1680441] : [-(c_List_Osublist(_1680435, hAPP(hAPP(c_List_Olist_OCons(_1680435), _1680437), _1680439), _1680441) = hAPP(hAPP(c_List_Oappend(_1680435), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1680435)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1680441)), hAPP(hAPP(c_List_Olist_OCons(_1680435), _1680437), c_List_Olist_ONil(_1680435))), c_List_Olist_ONil(_1680435))), c_List_Osublist(_1680435, _1680439, 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)), _1680441)))))], (23466 ^ _775212) ^ [_1182444, _1182446] : [-(c_Random_Olog(_1182444, _1182446) = 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(_1182444, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1182446), _1182444)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1182444), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1182446), _1182444)))], (3664 ^ _775212) ^ [_830614, _830616, _830618, _830620] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_830620, _830616) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_830618, _830614)), _830620 = _830618, _830616 = _830614], (1534 ^ _775212) ^ [_797243, _797245] : [-(class_Rings_Olinordered__semiring__strict(_797243)), _797245 = _797243, class_Rings_Olinordered__semiring__strict(_797245)], (3752 ^ _775212) ^ [_832084, _832086, _832088, _832090] : [-(c_Random_Oselect(_832090, _832086) = c_Random_Oselect(_832088, _832084)), _832090 = _832088, _832086 = _832084], (45623 ^ _775212) ^ [_1681210, _1681212, _1681214, _1681216, _1681218] : [hAPP(hAPP(c_List_Olist_OCons(_1681210), _1681212), _1681214) = hAPP(hAPP(c_List_Oappend(_1681210), _1681216), _1681218), 45628 ^ _775212 : [(45631 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1681210), _1681212), _1681214) = _1681218)], (45629 ^ _775212) ^ [] : [-(_1681216 = c_List_Olist_ONil(_1681210))]], 45633 ^ _775212 : [(45636 ^ _775212) ^ [] : [-(_1681214 = hAPP(hAPP(c_List_Oappend(_1681210), 45632 ^ [_1681210, _1681212, _1681214, _1681216, _1681218]), _1681218))], (45634 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1681210), _1681212), 45632 ^ [_1681210, _1681212, _1681214, _1681216, _1681218]) = _1681216)]]], (27822 ^ _775212) ^ [] : [-(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))))], (8673 ^ _775212) ^ [_915801, _915803] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _915801)), hAPP(c_Int_Onat, _915803)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _915803)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _915801), _915803))], (19531 ^ _775212) ^ [_1107925, _1107927, _1107929, _1107931] : [class_Fields_Ofield__inverse__zero(_1107925), -(_1107927 = c_Groups_Ozero__class_Ozero(_1107925)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107925), _1107927), _1107929)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107925), _1107927), _1107931)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107925), _1107929), _1107931))], (14433 ^ _775212) ^ [_1016208, _1016210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016208), _1016210)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016210), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016210), _1016208)) = _1016208)], (30782 ^ _775212) ^ [_1330947, _1330949, _1330951, _1330953, _1330955, _1330957] : [hBOOL(hAPP(hAPP(_1330947, _1330949), _1330951)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330953, tc_fun(_1330955, tc_HOL_Obool))), _1330957), _1330947), _1330949), _1330951)))], (29506 ^ _775212) ^ [_1300582, _1300584, _1300586, _1300588] : [hBOOL(hAPP(hAPP(c_member(_1300582), _1300584), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1300582, tc_HOL_Obool)), _1300586), _1300588))), -(hBOOL(hAPP(hAPP(c_member(_1300582), _1300584), _1300586))), -(hBOOL(hAPP(hAPP(c_member(_1300582), _1300584), _1300588)))], (16317 ^ _775212) ^ [_1052098, _1052100, _1052102, _1052104] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052098), hAPP(c_Int_Onumber__class_Onumber__of(_1052098), _1052100)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1052098), _1052102), _1052104)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1052098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052098), hAPP(c_Int_Onumber__class_Onumber__of(_1052098), _1052100)), _1052102)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052098), hAPP(c_Int_Onumber__class_Onumber__of(_1052098), _1052100)), _1052104))), class_Int_Onumber(_1052098), class_Rings_Oring(_1052098)], (48406 ^ _775212) ^ [_1744274, _1744276] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1744274))), c_List_Otranspose(_1744274, _1744276)) = c_List_Ofoldr(tc_List_Olist(_1744274), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1744274)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1744274))), _1744276, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34239 ^ _775212) ^ [_1402446, _1402448, _1402450, _1402452, _1402454, _1402456, _1402458] : [c_Equiv__Relations_Oequiv(_1402446, _1402448, _1402450), hBOOL(hAPP(hAPP(c_member(tc_fun(_1402446, tc_HOL_Obool)), _1402452), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1402446), _1402448), _1402450))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1402446, tc_HOL_Obool)), _1402454), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1402446), _1402448), _1402450))), hBOOL(hAPP(hAPP(c_member(_1402446), _1402456), _1402452)), hBOOL(hAPP(hAPP(c_member(_1402446), _1402458), _1402454)), 34258 ^ _775212 : [(34265 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1402446, _1402446)), hAPP(hAPP(c_Product__Type_OPair(_1402446, _1402446), _1402456), _1402458)), _1402450)), -(_1402452 = _1402454)], (34259 ^ _775212) ^ [] : [_1402452 = _1402454, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1402446, _1402446)), hAPP(hAPP(c_Product__Type_OPair(_1402446, _1402446), _1402456), _1402458)), _1402450)))]]], (26507 ^ _775212) ^ [_1241073] : [-(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)), _1241073)) = _1241073)], (12452 ^ _775212) ^ [_979988, _979990, _979992, _979994] : [class_Divides_Osemiring__div(_979988), -(c_Divides_Odiv__class_Omod(_979988, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979988), _979990), _979992), _979994) = c_Divides_Odiv__class_Omod(_979988, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979988), c_Divides_Odiv__class_Omod(_979988, _979990, _979994)), _979992), _979994))], (26688 ^ _775212) ^ [_1244156, _1244158, _1244160] : [class_Groups_Oordered__ab__group__add(_1244156), -(hAPP(c_Set_Oimage(_1244156, _1244156, c_Groups_Ouminus__class_Ouminus(_1244156)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1244156, _1244158, _1244160)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1244156, hAPP(c_Groups_Ouminus__class_Ouminus(_1244156), _1244160), hAPP(c_Groups_Ouminus__class_Ouminus(_1244156), _1244158)))], (37523 ^ _775212) ^ [_1474369, _1474371, _1474373, _1474375] : [-(hAPP(c_Set_Ovimage(_1474369, _1474371, _1474373), _1474375) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474371, tc_fun(_1474369, tc_HOL_Obool)), _1474375), hAPP(hAPP(c_COMBB(tc_fun(_1474371, tc_HOL_Obool), tc_fun(_1474369, tc_HOL_Obool), _1474371), c_Set_Ovimage(_1474369, _1474371, _1474373)), hAPP(hAPP(c_COMBC(_1474371, tc_fun(_1474371, tc_HOL_Obool), tc_fun(_1474371, tc_HOL_Obool)), c_Set_Oinsert(_1474371)), c_Orderings_Obot__class_Obot(tc_fun(_1474371, tc_HOL_Obool))))))], (48189 ^ _775212) ^ [_1738446, _1738448] : [-(c_List_Oconcat(_1738446, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1738446), tc_List_Olist(_1738446)), c_List_Olist_Olist__case(tc_List_Olist(_1738446), _1738446, c_List_Olist_ONil(_1738446), hAPP(hAPP(c_COMBB(tc_List_Olist(_1738446), tc_fun(tc_List_Olist(_1738446), tc_List_Olist(_1738446)), _1738446), c_COMBK(tc_List_Olist(_1738446), tc_List_Olist(_1738446))), hAPP(hAPP(c_COMBC(_1738446, tc_List_Olist(_1738446), tc_List_Olist(_1738446)), c_List_Olist_OCons(_1738446)), c_List_Olist_ONil(_1738446))))), _1738448)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1738446), _1738446), c_List_Ohd(_1738446)), hAPP(c_List_Ofilter(tc_List_Olist(_1738446), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1738446)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1738446), tc_List_Olist(_1738446), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1738446)))), _1738448)))], (52473 ^ _775212) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (7552 ^ _775212) ^ [_895717] : [-(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, _895717)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21809 ^ _775212) ^ [_1149141, _1149143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1149141), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1149143), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1149141), _1149143) = 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), _1149141), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1149143)))))], (23504 ^ _775212) ^ [_1183193, _1183195, _1183197] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1183193), _1183195))), -(c_Random_Ominus__shift(_1183197, _1183193, _1183195) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1183193), _1183195))], (30462 ^ _775212) ^ [_1323819, _1323821, _1323823] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1323819), _1323821)), 30465 ^ _775212 : [(30472 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1323819), _1323823), _1323821))), -(hAPP(c_Finite__Set_Ocard(_1323819), hAPP(hAPP(c_Set_Oinsert(_1323819), _1323823), _1323821)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1323819), _1323821)))], (30466 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1323819), _1323823), _1323821)), -(hAPP(c_Finite__Set_Ocard(_1323819), hAPP(hAPP(c_Set_Oinsert(_1323819), _1323823), _1323821)) = hAPP(c_Finite__Set_Ocard(_1323819), _1323821))]]], (3996 ^ _775212) ^ [_835850, _835852, _835854, _835856] : [-(c_List_Olistsp(_835856, _835852) = c_List_Olistsp(_835854, _835850)), _835856 = _835854, _835852 = _835850], (33755 ^ _775212) ^ [_1390756, _1390758, _1390760] : [hAPP(c_Set_Oimage(_1390758, tc_fun(_1390758, tc_HOL_Obool), _1390756), _1390760) = hAPP(c_Set_OPow(_1390758), _1390760)], (12440 ^ _775212) ^ [_979744, _979746, _979748] : [class_Divides_Osemiring__div(_979744), -(c_Divides_Odiv__class_Omod(_979744, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979744), _979746), _979748), _979746) = c_Divides_Odiv__class_Omod(_979744, _979748, _979746))], (28954 ^ _775212) ^ [_1289669, _1289671, _1289673, _1289675] : [class_Orderings_Oorder(_1289669), 28957 ^ _775212 : [(28966 ^ _775212) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1289669, _1289671, _1289673) = hAPP(hAPP(c_Set_Oinsert(_1289669), _1289675), c_Orderings_Obot__class_Obot(tc_fun(_1289669, tc_HOL_Obool)))), _1289671 = _1289673, _1289673 = _1289675], (28958 ^ _775212) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1289669, _1289671, _1289673) = hAPP(hAPP(c_Set_Oinsert(_1289669), _1289675), c_Orderings_Obot__class_Obot(tc_fun(_1289669, tc_HOL_Obool))), 28961 ^ _775212 : [(28964 ^ _775212) ^ [] : [-(_1289673 = _1289675)], (28962 ^ _775212) ^ [] : [-(_1289671 = _1289673)]]]]], (16237 ^ _775212) ^ [_1050553, _1050555, _1050557] : [class_Groups_Oordered__ab__group__add__abs(_1050553), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050553), hAPP(c_Groups_Oabs__class_Oabs(_1050553), _1050555)), _1050557)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050553), hAPP(c_Groups_Ouminus__class_Ouminus(_1050553), _1050555)), _1050557)))], (464 ^ _775212) ^ [_782306, _782308, _782310, _782312, _782314, _782316, _782318, _782320, _782322, _782324] : [-(c_Finite__Set_Ofolding__image(_782322, _782318, _782314, _782310, _782306)), c_Finite__Set_Ofolding__image(_782324, _782320, _782316, _782312, _782308), _782324 = _782322, _782320 = _782318, _782316 = _782314, _782312 = _782310, _782308 = _782306], (38040 ^ _775212) ^ [_1488052, _1488054, _1488056, _1488058] : [-(_1488052 = c_Orderings_Obot__class_Obot(tc_fun(_1488054, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1488056, _1488054), _1488056, c_Product__Type_Ofst(_1488056, _1488054)), hAPP(hAPP(c_Product__Type_OSigma(_1488056, _1488054), _1488058), hAPP(c_COMBK(tc_fun(_1488054, tc_HOL_Obool), _1488056), _1488052))) = _1488058)], (10011 ^ _775212) ^ [_937541, _937543, _937545] : [class_Rings_Olinordered__semidom(_937541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937541), c_Groups_Oone__class_Oone(_937541)), _937543)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937541), c_Groups_Oone__class_Oone(_937541)), _937545)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937541), c_Groups_Oone__class_Oone(_937541)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937541), _937543), _937545))))], (44278 ^ _775212) ^ [_1645245, _1645247, _1645249, _1645251] : [hBOOL(hAPP(hAPP(c_member(_1645245), _1645247), c_Wellfounded_Oacc(_1645245, _1645249))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1645245)), _1645251), c_Wellfounded_Oacc(tc_List_Olist(_1645245), c_List_Olistrel1(_1645245, _1645249)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1645245)), hAPP(hAPP(c_List_Olist_OCons(_1645245), _1645247), _1645251)), c_Wellfounded_Oacc(tc_List_Olist(_1645245), c_List_Olistrel1(_1645245, _1645249)))))], (47438 ^ _775212) ^ [_1721444, _1721446] : [-(hBOOL(hAPP(c_List_Olistsp(_1721444, _1721446), c_List_Olist_ONil(_1721444))))], (40614 ^ _775212) ^ [_1555987, _1555989, _1555991, _1555993, _1555995] : [class_Groups_Ocomm__monoid__mult(_1555987), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555989), _1555991)), c_Fun_Oinj__on(_1555989, _1555989, _1555993, _1555991), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555989, _1555987), _1555995), hAPP(c_Set_Oimage(_1555989, _1555989, _1555993), _1555991)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555989, _1555987), hAPP(c_Fun_Ocomp(_1555989, _1555987, _1555989, _1555995), _1555993)), _1555991))], (32977 ^ _775212) ^ [_1373380, _1373382, _1373384] : [class_Groups_Ocomm__monoid__mult(_1373380), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1373382, _1373380), _1373384), c_Orderings_Obot__class_Obot(tc_fun(_1373382, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1373380))], (11176 ^ _775212) ^ [_958599, _958601, _958603, _958605] : [class_Rings_Olinordered__ring__strict(_958599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958599), c_Groups_Ozero__class_Ozero(_958599)), _958601)), 11183 ^ _775212 : [(11190 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958599), _958603), _958605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958599), _958601), _958603)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958599), _958601), _958605))))], (11184 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958599), _958601), _958603)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958599), _958601), _958605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958599), _958603), _958605)))]]], (23072 ^ _775212) ^ [_1174596, _1174598, _1174600, _1174602] : [class_Orderings_Olinorder(_1174596), 23075 ^ _775212 : [(23076 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174596), _1174598), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174596), _1174600), _1174602))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174596), _1174598), _1174600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174596), _1174598), _1174602)))], (23086 ^ _775212) ^ [] : [23087 ^ _775212 : [(23090 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174596), _1174598), _1174602))], (23088 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174596), _1174598), _1174600))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174596), _1174598), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174596), _1174600), _1174602))))]]], (40043 ^ _775212) ^ [_1542744, _1542746, _1542748, _1542750] : [hBOOL(hAPP(hAPP(c_member(_1542744), _1542746), hAPP(c_Relation_ODomain(_1542744, _1542748), _1542750))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542744, _1542748)), hAPP(hAPP(c_Product__Type_OPair(_1542744, _1542748), _1542746), 40046 ^ [_1542744, _1542746, _1542748, _1542750])), _1542750)))], (28040 ^ _775212) ^ [_1271764, _1271766] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271764, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1271764, tc_HOL_Obool)), _1271766)), _1271766) = c_Orderings_Otop__class_Otop(tc_fun(_1271764, tc_HOL_Obool)))], (51555 ^ _775212) ^ [_1811916, _1811918] : [c_Predicate_Oreflp(_1811916, _1811918), c_Predicate_Osymp(_1811916, _1811918), c_Predicate_Otransp(_1811916, _1811918), -(c_Equiv__Relations_Oequivp(_1811916, _1811918))], (19343 ^ _775212) ^ [_1104866, _1104868, _1104870] : [class_Fields_Olinordered__field(_1104866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104866), _1104868), c_Groups_Ozero__class_Ozero(_1104866))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104866), _1104870), c_Groups_Ozero__class_Ozero(_1104866))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104866), c_Groups_Ozero__class_Ozero(_1104866)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104866), _1104868), _1104870))))], (12622 ^ _775212) ^ [_983431, _983433] : [class_Divides_Osemiring__div(_983431), -(c_Divides_Odiv__class_Omod(_983431, _983433, c_Groups_Oone__class_Oone(_983431)) = c_Groups_Ozero__class_Ozero(_983431))], (18179 ^ _775212) ^ [_1083854, _1083856] : [c_Int_OBit1(_1083854) = c_Int_OBit0(_1083856)], (13845 ^ _775212) ^ [_1005113, _1005115, _1005117] : [class_Divides_Osemiring__div(_1005113), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1005113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005113), _1005115), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1005113), _1005117), _1005115))), c_Divides_Odiv__class_Omod(_1005113, _1005117, _1005115)) = _1005117)], (43386 ^ _775212) ^ [_1622400, _1622402, _1622404, _1622406] : [-(hAPP(c_Set_Ovimage(_1622400, _1622402, _1622404), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1622402, tc_HOL_Obool), _1622406)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1622402, tc_HOL_Obool), tc_fun(_1622400, tc_HOL_Obool)), _1622406), c_Set_Ovimage(_1622400, _1622402, _1622404)))], (12352 ^ _775212) ^ [_978443] : [_978443 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _978443) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19329 ^ _775212) ^ [_1104611, _1104613, _1104615] : [class_Fields_Olinordered__field(_1104611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104611), _1104613), c_Groups_Ozero__class_Ozero(_1104611))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104611), c_Groups_Ozero__class_Ozero(_1104611)), _1104615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104611), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104611), _1104613), _1104615)), c_Groups_Ozero__class_Ozero(_1104611))))], (30398 ^ _775212) ^ [_1322439, _1322441, _1322443, _1322445, _1322447] : [class_Groups_Ocomm__monoid__add(_1322439), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322441), _1322443)), -(hBOOL(hAPP(hAPP(c_member(_1322441), _1322445), _1322443))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1322441, _1322439), _1322447), hAPP(hAPP(c_Set_Oinsert(_1322441), _1322445), _1322443)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1322439), hAPP(_1322447, _1322445)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1322441, _1322439), _1322447), _1322443)))], (6571 ^ _775212) ^ [_879340, _879342] : [class_Groups_Ocomm__monoid__add(_879340), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879340), c_Groups_Ozero__class_Ozero(_879340)), _879342) = _879342)], (28030 ^ _775212) ^ [_1271640, _1271642, _1271644, _1271646] : [class_Groups_Ocomm__monoid__add(_1271640), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1271642), _1271644))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1271642, _1271640), _1271646), _1271644) = c_Groups_Ozero__class_Ozero(_1271640))], (24702 ^ _775212) ^ [_1204093, _1204095, _1204097, _1204099] : [class_Divides_Osemiring__div(_1204093), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204093), _1204095), _1204097)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204093), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204093), _1204097), _1204095)), _1204099) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204093), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204093), _1204097), _1204099)), _1204095))], (17055 ^ _775212) ^ [_1065466] : [-(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, _1065466))))))], (23820 ^ _775212) ^ [_1189215, _1189217] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1189215), _1189217) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1189215)), hAPP(c_Code__Numeral_Onat__of, _1189217))))], (50566 ^ _775212) ^ [_1789245, _1789247, _1789249] : [c_List_Olist__all(_1789245, _1789247, _1789249), 50569 ^ _775212 : [(50570 ^ _775212) ^ [_1789326] : [hBOOL(hAPP(hAPP(c_member(_1789245), _1789326), hAPP(c_List_Oset(_1789245), _1789249))), -(hBOOL(hAPP(_1789247, _1789326)))]]], (7601 ^ _775212) ^ [_896674] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _896674)) = _896674)], (31931 ^ _775212) ^ [_1352586, _1352588, _1352590] : [class_Lattices_Olattice(_1352586), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352586), _1352588)), -(_1352588 = c_Orderings_Obot__class_Obot(tc_fun(_1352586, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352586), _1352590)), -(_1352590 = c_Orderings_Obot__class_Obot(tc_fun(_1352586, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1352586, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352586, tc_HOL_Obool)), _1352588), _1352590)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1352586), c_Big__Operators_Olattice__class_OSup__fin(_1352586, _1352588)), c_Big__Operators_Olattice__class_OSup__fin(_1352586, _1352590)))], (6701 ^ _775212) ^ [_881694, _881696] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _881694)), _881696) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881694), hAPP(c_Nat_OSuc, _881696)))], (42073 ^ _775212) ^ [_1588287, _1588289] : [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), _1588287), _1588289)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1588287), _1588289)))], (17773 ^ _775212) ^ [_1077006] : [-(c_Int_OBit1(_1077006) = 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)), _1077006)), _1077006))], (29931 ^ _775212) ^ [_1308674, _1308676, _1308678, _1308680, _1308682] : [hBOOL(hAPP(hAPP(c_member(_1308674), _1308676), c_SetInterval_Oord_OatLeastAtMost(_1308674, _1308678, _1308680, _1308682))), 29934 ^ _775212 : [(29937 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1308678, _1308676), _1308682)))], (29935 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1308678, _1308680), _1308676)))]]], (25587 ^ _775212) ^ [_1221197, _1221199, _1221201] : [class_Groups_Ocomm__monoid__add(_1221197), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221199, _1221197), hAPP(c_COMBK(_1221197, _1221199), c_Groups_Ozero__class_Ozero(_1221197))), _1221201) = c_Groups_Ozero__class_Ozero(_1221197))], (11855 ^ _775212) ^ [_969785, _969787, _969789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969787), _969789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969785), _969787)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969785), _969789))))], (1434 ^ _775212) ^ [_795993, _795995] : [-(class_Orderings_Otop(_795993)), _795995 = _795993, class_Orderings_Otop(_795995)], (8359 ^ _775212) ^ [_910248, _910250, _910252] : [class_Rings_Olinordered__semiring__strict(_910248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910248), c_Groups_Ozero__class_Ozero(_910248)), _910250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910248), _910252), c_Groups_Ozero__class_Ozero(_910248))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_910248), _910252), _910250)), c_Groups_Ozero__class_Ozero(_910248))))], (9339 ^ _775212) ^ [_926394, _926396, _926398] : [class_Orderings_Opreorder(_926394), 9342 ^ _775212 : [(9351 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926394), _926396), _926398))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926394), _926396), _926398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926394), _926398), _926396)))], (9343 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926394), _926396), _926398)), 9346 ^ _775212 : [(9349 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926394), _926398), _926396))], (9347 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926394), _926396), _926398)))]]]]], (23852 ^ _775212) ^ [_1189799, _1189801, _1189803] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1189799), _1189801)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1189799), _1189803))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1189799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1189801), _1189803)))], (52675 ^ _775212) ^ [_1828146, _1828148] : [-(hAPP(c_COMBI(_1828146), _1828148) = _1828148)], (40221 ^ _775212) ^ [_1547280, _1547282] : [c_Wellfounded_Owf(_1547280, _1547282), -(c_Wellfounded_Oacyclic(_1547280, _1547282))], (1834 ^ _775212) ^ [_800993, _800995] : [-(class_Orderings_Oord(_800993)), _800995 = _800993, class_Orderings_Oord(_800995)], (38955 ^ _775212) ^ [_1507930, _1507932, _1507934] : [hBOOL(hAPP(hAPP(c_member(_1507930), _1507932), hAPP(c_Set_OCollect(_1507930), _1507934))), -(hBOOL(hAPP(_1507934, _1507932)))], (46506 ^ _775212) ^ [_1701839, _1701841, _1701843] : [-(_1701839 = c_List_Olist_ONil(_1701841)), -(hAPP(c_List_Otl(_1701841), hAPP(hAPP(c_List_Oappend(_1701841), _1701839), _1701843)) = hAPP(hAPP(c_List_Oappend(_1701841), hAPP(c_List_Otl(_1701841), _1701839)), _1701843))], (23604 ^ _775212) ^ [_1185056, _1185058, _1185060, _1185062] : [-(c_HOL_OThe(tc_prod(_1185056, _1185058), hAPP(c_Product__Type_Oprod_Oprod__case(_1185056, _1185058, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1185056, tc_fun(_1185058, tc_HOL_Obool), tc_fun(_1185058, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1185058, tc_HOL_Obool), tc_fun(_1185058, tc_HOL_Obool)), _1185056), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1185058)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1185056), c_fconj), hAPP(c_fequal, _1185060)))), hAPP(c_fequal, _1185062)))) = hAPP(hAPP(c_Product__Type_OPair(_1185056, _1185058), _1185060), _1185062))], (31190 ^ _775212) ^ [_1339072, _1339074, _1339076, _1339078, _1339080] : [c_Finite__Set_Ofolding__one(_1339072, _1339074, _1339076), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339072), _1339078)), 31197 ^ _775212 : [(31204 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339072, tc_HOL_Obool)), _1339078), hAPP(hAPP(c_Set_Oinsert(_1339072), _1339080), c_Orderings_Obot__class_Obot(tc_fun(_1339072, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1339072, tc_HOL_Obool))), -(hAPP(_1339076, hAPP(hAPP(c_Set_Oinsert(_1339072), _1339080), _1339078)) = hAPP(hAPP(_1339074, _1339080), hAPP(_1339076, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339072, tc_HOL_Obool)), _1339078), hAPP(hAPP(c_Set_Oinsert(_1339072), _1339080), c_Orderings_Obot__class_Obot(tc_fun(_1339072, tc_HOL_Obool)))))))], (31198 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339072, tc_HOL_Obool)), _1339078), hAPP(hAPP(c_Set_Oinsert(_1339072), _1339080), c_Orderings_Obot__class_Obot(tc_fun(_1339072, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1339072, tc_HOL_Obool)), -(hAPP(_1339076, hAPP(hAPP(c_Set_Oinsert(_1339072), _1339080), _1339078)) = _1339080)]]], (21280 ^ _775212) ^ [_1139769, _1139771, _1139773] : [21282 ^ _775212 : [(21285 ^ _775212) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1139769, _1139771), 21281 ^ [_1139769, _1139771, _1139773]))], (21283 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1139771, 21281 ^ [_1139769, _1139771, _1139773]), _1139773)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1139769, _1139771), _1139773)))], (41267 ^ _775212) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (31238 ^ _775212) ^ [_1340200, _1340202, _1340204, _1340206, _1340208] : [class_Groups_Oordered__ab__semigroup__add(_1340200), class_Rings_Osemiring__1(_1340200), 31248 ^ _775212 : [(31251 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340200), hAPP(_1340206, 31247 ^ [_1340200, _1340202, _1340204, _1340206, _1340208])), _1340208))], (31249 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1340202), 31247 ^ [_1340200, _1340202, _1340204, _1340206, _1340208]), _1340204)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340200), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1340202, _1340200), _1340206), _1340204)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1340200), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1340200), hAPP(c_Finite__Set_Ocard(_1340202), _1340204))), _1340208))))], (5290 ^ _775212) ^ [_855961, _855963] : [_855963 = _855961, -(c_Relation_OId(_855963) = c_Relation_OId(_855961))], (16521 ^ _775212) ^ [_1056284, _1056286] : [class_Groups_Oordered__ab__group__add__abs(_1056284), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056284), _1056286), c_Groups_Ozero__class_Ozero(_1056284))), -(hAPP(c_Groups_Oabs__class_Oabs(_1056284), _1056286) = hAPP(c_Groups_Ouminus__class_Ouminus(_1056284), _1056286))], (12939 ^ _775212) ^ [_988905, _988907, _988909, _988911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _988905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _988907)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _988907), _988909)), -(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), _988909), c_Divides_Odiv__class_Omod(tc_Int_Oint, _988911, _988905))), _988907)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _988909), _988905))))], (37090 ^ _775212) ^ [_1465090, _1465092, _1465094, _1465096] : [c_Fun_Oinj__on(_1465090, _1465092, _1465094, c_Orderings_Otop__class_Otop(tc_fun(_1465090, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1465090, _1465092, c_Orderings_Otop__class_Otop(tc_fun(_1465090, tc_HOL_Obool)), _1465094), hAPP(_1465094, _1465096)) = _1465096)], (42353 ^ _775212) ^ [_1595478, _1595480, _1595482, _1595484, _1595486] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595478, tc_fun(_1595480, tc_HOL_Obool)), _1595482), hAPP(hAPP(c_COMBS(_1595478, tc_fun(_1595480, tc_HOL_Obool), tc_fun(_1595480, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1595480, tc_HOL_Obool), tc_fun(tc_fun(_1595480, tc_HOL_Obool), tc_fun(_1595480, tc_HOL_Obool)), _1595478), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1595480, tc_HOL_Obool))), _1595484)), _1595486)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1595480, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595478, tc_fun(_1595480, tc_HOL_Obool)), _1595482), _1595484)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595478, tc_fun(_1595480, tc_HOL_Obool)), _1595482), _1595486)))], (40959 ^ _775212) ^ [_1563873, _1563875, _1563877, _1563879] : [-(c_New__Random__Sequence_Oneg__map(_1563873, _1563875, _1563877, _1563879) = c_New__Random__Sequence_Oneg__bind(_1563873, _1563875, _1563879, hAPP(c_Fun_Ocomp(_1563875, 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(_1563875)))))), _1563873, c_New__Random__Sequence_Oneg__single(_1563875)), _1563877)))], (20105 ^ _775212) ^ [_1118220, _1118222, _1118224, _1118226] : [class_Fields_Ofield__inverse__zero(_1118220), -(_1118222 = c_Groups_Ozero__class_Ozero(_1118220)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118220), _1118224), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118220), _1118226), _1118222)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118220), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118220), _1118226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118220), _1118224), _1118222))), _1118222))], (23728 ^ _775212) ^ [_1187600, _1187602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1187600)), hAPP(c_Code__Numeral_Oof__nat, _1187602))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1187600), _1187602)))], (51747 ^ _775212) ^ [_1815657, _1815659] : [-(c_Relation_Osym(_1815657, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1815657, _1815657), tc_HOL_Obool)), _1815659), hAPP(c_Relation_Oconverse(_1815657, _1815657), _1815659))))], (10824 ^ _775212) ^ [_952039] : [-(hBOOL(hAPP(_952039, 10831 ^ [_952039]))), 10825 ^ _775212 : [(10826 ^ _775212) ^ [_952091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952091)), hBOOL(hAPP(_952039, hAPP(c_Int_Onat, _952091)))]]], (13290 ^ _775212) ^ [_995731, _995733] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _995731), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _995733)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _995731)), _995733))], (31881 ^ _775212) ^ [_1351750, _1351752, _1351754] : [class_Lattices_Olattice(_1351750), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351750), _1351752)), -(_1351754 = c_Orderings_Obot__class_Obot(tc_fun(_1351750, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1351750, tc_HOL_Obool)), _1351754), _1351752)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1351750), c_Big__Operators_Olattice__class_OSup__fin(_1351750, _1351754)), c_Big__Operators_Olattice__class_OSup__fin(_1351750, _1351752)) = c_Big__Operators_Olattice__class_OSup__fin(_1351750, _1351752))], (1124 ^ _775212) ^ [_792118, _792120] : [-(class_Rings_Oring__1__no__zero__divisors(_792118)), _792120 = _792118, class_Rings_Oring__1__no__zero__divisors(_792120)], (52439 ^ _775212) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (43835 ^ _775212) ^ [_1633387, _1633389, _1633391] : [43837 ^ _775212 : [(43840 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1633387), _1633391), 43836 ^ [_1633387, _1633389, _1633391]))], (43838 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1633387, tc_HOL_Obool)), 43836 ^ [_1633387, _1633389, _1633391]), _1633389)))]], -(hBOOL(hAPP(hAPP(c_member(_1633387), _1633391), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1633387, tc_HOL_Obool), _1633389))))], (32765 ^ _775212) ^ [_1369196, _1369198, _1369200, _1369202, _1369204, _1369206] : [class_Groups_Ocomm__monoid__mult(_1369196), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369198), _1369200)), 32772 ^ _775212 : [(32779 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1369198), _1369202), _1369200))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1369198, _1369196), hAPP(hAPP(c_COMBC(_1369198, _1369196, _1369196), hAPP(hAPP(c_COMBS(_1369198, _1369196, tc_fun(_1369196, _1369196)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1369196, tc_fun(_1369196, _1369196)), _1369198), c_If(_1369196)), hAPP(hAPP(c_COMBC(_1369198, _1369198, tc_HOL_Obool), c_fequal), _1369202))), _1369204)), _1369206)), _1369200) = hAPP(hAPP(c_Power_Opower__class_Opower(_1369196), _1369206), hAPP(c_Finite__Set_Ocard(_1369198), _1369200)))], (32773 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1369198), _1369202), _1369200)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1369198, _1369196), hAPP(hAPP(c_COMBC(_1369198, _1369196, _1369196), hAPP(hAPP(c_COMBS(_1369198, _1369196, tc_fun(_1369196, _1369196)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1369196, tc_fun(_1369196, _1369196)), _1369198), c_If(_1369196)), hAPP(hAPP(c_COMBC(_1369198, _1369198, tc_HOL_Obool), c_fequal), _1369202))), _1369204)), _1369206)), _1369200) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369196), hAPP(_1369204, _1369202)), hAPP(hAPP(c_Power_Opower__class_Opower(_1369196), _1369206), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1369198), _1369200)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (52639 ^ _775212) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (21947 ^ _775212) ^ [_1151794, _1151796] : [c_Code__Numeral_OSuc__code__numeral(_1151794) = c_Code__Numeral_OSuc__code__numeral(_1151796), -(_1151794 = _1151796)], (48043 ^ _775212) ^ [_1734570, _1734572] : [c_List_Olist_ONil(_1734570) = c_List_Oconcat(_1734570, _1734572), 48046 ^ _775212 : [(48047 ^ _775212) ^ [_1734661] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1734570)), _1734661), hAPP(c_List_Oset(tc_List_Olist(_1734570)), _1734572))), -(_1734661 = c_List_Olist_ONil(_1734570))]]], (41949 ^ _775212) ^ [_1585309, _1585311, _1585313, _1585315, _1585317] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585309, _1585309)), hAPP(hAPP(c_Product__Type_OPair(_1585309, _1585309), _1585311), _1585313)), _1585315)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585309, _1585309)), hAPP(hAPP(c_Product__Type_OPair(_1585309, _1585309), _1585313), _1585317)), c_Transitive__Closure_Ortrancl(_1585309, _1585315))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585309, _1585309)), hAPP(hAPP(c_Product__Type_OPair(_1585309, _1585309), _1585311), _1585317)), c_Transitive__Closure_Otrancl(_1585309, _1585315))))], (44606 ^ _775212) ^ [_1655100, _1655102, _1655104, _1655106] : [-(hAPP(hAPP(c_List_Onth(_1655100), hAPP(hAPP(c_List_Olist_OCons(_1655100), _1655102), _1655104)), _1655106) = c_Nat_Onat_Onat__case(_1655100, _1655102, hAPP(c_List_Onth(_1655100), _1655104), _1655106))], (41257 ^ _775212) ^ [_1570494, _1570496, _1570498, _1570500] : [class_Lattices_Osemilattice__inf(_1570494), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570494), _1570496)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1570494, _1570494, c_Lattices_Osemilattice__inf__class_Oinf(_1570494)), _1570498), hAPP(hAPP(c_Set_Oinsert(_1570494), _1570500), _1570496)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1570494), _1570500), hAPP(hAPP(c_Finite__Set_Ofold(_1570494, _1570494, c_Lattices_Osemilattice__inf__class_Oinf(_1570494)), _1570498), _1570496)))], (45654 ^ _775212) ^ [_1681874, _1681876, _1681878, _1681880, _1681882] : [hAPP(hAPP(c_List_Oappend(_1681874), _1681876), hAPP(hAPP(c_List_Olist_OCons(_1681874), _1681878), c_List_Olist_ONil(_1681874))) = hAPP(hAPP(c_List_Oappend(_1681874), _1681880), hAPP(hAPP(c_List_Olist_OCons(_1681874), _1681882), c_List_Olist_ONil(_1681874))), 45657 ^ _775212 : [(45660 ^ _775212) ^ [] : [-(_1681878 = _1681882)], (45658 ^ _775212) ^ [] : [-(_1681876 = _1681880)]]], (51012 ^ _775212) ^ [_1798824, _1798826, _1798828, _1798830] : [hBOOL(hAPP(hAPP(c_List_Omember(_1798824), hAPP(hAPP(c_List_Olist_OCons(_1798824), _1798826), _1798828)), _1798830)), -(_1798826 = _1798830), -(hBOOL(hAPP(hAPP(c_List_Omember(_1798824), _1798828), _1798830)))], (10361 ^ _775212) ^ [_943910, _943912, _943914, _943916] : [class_Rings_Oordered__ring(_943910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943910), _943912), _943914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943910), _943916), c_Groups_Ozero__class_Ozero(_943910))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943910), _943916), _943914)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943910), _943916), _943912))))], (6980 ^ _775212) ^ [_886394, _886396, _886398] : [class_Orderings_Opreorder(_886394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886394), _886396), _886398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886394), _886398), _886396))], (26499 ^ _775212) ^ [_1240874, _1240876, _1240878] : [-(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)), _1240874)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1240876), _1240878)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1240876), _1240874)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1240878), _1240874)))], (44758 ^ _775212) ^ [_1659179, _1659181, _1659183, _1659185] : [-(hAPP(c_List_Oset(_1659179), hAPP(hAPP(c_List_Omap(_1659181, _1659179), _1659183), _1659185)) = hAPP(c_Set_Oimage(_1659181, _1659179, _1659183), hAPP(c_List_Oset(_1659181), _1659185)))], (23268 ^ _775212) ^ [_1178692, _1178694, _1178696] : [class_Groups_Olinordered__ab__group__add(_1178692), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1178692), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178692), _1178694), _1178696)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1178692), hAPP(c_Groups_Ouminus__class_Ouminus(_1178692), _1178694)), hAPP(c_Groups_Ouminus__class_Ouminus(_1178692), _1178696)))], (5789 ^ _775212) ^ [_866547, _866549, _866551, _866553] : [c_Com_Ocom_OWhile(_866547, _866549) = c_Com_Ocom_OWhile(_866551, _866553), 5792 ^ _775212 : [(5795 ^ _775212) ^ [] : [-(_866549 = _866553)], (5793 ^ _775212) ^ [] : [-(_866547 = _866551)]]], (18165 ^ _775212) ^ [_1083668] : [c_Int_OPls = c_Int_OBit0(_1083668), -(c_Int_OPls = _1083668)], (42301 ^ _775212) ^ [_1594148, _1594150, _1594152, _1594154, _1594156, _1594158] : [class_Complete__Lattice_Ocomplete__lattice(_1594148), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594150, tc_fun(_1594152, _1594148)), _1594154), _1594156), _1594158) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594150, _1594148), _1594154), hAPP(hAPP(c_COMBC(_1594150, _1594152, _1594148), _1594156), _1594158)))], (8373 ^ _775212) ^ [_910503, _910505, _910507] : [class_Rings_Olinordered__semiring__strict(_910503), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910503), c_Groups_Ozero__class_Ozero(_910503)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_910503), _910505), _910507))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910503), c_Groups_Ozero__class_Ozero(_910503)), _910505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910503), c_Groups_Ozero__class_Ozero(_910503)), _910507)))], (48861 ^ _775212) ^ [_1752669, _1752671, _1752673] : [class_Orderings_Olinorder(_1752669), 48864 ^ _775212 : [(48877 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1752669, hAPP(hAPP(c_List_Olist_OCons(_1752669), _1752671), _1752673))), c_List_Olinorder__class_Osorted(_1752669, _1752673), 48883 ^ _775212 : [(48886 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1752669), _1752671), 48882 ^ [_1752669, _1752671, _1752673]))], (48884 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752669), 48882 ^ [_1752669, _1752671, _1752673]), hAPP(c_List_Oset(_1752669), _1752673))))]]], (48865 ^ _775212) ^ [] : [c_List_Olinorder__class_Osorted(_1752669, hAPP(hAPP(c_List_Olist_OCons(_1752669), _1752671), _1752673)), 48868 ^ _775212 : [(48871 ^ _775212) ^ [_1752855] : [hBOOL(hAPP(hAPP(c_member(_1752669), _1752855), hAPP(c_List_Oset(_1752669), _1752673))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1752669), _1752671), _1752855)))], (48869 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1752669, _1752673))]]]]], (16819 ^ _775212) ^ [_1062045] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062045))), -(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), _1062045)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17289 ^ _775212) ^ [_1069152] : [class_Int_Onumber__ring(_1069152), -(c_Groups_Ozero__class_Ozero(_1069152) = hAPP(c_Int_Onumber__class_Onumber__of(_1069152), c_Int_OPls))], (52433 ^ _775212) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (49626 ^ _775212) ^ [_1768729, _1768731] : [class_Orderings_Olinorder(_1768729), 49633 ^ _775212 : [(49638 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1768729), hAPP(hAPP(c_List_Onth(_1768729), _1768731), 49631 ^ [_1768729, _1768731])), hAPP(hAPP(c_List_Onth(_1768729), _1768731), 49632 ^ [_1768729, _1768731])))], (49636 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49632 ^ [_1768729, _1768731]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768729)), _1768731))))], (49634 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 49631 ^ [_1768729, _1768731]), 49632 ^ [_1768729, _1768731])))]], -(c_List_Olinorder__class_Osorted(_1768729, _1768731))], (40993 ^ _775212) ^ [_1564758, _1564760, _1564762] : [-(hBOOL(hAPP(hAPP(c_member(_1564758), _1564760), c_Wellfounded_Oacc(_1564758, _1564762)))), 40997 ^ _775212 : [(41000 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1564758), 40996 ^ [_1564758, _1564760, _1564762]), c_Wellfounded_Oacc(_1564758, _1564762)))], (40998 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564758, _1564758)), hAPP(hAPP(c_Product__Type_OPair(_1564758, _1564758), 40996 ^ [_1564758, _1564760, _1564762]), _1564760)), _1564762)))]]], (22798 ^ _775212) ^ [_1169450, _1169452] : [-(_1169450 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22801 ^ _775212 : [(22808 ^ _775212) ^ [] : [-(_1169452 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1169450, _1169452) = 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, _1169452))), 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, _1169450)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1169452))), c_Divides_Opdivmod(_1169450, _1169452)), 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), _1169452))))), c_Divides_Opdivmod(_1169450, _1169452)))))], (22802 ^ _775212) ^ [] : [_1169452 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1169450, _1169452) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1169450))]]], (52299 ^ _775212) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (5316 ^ _775212) ^ [_856344, _856346, _856348, _856350] : [-(c_Transitive__Closure_Ortrancl(_856350, _856346) = c_Transitive__Closure_Ortrancl(_856348, _856344)), _856350 = _856348, _856346 = _856344], (23740 ^ _775212) ^ [_1187816, _1187818] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1187816)), hAPP(c_Code__Numeral_Oof__nat, _1187818)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1187816), _1187818)))], (46230 ^ _775212) ^ [_1695738, _1695740, _1695742, _1695744] : [-(hAPP(hAPP(c_List_Odrop(_1695738), hAPP(c_Nat_OSuc, _1695740)), hAPP(hAPP(c_List_Olist_OCons(_1695738), _1695742), _1695744)) = hAPP(hAPP(c_List_Odrop(_1695738), _1695740), _1695744))], (49349 ^ _775212) ^ [_1762739, _1762741, _1762743] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1762739), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1762739))), _1762741))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1762743), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1762739))), _1762741))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1762739))), hAPP(c_List_Ofilter(tc_List_Olist(_1762739), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1762739)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1762743)), c_Nat_Osize__class_Osize(tc_List_Olist(_1762739)))), c_List_Otranspose(_1762739, _1762741))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762739)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1762739)), _1762741), _1762743)))], (38808 ^ _775212) ^ [_1504788] : [class_Lattices_Oab__semigroup__idem__mult(_1504788), -(c_Finite__Set_Ofun__left__comm__idem(_1504788, _1504788, c_Groups_Otimes__class_Otimes(_1504788)))], (25104 ^ _775212) ^ [_1211960, _1211962, _1211964, _1211966, _1211968] : [-(hAPP(c_New__DSequence_Opos__bind(_1211960, _1211962, _1211964, _1211966), _1211968) = hAPP(c_Lazy__Sequence_Obind(_1211960, _1211962, hAPP(_1211964, _1211968)), hAPP(hAPP(c_COMBC(_1211960, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1211962)), _1211966), _1211968)))], (43214 ^ _775212) ^ [_1618626, _1618628, _1618630] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1618626, tc_HOL_Obool)), _1618628), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1618626, tc_HOL_Obool), _1618630)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1618626, tc_HOL_Obool), tc_fun(_1618626, tc_HOL_Obool)), _1618630), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1618626, tc_HOL_Obool)), _1618628)))], (47941 ^ _775212) ^ [_1732575, _1732577, _1732579, _1732581] : [-(c_Lazy__Sequence_Oproduct(_1732575, _1732577, _1732579, _1732581) = hAPP(c_Lazy__Sequence_Obind(_1732575, tc_prod(_1732575, _1732577), _1732579), hAPP(hAPP(c_COMBB(tc_fun(_1732577, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1732575, _1732577))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1732575, _1732577)), _1732575), c_Lazy__Sequence_Obind(_1732577, tc_prod(_1732575, _1732577), _1732581)), hAPP(hAPP(c_COMBB(tc_fun(_1732577, tc_prod(_1732575, _1732577)), tc_fun(_1732577, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1732575, _1732577))), _1732575), hAPP(c_COMBB(tc_prod(_1732575, _1732577), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1732575, _1732577)), _1732577), c_Lazy__Sequence_Osingle(tc_prod(_1732575, _1732577)))), c_Product__Type_OPair(_1732575, _1732577)))))], (6673 ^ _775212) ^ [_881265, _881267] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881265), _881267) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 6676 ^ _775212 : [(6679 ^ _775212) ^ [] : [-(_881267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6677 ^ _775212) ^ [] : [-(_881265 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (49107 ^ _775212) ^ [_1757751, _1757753] : [hBOOL(hAPP(c_List_Odistinct(_1757751), hAPP(c_List_Orev(_1757751), _1757753))), -(hBOOL(hAPP(c_List_Odistinct(_1757751), _1757753)))], (44553 ^ _775212) ^ [_1653492, _1653494, _1653496] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653492)), _1653494), c_Wellfounded_Oacc(tc_List_Olist(_1653492), c_List_Olistrel1(_1653492, _1653496)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653492)), _1653494), c_List_Olists(_1653492, c_Wellfounded_Oacc(_1653492, _1653496)))))], (44947 ^ _775212) ^ [_1663532, _1663534, _1663536, _1663538, _1663540] : [hBOOL(hAPP(hAPP(c_member(_1663532), _1663534), hAPP(c_List_Oset(_1663532), _1663536))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663538), hAPP(_1663540, _1663534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663538), c_List_Olist_Olist__size(_1663532, _1663540, _1663536))))], (52591 ^ _775212) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (47909 ^ _775212) ^ [_1731805, _1731807, _1731809, _1731811] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1731805)), _1731807), hAPP(c_List_Oset(tc_List_Olist(_1731805)), c_Enum_On__lists(_1731805, _1731809, _1731811)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731805)), _1731807) = _1731809)], (37818 ^ _775212) ^ [_1481636, _1481638, _1481640, _1481642, _1481644] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1481636, _1481638, hAPP(hAPP(c_Set_Oinsert(_1481636), _1481640), _1481642)), _1481644))), 37819 ^ _775212 : [(37820 ^ _775212) ^ [_1481740, _1481742] : [hAPP(hAPP(c_Set_Oinsert(_1481636), _1481640), _1481642) = hAPP(hAPP(c_Set_Oinsert(_1481636), _1481742), _1481740), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1481636, _1481636, _1481638, _1481742, _1481740), _1481644)), -(hBOOL(hAPP(hAPP(c_member(_1481636), _1481742), _1481740)))]]], (31561 ^ _775212) ^ [_1346551, _1346553] : [class_Groups_Olinordered__ab__group__add(_1346551), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346551), _1346553)), -(_1346553 = c_Orderings_Obot__class_Obot(tc_fun(_1346551, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1346551), c_Big__Operators_Olinorder__class_OMax(_1346551, _1346553)) = c_Big__Operators_Olinorder__class_OMin(_1346551, hAPP(c_Set_Oimage(_1346551, _1346551, c_Groups_Ouminus__class_Ouminus(_1346551)), _1346553)))], (42193 ^ _775212) ^ [_1590942, _1590944, _1590946, _1590948, _1590950, _1590952] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590942, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1590944, _1590942, _1590946), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590948, tc_fun(_1590944, tc_HOL_Obool)), _1590950), _1590952))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590948, tc_fun(_1590942, tc_HOL_Obool)), _1590950), hAPP(hAPP(c_COMBB(tc_fun(_1590944, tc_HOL_Obool), tc_fun(_1590942, tc_HOL_Obool), _1590948), c_Relation_OImage(_1590944, _1590942, _1590946)), _1590952)))))], (19945 ^ _775212) ^ [_1115257, _1115259, _1115261, _1115263] : [class_Fields_Olinordered__field(_1115257), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115257), c_Groups_Ozero__class_Ozero(_1115257)), _1115259)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115257), _1115261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115257), _1115263), _1115259))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115257), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115257), _1115261), _1115259)), _1115263)))], (12785 ^ _775212) ^ [_986116, _986118, _986120, _986122] : [class_Groups_Ouminus(_986116), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_986118, _986116)), _986120), _986122) = hAPP(c_Groups_Ouminus__class_Ouminus(_986116), hAPP(_986120, _986122)))], (10167 ^ _775212) ^ [_940379, _940381, _940383] : [class_Rings_Olinordered__ring__strict(_940379), 10170 ^ _775212 : [(10185 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940379), c_Groups_Ozero__class_Ozero(_940379)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940379), _940381), _940383)))), 10186 ^ _775212 : [(10193 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940379), _940381), c_Groups_Ozero__class_Ozero(_940379))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940379), _940383), c_Groups_Ozero__class_Ozero(_940379)))], (10187 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940379), c_Groups_Ozero__class_Ozero(_940379)), _940381)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940379), c_Groups_Ozero__class_Ozero(_940379)), _940383))]]], (10171 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940379), c_Groups_Ozero__class_Ozero(_940379)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940379), _940381), _940383))), 10176 ^ _775212 : [(10179 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940379), c_Groups_Ozero__class_Ozero(_940379)), _940383)))], (10177 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940379), c_Groups_Ozero__class_Ozero(_940379)), _940381)))]], 10180 ^ _775212 : [(10183 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940379), _940383), c_Groups_Ozero__class_Ozero(_940379))))], (10181 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940379), _940381), c_Groups_Ozero__class_Ozero(_940379))))]]]]], (18077 ^ _775212) ^ [_1082105, _1082107] : [class_Rings_Osemiring__1(_1082105), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1082107)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1082105), 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)))), _1082107))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082105), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1082105), hAPP(c_Int_Onat, _1082107))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1082105), hAPP(c_Int_Onat, _1082107))))], (23484 ^ _775212) ^ [_1182756, _1182758, _1182760] : [-(c_Nitpick_Otimes__frac(_1182756, _1182758, _1182760) = hAPP(hAPP(c_Nitpick_Ofrac(_1182756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1182756), _1182758)), hAPP(c_Nitpick_Onum(_1182756), _1182760))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1182756), _1182758)), hAPP(c_Nitpick_Odenom(_1182756), _1182760))))], (4946 ^ _775212) ^ [_850631, _850633] : [_850633 = _850631, -(c_Lazy__Sequence_Oyield(_850633) = c_Lazy__Sequence_Oyield(_850631))], (23220 ^ _775212) ^ [_1177545, _1177547, _1177549, _1177551, _1177553, _1177555] : [hAPP(c_Product__Type_Oapfst(_1177545, _1177547, _1177549, _1177551), _1177553) = hAPP(c_Product__Type_Oapfst(_1177545, _1177547, _1177549, _1177555), _1177553), -(hAPP(_1177551, hAPP(c_Product__Type_Ofst(_1177545, _1177549), _1177553)) = hAPP(_1177555, hAPP(c_Product__Type_Ofst(_1177545, _1177549), _1177553)))], (44074 ^ _775212) ^ [_1638954, _1638956, _1638958] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1638954), _1638956)), hBOOL(hAPP(_1638958, c_Orderings_Obot__class_Obot(tc_fun(_1638954, tc_HOL_Obool)))), 44085 ^ _775212 : [(44088 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1638954), 44083 ^ [_1638954, _1638956, _1638958]), 44084 ^ [_1638954, _1638956, _1638958]))], (44090 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1638958, 44084 ^ [_1638954, _1638956, _1638958])))], (44092 ^ _775212) ^ [] : [hBOOL(hAPP(_1638958, hAPP(hAPP(c_Set_Oinsert(_1638954), 44083 ^ [_1638954, _1638956, _1638958]), 44084 ^ [_1638954, _1638956, _1638958])))], (44086 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1638954), 44084 ^ [_1638954, _1638956, _1638958])))]], -(hBOOL(hAPP(_1638958, _1638956)))], (35157 ^ _775212) ^ [_1422690, _1422692, _1422694] : [class_Lattices_Olattice(_1422690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422690), _1422692)), hBOOL(hAPP(hAPP(c_member(_1422690), _1422694), _1422692)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1422690), _1422694), c_Big__Operators_Olattice__class_OSup__fin(_1422690, _1422692)) = _1422694)], (12105 ^ _775212) ^ [_974124, _974126, _974128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974126), _974128)), -(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, _974124)), _974126)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974124)), _974128))))], (3040 ^ _775212) ^ [_820720, _820722, _820724, _820726, _820728, _820730] : [-(c_SetInterval_Oord_OatMost(_820730, _820726, _820722) = c_SetInterval_Oord_OatMost(_820728, _820724, _820720)), _820730 = _820728, _820726 = _820724, _820722 = _820720], (30955 ^ _775212) ^ [_1334269, _1334271, _1334273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334269)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1334271), _1334273)), 30962 ^ _775212 : [(30963 ^ _775212) ^ [_1334465] : [30965 ^ _775212 : [(30971 ^ _775212) ^ [] : [-(_1334465 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30967 ^ [_1334269, _1334271, _1334273, _1334465]), 30964 ^ [_1334269, _1334271, _1334273, _1334465]))], (30969 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30967 ^ [_1334269, _1334271, _1334273, _1334465]), _1334273)))], (30966 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30964 ^ [_1334269, _1334271, _1334273, _1334465]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1334269))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334271), _1334465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334271), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1334465), _1334269))))]]], (49984 ^ _775212) ^ [_1776446, _1776448, _1776450, _1776452, _1776454] : [49985 ^ _775212 : [(49988 ^ _775212) ^ [] : [hBOOL(hAPP(_1776454, hAPP(hAPP(c_List_Ozip(_1776446, _1776450), hAPP(hAPP(c_List_Otake(_1776446), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776446)), _1776448)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776450)), _1776452))), _1776448)), hAPP(hAPP(c_List_Otake(_1776450), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776446)), _1776448)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776450)), _1776452))), _1776452))))], (49986 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776446)), hAPP(hAPP(c_List_Otake(_1776446), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776446)), _1776448)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776450)), _1776452))), _1776448)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776450)), hAPP(hAPP(c_List_Otake(_1776450), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776446)), _1776448)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776450)), _1776452))), _1776452)))]], -(hBOOL(hAPP(_1776454, hAPP(hAPP(c_List_Ozip(_1776446, _1776450), _1776448), _1776452))))], (44372 ^ _775212) ^ [_1648223, _1648225, _1648227] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1648223, _1648223)), hAPP(hAPP(c_Product__Type_OPair(_1648223, _1648223), 44373 ^ [_1648223, _1648225, _1648227]), 44373 ^ [_1648223, _1648225, _1648227])), _1648225))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648223), tc_List_Olist(_1648223))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648223), tc_List_Olist(_1648223)), _1648227), _1648227)), c_List_Olexord(_1648223, _1648225)))], (37320 ^ _775212) ^ [_1469672, _1469674, _1469676, _1469678, _1469680, _1469682] : [c_Typedef_Otype__definition(_1469672, _1469674, _1469676, _1469678, _1469680), hBOOL(hAPP(hAPP(c_member(_1469674), _1469682), _1469680)), -(hAPP(_1469676, hAPP(_1469678, _1469682)) = _1469682)], (2034 ^ _775212) ^ [_804563, _804565, _804567, _804569] : [-(c_Int_Onat__aux(_804569, _804565) = c_Int_Onat__aux(_804567, _804563)), _804569 = _804567, _804565 = _804563], (39548 ^ _775212) ^ [_1529284, _1529286, _1529288] : [_1529288 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529284, _1529286), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1529284, _1529286), _1529288) = c_Orderings_Obot__class_Obot(tc_fun(_1529286, tc_HOL_Obool)))], (22128 ^ _775212) ^ [_1155154, _1155156, _1155158, _1155160] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1155154, _1155156, _1155158, c_Code__Numeral_OSuc__code__numeral(_1155160)) = hAPP(_1155158, _1155160))], (22188 ^ _775212) ^ [_1156459, _1156461] : [class_Rings_Osemiring__1(_1156459), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1156459), _1156461) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1156459, hAPP(hAPP(c_COMBC(_1156459, _1156459, _1156459), c_Groups_Oplus__class_Oplus(_1156459)), c_Groups_Oone__class_Oone(_1156459)), _1156461, c_Groups_Ozero__class_Ozero(_1156459)))], (7094 ^ _775212) ^ [_888216, _888218, _888220] : [class_Orderings_Oorder(_888216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888216), _888218), _888220)), _888220 = _888218], (17957 ^ _775212) ^ [_1079880, _1079882] : [class_Int_Onumber__ring(_1079880), class_Rings_Olinordered__idom(_1079880), 17964 ^ _775212 : [(17971 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079882), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079880), hAPP(c_Int_Onumber__class_Onumber__of(_1079880), _1079882)), c_Groups_Oone__class_Oone(_1079880))))], (17965 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079880), hAPP(c_Int_Onumber__class_Onumber__of(_1079880), _1079882)), c_Groups_Oone__class_Oone(_1079880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079882), c_Int_OBit1(c_Int_OPls))))]]], (42189 ^ _775212) ^ [_1590778, _1590780, _1590782, _1590784] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1590778, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590780, tc_fun(_1590778, tc_HOL_Obool)), _1590782), _1590784)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1590780, tc_fun(_1590778, tc_HOL_Obool)), _1590782), hAPP(hAPP(c_COMBB(tc_fun(_1590778, tc_HOL_Obool), tc_fun(_1590778, tc_HOL_Obool), _1590780), c_Groups_Ouminus__class_Ouminus(tc_fun(_1590778, tc_HOL_Obool))), _1590784)))], (32379 ^ _775212) ^ [_1361771, _1361773, _1361775] : [class_Orderings_Olinorder(_1361771), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361771), _1361773)), hBOOL(hAPP(hAPP(c_member(_1361771), _1361775), _1361773)), 32390 ^ _775212 : [(32397 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361771, tc_HOL_Obool)), _1361773), hAPP(hAPP(c_Set_Oinsert(_1361771), _1361775), c_Orderings_Obot__class_Obot(tc_fun(_1361771, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1361771, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1361771, c_Orderings_Oord__class_Omax(_1361771), _1361773) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361771), _1361775), c_Big__Operators_Olattice_OSup__fin(_1361771, c_Orderings_Oord__class_Omax(_1361771), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361771, tc_HOL_Obool)), _1361773), hAPP(hAPP(c_Set_Oinsert(_1361771), _1361775), c_Orderings_Obot__class_Obot(tc_fun(_1361771, tc_HOL_Obool)))))))], (32391 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361771, tc_HOL_Obool)), _1361773), hAPP(hAPP(c_Set_Oinsert(_1361771), _1361775), c_Orderings_Obot__class_Obot(tc_fun(_1361771, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1361771, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1361771, c_Orderings_Oord__class_Omax(_1361771), _1361773) = _1361775)]]], (45592 ^ _775212) ^ [_1680546, _1680548, _1680550, _1680552, _1680554] : [hAPP(hAPP(c_List_Oappend(_1680546), _1680548), _1680550) = hAPP(hAPP(c_List_Olist_OCons(_1680546), _1680552), _1680554), 45597 ^ _775212 : [(45600 ^ _775212) ^ [] : [-(_1680550 = hAPP(hAPP(c_List_Olist_OCons(_1680546), _1680552), _1680554))], (45598 ^ _775212) ^ [] : [-(_1680548 = c_List_Olist_ONil(_1680546))]], 45602 ^ _775212 : [(45605 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1680546), 45601 ^ [_1680546, _1680548, _1680550, _1680552, _1680554]), _1680550) = _1680554)], (45603 ^ _775212) ^ [] : [-(_1680548 = hAPP(hAPP(c_List_Olist_OCons(_1680546), _1680552), 45601 ^ [_1680546, _1680548, _1680550, _1680552, _1680554]))]]], (11266 ^ _775212) ^ [_960210] : [_960210 = 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), _960210)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23446 ^ _775212) ^ [_1182115, _1182117, _1182119, _1182121, _1182123] : [_1182115 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1182117, _1182119, _1182115, _1182121), _1182123) = hAPP(c_Product__Type_OPair(_1182117, _1182119), _1182123))], (132 ^ _775212) ^ [_777056, _777058, _777060, _777062, _777064, _777066, _777068, _777070] : [-(c_Orderings_Oorder_Ostrict__mono(_777068, _777064, _777060, _777056)), c_Orderings_Oorder_Ostrict__mono(_777070, _777066, _777062, _777058), _777070 = _777068, _777066 = _777064, _777062 = _777060, _777058 = _777056], (15585 ^ _775212) ^ [_1038663, _1038665, _1038667] : [class_Rings_Olinordered__semidom(_1038663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038663), c_Groups_Ozero__class_Ozero(_1038663)), _1038665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038663), _1038665), c_Groups_Oone__class_Oone(_1038663))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038663), _1038665), hAPP(hAPP(c_Power_Opower__class_Opower(_1038663), _1038665), _1038667))), hAPP(hAPP(c_Power_Opower__class_Opower(_1038663), _1038665), _1038667))))], (11766 ^ _775212) ^ [_968360, _968362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968360), _968362)), 11769 ^ _775212 : [(11772 ^ _775212) ^ [] : [_968360 = _968362], (11770 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968360), _968362)))]]], (9855 ^ _775212) ^ [_934701, _934703] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934701), _934703))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _934701), _934703)), -(_934701 = _934703)], (50010 ^ _775212) ^ [_1777428, _1777430, _1777432, _1777434] : [50012 ^ _775212 : [(50015 ^ _775212) ^ [] : [hBOOL(hAPP(_1777432, 50011 ^ [_1777428, _1777430, _1777432, _1777434]))], (50013 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777428), 50011 ^ [_1777428, _1777430, _1777432, _1777434]), hAPP(c_List_Oset(_1777428), _1777430))))]], -(c_List_OdropWhile(_1777428, _1777432, hAPP(hAPP(c_List_Oappend(_1777428), _1777430), _1777434)) = c_List_OdropWhile(_1777428, _1777432, _1777434))], (19611 ^ _775212) ^ [_1109174, _1109176, _1109178] : [class_Rings_Odivision__ring(_1109174), -(_1109176 = c_Groups_Ozero__class_Ozero(_1109174)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109174), hAPP(c_Groups_Ouminus__class_Ouminus(_1109174), _1109178)), hAPP(c_Groups_Ouminus__class_Ouminus(_1109174), _1109176)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109174), _1109178), _1109176))], (49173 ^ _775212) ^ [_1759057, _1759059, _1759061, _1759063] : [-(hAPP(c_List_Orev(_1759057), hAPP(hAPP(c_List_Omap(_1759059, _1759057), _1759061), _1759063)) = hAPP(hAPP(c_List_Omap(_1759059, _1759057), _1759061), hAPP(c_List_Orev(_1759059), _1759063)))], (39878 ^ _775212) ^ [_1538340, _1538342, _1538344] : [c_Wellfounded_Owf(_1538340, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1538340, _1538340), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1538340, _1538340), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1538340, _1538340, _1538340), _1538342), _1538342)), hAPP(hAPP(c_Relation_Orel__comp(_1538340, _1538340, _1538340), _1538344), _1538342))), _1538344)), -(c_Wellfounded_Owf(_1538340, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1538340, _1538340), tc_HOL_Obool)), _1538342), _1538344)))], (32423 ^ _775212) ^ [_1362655, _1362657, _1362659] : [class_Orderings_Olinorder(_1362655), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362655), _1362657)), -(_1362657 = c_Orderings_Obot__class_Obot(tc_fun(_1362655, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1362655, c_Orderings_Oord__class_Omax(_1362655), hAPP(hAPP(c_Set_Oinsert(_1362655), _1362659), _1362657)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362655), _1362659), c_Big__Operators_Olattice_OSup__fin(_1362655, c_Orderings_Oord__class_Omax(_1362655), _1362657)))], (16043 ^ _775212) ^ [_1047071, _1047073] : [class_Int_Onumber__ring(_1047071), 16046 ^ _775212 : [(16053 ^ _775212) ^ [] : [-(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), _1047073)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1047071), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1047073)) = c_Groups_Ozero__class_Ozero(_1047071))], (16047 ^ _775212) ^ [] : [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), _1047073))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1047071), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1047073)) = hAPP(c_Int_Onumber__class_Onumber__of(_1047071), _1047073))]]], (31489 ^ _775212) ^ [_1345033, _1345035, _1345037] : [class_Lattices_Olattice(_1345033), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345033), _1345035)), hBOOL(hAPP(hAPP(c_member(_1345033), _1345037), _1345035)), 31500 ^ _775212 : [(31507 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345033, tc_HOL_Obool)), _1345035), hAPP(hAPP(c_Set_Oinsert(_1345033), _1345037), c_Orderings_Obot__class_Obot(tc_fun(_1345033, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1345033, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1345033, _1345035) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1345033), _1345037), c_Big__Operators_Olattice__class_OSup__fin(_1345033, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345033, tc_HOL_Obool)), _1345035), hAPP(hAPP(c_Set_Oinsert(_1345033), _1345037), c_Orderings_Obot__class_Obot(tc_fun(_1345033, tc_HOL_Obool)))))))], (31501 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345033, tc_HOL_Obool)), _1345035), hAPP(hAPP(c_Set_Oinsert(_1345033), _1345037), c_Orderings_Obot__class_Obot(tc_fun(_1345033, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1345033, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1345033, _1345035) = _1345037)]]], (20733 ^ _775212) ^ [_1129547, _1129549, _1129551, _1129553] : [class_Fields_Olinordered__field__inverse__zero(_1129547), class_Int_Onumber(_1129547), 20740 ^ _775212 : [(20741 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129547), _1129549), _1129551)), hAPP(c_Int_Onumber__class_Onumber__of(_1129547), _1129553))), 20744 ^ _775212 : [(20751 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), c_Groups_Ozero__class_Ozero(_1129547)), _1129551))), 20754 ^ _775212 : [(20761 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), _1129551), c_Groups_Ozero__class_Ozero(_1129547)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), c_Groups_Ozero__class_Ozero(_1129547)), hAPP(c_Int_Onumber__class_Onumber__of(_1129547), _1129553))))], (20755 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), _1129551), c_Groups_Ozero__class_Ozero(_1129547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129547), hAPP(c_Int_Onumber__class_Onumber__of(_1129547), _1129553)), _1129551)), _1129549)))]]], (20745 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), c_Groups_Ozero__class_Ozero(_1129547)), _1129551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), _1129549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129547), hAPP(c_Int_Onumber__class_Onumber__of(_1129547), _1129553)), _1129551))))]]], (20767 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129547), _1129549), _1129551)), hAPP(c_Int_Onumber__class_Onumber__of(_1129547), _1129553)))), 20770 ^ _775212 : [(20773 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), _1129549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129547), hAPP(c_Int_Onumber__class_Onumber__of(_1129547), _1129553)), _1129551)))], (20771 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), c_Groups_Ozero__class_Ozero(_1129547)), _1129551)))]], 20774 ^ _775212 : [(20777 ^ _775212) ^ [] : [20778 ^ _775212 : [(20781 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129547), hAPP(c_Int_Onumber__class_Onumber__of(_1129547), _1129553)), _1129551)), _1129549))], (20779 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), _1129551), c_Groups_Ozero__class_Ozero(_1129547))))]], 20782 ^ _775212 : [(20785 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), c_Groups_Ozero__class_Ozero(_1129547)), hAPP(c_Int_Onumber__class_Onumber__of(_1129547), _1129553)))], (20783 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), _1129551), c_Groups_Ozero__class_Ozero(_1129547)))]]], (20775 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129547), c_Groups_Ozero__class_Ozero(_1129547)), _1129551))]]]]], (13260 ^ _775212) ^ [_995101, _995103, _995105] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995101), _995103)), _995105) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995101), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _995103), _995105))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995101), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _995103, _995105))), _995105)))], (29160 ^ _775212) ^ [_1293389, _1293391, _1293393, _1293395, _1293397] : [-(_1293389 = c_Orderings_Obot__class_Obot(tc_fun(_1293391, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293391, tc_fun(_1293393, tc_HOL_Obool)), _1293389), hAPP(hAPP(c_COMBC(_1293391, tc_fun(_1293393, tc_HOL_Obool), tc_fun(_1293393, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1293393, tc_HOL_Obool), tc_fun(tc_fun(_1293393, tc_HOL_Obool), tc_fun(_1293393, tc_HOL_Obool)), _1293391), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293393, tc_HOL_Obool))), _1293395)), _1293397)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293393, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293391, tc_fun(_1293393, tc_HOL_Obool)), _1293389), _1293395)), _1293397))], (31063 ^ _775212) ^ [_1336448, _1336450, _1336452, _1336454, _1336456] : [c_Finite__Set_Ofolding__one(_1336448, _1336450, _1336452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336448), _1336454)), hBOOL(hAPP(hAPP(c_member(_1336448), _1336456), _1336454)), 31074 ^ _775212 : [(31081 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336448, tc_HOL_Obool)), _1336454), hAPP(hAPP(c_Set_Oinsert(_1336448), _1336456), c_Orderings_Obot__class_Obot(tc_fun(_1336448, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1336448, tc_HOL_Obool))), -(hAPP(_1336452, _1336454) = hAPP(hAPP(_1336450, _1336456), hAPP(_1336452, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336448, tc_HOL_Obool)), _1336454), hAPP(hAPP(c_Set_Oinsert(_1336448), _1336456), c_Orderings_Obot__class_Obot(tc_fun(_1336448, tc_HOL_Obool)))))))], (31075 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336448, tc_HOL_Obool)), _1336454), hAPP(hAPP(c_Set_Oinsert(_1336448), _1336456), c_Orderings_Obot__class_Obot(tc_fun(_1336448, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1336448, tc_HOL_Obool)), -(hAPP(_1336452, _1336454) = _1336456)]]], (6156 ^ _775212) ^ [_872479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872479), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (35097 ^ _775212) ^ [_1421246, _1421248, _1421250, _1421252] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421246, tc_HOL_Obool)), _1421248), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421246, tc_HOL_Obool)), _1421250), _1421252)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421246, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421246, tc_HOL_Obool)), _1421248), _1421250)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421246, tc_HOL_Obool)), _1421248), _1421252)))], (14269 ^ _775212) ^ [_1012997, _1012999, _1013001] : [class_Rings_Oring__1__no__zero__divisors(_1012997), -(_1012999 = c_Groups_Ozero__class_Ozero(_1012997)), hAPP(hAPP(c_Power_Opower__class_Opower(_1012997), _1012999), _1013001) = c_Groups_Ozero__class_Ozero(_1012997)], (36012 ^ _775212) ^ [_1442850, _1442852, _1442854, _1442856, _1442858, _1442860] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442850, tc_fun(_1442852, tc_HOL_Obool))), _1442854), _1442856), _1442858), _1442860)), 36015 ^ _775212 : [(36018 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1442856, _1442858), _1442860)))], (36016 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1442854, _1442858), _1442860)))]]], (25236 ^ _775212) ^ [_1214228, _1214230, _1214232, _1214234, _1214236] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1214228), _1214230)), 25239 ^ _775212 : [(25246 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1214228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1214236), _1214230))), _1214234))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1214228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214232), _1214234))))], (25240 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1214228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214232), _1214234))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1214228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1214236), _1214230))), _1214234))))]]], (34061 ^ _775212) ^ [] : [-(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))))))], (48301 ^ _775212) ^ [_1740866, _1740868, _1740870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1740866), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1740868))), c_List_Otranspose(_1740868, _1740870)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1740868)), c_List_Otranspose(_1740868, _1740870)), _1740866) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1740868), _1740868), hAPP(hAPP(c_COMBC(tc_List_Olist(_1740868), tc_Nat_Onat, _1740868), c_List_Onth(_1740868)), _1740866)), hAPP(c_List_Ofilter(tc_List_Olist(_1740868), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1740868)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1740866)), c_Nat_Osize__class_Osize(tc_List_Olist(_1740868)))), _1740870)))], (2898 ^ _775212) ^ [_818449, _818451] : [_818451 = _818449, -(c_New__DSequence_Opos__empty(_818451) = c_New__DSequence_Opos__empty(_818449))], (11466 ^ _775212) ^ [_963266, _963268, _963270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _963266)), _963266 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _963268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _963266), _963270)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _963268), _963266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _963270)))], (28369 ^ _775212) ^ [_1278300, _1278302, _1278304] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278300), _1278302)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278300), _1278304)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1278300), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278300, tc_HOL_Obool)), _1278302), _1278304))))], (13127 ^ _775212) ^ [_992576, _992578, _992580] : [-(hBOOL(hAPP(_992576, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _992578), _992580)))), 13130 ^ _775212 : [(13133 ^ _775212) ^ [] : [hBOOL(hAPP(_992576, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (13131 ^ _775212) ^ [] : [-(_992580 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 13136 ^ _775212 : [(13137 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _992580)))], (13143 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 13139 ^ [_992576, _992578, _992580]), _992580)))], (13147 ^ _775212) ^ [] : [hBOOL(hAPP(_992576, 13138 ^ [_992576, _992578, _992580]))], (13145 ^ _775212) ^ [] : [-(_992578 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _992580), 13138 ^ [_992576, _992578, _992580])), 13139 ^ [_992576, _992578, _992580]))], (13141 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13139 ^ [_992576, _992578, _992580])))]], 13148 ^ _775212 : [(13149 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992580), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13155 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 13151 ^ [_992576, _992578, _992580]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13159 ^ _775212) ^ [] : [hBOOL(hAPP(_992576, 13150 ^ [_992576, _992578, _992580]))], (13157 ^ _775212) ^ [] : [-(_992578 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _992580), 13150 ^ [_992576, _992578, _992580])), 13151 ^ [_992576, _992578, _992580]))], (13153 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992580), 13151 ^ [_992576, _992578, _992580])))]]], (20331 ^ _775212) ^ [_1121996, _1121998, _1122000] : [class_Fields_Olinordered__field__inverse__zero(_1121996), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121996), c_Groups_Ozero__class_Ozero(_1121996)), _1121998)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121996), hAPP(c_Groups_Oabs__class_Oabs(_1121996), _1122000)), _1121998) = hAPP(c_Groups_Oabs__class_Oabs(_1121996), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121996), _1122000), _1121998)))], (52423 ^ _775212) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (45752 ^ _775212) ^ [_1684141, _1684143, _1684145, _1684147] : [_1684143 = c_List_Olist_ONil(_1684141), -(hAPP(hAPP(c_List_Olist__update(_1684141, _1684143), _1684145), _1684147) = c_List_Olist_ONil(_1684141))], (46176 ^ _775212) ^ [_1694425, _1694427, _1694429, _1694431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1694425), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694427)), _1694429))), -(hAPP(hAPP(c_List_Olist__update(_1694427, _1694429), _1694425), _1694431) = hAPP(hAPP(c_List_Oappend(_1694427), hAPP(hAPP(c_List_Otake(_1694427), _1694425), _1694429)), hAPP(hAPP(c_List_Olist_OCons(_1694427), _1694431), hAPP(hAPP(c_List_Odrop(_1694427), hAPP(c_Nat_OSuc, _1694425)), _1694429))))], (39500 ^ _775212) ^ [_1527970, _1527972, _1527974, _1527976] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527970, _1527972, _1527974), _1527976), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527972, _1527974), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527970, _1527974), tc_HOL_Obool)))], (47804 ^ _775212) ^ [_1729310, _1729312, _1729314, _1729316, _1729318] : [c_List_Olist__all2(_1729310, _1729312, _1729314, _1729316, _1729318), 47807 ^ _775212 : [(47810 ^ _775212) ^ [_1729473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729473), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729310)), _1729316))), -(hBOOL(hAPP(hAPP(_1729314, hAPP(hAPP(c_List_Onth(_1729310), _1729316), _1729473)), hAPP(hAPP(c_List_Onth(_1729312), _1729318), _1729473))))], (47808 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729310)), _1729316) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729312)), _1729318))]]], (37668 ^ _775212) ^ [_1478123, _1478125, _1478127] : [hBOOL(hAPP(hAPP(c_member(_1478123), _1478125), c_Wellfounded_Oacc(_1478123, _1478127))), 37671 ^ _775212 : [(37672 ^ _775212) ^ [_1478237] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1478123, _1478123)), hAPP(hAPP(c_Product__Type_OPair(_1478123, _1478123), _1478237), _1478125)), _1478127)), -(hBOOL(hAPP(hAPP(c_member(_1478123), _1478237), c_Wellfounded_Oacc(_1478123, _1478127))))]]], (1424 ^ _775212) ^ [_795868, _795870] : [-(class_Lattices_Olattice(_795868)), _795870 = _795868, class_Lattices_Olattice(_795870)], (27397 ^ _775212) ^ [_1258239, _1258241, _1258243, _1258245] : [class_Orderings_Olinorder(_1258239), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258239), _1258241), _1258243)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258239), _1258243), _1258245)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258239, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1258239, _1258241, _1258243)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1258239, _1258243, _1258245)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1258239, _1258241, _1258245))], (39003 ^ _775212) ^ [_1509010, _1509012, _1509014] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509010, tc_HOL_Obool)), _1509012), _1509014) = hAPP(c_Set_OCollect(_1509010), hAPP(hAPP(c_COMBS(_1509010, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509010), c_fconj), hAPP(hAPP(c_COMBC(_1509010, tc_fun(_1509010, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509010)), _1509012))), hAPP(hAPP(c_COMBC(_1509010, tc_fun(_1509010, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509010)), _1509014))))], (39430 ^ _775212) ^ [_1525829, _1525831] : [-(hAPP(c_Set_Oimage(_1525829, _1525829, c_Fun_Oid(_1525829)), _1525831) = _1525831)], (12265 ^ _775212) ^ [_976941, _976943, _976945] : [class_Lattices_Oboolean__algebra(_976941), 12268 ^ _775212 : [(12275 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976941), _976945), _976943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976941), hAPP(c_Groups_Ouminus__class_Ouminus(_976941), _976943)), hAPP(c_Groups_Ouminus__class_Ouminus(_976941), _976945))))], (12269 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976941), hAPP(c_Groups_Ouminus__class_Ouminus(_976941), _976943)), hAPP(c_Groups_Ouminus__class_Ouminus(_976941), _976945))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976941), _976945), _976943)))]]], (10277 ^ _775212) ^ [_942324, _942326, _942328] : [class_Rings_Oordered__cancel__semiring(_942324), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942324), _942326), c_Groups_Ozero__class_Ozero(_942324))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942324), c_Groups_Ozero__class_Ozero(_942324)), _942328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942324), _942326), _942328)), c_Groups_Ozero__class_Ozero(_942324))))], (36449 ^ _775212) ^ [_1451879, _1451881, _1451883, _1451885] : [c_Equiv__Relations_Oequivp(_1451879, _1451881), hBOOL(hAPP(hAPP(_1451881, _1451883), _1451885)), -(hBOOL(hAPP(hAPP(_1451881, _1451885), _1451883)))], (47979 ^ _775212) ^ [_1733380, _1733382] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733380)), c_List_Oremdups(_1733380, _1733382)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733380)), _1733382), -(c_List_Oremdups(_1733380, _1733382) = _1733382)], (31899 ^ _775212) ^ [_1352064, _1352066, _1352068] : [class_Orderings_Olinorder(_1352064), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352064), _1352066)), -(_1352066 = c_Orderings_Obot__class_Obot(tc_fun(_1352064, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1352064, hAPP(hAPP(c_Set_Oinsert(_1352064), _1352068), _1352066)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352064), _1352068), c_Big__Operators_Olinorder__class_OMax(_1352064, _1352066)))], (12021 ^ _775212) ^ [_972708, _972710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972708), _972710)), 12024 ^ _775212 : [(12031 ^ _775212) ^ [] : [_972710 = _972708, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972710), hAPP(c_Nat_OSuc, _972708))))], (12025 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972710), hAPP(c_Nat_OSuc, _972708))), -(_972710 = _972708)]]], (28946 ^ _775212) ^ [_1289514, _1289516] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289514, tc_HOL_Obool)), _1289516), c_Orderings_Otop__class_Otop(tc_fun(_1289514, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1289514, tc_HOL_Obool)))], (38826 ^ _775212) ^ [_1505025] : [class_Orderings_Olinorder(_1505025), -(c_Finite__Set_Ofun__left__comm__idem(_1505025, _1505025, c_Orderings_Oord__class_Omin(_1505025)))], (13071 ^ _775212) ^ [_991451, _991453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991451)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_991451, _991453))))], (9635 ^ _775212) ^ [_930816, _930818, _930820, _930822] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_930816), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930816), _930818), _930820)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930816), _930822), _930820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930816), _930818), _930822)))], (9841 ^ _775212) ^ [_934460, _934462, _934464] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _934460), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _934462), _934464)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _934460), _934462)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _934460), _934464)))], (31913 ^ _775212) ^ [_1352272, _1352274, _1352276] : [class_Orderings_Olinorder(_1352272), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352272), _1352274)), -(_1352276 = c_Orderings_Obot__class_Obot(tc_fun(_1352272, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1352272, tc_HOL_Obool)), _1352276), _1352274)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1352272), c_Big__Operators_Olinorder__class_OMin(_1352272, _1352276)), c_Big__Operators_Olinorder__class_OMin(_1352272, _1352274)) = c_Big__Operators_Olinorder__class_OMin(_1352272, _1352274))], (7427 ^ _775212) ^ [_893378, _893380, _893382, _893384] : [class_Rings_Ocomm__semiring__1(_893378), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893378), _893380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893378), _893382), _893384)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893378), _893382), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893378), _893380), _893384)))], (40395 ^ _775212) ^ [_1551171, _1551173, _1551175, _1551177, _1551179, _1551181, _1551183] : [hAPP(c_Fun_Ocomp(_1551171, _1551173, _1551175, _1551177), _1551179) = hAPP(c_Fun_Ocomp(_1551173, _1551173, _1551175, c_Fun_Oid(_1551173)), _1551181), -(hAPP(_1551177, hAPP(_1551179, _1551183)) = hAPP(_1551181, _1551183))], (3286 ^ _775212) ^ [_824633, _824635, _824637, _824639, _824641, _824643] : [-(c_Predicate_ODomainP(_824643, _824639, _824635) = c_Predicate_ODomainP(_824641, _824637, _824633)), _824643 = _824641, _824639 = _824637, _824635 = _824633], (52297 ^ _775212) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (35421 ^ _775212) ^ [_1428924, _1428926, _1428928, _1428930, _1428932] : [c_Equiv__Relations_Oequiv(_1428924, _1428926, _1428928), hBOOL(hAPP(hAPP(c_member(tc_fun(_1428924, tc_HOL_Obool)), _1428930), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1428924), _1428926), _1428928))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1428924, tc_HOL_Obool)), _1428932), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1428924), _1428926), _1428928))), -(_1428930 = _1428932), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428924, tc_HOL_Obool)), _1428930), _1428932) = c_Orderings_Obot__class_Obot(tc_fun(_1428924, tc_HOL_Obool)))], (48321 ^ _775212) ^ [_1741439, _1741441, _1741443] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1741439, tc_HOL_Obool)), hAPP(c_List_Oset(_1741439), _1741441)), hAPP(hAPP(c_Set_Oinsert(_1741439), _1741443), c_Orderings_Obot__class_Obot(tc_fun(_1741439, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1741439), hAPP(c_List_Ofilter(_1741439, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1741439), c_fNot), hAPP(hAPP(c_COMBC(_1741439, _1741439, tc_HOL_Obool), c_fequal), _1741443))), _1741441)))], (1284 ^ _775212) ^ [_794118, _794120] : [-(class_Groups_Osgn__if(_794118)), _794120 = _794118, class_Groups_Osgn__if(_794120)], (33921 ^ _775212) ^ [_1394372, _1394374, _1394376, _1394378] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1394372), _1394374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1394372, tc_HOL_Obool)), _1394374), _1394376)), hBOOL(hAPP(_1394378, c_Orderings_Obot__class_Obot(tc_fun(_1394372, tc_HOL_Obool)))), 33936 ^ _775212 : [(33937 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1394372), 33935 ^ [_1394372, _1394374, _1394376, _1394378])))], (33941 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1394372), 33934 ^ [_1394372, _1394374, _1394376, _1394378]), 33935 ^ [_1394372, _1394374, _1394376, _1394378]))], (33945 ^ _775212) ^ [] : [hBOOL(hAPP(_1394378, hAPP(hAPP(c_Set_Oinsert(_1394372), 33934 ^ [_1394372, _1394374, _1394376, _1394378]), 33935 ^ [_1394372, _1394374, _1394376, _1394378])))], (33943 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1394378, 33935 ^ [_1394372, _1394374, _1394376, _1394378])))], (33939 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394372), 33934 ^ [_1394372, _1394374, _1394376, _1394378]), _1394376)))]], -(hBOOL(hAPP(_1394378, _1394374)))], (39906 ^ _775212) ^ [_1539062, _1539064, _1539066] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539062, _1539064)), _1539066)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1539062), hAPP(c_Relation_ODomain(_1539062, _1539064), _1539066))))], (48572 ^ _775212) ^ [_1747520, _1747522, _1747524, _1747526] : [class_Groups_Ocomm__monoid__add(_1747520), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1747520), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1747520), _1747522), c_List_Oupt(_1747524, _1747526))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1747520), _1747522), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1747524, _1747526))))], (23274 ^ _775212) ^ [_1178831, _1178833, _1178835] : [class_Groups_Olinordered__ab__group__add(_1178831), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1178831), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1178831), _1178833), _1178835)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178831), hAPP(c_Groups_Ouminus__class_Ouminus(_1178831), _1178833)), hAPP(c_Groups_Ouminus__class_Ouminus(_1178831), _1178835)))], (15093 ^ _775212) ^ [_1028462, _1028464, _1028466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028462), _1028464)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028466), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028464), _1028462)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028466), _1028462)), _1028464))], (27427 ^ _775212) ^ [_1258815, _1258817, _1258819, _1258821] : [class_Orderings_Olinorder(_1258815), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258815), _1258817), _1258819)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258815), _1258819), _1258821)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258815, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1258815, _1258817), _1258819)), c_SetInterval_Oord__class_OatLeastAtMost(_1258815, _1258819, _1258821)) = c_SetInterval_Oord__class_OatLeastAtMost(_1258815, _1258817, _1258821))], (10629 ^ _775212) ^ [_948680, _948682, _948684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948680), _948682)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948684), _948682))), 10632 ^ _775212 : [(10635 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948680), _948684)))], (10633 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _948682)))]]], (12137 ^ _775212) ^ [] : [-(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))], (34997 ^ _775212) ^ [_1418965, _1418967] : [class_Lattices_Oboolean__algebra(_1418965), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418965), _1418967), hAPP(c_Groups_Ouminus__class_Ouminus(_1418965), _1418967)) = c_Orderings_Obot__class_Obot(_1418965))], (38263 ^ _775212) ^ [_1494606, _1494608, _1494610] : [class_Groups_Oab__semigroup__mult(_1494606), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494606), _1494608)), -(_1494608 = c_Orderings_Obot__class_Obot(tc_fun(_1494606, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494606), _1494610)), -(_1494610 = c_Orderings_Obot__class_Obot(tc_fun(_1494606, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494606, tc_HOL_Obool)), _1494608), _1494610) = c_Orderings_Obot__class_Obot(tc_fun(_1494606, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1494606, c_Groups_Otimes__class_Otimes(_1494606)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494606, tc_HOL_Obool)), _1494608), _1494610)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1494606), hAPP(c_Finite__Set_Ofold1(_1494606, c_Groups_Otimes__class_Otimes(_1494606)), _1494608)), hAPP(c_Finite__Set_Ofold1(_1494606, c_Groups_Otimes__class_Otimes(_1494606)), _1494610)))], (6949 ^ _775212) ^ [_885948, _885950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885948), _885950)), -(_885950 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885948), 6952 ^ [_885948, _885950])))], (33050 ^ _775212) ^ [_1374669, _1374671, _1374673, _1374675, _1374677] : [class_Fields_Ofield__inverse__zero(_1374669), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374671), _1374673)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1374671, _1374669), hAPP(hAPP(c_COMBS(_1374671, _1374669, _1374669), hAPP(hAPP(c_COMBB(_1374669, tc_fun(_1374669, _1374669), _1374671), c_Rings_Oinverse__class_Odivide(_1374669)), _1374675)), _1374677)), _1374673) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1374669), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1374671, _1374669), _1374675), _1374673)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1374671, _1374669), _1374677), _1374673)))], (9119 ^ _775212) ^ [_922954, _922956] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _922954), _922956))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _922956), _922954)))], (28251 ^ _775212) ^ [_1276134, _1276136] : [class_Finite__Set_Ofinite(_1276134), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1276134), _1276136)))], (1164 ^ _775212) ^ [_792618, _792620] : [-(class_Groups_Oordered__ab__group__add(_792618)), _792620 = _792618, class_Groups_Oordered__ab__group__add(_792620)], (52697 ^ _775212) ^ [] : [hBOOL(c_fFalse)], (47770 ^ _775212) ^ [_1728481, _1728483, _1728485, _1728487, _1728489, _1728491, _1728493] : [c_List_Olist__all2(_1728481, _1728489, hAPP(hAPP(c_COMBC(_1728481, tc_fun(_1728489, _1728483), tc_fun(_1728489, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1728483, tc_HOL_Obool), tc_fun(tc_fun(_1728489, _1728483), tc_fun(_1728489, tc_HOL_Obool)), _1728481), c_COMBB(_1728483, tc_HOL_Obool, _1728489)), _1728485)), _1728491), _1728487, _1728493), -(c_List_Olist__all2(_1728481, _1728483, _1728485, _1728487, hAPP(hAPP(c_List_Omap(_1728489, _1728483), _1728491), _1728493)))], (9383 ^ _775212) ^ [_927049, _927051, _927053] : [class_Orderings_Olinorder(_927049), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927049), _927051), _927053))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927049), _927053), _927051)))], (26399 ^ _775212) ^ [_1238864, _1238866, _1238868] : [class_Groups_Oordered__ab__group__add(_1238864), -(hAPP(c_Set_Oimage(_1238864, _1238864, c_Groups_Ouminus__class_Ouminus(_1238864)), c_SetInterval_Oord__class_OatLeastAtMost(_1238864, _1238866, _1238868)) = c_SetInterval_Oord__class_OatLeastAtMost(_1238864, hAPP(c_Groups_Ouminus__class_Ouminus(_1238864), _1238868), hAPP(c_Groups_Ouminus__class_Ouminus(_1238864), _1238866)))], (25252 ^ _775212) ^ [_1214580, _1214582] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214580), _1214582)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1214580)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1214582))))], (50953 ^ _775212) ^ [_1797319, _1797321, _1797323] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1797319)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1797319, _1797321, _1797323)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1797319)), _1797323)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45638 ^ _775212) ^ [_1681503, _1681505, _1681507, _1681509, _1681511] : [-(hAPP(hAPP(c_List_Olist_OCons(_1681503), _1681505), _1681507) = hAPP(hAPP(c_List_Oappend(_1681503), _1681509), _1681511)), 45639 ^ _775212 : [(45646 ^ _775212) ^ [_1681686] : [hAPP(hAPP(c_List_Olist_OCons(_1681503), _1681505), _1681686) = _1681509, _1681507 = hAPP(hAPP(c_List_Oappend(_1681503), _1681686), _1681511)], (45640 ^ _775212) ^ [] : [_1681509 = c_List_Olist_ONil(_1681503), hAPP(hAPP(c_List_Olist_OCons(_1681503), _1681505), _1681507) = _1681511]]], (45369 ^ _775212) ^ [_1674684, _1674686] : [-(c_List_Oset__Cons(_1674684, _1674686, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1674684)), c_List_Olist_ONil(_1674684)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1674684), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1674684, tc_List_Olist(_1674684), hAPP(hAPP(c_COMBC(_1674684, tc_List_Olist(_1674684), tc_List_Olist(_1674684)), c_List_Olist_OCons(_1674684)), c_List_Olist_ONil(_1674684))), _1674686))], (52371 ^ _775212) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (44334 ^ _775212) ^ [_1647063, _1647065, _1647067, _1647069, _1647071] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1647063, _1647063)), hAPP(hAPP(c_Product__Type_OPair(_1647063, _1647063), _1647065), _1647067)), _1647069)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647063), tc_List_Olist(_1647063))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647063), tc_List_Olist(_1647063)), hAPP(hAPP(c_List_Olist_OCons(_1647063), _1647065), _1647071)), hAPP(hAPP(c_List_Olist_OCons(_1647063), _1647067), _1647071))), c_List_Olistrel1(_1647063, _1647069))))], (14495 ^ _775212) ^ [_1017311, _1017313, _1017315] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1017311), _1017313)), _1017315) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017311), _1017315)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017313), _1017315)))], (24560 ^ _775212) ^ [_1201638, _1201640] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201638), _1201640)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201638), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1201640), _1201638))))], (50723 ^ _775212) ^ [_1792381, _1792383, _1792385, _1792387] : [-(hAPP(hAPP(c_List_Omap(_1792381, _1792383), hAPP(c_COMBK(_1792383, _1792381), _1792385)), _1792387) = c_List_Oreplicate(_1792383, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792381)), _1792387), _1792385))], (51002 ^ _775212) ^ [_1798611, _1798613, _1798615] : [hBOOL(hAPP(hAPP(c_List_Omember(_1798611), _1798615), _1798613)), -(hBOOL(hAPP(hAPP(c_member(_1798611), _1798613), hAPP(c_List_Oset(_1798611), _1798615))))], (9437 ^ _775212) ^ [_927808, _927810, _927812] : [class_Orderings_Oorder(_927808), -(_927810 = _927812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927808), _927812), _927810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927808), _927812), _927810)))], (39981 ^ _775212) ^ [_1540798, _1540800] : [-(c_FunDef_Oreduction__pair(_1540798, _1540800)), c_Wellfounded_Owf(_1540798, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1540798, _1540798), tc_HOL_Obool), tc_fun(tc_prod(_1540798, _1540798), tc_HOL_Obool)), _1540800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1540798, _1540798), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1540798, _1540798, _1540798), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1540798, _1540798), tc_HOL_Obool), tc_fun(tc_prod(_1540798, _1540798), tc_HOL_Obool)), _1540800)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1540798, _1540798), tc_HOL_Obool), tc_fun(tc_prod(_1540798, _1540798), tc_HOL_Obool)), _1540800))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1540798, _1540798), tc_HOL_Obool), tc_fun(tc_prod(_1540798, _1540798), tc_HOL_Obool)), _1540800)))], (706 ^ _775212) ^ [_786067, _786069, _786071, _786073, _786075, _786077] : [-(c_Finite__Set_Ofun__left__comm__idem(_786075, _786071, _786067)), c_Finite__Set_Ofun__left__comm__idem(_786077, _786073, _786069), _786077 = _786075, _786073 = _786071, _786069 = _786067], (17793 ^ _775212) ^ [_1077331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1077331), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1077331)), c_Int_OMin)))], (45224 ^ _775212) ^ [_1670669, _1670671] : [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(_1670669)), _1670671))), _1670671 = c_List_Olist_ONil(_1670669)], (5306 ^ _775212) ^ [_856195, _856197, _856199, _856201] : [-(c_Transitive__Closure_Otrancl(_856201, _856197) = c_Transitive__Closure_Otrancl(_856199, _856195)), _856201 = _856199, _856197 = _856195], (51391 ^ _775212) ^ [_1807210, _1807212] : [-(c_Relation_Otrans(_1807210, c_Transitive__Closure_Otrancl(_1807210, _1807212)))], (29636 ^ _775212) ^ [_1303082, _1303084, _1303086] : [hBOOL(hAPP(hAPP(c_member(_1303082), _1303084), _1303086)), -(hAPP(hAPP(c_Set_Oinsert(_1303082), _1303084), _1303086) = _1303086)], (35371 ^ _775212) ^ [_1427533, _1427535, _1427537, _1427539, _1427541] : [class_Groups_Ocomm__monoid__mult(_1427533), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427535), _1427537)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427535), _1427539)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427533), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1427535, _1427533), _1427541), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427535, tc_HOL_Obool)), _1427537), _1427539))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1427535, _1427533), _1427541), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427535, tc_HOL_Obool)), _1427537), _1427539))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427533), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1427535, _1427533), _1427541), _1427537)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1427535, _1427533), _1427541), _1427539)))], (240 ^ _775212) ^ [_778750, _778752] : [-(c_Nat__Transfer_Ois__nat(_778750)), _778752 = _778750, c_Nat__Transfer_Ois__nat(_778752)], (32329 ^ _775212) ^ [_1360673, _1360675, _1360677, _1360679] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1360673, _1360675)), c_Sum__Type_OPlus(_1360673, _1360675, _1360677, _1360679)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360673), _1360677)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360675), _1360679))], (6014 ^ _775212) ^ [_870634] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _870634))))], (42334 ^ _775212) ^ [_1595019, _1595021, _1595023, _1595025] : [c_Orderings_Otop__class_Otop(tc_fun(_1595019, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595021, tc_fun(_1595019, tc_HOL_Obool)), _1595023), _1595025), 42337 ^ _775212 : [(42338 ^ _775212) ^ [_1595135] : [hBOOL(hAPP(hAPP(c_member(_1595021), _1595135), _1595023)), -(hAPP(_1595025, _1595135) = c_Orderings_Otop__class_Otop(tc_fun(_1595019, tc_HOL_Obool)))]]], (14401 ^ _775212) ^ [_1015509, _1015511, _1015513, _1015515] : [class_Groups_Omonoid__mult(_1015509), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1015509), _1015511), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015513), _1015515)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1015509), hAPP(hAPP(c_Power_Opower__class_Opower(_1015509), _1015511), _1015513)), _1015515))], (3944 ^ _775212) ^ [_835038, _835040, _835042, _835044] : [-(c_Big__Operators_Olinorder__class_OMax(_835044, _835040) = c_Big__Operators_Olinorder__class_OMax(_835042, _835038)), _835044 = _835042, _835040 = _835038], (7018 ^ _775212) ^ [_887020, _887022, _887024, _887026] : [class_Orderings_Oorder(_887020), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887020), _887022), _887024)), _887022 = _887026, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887020), _887026), _887024)))], (16643 ^ _775212) ^ [_1058825] : [-(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), _1058825)) = 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), _1058825))))], (46544 ^ _775212) ^ [_1702554, _1702556] : [hAPP(c_Finite__Set_Ocard(_1702554), hAPP(c_List_Oset(_1702554), _1702556)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702554)), _1702556), -(hBOOL(hAPP(c_List_Odistinct(_1702554), _1702556)))], (42822 ^ _775212) ^ [_1609026, _1609028] : [-(c_Transitive__Closure_Ortrancl(_1609026, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1609026, _1609026), tc_HOL_Obool)), _1609028), c_Relation_OId(_1609026))) = c_Transitive__Closure_Ortrancl(_1609026, _1609028))], (47601 ^ _775212) ^ [_1724808, _1724810, _1724812] : [class_Orderings_Olinorder(_1724808), hBOOL(hAPP(hAPP(c_member(_1724808), _1724810), hAPP(c_List_Oset(_1724808), _1724812))), -(c_List_Olinorder__class_Oinsort__insert__key(_1724808, _1724808, c_COMBI(_1724808), _1724810, _1724812) = _1724812)], (8798 ^ _775212) ^ [_917896] : [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, _917896)))))], (16383 ^ _775212) ^ [_1053415, _1053417, _1053419] : [class_Int_Onumber__ring(_1053415), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053415), hAPP(c_Int_Onumber__class_Onumber__of(_1053415), _1053417)), hAPP(c_Int_Onumber__class_Onumber__of(_1053415), _1053419)) = hAPP(c_Int_Onumber__class_Onumber__of(_1053415), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1053417), _1053419)))], (2568 ^ _775212) ^ [_812886, _812888, _812890, _812892, _812894, _812896, _812898, _812900, _812902, _812904] : [-(c_Nitpick_Opair__box_Opair__box__rec(_812904, _812900, _812896, _812892, _812888) = c_Nitpick_Opair__box_Opair__box__rec(_812902, _812898, _812894, _812890, _812886)), _812904 = _812902, _812900 = _812898, _812896 = _812894, _812892 = _812890, _812888 = _812886], (44310 ^ _775212) ^ [_1646230, _1646232, _1646234, _1646236] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646230), tc_List_Olist(_1646230))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646230), tc_List_Olist(_1646230)), _1646232), _1646234)), c_List_Olistrel1(_1646230, _1646236))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646230)), _1646232) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646230)), _1646234))], (32785 ^ _775212) ^ [_1369808, _1369810, _1369812, _1369814, _1369816] : [class_Groups_Oordered__ab__group__add(_1369808), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369810), _1369812)), 32795 ^ _775212 : [(32798 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369808), c_Groups_Ozero__class_Ozero(_1369808)), hAPP(_1369814, 32794 ^ [_1369808, _1369810, _1369812, _1369814, _1369816])))], (32796 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1369810), 32794 ^ [_1369808, _1369810, _1369812, _1369814, _1369816]), _1369812)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1369810, _1369808), _1369814), _1369812) = c_Groups_Ozero__class_Ozero(_1369808), hBOOL(hAPP(hAPP(c_member(_1369810), _1369816), _1369812)), -(hAPP(_1369814, _1369816) = c_Groups_Ozero__class_Ozero(_1369808))], (49410 ^ _775212) ^ [_1764165, _1764167, _1764169, _1764171, _1764173] : [-(c_List_OtakeWhile(_1764165, _1764167, hAPP(hAPP(c_List_Omap(_1764169, _1764165), _1764171), _1764173)) = hAPP(hAPP(c_List_Omap(_1764169, _1764165), _1764171), c_List_OtakeWhile(_1764169, hAPP(c_Fun_Ocomp(_1764165, tc_HOL_Obool, _1764169, _1764167), _1764171), _1764173)))], (11438 ^ _775212) ^ [_962813, _962815] : [-(hAPP(c_Int_Onat, _962813) = _962815), 11441 ^ _775212 : [(11444 ^ _775212) ^ [] : [_962813 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _962815)], (11442 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _962813)))]], 11445 ^ _775212 : [(11448 ^ _775212) ^ [] : [_962815 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11446 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _962813))]]], (8649 ^ _775212) ^ [_915392, _915394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _915392)), 8652 ^ _775212 : [(8659 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _915394), _915392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _915394)), hAPP(c_Int_Onat, _915392))))], (8653 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _915394)), hAPP(c_Int_Onat, _915392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _915394), _915392)))]]], (35895 ^ _775212) ^ [_1438911, _1438913, _1438915, _1438917, _1438919, _1438921, _1438923, _1438925, _1438927, _1438929, _1438931] : [c_Equiv__Relations_Oequiv(_1438911, _1438913, _1438915), c_Equiv__Relations_Oequiv(_1438917, _1438919, _1438921), c_Equiv__Relations_Ocongruent2(_1438911, _1438917, tc_fun(_1438923, tc_HOL_Obool), _1438915, _1438921, _1438925), hBOOL(hAPP(hAPP(c_member(tc_fun(_1438911, tc_HOL_Obool)), _1438927), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1438911), _1438913), _1438915))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1438917, tc_HOL_Obool)), _1438929), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1438917), _1438919), _1438921))), 35917 ^ _775212 : [(35923 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1438923, tc_HOL_Obool)), hAPP(hAPP(_1438925, 35916 ^ [_1438911, _1438913, _1438915, _1438917, _1438919, _1438921, _1438923, _1438925, _1438927, _1438929, _1438931]), 35919 ^ [_1438911, _1438913, _1438915, _1438917, _1438919, _1438921, _1438923, _1438925, _1438927, _1438929, _1438931])), _1438931))], (35921 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1438917), 35919 ^ [_1438911, _1438913, _1438915, _1438917, _1438919, _1438921, _1438923, _1438925, _1438927, _1438929, _1438931]), _1438919)))], (35918 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1438911), 35916 ^ [_1438911, _1438913, _1438915, _1438917, _1438919, _1438921, _1438923, _1438925, _1438927, _1438929, _1438931]), _1438913)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1438923, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1438911, tc_fun(_1438923, tc_HOL_Obool)), _1438927), hAPP(hAPP(c_COMBB(tc_fun(_1438917, tc_fun(_1438923, tc_HOL_Obool)), tc_fun(_1438923, tc_HOL_Obool), _1438911), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1438917, tc_fun(_1438923, tc_HOL_Obool)), _1438929)), _1438925))), _1438931)))], (47784 ^ _775212) ^ [_1728852, _1728854, _1728856, _1728858, _1728860, _1728862] : [c_List_Olist__all2(_1728852, _1728854, _1728856, _1728858, _1728860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728862), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728854)), _1728860))), -(hBOOL(hAPP(hAPP(_1728856, hAPP(hAPP(c_List_Onth(_1728852), _1728858), _1728862)), hAPP(hAPP(c_List_Onth(_1728854), _1728860), _1728862))))], (42877 ^ _775212) ^ [_1610475, _1610477] : [-(c_Relation_Osingle__valued(_1610475, _1610475, c_Relation_OId__on(_1610475, _1610477)))], (23188 ^ _775212) ^ [_1176769, _1176771, _1176773, _1176775] : [class_Orderings_Olinorder(_1176769), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176769), _1176771), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176769), _1176773), _1176775)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176769), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176769), _1176771), _1176773)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176769), _1176771), _1176775)))], (38091 ^ _775212) ^ [_1489679, _1489681, _1489683, _1489685] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1489681, _1489679), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1489679, tc_prod(_1489681, _1489679), 38087 ^ [_1489679, _1489681, _1489683, _1489685]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1489681, tc_fun(_1489679, tc_HOL_Obool)), _1489683), _1489685))), hAPP(hAPP(c_Product__Type_OSigma(_1489681, _1489679), _1489683), _1489685))))], (6423 ^ _775212) ^ [_876776, _876778, _876780, _876782] : [class_Groups_Oab__semigroup__add(_876776), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876776), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876776), _876778), _876780)), _876782) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876776), _876778), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876776), _876780), _876782)))], (6164 ^ _775212) ^ [_872616, _872618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _872616)), _872618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872616), _872618)))], (5032 ^ _775212) ^ [_851894, _851896, _851898, _851900, _851902, _851904, _851906, _851908, _851910, _851912] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_851912, _851908, _851904, _851900, _851896) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_851910, _851906, _851902, _851898, _851894)), _851912 = _851910, _851908 = _851906, _851904 = _851902, _851900 = _851898, _851896 = _851894], (33590 ^ _775212) ^ [_1387234] : [-(c_Relation_OId__on(_1387234, c_Orderings_Obot__class_Obot(tc_fun(_1387234, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1387234, _1387234), tc_HOL_Obool)))], (21565 ^ _775212) ^ [_1144570, _1144572, _1144574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1144570, tc_HOL_Obool)), _1144572), _1144574)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1144570, tc_HOL_Obool)), _1144574), _1144572)), -(_1144572 = _1144574)], (21733 ^ _775212) ^ [_1147646, _1147648, _1147650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1147646, tc_HOL_Obool)), _1147648), _1147650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1147646, tc_HOL_Obool)), _1147648), _1147650))), -(_1147648 = _1147650)], (27471 ^ _775212) ^ [_1259709, _1259711, _1259713] : [class_Orderings_Olinorder(_1259709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259709), _1259711), _1259713)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259709, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1259709), _1259711)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1259709, _1259711, _1259713)) = hAPP(c_SetInterval_Oord__class_OatMost(_1259709), _1259713))], (28775 ^ _775212) ^ [_1286524, _1286526, _1286528] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1286524, tc_fun(_1286526, tc_HOL_Obool)), _1286528), hAPP(c_COMBK(tc_fun(_1286526, tc_HOL_Obool), _1286524), c_Orderings_Obot__class_Obot(tc_fun(_1286526, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1286526, tc_HOL_Obool)))], (37102 ^ _775212) ^ [_1465340, _1465342, _1465344, _1465346] : [c_Fun_Oinj__on(_1465340, _1465342, _1465344, _1465346), -(c_Fun_Oinj__on(_1465342, _1465340, c_Fun_Othe__inv__into(_1465340, _1465342, _1465346, _1465344), hAPP(c_Set_Oimage(_1465340, _1465342, _1465344), _1465346)))], (14355 ^ _775212) ^ [_1014740] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1014740) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1134 ^ _775212) ^ [_792243, _792245] : [-(class_Rings_Olinordered__ring__strict(_792243)), _792245 = _792243, class_Rings_Olinordered__ring__strict(_792245)], (40206 ^ _775212) ^ [_1547004, _1547006] : [40208 ^ _775212 : [(40211 ^ _775212) ^ [] : [hBOOL(hAPP(_1547004, hAPP(c_Int_OAbs__Integ, 40207 ^ [_1547004, _1547006])))], (40209 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40207 ^ [_1547004, _1547006]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1547004, _1547006)))], (17677 ^ _775212) ^ [_1075431, _1075433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1075431), _1075433)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1075431)), c_Int_OBit1(_1075433))))], (44473 ^ _775212) ^ [_1651571, _1651573, _1651575, _1651577, _1651579, _1651581] : [c_List_Olistrelp(_1651571, _1651573, hAPP(hAPP(c_List_Olist_OCons(_1651571), _1651575), _1651577), hAPP(hAPP(c_List_Olist_OCons(_1651571), _1651579), _1651581)), 44476 ^ _775212 : [(44479 ^ _775212) ^ [] : [-(c_List_Olistrelp(_1651571, _1651573, _1651577, _1651581))], (44477 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1651573, _1651575), _1651579)))]]], (36667 ^ _775212) ^ [_1455999, _1456001, _1456003, _1456005, _1456007] : [c_Fun_Oinj__on(_1455999, _1456001, _1456003, c_Orderings_Otop__class_Otop(tc_fun(_1455999, tc_HOL_Obool))), 36670 ^ _775212 : [(36677 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1455999), _1456005), _1456007)), -(hBOOL(hAPP(hAPP(c_member(_1456001), hAPP(_1456003, _1456005)), hAPP(c_Set_Oimage(_1455999, _1456001, _1456003), _1456007))))], (36671 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1456001), hAPP(_1456003, _1456005)), hAPP(c_Set_Oimage(_1455999, _1456001, _1456003), _1456007))), -(hBOOL(hAPP(hAPP(c_member(_1455999), _1456005), _1456007)))]]], (41754 ^ _775212) ^ [_1580721, _1580723, _1580725, _1580727, _1580729, _1580731] : [c_Finite__Set_Ofun__left__comm(_1580721, _1580723, _1580725), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1580721, _1580723, _1580725, _1580727, _1580729), _1580731)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1580721, _1580723, _1580725), _1580727), _1580729) = _1580731)], (50827 ^ _775212) ^ [_1794417, _1794419, _1794421, _1794423, _1794425] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1794417, _1794419, _1794421), _1794423), _1794425)), -(hBOOL(hAPP(hAPP(_1794421, _1794425), _1794423)))], (34361 ^ _775212) ^ [_1405153, _1405155, _1405157, _1405159, _1405161, _1405163, _1405165, _1405167, _1405169, _1405171] : [c_Equiv__Relations_Oequiv(_1405153, _1405155, _1405157), c_Equiv__Relations_Oequiv(_1405159, _1405161, _1405163), c_Equiv__Relations_Ocongruent2(_1405153, _1405159, tc_fun(_1405165, tc_HOL_Obool), _1405157, _1405163, _1405167), hBOOL(hAPP(hAPP(c_member(_1405153), _1405169), _1405155)), hBOOL(hAPP(hAPP(c_member(_1405159), _1405171), _1405161)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405153, tc_fun(_1405165, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1405153, _1405153, _1405157), hAPP(hAPP(c_Set_Oinsert(_1405153), _1405169), c_Orderings_Obot__class_Obot(tc_fun(_1405153, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1405159, tc_fun(_1405165, tc_HOL_Obool)), tc_fun(_1405165, tc_HOL_Obool), _1405153), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405159, tc_fun(_1405165, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1405159, _1405159, _1405163), hAPP(hAPP(c_Set_Oinsert(_1405159), _1405171), c_Orderings_Obot__class_Obot(tc_fun(_1405159, tc_HOL_Obool)))))), _1405167)) = hAPP(hAPP(_1405167, _1405169), _1405171))], (39731 ^ _775212) ^ [_1535586, _1535588, _1535590, _1535592, _1535594] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1535586, _1535588)), hAPP(hAPP(c_Product__Type_OPair(_1535586, _1535588), _1535590), _1535592)), _1535594)), -(hBOOL(hAPP(hAPP(c_member(_1535586), _1535590), hAPP(c_Relation_ODomain(_1535586, _1535588), _1535594))))], (29379 ^ _775212) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3244 ^ _775212) ^ [_823962, _823964, _823966, _823968, _823970, _823972, _823974, _823976] : [-(c_Recdef_Osame__fst(_823976, _823972, _823968, _823964) = c_Recdef_Osame__fst(_823974, _823970, _823966, _823962)), _823976 = _823974, _823972 = _823970, _823968 = _823966, _823964 = _823962], (18389 ^ _775212) ^ [_1087516, _1087518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1087516)), c_Int_OBit0(_1087518))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087516), _1087518)))], (20569 ^ _775212) ^ [_1126411, _1126413, _1126415, _1126417] : [class_Fields_Olinordered__field__inverse__zero(_1126411), 20572 ^ _775212 : [(20573 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126411), _1126413), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126411), _1126415), _1126417))), 20576 ^ _775212 : [(20583 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126411), c_Groups_Ozero__class_Ozero(_1126411)), _1126417))), 20586 ^ _775212 : [(20593 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126411), _1126417), c_Groups_Ozero__class_Ozero(_1126411)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126411), _1126413), c_Groups_Ozero__class_Ozero(_1126411))))], (20587 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126411), _1126417), c_Groups_Ozero__class_Ozero(_1126411))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126411), _1126415), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126411), _1126413), _1126417))))]]], (20577 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126411), c_Groups_Ozero__class_Ozero(_1126411)), _1126417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126411), _1126413), _1126417)), _1126415)))]]], (20599 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126411), _1126413), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126411), _1126415), _1126417)))), 20602 ^ _775212 : [(20605 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126411), _1126413), _1126417)), _1126415))], (20603 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126411), c_Groups_Ozero__class_Ozero(_1126411)), _1126417)))]], 20606 ^ _775212 : [(20609 ^ _775212) ^ [] : [20610 ^ _775212 : [(20613 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126411), _1126415), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126411), _1126413), _1126417)))], (20611 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126411), _1126417), c_Groups_Ozero__class_Ozero(_1126411))))]], 20614 ^ _775212 : [(20617 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126411), _1126413), c_Groups_Ozero__class_Ozero(_1126411)))], (20615 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126411), _1126417), c_Groups_Ozero__class_Ozero(_1126411)))]]], (20607 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126411), c_Groups_Ozero__class_Ozero(_1126411)), _1126417))]]]]], (45162 ^ _775212) ^ [_1669430, _1669432] : [-(c_List_Olistrelp(_1669430, _1669432, c_List_Olist_ONil(_1669430), c_List_Olist_ONil(_1669430)))], (14069 ^ _775212) ^ [_1009293, _1009295, _1009297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009293)), 14075 ^ _775212 : [(14078 ^ _775212) ^ [] : [hBOOL(hAPP(_1009295, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 14074 ^ [_1009293, _1009295, _1009297]), _1009293)))], (14076 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1009295, 14074 ^ [_1009293, _1009295, _1009297])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009297)), 14083 ^ _775212 : [(14084 ^ _775212) ^ [_1009582] : [hBOOL(hAPP(_1009295, _1009582)), -(hBOOL(hAPP(_1009295, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1009582), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1009297), _1009293)))))]]], (49452 ^ _775212) ^ [_1764866, _1764868, _1764870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764866)), c_List_OtakeWhile(_1764866, _1764868, _1764870))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764866)), _1764870))), hBOOL(hAPP(_1764868, hAPP(hAPP(c_List_Onth(_1764866), _1764870), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764866)), c_List_OtakeWhile(_1764866, _1764868, _1764870)))))], (46123 ^ _775212) ^ [_1693010, _1693012, _1693014, _1693016] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693010), tc_List_Olist(_1693010))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693010), tc_List_Olist(_1693010)), _1693012), _1693014)), c_List_Olistrel1(_1693010, _1693016)))), 46124 ^ _775212 : [(46125 ^ _775212) ^ [_1693143, _1693145] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1693010, _1693010)), hAPP(hAPP(c_Product__Type_OPair(_1693010, _1693010), hAPP(hAPP(c_List_Onth(_1693010), _1693012), _1693143)), _1693145)), _1693016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1693143), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693010)), _1693012))), _1693014 = hAPP(hAPP(c_List_Olist__update(_1693010, _1693012), _1693143), _1693145)]]], (41540 ^ _775212) ^ [_1576009, _1576011, _1576013] : [class_Orderings_Olinorder(_1576009), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576009), _1576011)), -(hBOOL(hAPP(hAPP(c_member(_1576009), _1576013), _1576011))), -(c_Big__Operators_Olinorder__class_OMin(_1576009, hAPP(hAPP(c_Set_Oinsert(_1576009), _1576013), _1576011)) = hAPP(hAPP(c_Finite__Set_Ofold(_1576009, _1576009, c_Orderings_Oord__class_Omin(_1576009)), _1576013), _1576011))], (40087 ^ _775212) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (44726 ^ _775212) ^ [_1658244, _1658246, _1658248] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1658244), _1658246)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1658244)), hAPP(c_Set_OCollect(tc_List_Olist(_1658244)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1658244), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1658244)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1658244), tc_fun(_1658244, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1658244, tc_HOL_Obool), tc_fun(tc_fun(_1658244, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1658244)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1658244, tc_HOL_Obool))), c_List_Oset(_1658244))), _1658246))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1658244), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1658244)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1658244)))), _1658248))))))], (17263 ^ _775212) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (49812 ^ _775212) ^ [_1772369, _1772371, _1772373] : [-(hAPP(c_List_Oset(_1772369), c_List_Oinsert(_1772369, _1772371, _1772373)) = hAPP(hAPP(c_Set_Oinsert(_1772369), _1772371), hAPP(c_List_Oset(_1772369), _1772373)))], (47529 ^ _775212) ^ [_1723342, _1723344, _1723346, _1723348, _1723350] : [class_Orderings_Olinorder(_1723342), 47532 ^ _775212 : [(47541 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1723344), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1723344, _1723342, _1723346), _1723348), _1723350)))), -(hBOOL(hAPP(hAPP(c_member(_1723344), _1723348), hAPP(c_List_Oset(_1723344), _1723350)))), hBOOL(hAPP(c_List_Odistinct(_1723344), _1723350))], (47533 ^ _775212) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1723344), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1723344, _1723342, _1723346), _1723348), _1723350))), 47536 ^ _775212 : [(47539 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1723344), _1723350)))], (47537 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1723344), _1723348), hAPP(c_List_Oset(_1723344), _1723350)))]]]]], (49464 ^ _775212) ^ [_1765186, _1765188] : [-(_1765186 = c_List_Olist_ONil(_1765188)), hBOOL(hAPP(c_List_Odistinct(_1765188), _1765186)), -(c_List_OtakeWhile(_1765188, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1765188), c_fNot), hAPP(hAPP(c_COMBC(_1765188, _1765188, tc_HOL_Obool), c_fequal), c_List_Olast(_1765188, _1765186))), _1765186) = c_List_Obutlast(_1765188, _1765186))], (43503 ^ _775212) ^ [_1625282, _1625284] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1625282), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625282, tc_HOL_Obool), _1625284))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1625282, tc_HOL_Obool)), _1625284)))], (51140 ^ _775212) ^ [_1801781, _1801783, _1801785, _1801787, _1801789, _1801791, _1801793] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1801781, tc_fun(_1801783, tc_fun(_1801785, tc_HOL_Obool))), _1801787), _1801789), _1801791), _1801793)), 51144 ^ _775212 : [(51147 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1801789, 51143 ^ [_1801781, _1801783, _1801785, _1801787, _1801789, _1801791, _1801793]), _1801791), _1801793)))], (51145 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801781), 51143 ^ [_1801781, _1801783, _1801785, _1801787, _1801789, _1801791, _1801793]), _1801787)))]]], (6966 ^ _775212) ^ [_886259, _886261, _886263] : [class_Orderings_Olinorder(_886259), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886259), _886261), _886263))), -(_886261 = _886263), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886259), _886263), _886261)))], (42990 ^ _775212) ^ [_1613101, _1613103, _1613105] : [c_Wellfounded_Owf(_1613101, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613101, _1613101), tc_HOL_Obool), _1613103), _1613105)), -(c_Wellfounded_Owf(_1613101, _1613105))], (28075 ^ _775212) ^ [_1272487, _1272489, _1272491, _1272493, _1272495] : [class_Groups_Ocomm__monoid__add(_1272487), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272489), _1272491)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1272489, _1272487), hAPP(hAPP(c_COMBS(_1272489, _1272487, _1272487), hAPP(hAPP(c_COMBB(_1272487, tc_fun(_1272487, _1272487), _1272489), c_Groups_Oplus__class_Oplus(_1272487)), _1272493)), _1272495)), _1272491) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272487), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1272489, _1272487), _1272493), _1272491)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1272489, _1272487), _1272495), _1272491)))], (27824 ^ _775212) ^ [_1267833] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1267833)) = 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), _1267833))))], (19925 ^ _775212) ^ [_1114876, _1114878, _1114880, _1114882] : [class_Fields_Olinordered__field(_1114876), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114876), c_Groups_Ozero__class_Ozero(_1114876)), _1114878)), 19932 ^ _775212 : [(19939 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114876), _1114880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114876), _1114882), _1114878))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114876), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114876), _1114880), _1114878)), _1114882)))], (19933 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114876), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114876), _1114880), _1114878)), _1114882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114876), _1114880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114876), _1114882), _1114878))))]]], (22286 ^ _775212) ^ [_1158945, _1158947, _1158949] : [class_Int_Onumber__ring(_1158945), 22289 ^ _775212 : [(22296 ^ _775212) ^ [] : [-(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), _1158947)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1158945), _1158949), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1158947))) = c_Groups_Oone__class_Oone(_1158945))], (22290 ^ _775212) ^ [] : [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), _1158947))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1158945), _1158949), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1158947))) = hAPP(hAPP(c_HOL_OLet(_1158945, _1158945), hAPP(hAPP(c_Power_Opower__class_Opower(_1158945), _1158949), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158947))), hAPP(hAPP(c_COMBS(_1158945, _1158945, _1158945), hAPP(hAPP(c_COMBB(_1158945, tc_fun(_1158945, _1158945), _1158945), c_Groups_Otimes__class_Otimes(_1158945)), hAPP(c_Groups_Otimes__class_Otimes(_1158945), _1158949))), c_COMBI(_1158945))))]]], (14221 ^ _775212) ^ [_1012183, _1012185, _1012187] : [class_Groups_Ogroup__add(_1012183), 14224 ^ _775212 : [(14231 ^ _775212) ^ [] : [_1012185 = _1012187, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1012183), _1012185), _1012187) = c_Groups_Ozero__class_Ozero(_1012183))], (14225 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1012183), _1012185), _1012187) = c_Groups_Ozero__class_Ozero(_1012183), -(_1012185 = _1012187)]]], (31051 ^ _775212) ^ [_1336224, _1336226, _1336228, _1336230] : [hBOOL(hAPP(hAPP(c_member(_1336224), _1336226), c_SetInterval_Oord_OatMost(_1336224, _1336228, _1336230))), -(hBOOL(hAPP(hAPP(_1336228, _1336226), _1336230)))], (43792 ^ _775212) ^ [_1632399, _1632401, _1632403, _1632405] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632399, _1632399)), hAPP(hAPP(c_Product__Type_OPair(_1632399, _1632399), _1632401), _1632403)), c_Transitive__Closure_Otrancl(_1632399, _1632405))), 43796 ^ _775212 : [(43799 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632399, _1632399)), hAPP(hAPP(c_Product__Type_OPair(_1632399, _1632399), 43795 ^ [_1632399, _1632401, _1632403, _1632405]), _1632403)), _1632405)))], (43797 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632399, _1632399)), hAPP(hAPP(c_Product__Type_OPair(_1632399, _1632399), _1632401), 43795 ^ [_1632399, _1632401, _1632403, _1632405])), c_Transitive__Closure_Ortrancl(_1632399, _1632405))))]]], (26762 ^ _775212) ^ [_1245538, _1245540] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1245538, _1245540)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1245540), _1245538)))], (19205 ^ _775212) ^ [_1102383, _1102385, _1102387, _1102389] : [class_Fields_Olinordered__field__inverse__zero(_1102383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102383), _1102385), _1102387)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102383), c_Groups_Ozero__class_Ozero(_1102383)), _1102389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102383), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102383), _1102385), _1102389)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102383), _1102387), _1102389))))], (14371 ^ _775212) ^ [_1015053, _1015055, _1015057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015053), _1015055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015053), _1015057)), _1015055)))], (37222 ^ _775212) ^ [_1468075, _1468077] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1468075), _1468077))), -(hAPP(c_Finite__Set_Ocard(_1468075), _1468077) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5054 ^ _775212) ^ [_852283, _852285, _852287, _852289, _852291, _852293] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_852293, _852289, _852285) = c_Lazy__Sequence_Olazy__sequence_OInsert(_852291, _852287, _852283)), _852293 = _852291, _852289 = _852287, _852285 = _852283], (51169 ^ _775212) ^ [_1802505] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1802505)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1802505)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28559 ^ _775212) ^ [_1282192, _1282194, _1282196] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1282192), _1282194))), 28562 ^ _775212 : [(28569 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1282196), _1282194))), -(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)), _1282192)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1282196), _1282194)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (28563 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1282196), _1282194)), -(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)), _1282192)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1282196), _1282194)) = 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))))]]], (40069 ^ _775212) ^ [] : [-(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))))], (19037 ^ _775212) ^ [_1099405, _1099407, _1099409, _1099411, _1099413] : [class_Fields_Ofield__inverse__zero(_1099405), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099405), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099405), _1099407), _1099409)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099405), _1099411), _1099413)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099405), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099405), _1099407), _1099411)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099405), _1099409), _1099413)))], (51226 ^ _775212) ^ [_1803585, _1803587, _1803589, _1803591, _1803593] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1803585), tc_List_Olist(_1803585))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1803585), tc_List_Olist(_1803585)), _1803587), _1803589)), c_List_Olexord(_1803585, _1803591))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1803585), tc_List_Olist(_1803585))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1803585), tc_List_Olist(_1803585)), _1803589), _1803593)), c_List_Olexord(_1803585, _1803591))), c_Relation_Otrans(_1803585, _1803591), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1803585), tc_List_Olist(_1803585))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1803585), tc_List_Olist(_1803585)), _1803587), _1803593)), c_List_Olexord(_1803585, _1803591))))], (48488 ^ _775212) ^ [_1745904, _1745906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1745904), _1745906)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1745904, _1745906)) = _1745904)], (24042 ^ _775212) ^ [_1192958, _1192960] : [24049 ^ _775212 : [(24052 ^ _775212) ^ [] : [_1192958 = _1192960], (24050 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192958), _1192960)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192958), _1192960)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192960), _1192958)))], (39811 ^ _775212) ^ [_1537084, _1537086] : [c_Wellfounded_Owf(_1537084, _1537086), -(c_Wellfounded_Owf(tc_fun(_1537084, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1537084, _1537086)))], (15876 ^ _775212) ^ [_1044089] : [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), _1044089))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1044089) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1044089)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (37294 ^ _775212) ^ [] : [-(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))))], (9917 ^ _775212) ^ [_935830, _935832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935830)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _935830), _935832)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _935830)), hAPP(c_Int_Onat, _935832)))], (50965 ^ _775212) ^ [_1797560, _1797562, _1797564, _1797566, _1797568] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1797560, _1797562, _1797564) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1797560, _1797566, _1797568)), _1797562 = _1797566, _1797564 = _1797568], (34841 ^ _775212) ^ [_1415077, _1415079] : [class_Lattices_Osemilattice__inf(_1415077), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415077), _1415079), _1415079) = _1415079)], (46796 ^ _775212) ^ [_1708067] : [class_Groups_Omonoid__add(_1708067), -(c_List_Omonoid__add__class_Olistsum(_1708067) = c_List_Ofoldl(_1708067, _1708067, c_Groups_Oplus__class_Oplus(_1708067), c_Groups_Ozero__class_Ozero(_1708067)))], (29907 ^ _775212) ^ [_1308227, _1308229, _1308231] : [hBOOL(hAPP(hAPP(c_member(_1308227), _1308229), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308227, tc_HOL_Obool)), _1308231))), hBOOL(hAPP(hAPP(c_member(_1308227), _1308229), _1308231))], (4990 ^ _775212) ^ [_851269, _851271, _851273, _851275, _851277, _851279] : [-(c_FunDef_OTHE__default(_851279, _851275, _851271) = c_FunDef_OTHE__default(_851277, _851273, _851269)), _851279 = _851277, _851275 = _851273, _851271 = _851269], (37445 ^ _775212) ^ [_1472568, _1472570, _1472572] : [-(hAPP(c_Set_Ovimage(_1472568, _1472570, _1472572), c_Orderings_Otop__class_Otop(tc_fun(_1472570, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1472568, tc_HOL_Obool)))], (27573 ^ _775212) ^ [_1261692, _1261694, _1261696] : [class_Orderings_Olinorder(_1261692), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261692), _1261694), _1261696)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261692, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1261692, _1261694, _1261696)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1261692), _1261696)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1261692), _1261694))], (40656 ^ _775212) ^ [_1556936] : [-(c_Nitpick_Odenom(_1556936) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1556936, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1556936)))], (45734 ^ _775212) ^ [_1683776, _1683778, _1683780] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683776)), hAPP(hAPP(c_List_Oappend(_1683776), _1683778), _1683780)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683776)), _1683778)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683776)), _1683780)))], (37330 ^ _775212) ^ [_1469849, _1469851, _1469853, _1469855, _1469857, _1469859] : [c_Typedef_Otype__definition(_1469849, _1469851, _1469853, _1469855, _1469857), -(hBOOL(hAPP(hAPP(c_member(_1469851), hAPP(_1469853, _1469859)), _1469857)))], (52261 ^ _775212) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (48989 ^ _775212) ^ [_1755078, _1755080, _1755082] : [class_Orderings_Olinorder(_1755078), hBOOL(hAPP(hAPP(c_member(_1755078), _1755080), hAPP(c_List_Oset(_1755078), _1755082))), c_List_Olinorder__class_Osorted(_1755078, _1755082), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1755078, _1755078, c_COMBI(_1755078)), _1755080), c_List_Oremove1(_1755078, _1755080, _1755082)) = _1755082)], (45554 ^ _775212) ^ [_1679754, _1679756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1679754), _1679756)), -(c_List_Oupto(_1679754, _1679756) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1679754), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1679754), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1679756)))], (37922 ^ _775212) ^ [_1484936, _1484938, _1484940, _1484942, _1484944] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1484936, _1484938), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484936, tc_HOL_Obool)), _1484940), _1484942)), _1484944) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1484936, _1484938), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1484936, _1484938), _1484940), _1484944)), hAPP(hAPP(c_Product__Type_OSigma(_1484936, _1484938), _1484942), _1484944)))], (47627 ^ _775212) ^ [_1725303, _1725305, _1725307, _1725309, _1725311] : [-(c_Enum_Oproduct(_1725303, _1725305, hAPP(hAPP(c_List_Olist_OCons(_1725303), _1725307), _1725309), _1725311) = hAPP(hAPP(c_List_Oappend(tc_prod(_1725303, _1725305)), hAPP(hAPP(c_List_Omap(_1725305, tc_prod(_1725303, _1725305)), hAPP(c_Product__Type_OPair(_1725303, _1725305), _1725307)), _1725311)), c_Enum_Oproduct(_1725303, _1725305, _1725309, _1725311)))], (25581 ^ _775212) ^ [_1221048, _1221050, _1221052, _1221054] : [class_Rings_Osemiring__1(_1221048), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1221048), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221050, tc_Nat_Onat), _1221052), _1221054)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221050, _1221048), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1221048, _1221050), c_Nat_Osemiring__1__class_Oof__nat(_1221048)), _1221052)), _1221054))], (30292 ^ _775212) ^ [_1319122, _1319124, _1319126, _1319128, _1319130] : [hBOOL(hAPP(hAPP(c_member(_1319122), _1319124), _1319126)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319128, tc_HOL_Obool)), hAPP(_1319130, _1319124)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1319122, tc_fun(_1319128, tc_HOL_Obool)), _1319126), _1319130)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1319122, tc_fun(_1319128, tc_HOL_Obool)), _1319126), _1319130))], (51901 ^ _775212) ^ [_1818299, _1818301] : [c_Relation_Osym(_1818299, hAPP(c_Set_OCollect(tc_prod(_1818299, _1818299)), hAPP(c_Product__Type_Oprod_Oprod__case(_1818299, _1818299, tc_HOL_Obool), _1818301))), -(c_Predicate_Osymp(_1818299, _1818301))], (23236 ^ _775212) ^ [_1177954, _1177956, _1177958] : [class_Int_Onumber(_1177954), class_Orderings_Oord(_1177954), 23243 ^ _775212 : [(23250 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177954), hAPP(c_Int_Onumber__class_Onumber__of(_1177954), _1177956)), hAPP(c_Int_Onumber__class_Onumber__of(_1177954), _1177958)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177954), hAPP(c_Int_Onumber__class_Onumber__of(_1177954), _1177956)), hAPP(c_Int_Onumber__class_Onumber__of(_1177954), _1177958)) = hAPP(c_Int_Onumber__class_Onumber__of(_1177954), _1177956))], (23244 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177954), hAPP(c_Int_Onumber__class_Onumber__of(_1177954), _1177956)), hAPP(c_Int_Onumber__class_Onumber__of(_1177954), _1177958))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177954), hAPP(c_Int_Onumber__class_Onumber__of(_1177954), _1177956)), hAPP(c_Int_Onumber__class_Onumber__of(_1177954), _1177958)) = hAPP(c_Int_Onumber__class_Onumber__of(_1177954), _1177958))]]], (4228 ^ _775212) ^ [_839408, _839410, _839412, _839414, _839416, _839418] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_839418, _839414, _839410) = c_SetInterval_Oord__class_OgreaterThanLessThan(_839416, _839412, _839408)), _839418 = _839416, _839414 = _839412, _839410 = _839408], (26748 ^ _775212) ^ [_1245253] : [c_Nat__Transfer_Onat__set(_1245253), -(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), _1245253)) = _1245253)], (27872 ^ _775212) ^ [_1268781, _1268783] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1268781, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1268781, tc_HOL_Obool))), _1268783) = c_Orderings_Otop__class_Otop(tc_fun(_1268781, tc_HOL_Obool)))], (45921 ^ _775212) ^ [_1687692, _1687694, _1687696, _1687698, _1687700, _1687702] : [-(_1687692 = _1687694), -(hAPP(hAPP(c_List_Olist__update(_1687696, hAPP(hAPP(c_List_Olist__update(_1687696, _1687698), _1687692), _1687700)), _1687694), _1687702) = hAPP(hAPP(c_List_Olist__update(_1687696, hAPP(hAPP(c_List_Olist__update(_1687696, _1687698), _1687694), _1687702)), _1687692), _1687700))], (38885 ^ _775212) ^ [_1506309] : [-(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)), _1506309)))))], (28257 ^ _775212) ^ [_1276217, _1276219] : [class_Finite__Set_Ofinite(_1276217), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1276217), _1276219)))], (27992 ^ _775212) ^ [_1271143, _1271145] : [class_Lattices_Obounded__lattice__top(_1271143), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271143), c_Orderings_Otop__class_Otop(_1271143)), _1271145) = c_Orderings_Otop__class_Otop(_1271143))], (27739 ^ _775212) ^ [_1265572, _1265574, _1265576, _1265578, _1265580, _1265582] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265572, tc_fun(_1265574, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265576, tc_fun(_1265572, tc_HOL_Obool)), _1265578), _1265580)), _1265582) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265576, tc_fun(_1265574, tc_HOL_Obool)), _1265578), hAPP(hAPP(c_COMBC(_1265576, tc_fun(_1265572, tc_fun(_1265574, tc_HOL_Obool)), tc_fun(_1265574, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1265572, tc_HOL_Obool), tc_fun(tc_fun(_1265572, tc_fun(_1265574, tc_HOL_Obool)), tc_fun(_1265574, tc_HOL_Obool)), _1265576), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265572, tc_fun(_1265574, tc_HOL_Obool))), _1265580)), _1265582)))], (11612 ^ _775212) ^ [_965958, _965960, _965962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965958)), 11615 ^ _775212 : [(11622 ^ _775212) ^ [] : [_965960 = _965962, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965958), _965960) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965958), _965962))], (11616 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965958), _965960) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965958), _965962), -(_965960 = _965962)]]], (1484 ^ _775212) ^ [_796618, _796620] : [-(class_Enum_Oenum(_796618)), _796620 = _796618, class_Enum_Oenum(_796620)], (23838 ^ _775212) ^ [_1189566, _1189568, _1189570, _1189572, _1189574] : [_1189566 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1189568, _1189570, _1189572, _1189574), _1189566) = c_Lazy__Sequence_Oempty(_1189570))], (29606 ^ _775212) ^ [_1302438, _1302440, _1302442, _1302444] : [hBOOL(hAPP(hAPP(c_member(_1302438), _1302440), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1302438, tc_HOL_Obool)), _1302442), _1302444))), 29609 ^ _775212 : [(29612 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1302438), _1302440), _1302444))], (29610 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1302438), _1302440), _1302442)))]]], (51669 ^ _775212) ^ [_1813883] : [-(c_Relation_Oantisym(_1813883, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1813883, _1813883), tc_HOL_Obool))))], (696 ^ _775212) ^ [_785942, _785944] : [-(class_Lattices_Oab__semigroup__idem__mult(_785942)), _785944 = _785942, class_Lattices_Oab__semigroup__idem__mult(_785944)], (28020 ^ _775212) ^ [_1271516, _1271518, _1271520, _1271522] : [class_Groups_Ocomm__monoid__add(_1271516), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1271518), _1271520))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1271518, _1271516), _1271522), _1271520) = c_Groups_Ozero__class_Ozero(_1271516))], (6549 ^ _775212) ^ [_879004, _879006] : [class_Groups_Omonoid__add(_879004), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879004), _879006), c_Groups_Ozero__class_Ozero(_879004)) = _879006)], (17195 ^ _775212) ^ [_1067748, _1067750] : [class_Int_Onumber__ring(_1067748), 17198 ^ _775212 : [(17205 ^ _775212) ^ [] : [c_Int_Oiszero(_1067748, hAPP(c_Int_Onumber__class_Onumber__of(_1067748), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067750), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1067748), _1067750) = c_Groups_Ozero__class_Ozero(_1067748))], (17199 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1067748), _1067750) = c_Groups_Ozero__class_Ozero(_1067748), -(c_Int_Oiszero(_1067748, hAPP(c_Int_Onumber__class_Onumber__of(_1067748), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067750), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (3158 ^ _775212) ^ [_822645, _822647] : [_822647 = _822645, -(c_Rings_Oinverse__class_Odivide(_822647) = c_Rings_Oinverse__class_Odivide(_822645))], (51589 ^ _775212) ^ [_1812406, _1812408, _1812410, _1812412] : [c_Wellfounded_Omax__extp(_1812406, _1812408, _1812410, _1812412), 51592 ^ _775212 : [(51595 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1812406), _1812412)))], (51597 ^ _775212) ^ [] : [_1812412 = c_Orderings_Obot__class_Obot(tc_fun(_1812406, tc_HOL_Obool))], (51599 ^ _775212) ^ [_1812622] : [hBOOL(hAPP(hAPP(c_member(_1812406), _1812622), _1812410)), 51603 ^ _775212 : [(51606 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1812408, _1812622), 51602 ^ [_1812406, _1812408, _1812410, _1812412, _1812622])))], (51604 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1812406), 51602 ^ [_1812406, _1812408, _1812410, _1812412, _1812622]), _1812412)))]]], (51593 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1812406), _1812410)))]]], (47024 ^ _775212) ^ [_1712621, _1712623] : [-(_1712621 = c_List_Olist_ONil(_1712623)), -(hBOOL(hAPP(hAPP(c_member(_1712623), c_List_Olast(_1712623, _1712621)), hAPP(c_List_Oset(_1712623), _1712621))))], (49113 ^ _775212) ^ [_1757850, _1757852] : [hBOOL(hAPP(c_List_Odistinct(_1757850), _1757852)), -(hBOOL(hAPP(c_List_Odistinct(_1757850), hAPP(c_List_Orev(_1757850), _1757852))))], (36481 ^ _775212) ^ [_1452438, _1452440] : [-(c_Equiv__Relations_Oequivp(_1452438, _1452440)), 36486 ^ _775212 : [(36489 ^ _775212) ^ [] : [hAPP(_1452440, 36482 ^ [_1452438, _1452440]) = hAPP(_1452440, 36483 ^ [_1452438, _1452440])], (36487 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1452440, 36482 ^ [_1452438, _1452440]), 36483 ^ [_1452438, _1452440])))]], 36490 ^ _775212 : [(36493 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1452440, 36482 ^ [_1452438, _1452440]), 36483 ^ [_1452438, _1452440]))], (36491 ^ _775212) ^ [] : [-(hAPP(_1452440, 36482 ^ [_1452438, _1452440]) = hAPP(_1452440, 36483 ^ [_1452438, _1452440]))]]], (47971 ^ _775212) ^ [_1733212, _1733214, _1733216] : [hBOOL(hAPP(c_List_Odistinct(_1733212), _1733214)), -(c_List_Oremove1(_1733212, _1733216, c_List_Oremdups(_1733212, _1733214)) = c_List_Oremdups(_1733212, c_List_Oremove1(_1733212, _1733216, _1733214)))], (51193 ^ _775212) ^ [_1802946, _1802948, _1802950] : [c_List_Olist__ex(tc_Int_Oint, _1802946, c_List_Oupto(_1802948, _1802950)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1802946), _1802948, _1802950)], (47873 ^ _775212) ^ [_1730937] : [-(c_Enum_Osublists(_1730937, c_List_Olist_ONil(_1730937)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1730937)), c_List_Olist_ONil(_1730937)), c_List_Olist_ONil(tc_List_Olist(_1730937))))], (6110 ^ _775212) ^ [_871969, _871971] : [-(_871969 = _871971), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871969), _871971))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871971), _871969)))], (12981 ^ _775212) ^ [_989709, _989711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989709)), -(c_SMT_Oz3mod(_989711, _989709) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _989711, _989709))], (37942 ^ _775212) ^ [_1485466, _1485468, _1485470, _1485472, _1485474] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1485466, _1485468), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485466, tc_HOL_Obool)), _1485470), _1485472)), _1485474) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1485466, _1485468), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1485466, _1485468), _1485470), _1485474)), hAPP(hAPP(c_Product__Type_OSigma(_1485466, _1485468), _1485472), _1485474)))], (49163 ^ _775212) ^ [_1758810, _1758812, _1758814] : [_1758812 = hAPP(hAPP(c_List_Olist_OCons(_1758810), _1758814), c_List_Olist_ONil(_1758810)), -(hAPP(c_List_Orev(_1758810), _1758812) = hAPP(hAPP(c_List_Olist_OCons(_1758810), _1758814), c_List_Olist_ONil(_1758810)))], (52331 ^ _775212) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (7032 ^ _775212) ^ [_887239, _887241, _887243, _887245] : [class_Orderings_Oord(_887239), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887239), _887241), _887243)), _887243 = _887245, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887239), _887241), _887245)))], (29154 ^ _775212) ^ [_1293182, _1293184, _1293186, _1293188, _1293190] : [_1293182 = c_Orderings_Obot__class_Obot(tc_fun(_1293184, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293184, tc_fun(_1293186, tc_HOL_Obool)), _1293182), hAPP(hAPP(c_COMBC(_1293184, tc_fun(_1293186, tc_HOL_Obool), tc_fun(_1293186, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1293186, tc_HOL_Obool), tc_fun(tc_fun(_1293186, tc_HOL_Obool), tc_fun(_1293186, tc_HOL_Obool)), _1293184), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293186, tc_HOL_Obool))), _1293188)), _1293190)) = c_Orderings_Obot__class_Obot(tc_fun(_1293186, tc_HOL_Obool)))], (32311 ^ _775212) ^ [_1360332, _1360334, _1360336, _1360338] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1360332), _1360334)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360336), _1360338)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1360332, _1360336)), c_Sum__Type_OPlus(_1360332, _1360336, _1360334, _1360338))))], (48526 ^ _775212) ^ [_1746621, _1746623, _1746625, _1746627] : [-(c_List_Oupt(_1746621, _1746623) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1746625), _1746627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746621), _1746623)), _1746621 = _1746625, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1746621), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1746623) = _1746627], (36055 ^ _775212) ^ [_1443815, _1443817, _1443819, _1443821, _1443823] : [class_Groups_Ocomm__monoid__mult(_1443815), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443817), _1443819)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443817), _1443821)), 36069 ^ _775212 : [(36072 ^ _775212) ^ [] : [hAPP(_1443823, 36068 ^ [_1443815, _1443817, _1443819, _1443821, _1443823]) = c_Groups_Oone__class_Oone(_1443815)], (36070 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1443817), 36068 ^ [_1443815, _1443817, _1443819, _1443821, _1443823]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443817, tc_HOL_Obool)), _1443819), _1443821))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443817, _1443815), _1443823), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1443817, tc_HOL_Obool)), _1443819), _1443821)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1443815), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443817, _1443815), _1443823), _1443819)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443817, _1443815), _1443823), _1443821)))], (7733 ^ _775212) ^ [_899394, _899396] : [class_Groups_Ogroup__add(_899394), -(hAPP(c_Groups_Ouminus__class_Ouminus(_899394), hAPP(c_Groups_Ouminus__class_Ouminus(_899394), _899396)) = _899396)], (27978 ^ _775212) ^ [_1270879, _1270881, _1270883, _1270885, _1270887] : [-(hAPP(c_Set_Oimage(_1270879, _1270881, hAPP(hAPP(c_COMBB(_1270883, _1270881, _1270879), _1270885), _1270887)), c_Orderings_Otop__class_Otop(tc_fun(_1270879, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1270883, _1270881, _1270885), hAPP(c_Set_Oimage(_1270879, _1270883, _1270887), c_Orderings_Otop__class_Otop(tc_fun(_1270879, tc_HOL_Obool)))))], (45054 ^ _775212) ^ [_1667236, _1667238] : [-(_1667236 = c_List_Olist_ONil(_1667238)), -(c_Random_Oselect__weight(_1667238, hAPP(hAPP(c_List_Omap(_1667238, tc_prod(tc_Code__Numeral_Ocode__numeral, _1667238)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1667238), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1667236)) = c_Random_Oselect(_1667238, _1667236))], (2940 ^ _775212) ^ [_819136, _819138] : [_819138 = _819136, -(c_Int_OBit0(_819138) = c_Int_OBit0(_819136))], (1384 ^ _775212) ^ [_795368, _795370] : [-(class_Lattices_Osemilattice__sup(_795368)), _795370 = _795368, class_Lattices_Osemilattice__sup(_795370)], (50505 ^ _775212) ^ [_1788124, _1788126, _1788128] : [c_List_Olist__all(_1788124, _1788126, _1788128), -(c_List_Olist__all(_1788124, _1788126, hAPP(c_List_Orev(_1788124), _1788128)))], (47326 ^ _775212) ^ [_1718616] : [class_Orderings_Olinorder(_1718616), -(c_List_Olinorder__class_Osorted__list__of__set(_1718616, c_Orderings_Obot__class_Obot(tc_fun(_1718616, tc_HOL_Obool))) = c_List_Olist_ONil(_1718616))], (10419 ^ _775212) ^ [_945025, _945027, _945029] : [class_Rings_Oordered__ring(_945025), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945025), c_Groups_Ozero__class_Ozero(_945025)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945025), _945027), _945029)))), 10424 ^ _775212 : [(10431 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945025), _945027), c_Groups_Ozero__class_Ozero(_945025))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945025), _945029), c_Groups_Ozero__class_Ozero(_945025)))], (10425 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945025), c_Groups_Ozero__class_Ozero(_945025)), _945027)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945025), c_Groups_Ozero__class_Ozero(_945025)), _945029))]]], (31953 ^ _775212) ^ [_1352935, _1352937, _1352939] : [class_Orderings_Olinorder(_1352935), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352935), _1352937)), -(_1352939 = c_Orderings_Obot__class_Obot(tc_fun(_1352935, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1352935, tc_HOL_Obool)), _1352939), _1352937)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352935), c_Big__Operators_Olinorder__class_OMax(_1352935, _1352939)), c_Big__Operators_Olinorder__class_OMax(_1352935, _1352937)) = c_Big__Operators_Olinorder__class_OMax(_1352935, _1352937))], (29997 ^ _775212) ^ [_1312218, _1312220, _1312222, _1312224] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312218, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1312218, tc_fun(_1312218, tc_HOL_Obool), tc_HOL_Obool), c_member(_1312218)), _1312220)), hAPP(hAPP(c_COMBC(_1312218, tc_fun(_1312218, tc_HOL_Obool), tc_HOL_Obool), c_member(_1312218)), _1312222)), _1312224)), -(hBOOL(hAPP(hAPP(c_member(_1312218), _1312224), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312218, tc_HOL_Obool)), _1312220), _1312222))))], (29566 ^ _775212) ^ [_1301722, _1301724, _1301726, _1301728, _1301730, _1301732, _1301734] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1301722, _1301724)), hAPP(hAPP(c_Product__Type_OPair(_1301722, _1301724), _1301726), _1301728)), _1301730)), -(hBOOL(hAPP(hAPP(c_member(_1301732), hAPP(hAPP(_1301734, _1301726), _1301728)), hAPP(c_Set_Oimage(tc_prod(_1301722, _1301724), _1301732, hAPP(c_Product__Type_Oprod_Oprod__case(_1301722, _1301724, _1301732), _1301734)), _1301730))))], (13282 ^ _775212) ^ [_995548, _995550] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _995548, _995550)), _995548)))], (17177 ^ _775212) ^ [_1067533, _1067535] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1067533)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067533)), _1067535)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1067533))), _1067535))], (22910 ^ _775212) ^ [_1171745, _1171747, _1171749] : [class_Orderings_Olinorder(_1171745), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171745), _1171747), _1171749) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171745), _1171749), _1171747))], (40796 ^ _775212) ^ [_1560131, _1560133, _1560135, _1560137, _1560139, _1560141] : [c_Finite__Set_Ofolding(_1560131, _1560133, _1560135, _1560137), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560131), _1560139)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560131), _1560141)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1560131, tc_HOL_Obool)), _1560139), _1560141) = c_Orderings_Obot__class_Obot(tc_fun(_1560131, tc_HOL_Obool)), -(hAPP(_1560137, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1560131, tc_HOL_Obool)), _1560139), _1560141)) = hAPP(c_Fun_Ocomp(_1560133, _1560133, _1560133, hAPP(_1560137, _1560139)), hAPP(_1560137, _1560141)))], (25058 ^ _775212) ^ [_1211007, _1211009, _1211011] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211007), _1211009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211007), _1211011))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211007)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211009), _1211011)))], (38216 ^ _775212) ^ [_1493165, _1493167, _1493169, _1493171, _1493173, _1493175] : [-(c_Product__Type_Omap__pair(_1493165, _1493167, _1493169, _1493171, _1493173, _1493175) = hAPP(c_Product__Type_Oprod_Oprod__case(_1493165, _1493169, tc_prod(_1493167, _1493171)), hAPP(hAPP(c_COMBC(_1493165, tc_fun(_1493169, _1493171), tc_fun(_1493169, tc_prod(_1493167, _1493171))), hAPP(hAPP(c_COMBB(tc_fun(_1493171, tc_prod(_1493167, _1493171)), tc_fun(tc_fun(_1493169, _1493171), tc_fun(_1493169, tc_prod(_1493167, _1493171))), _1493165), c_COMBB(_1493171, tc_prod(_1493167, _1493171), _1493169)), hAPP(hAPP(c_COMBB(_1493167, tc_fun(_1493171, tc_prod(_1493167, _1493171)), _1493165), c_Product__Type_OPair(_1493167, _1493171)), _1493173))), _1493175)))], (39075 ^ _775212) ^ [_1511139, _1511141, _1511143, _1511145, _1511147, _1511149] : [-(hAPP(c_Set_Oimage(_1511139, _1511141, hAPP(hAPP(c_COMBS(_1511139, _1511141, _1511141), hAPP(hAPP(c_COMBS(_1511139, _1511141, tc_fun(_1511141, _1511141)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1511141, tc_fun(_1511141, _1511141)), _1511139), c_If(_1511141)), _1511143)), _1511145)), _1511147)), _1511149) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1511141, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1511139, _1511141, _1511145), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511139, tc_HOL_Obool)), _1511149), hAPP(c_Set_OCollect(_1511139), _1511143)))), hAPP(c_Set_Oimage(_1511139, _1511141, _1511147), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511139, tc_HOL_Obool)), _1511149), hAPP(c_Set_OCollect(_1511139), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1511139), c_fNot), _1511143))))))], (22074 ^ _775212) ^ [_1154112] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1154112)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1154112)], (25673 ^ _775212) ^ [_1223488, _1223490, _1223492, _1223494] : [class_Rings_Ocomm__semiring__1(_1223488), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223488), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223488), c_Groups_Oone__class_Oone(_1223488)), c_Groups_Oone__class_Oone(_1223488))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223488), hAPP(hAPP(c_COMBB(_1223488, _1223488, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1223488), _1223490)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1223488, _1223488), hAPP(hAPP(c_COMBB(_1223488, tc_fun(_1223488, _1223488), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1223488)), c_Nat_Osemiring__1__class_Oof__nat(_1223488))), _1223492))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1223494))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223488), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223488), _1223494)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223488), _1223490), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223488), _1223490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223488), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223488), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223494), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1223492)))))], (33626 ^ _775212) ^ [_1388014, _1388016, _1388018, _1388020] : [_1388014 = _1388016, hBOOL(hAPP(hAPP(c_member(_1388018), _1388014), _1388020)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1388018, _1388018)), hAPP(hAPP(c_Product__Type_OPair(_1388018, _1388018), _1388014), _1388016)), c_Relation_OId__on(_1388018, _1388020))))], (23438 ^ _775212) ^ [_1181876, _1181878, _1181880, _1181882] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1181876, _1181878, _1181880, tc_prod(_1181878, _1181880)), _1181882), c_Product__Type_OPair(_1181878, _1181880)) = _1181882)], (7959 ^ _775212) ^ [_903156, _903158, _903160] : [class_Rings_Ono__zero__divisors(_903156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903156), _903158), _903160) = c_Groups_Ozero__class_Ozero(_903156), -(_903158 = c_Groups_Ozero__class_Ozero(_903156)), -(_903160 = c_Groups_Ozero__class_Ozero(_903156))], (40642 ^ _775212) ^ [_1556625, _1556627, _1556629, _1556631, _1556633, _1556635, _1556637] : [class_Groups_Oab__semigroup__mult(_1556625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556627), _1556629)), c_Fun_Oinj__on(_1556627, _1556631, _1556633, _1556629), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1556625, _1556631, c_Groups_Otimes__class_Otimes(_1556625)), _1556635), _1556637), hAPP(c_Set_Oimage(_1556627, _1556631, _1556633), _1556629)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1556625, _1556627, c_Groups_Otimes__class_Otimes(_1556625)), hAPP(c_Fun_Ocomp(_1556631, _1556625, _1556627, _1556635), _1556633)), _1556637), _1556629))], (49359 ^ _775212) ^ [_1763048, _1763050] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1763048), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1763048))), _1763050))), -(c_List_Otranspose(_1763048, c_List_Otranspose(_1763048, _1763050)) = c_List_OtakeWhile(tc_List_Olist(_1763048), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1763048)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1763048), tc_List_Olist(_1763048), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1763048))), _1763050))], (46111 ^ _775212) ^ [_1692662, _1692664, _1692666, _1692668] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692662), tc_List_Olist(_1692662))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692662), tc_List_Olist(_1692662)), _1692664), _1692666)), c_List_Olistrel1(_1692662, _1692668))), 46116 ^ _775212 : [(46121 ^ _775212) ^ [] : [-(_1692666 = hAPP(hAPP(c_List_Olist__update(_1692662, _1692664), 46115 ^ [_1692662, _1692664, _1692666, _1692668]), 46114 ^ [_1692662, _1692664, _1692666, _1692668]))], (46119 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46115 ^ [_1692662, _1692664, _1692666, _1692668]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692662)), _1692664))))], (46117 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1692662, _1692662)), hAPP(hAPP(c_Product__Type_OPair(_1692662, _1692662), hAPP(hAPP(c_List_Onth(_1692662), _1692664), 46115 ^ [_1692662, _1692664, _1692666, _1692668])), 46114 ^ [_1692662, _1692664, _1692666, _1692668])), _1692668)))]]], (28694 ^ _775212) ^ [_1284906, _1284908, _1284910] : [class_Orderings_Obot(_1284906), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1284908, _1284906)), _1284910) = c_Orderings_Obot__class_Obot(_1284906))], (33757 ^ _775212) ^ [_1390798, _1390800, _1390802, _1390804, _1390806] : [hAPP(c_Set_Oimage(_1390798, _1390800, _1390802), _1390804) = _1390806, -(hAPP(c_Set_Oimage(tc_fun(_1390798, tc_HOL_Obool), tc_fun(_1390800, tc_HOL_Obool), c_Set_Oimage(_1390798, _1390800, _1390802)), hAPP(c_Set_OPow(_1390798), _1390804)) = hAPP(c_Set_OPow(_1390800), _1390806))], (42651 ^ _775212) ^ [_1604191, _1604193, _1604195, _1604197] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604191, _1604191)), hAPP(hAPP(c_Product__Type_OPair(_1604191, _1604191), _1604193), _1604195)), hAPP(c_Relation_Oconverse(_1604191, _1604191), c_Transitive__Closure_Otrancl(_1604191, _1604197)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604191, _1604191)), hAPP(hAPP(c_Product__Type_OPair(_1604191, _1604191), _1604193), _1604195)), c_Transitive__Closure_Otrancl(_1604191, hAPP(c_Relation_Oconverse(_1604191, _1604191), _1604197)))))], (31667 ^ _775212) ^ [_1348330, _1348332] : [class_Rings_Oring__1(_1348330), hBOOL(hAPP(hAPP(c_member(_1348330), _1348332), c_Int_Oring__1__class_OInts(_1348330))), -(hBOOL(hAPP(hAPP(c_member(_1348330), hAPP(c_Groups_Ouminus__class_Ouminus(_1348330), _1348332)), c_Int_Oring__1__class_OInts(_1348330))))], (5699 ^ _775212) ^ [_865074, _865076, _865078, _865080] : [-(hAPP(c_Nat_Onat_Onat__rec(_865074, _865076, _865078), hAPP(c_Nat_OSuc, _865080)) = hAPP(hAPP(_865078, _865080), hAPP(c_Nat_Onat_Onat__rec(_865074, _865076, _865078), _865080)))], (42359 ^ _775212) ^ [_1595751, _1595753, _1595755, _1595757, _1595759, _1595761] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595751, tc_fun(_1595753, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1595755, _1595751, _1595757), _1595759)), _1595761) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595755, tc_fun(_1595753, tc_HOL_Obool)), _1595759), hAPP(hAPP(c_COMBB(_1595751, tc_fun(_1595753, tc_HOL_Obool), _1595755), _1595761), _1595757)))], (12604 ^ _775212) ^ [_983072, _983074, _983076] : [class_Divides_Osemiring__div(_983072), -(c_Divides_Odiv__class_Omod(_983072, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983072), _983074), _983076), _983076) = c_Groups_Ozero__class_Ozero(_983072))], (2198 ^ _775212) ^ [_807161, _807163, _807165, _807167, _807169, _807171] : [-(c_Nat_Onat_Onat__rec(_807171, _807167, _807163) = c_Nat_Onat_Onat__rec(_807169, _807165, _807161)), _807171 = _807169, _807167 = _807165, _807163 = _807161], (42527 ^ _775212) ^ [_1600598, _1600600, _1600602, _1600604, _1600606, _1600608] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600598, tc_fun(_1600600, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1600602, tc_fun(_1600598, tc_HOL_Obool)), _1600604), _1600606)), _1600608) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600602, tc_fun(_1600600, tc_HOL_Obool)), _1600604), hAPP(hAPP(c_COMBC(_1600602, tc_fun(_1600598, tc_fun(_1600600, tc_HOL_Obool)), tc_fun(_1600600, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1600598, tc_HOL_Obool), tc_fun(tc_fun(_1600598, tc_fun(_1600600, tc_HOL_Obool)), tc_fun(_1600600, tc_HOL_Obool)), _1600602), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600598, tc_fun(_1600600, tc_HOL_Obool))), _1600606)), _1600608)))], (30128 ^ _775212) ^ [_1315209, _1315211, _1315213, _1315215, _1315217] : [hBOOL(hAPP(hAPP(c_member(_1315209), _1315211), c_SetInterval_Oord_OgreaterThanLessThan(_1315209, _1315213, _1315215, _1315217))), 30131 ^ _775212 : [(30134 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1315213, _1315211), _1315217)))], (30132 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1315213, _1315215), _1315211)))]]], (45879 ^ _775212) ^ [_1686760, _1686762, _1686764, _1686766, _1686768] : [-(hAPP(hAPP(c_List_Oappend(_1686760), _1686762), _1686764) = hAPP(hAPP(c_List_Oappend(_1686760), _1686766), _1686768)), 45880 ^ _775212 : [(45887 ^ _775212) ^ [_1686984] : [hAPP(hAPP(c_List_Oappend(_1686760), _1686762), _1686984) = _1686766, _1686764 = hAPP(hAPP(c_List_Oappend(_1686760), _1686984), _1686768)], (45881 ^ _775212) ^ [_1686872] : [_1686762 = hAPP(hAPP(c_List_Oappend(_1686760), _1686766), _1686872), hAPP(hAPP(c_List_Oappend(_1686760), _1686872), _1686764) = _1686768]]], (6336 ^ _775212) ^ [_875348, _875350] : [class_Rings_Olinordered__semidom(_875348), 6339 ^ _775212 : [(6346 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _875350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875348), c_Groups_Ozero__class_Ozero(_875348)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_875348), _875350))))], (6340 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875348), c_Groups_Ozero__class_Ozero(_875348)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_875348), _875350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _875350)))]]], (23452 ^ _775212) ^ [_1182220, _1182222, _1182224, _1182226, _1182228] : [-(_1182220 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1182222, _1182224, _1182220, _1182226), _1182228) = hAPP(hAPP(c_Product__Type_Oscomp(_1182224, _1182222, _1182224, tc_prod(_1182222, _1182224)), hAPP(_1182226, _1182228)), c_Random_Oiterate(_1182222, _1182224, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1182220), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1182226)))], (4554 ^ _775212) ^ [_844513, _844515, _844517, _844519, _844521, _844523, _844525, _844527] : [-(c_Lazy__Sequence_Oproduct(_844527, _844523, _844519, _844515) = c_Lazy__Sequence_Oproduct(_844525, _844521, _844517, _844513)), _844527 = _844525, _844523 = _844521, _844519 = _844517, _844515 = _844513], (49191 ^ _775212) ^ [_1759519, _1759521, _1759523, _1759525, _1759527] : [c_List_Olist__all2(_1759519, _1759521, _1759523, _1759525, hAPP(c_List_Orev(_1759521), _1759527)), -(c_List_Olist__all2(_1759519, _1759521, _1759523, hAPP(c_List_Orev(_1759519), _1759525), _1759527))], (40462 ^ _775212) ^ [_1552443, _1552445, _1552447, _1552449, _1552451, _1552453, _1552455, _1552457] : [hAPP(c_Fun_Ocomp(_1552443, _1552445, _1552447, _1552449), _1552451) = hAPP(c_Fun_Ocomp(_1552453, _1552445, _1552447, _1552455), _1552457), 40465 ^ _775212 : [(40466 ^ _775212) ^ [_1552558] : [-(hAPP(_1552449, hAPP(_1552451, _1552558)) = hAPP(_1552455, hAPP(_1552457, _1552558)))]]], (25975 ^ _775212) ^ [_1229963, _1229965, _1229967, _1229969] : [class_Groups_Ocomm__monoid__add(_1229963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1229965), _1229967)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1229963), _1229969), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1229965, _1229967)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229963), hAPP(_1229969, _1229965)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1229963), _1229969), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1229965), _1229967))))], (22478 ^ _775212) ^ [_1163254, _1163256, _1163258, _1163260] : [class_Orderings_Olinorder(_1163254), 22481 ^ _775212 : [(22482 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163254), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1163254), _1163256), _1163258)), _1163260)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163254), _1163256), _1163260))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163254), _1163258), _1163260)))], (22492 ^ _775212) ^ [] : [22493 ^ _775212 : [(22496 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163254), _1163258), _1163260))], (22494 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163254), _1163256), _1163260))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163254), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1163254), _1163256), _1163258)), _1163260)))]]], (49824 ^ _775212) ^ [_1772651, _1772653] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1772651)), _1772653)), 49830 ^ _775212 : [(49833 ^ _775212) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1772651), 49829 ^ [_1772651, _1772653]))], (49831 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772651)), 49829 ^ [_1772651, _1772653]), hAPP(c_List_Oset(tc_List_Olist(_1772651)), _1772653))))]], 49837 ^ _775212 : [(49841 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772651)), 49839 ^ [_1772651, _1772653]), hAPP(c_List_Oset(tc_List_Olist(_1772651)), _1772653))))], (49843 ^ _775212) ^ [] : [49836 ^ [_1772651, _1772653] = 49839 ^ [_1772651, _1772653]], (49845 ^ _775212) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1772651, tc_HOL_Obool)), hAPP(c_List_Oset(_1772651), 49836 ^ [_1772651, _1772653])), hAPP(c_List_Oset(_1772651), 49839 ^ [_1772651, _1772653])) = c_Orderings_Obot__class_Obot(tc_fun(_1772651, tc_HOL_Obool))], (49838 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772651)), 49836 ^ [_1772651, _1772653]), hAPP(c_List_Oset(tc_List_Olist(_1772651)), _1772653))))]], -(hBOOL(hAPP(c_List_Odistinct(_1772651), c_List_Oconcat(_1772651, _1772653))))], (1104 ^ _775212) ^ [_791868, _791870] : [-(class_Groups_Oordered__ab__group__add__abs(_791868)), _791870 = _791868, class_Groups_Oordered__ab__group__add__abs(_791870)], (37228 ^ _775212) ^ [_1468122, _1468124] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468122), _1468124)), -(hAPP(c_Finite__Set_Ocard(_1468122), _1468124) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1468122, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1468122), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1468124))], (1304 ^ _775212) ^ [_794368, _794370] : [-(class_Rings_Oring__1(_794368)), _794370 = _794368, class_Rings_Oring__1(_794370)], (44114 ^ _775212) ^ [_1639826, _1639828] : [-(c_FunDef_Ois__measure(_1639826, _1639828))], (28267 ^ _775212) ^ [_1276360, _1276362, _1276364] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276360), hAPP(hAPP(c_Set_Oinsert(_1276360), _1276362), _1276364))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1276360), _1276364)))], (6023 ^ _775212) ^ [_870700, _870702] : [hBOOL(hAPP(_870700, _870702)), 6029 ^ _775212 : [(6032 ^ _775212) ^ [] : [hBOOL(hAPP(_870700, 6028 ^ [_870700, _870702]))], (6030 ^ _775212) ^ [] : [-(hBOOL(hAPP(_870700, hAPP(c_Nat_OSuc, 6028 ^ [_870700, _870702]))))]], -(hBOOL(hAPP(_870700, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44031 ^ _775212) ^ [_1637949, _1637951, _1637953, _1637955] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637949, _1637951)), _1637953), hAPP(c_Relation_Oconverse(_1637951, _1637949), _1637955))), 44036 ^ _775212 : [(44039 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637951, _1637949)), hAPP(hAPP(c_Product__Type_OPair(_1637951, _1637949), 44034 ^ [_1637949, _1637951, _1637953, _1637955]), 44035 ^ [_1637949, _1637951, _1637953, _1637955])), _1637955)))], (44037 ^ _775212) ^ [] : [-(_1637953 = hAPP(hAPP(c_Product__Type_OPair(_1637949, _1637951), 44035 ^ [_1637949, _1637951, _1637953, _1637955]), 44034 ^ [_1637949, _1637951, _1637953, _1637955]))]]], (25541 ^ _775212) ^ [_1220093, _1220095, _1220097, _1220099] : [class_Groups_Oordered__ab__group__add__abs(_1220093), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220093), c_Groups_Ozero__class_Ozero(_1220093)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1220095, _1220093), hAPP(hAPP(c_COMBB(_1220093, _1220093, _1220095), c_Groups_Oabs__class_Oabs(_1220093)), _1220097)), _1220099))))], (29391 ^ _775212) ^ [_1298216, _1298218] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1298216), _1298218))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1298218, _1298216) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1298218), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1298218), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1298216)))], (7510 ^ _775212) ^ [_895009, _895011] : [class_Rings_Olinordered__idom(_895009), 7513 ^ _775212 : [(7520 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _895011), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_895009), hAPP(c_Int_Oring__1__class_Oof__int(_895009), _895011)), c_Groups_Ozero__class_Ozero(_895009))))], (7514 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_895009), hAPP(c_Int_Oring__1__class_Oof__int(_895009), _895011)), c_Groups_Ozero__class_Ozero(_895009))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _895011), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (13292 ^ _775212) ^ [_995774, _995776] : [class_Divides_Osemiring__div(_995774), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_995774), _995776), c_Groups_Ozero__class_Ozero(_995774)) = c_Groups_Ozero__class_Ozero(_995774))], (12233 ^ _775212) ^ [_976418, _976420, _976422] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _976418), _976420) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _976418), _976422), -(_976418 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_976420 = _976422)], (37788 ^ _775212) ^ [_1480860, _1480862, _1480864, _1480866] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1480860, _1480862, _1480864), _1480866)), _1480864 = c_Orderings_Obot__class_Obot(tc_fun(_1480860, tc_HOL_Obool))], (5192 ^ _775212) ^ [_854404, _854406, _854408, _854410] : [-(c_Complete__Lattice_OSup__class_OSup(_854410, _854406) = c_Complete__Lattice_OSup__class_OSup(_854408, _854404)), _854410 = _854408, _854406 = _854404], (15517 ^ _775212) ^ [_1037438, _1037440, _1037442, _1037444, _1037446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037438), _1037440)), -(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), _1037438), _1037442)), _1037444)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037440), _1037442)), _1037446)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037444), 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), _1037440), _1037438)), _1037442)), _1037446)))], (3636 ^ _775212) ^ [_830140, _830142] : [_830142 = _830140, -(c_Relation_OField(_830142) = c_Relation_OField(_830140))], (5170 ^ _775212) ^ [_854085, _854087] : [_854087 = _854085, -(c_Wellfounded_Ofinite__psubset(_854087) = c_Wellfounded_Ofinite__psubset(_854085))], (52491 ^ _775212) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (14157 ^ _775212) ^ [_1011069, _1011071, _1011073] : [class_Rings_Oring__1(_1011069), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1011071), _1011073)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1011069), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1011073), _1011071)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1011069), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1011069), _1011073)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1011069), _1011071)))], (26841 ^ _775212) ^ [_1247059, _1247061, _1247063, _1247065] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247059, _1247061)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247063, _1247065)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247063), _1247065)), 26844 ^ _775212 : [(26847 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247063), _1247059)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247061), _1247065)), 26854 ^ _775212 : [(26861 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247061), _1247065)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247065), _1247061)))], (26855 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247063), _1247059)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247059), _1247063)))]]], (26845 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247059), _1247061)))]]], (27021 ^ _775212) ^ [_1250943, _1250945] : [class_Lattices_Osemilattice__sup(_1250943), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1250943), _1250945), _1250945) = _1250945)], (25761 ^ _775212) ^ [_1225666, _1225668, _1225670, _1225672, _1225674] : [class_Orderings_Olinorder(_1225666), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1225666, _1225668), _1225670) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1225666, _1225672), _1225674), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225666), _1225668), _1225670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225666), _1225672), _1225674)), -(_1225668 = _1225672)], (26336 ^ _775212) ^ [_1237503, _1237505, _1237507, _1237509, _1237511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1237503, tc_HOL_Obool)), _1237505), _1237507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1237509, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1237503, _1237509, _1237511), _1237505)), hAPP(c_Set_Oimage(_1237503, _1237509, _1237511), _1237507))))], (28213 ^ _775212) ^ [_1275367, _1275369, _1275371] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1275367), _1275369)), -(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(_1275367), _1275371)), hAPP(c_Finite__Set_Ocard(_1275367), _1275369))), hAPP(c_Finite__Set_Ocard(_1275367), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1275367, tc_HOL_Obool)), _1275371), _1275369)))))], (30658 ^ _775212) ^ [_1328197, _1328199, _1328201] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1328197), _1328199)), hBOOL(hAPP(hAPP(c_member(_1328197), _1328201), _1328199)), -(hAPP(c_Finite__Set_Ocard(_1328197), _1328199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1328197), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1328197, tc_HOL_Obool)), _1328199), hAPP(hAPP(c_Set_Oinsert(_1328197), _1328201), c_Orderings_Obot__class_Obot(tc_fun(_1328197, tc_HOL_Obool)))))))], (31817 ^ _775212) ^ [_1350722, _1350724, _1350726] : [class_Orderings_Olinorder(_1350722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350722, tc_HOL_Obool)), _1350724), _1350726)), -(_1350724 = c_Orderings_Obot__class_Obot(tc_fun(_1350722, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350722), _1350726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350722), c_Big__Operators_Olinorder__class_OMax(_1350722, _1350724)), c_Big__Operators_Olinorder__class_OMax(_1350722, _1350726))))], (18525 ^ _775212) ^ [] : [-(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))))], (4864 ^ _775212) ^ [_849292, _849294] : [_849294 = _849292, -(c_Set_Oinsert(_849294) = c_Set_Oinsert(_849292))], (47629 ^ _775212) ^ [_1725405, _1725407, _1725409, _1725411, _1725413] : [c_List_Olist__all2(_1725405, _1725407, _1725409, _1725411, _1725413), 47632 ^ _775212 : [(47635 ^ _775212) ^ [_1725571] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1725405, _1725407)), _1725571), hAPP(c_List_Oset(tc_prod(_1725405, _1725407)), hAPP(hAPP(c_List_Ozip(_1725405, _1725407), _1725411), _1725413)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1725405, _1725407, tc_HOL_Obool), _1725409), _1725571)))], (47633 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725405)), _1725411) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725407)), _1725413))]]], (41821 ^ _775212) ^ [_1582226, _1582228, _1582230] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582226, _1582226)), _1582228), _1582230)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582226, _1582226)), _1582228), c_Transitive__Closure_Ortrancl(_1582226, _1582230))))], (50809 ^ _775212) ^ [_1794099, _1794101, _1794103] : [-(_1794101 = _1794103), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1794099, _1794099, hAPP(hAPP(c_COMBB(tc_fun(_1794099, tc_HOL_Obool), tc_fun(_1794099, tc_HOL_Obool), _1794099), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1794099), c_fNot)), c_fequal)), _1794101), _1794103)))], (10755 ^ _775212) ^ [_950951, _950953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950951)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950953)), 10762 ^ _775212 : [(10769 ^ _775212) ^ [] : [_950951 = _950953, -(hAPP(c_Int_Onat, _950951) = hAPP(c_Int_Onat, _950953))], (10763 ^ _775212) ^ [] : [hAPP(c_Int_Onat, _950951) = hAPP(c_Int_Onat, _950953), -(_950951 = _950953)]]], (22814 ^ _775212) ^ [_1169762] : [class_Orderings_Oord(_1169762), -(c_Orderings_Oord__class_Omin(_1169762) = c_Orderings_Oord_Omin(_1169762, c_Orderings_Oord__class_Oless__eq(_1169762)))], (45744 ^ _775212) ^ [_1683977, _1683979, _1683981] : [-(hAPP(hAPP(c_List_Olist__update(_1683977, c_List_Olist_ONil(_1683977)), _1683979), _1683981) = c_List_Olist_ONil(_1683977))], (18439 ^ _775212) ^ [_1088452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1088452)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088452), c_Int_OMin)))], (6374 ^ _775212) ^ [_876014, _876016, _876018, _876020] : [class_Orderings_Oorder(_876014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876014), hAPP(_876016, 6379 ^ [_876014, _876016, _876018, _876020])), hAPP(_876016, hAPP(c_Nat_OSuc, 6379 ^ [_876014, _876016, _876018, _876020])))), 6382 ^ _775212 : [(6389 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _876018), _876020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876014), hAPP(_876016, _876018)), hAPP(_876016, _876020))))], (6383 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876014), hAPP(_876016, _876018)), hAPP(_876016, _876020))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _876018), _876020)))]]], (26686 ^ _775212) ^ [_1244124] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1244124)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1244124))], (50511 ^ _775212) ^ [_1788237, _1788239, _1788241] : [c_List_Olist__all(_1788237, _1788239, _1788241), 50514 ^ _775212 : [(50515 ^ _775212) ^ [_1788318] : [hBOOL(hAPP(hAPP(c_member(_1788237), _1788318), hAPP(c_List_Oset(_1788237), _1788241))), -(hBOOL(hAPP(_1788239, _1788318)))]]], (46502 ^ _775212) ^ [_1701773, _1701775] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1701773, _1701775))))], (18995 ^ _775212) ^ [_1098597] : [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), _1098597))), 18998 ^ _775212 : [(19005 ^ _775212) ^ [] : [-(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), _1098597))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1098597)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1098597)), 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), _1098597)))))], (18999 ^ _775212) ^ [] : [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), _1098597)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1098597)) = 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), _1098597))))]]], (17011 ^ _775212) ^ [_1064840, _1064842] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1064840), _1064842) = c_Groups_Oone__class_Oone(tc_Int_Oint), 17016 ^ _775212 : [(17019 ^ _775212) ^ [] : [-(_1064842 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (17017 ^ _775212) ^ [] : [-(_1064840 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 17020 ^ _775212 : [(17023 ^ _775212) ^ [] : [-(_1064842 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (17021 ^ _775212) ^ [] : [-(_1064840 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (31033 ^ _775212) ^ [_1335851, _1335853] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335851), _1335853)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1335851), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335853))))], (11931 ^ _775212) ^ [_971232, _971234, _971236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971232), _971234)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971236), _971232)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971236), _971234))))], (35171 ^ _775212) ^ [_1422937, _1422939, _1422941] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422937, tc_HOL_Obool)), _1422939), _1422941) = c_Orderings_Obot__class_Obot(tc_fun(_1422937, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1422937, tc_HOL_Obool)), _1422939), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1422937, tc_HOL_Obool)), _1422941))))], (49227 ^ _775212) ^ [_1760215, _1760217, _1760219] : [_1760217 = hAPP(c_List_Orev(_1760215), _1760219), -(hAPP(c_List_Orev(_1760215), _1760217) = _1760219)], (3238 ^ _775212) ^ [_823877, _823879] : [_823879 = _823877, -(c_Int_Oint__ge__less__than(_823879) = c_Int_Oint__ge__less__than(_823877))], (25188 ^ _775212) ^ [_1213398, _1213400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213398), _1213400)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1213400), _1213398))], (50350 ^ _775212) ^ [_1784815, _1784817, _1784819] : [c_List_Olist__ex(_1784815, _1784817, _1784819), 50354 ^ _775212 : [(50357 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1784817, 50353 ^ [_1784815, _1784817, _1784819])))], (50355 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1784815), 50353 ^ [_1784815, _1784817, _1784819]), hAPP(c_List_Oset(_1784815), _1784819))))]]], (15671 ^ _775212) ^ [_1040260, _1040262, _1040264, _1040266] : [class_Rings_Olinordered__semidom(_1040260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040260), c_Groups_Oone__class_Oone(_1040260)), _1040262)), 15678 ^ _775212 : [(15685 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040264), _1040266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040260), hAPP(hAPP(c_Power_Opower__class_Opower(_1040260), _1040262), _1040264)), hAPP(hAPP(c_Power_Opower__class_Opower(_1040260), _1040262), _1040266))))], (15679 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040260), hAPP(hAPP(c_Power_Opower__class_Opower(_1040260), _1040262), _1040264)), hAPP(hAPP(c_Power_Opower__class_Opower(_1040260), _1040262), _1040266))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040264), _1040266)))]]], (842 ^ _775212) ^ [_788099, _788101, _788103, _788105, _788107, _788109] : [-(c_List_Oall__interval__int(_788107, _788103, _788099)), c_List_Oall__interval__int(_788109, _788105, _788101), _788109 = _788107, _788105 = _788103, _788101 = _788099], (30867 ^ _775212) ^ [_1332650, _1332652, _1332654, _1332656] : [hBOOL(hAPP(hAPP(c_member(_1332650), _1332652), c_SetInterval_Oord_OgreaterThan(_1332650, _1332654, _1332656))), -(hBOOL(hAPP(hAPP(_1332654, _1332656), _1332652)))], (2014 ^ _775212) ^ [_804257, _804259, _804261, _804263, _804265, _804267] : [-(c_Com_Ocom_OLocal(_804267, _804263, _804259) = c_Com_Ocom_OLocal(_804265, _804261, _804257)), _804267 = _804265, _804263 = _804261, _804259 = _804257], (41172 ^ _775212) ^ [_1568770, _1568772, _1568774, _1568776, _1568778, _1568780, _1568782, _1568784] : [class_Groups_Ocomm__monoid__add(_1568770), c_Fun_Oinj__on(_1568772, _1568774, _1568776, _1568778), _1568780 = hAPP(c_Set_Oimage(_1568772, _1568774, _1568776), _1568778), 41186 ^ _775212 : [(41189 ^ _775212) ^ [] : [hAPP(_1568782, 41185 ^ [_1568770, _1568772, _1568774, _1568776, _1568778, _1568780, _1568782, _1568784]) = hAPP(_1568784, hAPP(_1568776, 41185 ^ [_1568770, _1568772, _1568774, _1568776, _1568778, _1568780, _1568782, _1568784]))], (41187 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568772), 41185 ^ [_1568770, _1568772, _1568774, _1568776, _1568778, _1568780, _1568782, _1568784]), _1568778)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1568774, _1568770), _1568784), _1568780) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1568772, _1568770), _1568782), _1568778))], (39152 ^ _775212) ^ [_1513975, _1513977, _1513979] : [class_Orderings_Olinorder(_1513975), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513975), _1513977)), -(_1513977 = c_Orderings_Obot__class_Obot(tc_fun(_1513975, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513975), _1513979)), -(_1513979 = c_Orderings_Obot__class_Obot(tc_fun(_1513975, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1513975), c_Big__Operators_Olattice_OInf__fin(_1513975, c_Orderings_Oord__class_Omin(_1513975), _1513977)), c_Big__Operators_Olattice_OInf__fin(_1513975, c_Orderings_Oord__class_Omin(_1513975), _1513979)) = c_Big__Operators_Olattice_OInf__fin(_1513975, c_Orderings_Oord__class_Omin(_1513975), hAPP(c_Set_OCollect(_1513975), hAPP(hAPP(c_COMBB(tc_fun(_1513975, tc_HOL_Obool), tc_HOL_Obool, _1513975), c_HOL_OEx(_1513975)), hAPP(hAPP(c_COMBB(tc_fun(_1513975, tc_fun(_1513975, tc_HOL_Obool)), tc_fun(_1513975, tc_HOL_Obool), _1513975), hAPP(c_COMBB(tc_fun(_1513975, tc_HOL_Obool), tc_HOL_Obool, _1513975), c_HOL_OEx(_1513975))), hAPP(hAPP(c_COMBC(_1513975, tc_fun(_1513975, tc_fun(_1513975, tc_HOL_Obool)), tc_fun(_1513975, tc_fun(_1513975, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1513975, tc_fun(tc_fun(_1513975, tc_HOL_Obool), tc_fun(_1513975, tc_HOL_Obool))), tc_fun(tc_fun(_1513975, tc_fun(_1513975, tc_HOL_Obool)), tc_fun(_1513975, tc_fun(_1513975, tc_HOL_Obool))), _1513975), c_COMBS(_1513975, tc_fun(_1513975, tc_HOL_Obool), tc_fun(_1513975, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1513975, tc_fun(_1513975, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1513975, tc_fun(tc_fun(_1513975, tc_HOL_Obool), tc_fun(_1513975, tc_HOL_Obool))), _1513975), hAPP(c_COMBB(tc_fun(_1513975, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1513975, tc_HOL_Obool), tc_fun(_1513975, tc_HOL_Obool)), _1513975), c_COMBS(_1513975, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1513975, tc_fun(_1513975, tc_HOL_Obool)), tc_fun(_1513975, tc_fun(_1513975, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1513975), hAPP(c_COMBB(tc_fun(_1513975, tc_HOL_Obool), tc_fun(_1513975, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1513975), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513975), c_fconj))), hAPP(hAPP(c_COMBC(_1513975, tc_fun(_1513975, tc_fun(_1513975, _1513975)), tc_fun(_1513975, tc_fun(_1513975, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513975, _1513975), tc_fun(_1513975, tc_HOL_Obool)), tc_fun(tc_fun(_1513975, tc_fun(_1513975, _1513975)), tc_fun(_1513975, tc_fun(_1513975, tc_HOL_Obool))), _1513975), c_COMBB(tc_fun(_1513975, _1513975), tc_fun(_1513975, tc_HOL_Obool), _1513975)), hAPP(hAPP(c_COMBB(tc_fun(_1513975, tc_HOL_Obool), tc_fun(tc_fun(_1513975, _1513975), tc_fun(_1513975, tc_HOL_Obool)), _1513975), c_COMBB(_1513975, tc_HOL_Obool, _1513975)), c_fequal))), c_Orderings_Oord__class_Omax(_1513975)))))), hAPP(hAPP(c_COMBC(_1513975, tc_fun(_1513975, tc_HOL_Obool), tc_fun(_1513975, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1513975, tc_HOL_Obool), tc_fun(_1513975, tc_HOL_Obool)), _1513975), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1513975)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513975), c_fconj), hAPP(hAPP(c_COMBC(_1513975, tc_fun(_1513975, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513975)), _1513977)))), hAPP(hAPP(c_COMBC(_1513975, tc_fun(_1513975, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513975)), _1513979))))))))], (51114 ^ _775212) ^ [_1801262, _1801264, _1801266] : [-(c_FunDef_OTHE__default(_1801264, _1801266, _1801262) = c_HOL_OThe(_1801264, _1801262)), 51115 ^ _775212 : [(51116 ^ _775212) ^ [_1801326] : [hBOOL(hAPP(_1801262, _1801326)), 51120 ^ _775212 : [(51123 ^ _775212) ^ [] : [51119 ^ [_1801262, _1801264, _1801266, _1801326] = _1801326], (51121 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1801262, 51119 ^ [_1801262, _1801264, _1801266, _1801326])))]]]]], (14299 ^ _775212) ^ [_1013558, _1013560, _1013562, _1013564] : [class_Divides_Oring__div(_1013558), -(c_Divides_Odiv__class_Omod(_1013558, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1013558), _1013560), _1013562), _1013564) = c_Divides_Odiv__class_Omod(_1013558, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1013558), c_Divides_Odiv__class_Omod(_1013558, _1013560, _1013564)), c_Divides_Odiv__class_Omod(_1013558, _1013562, _1013564)), _1013564))], (41322 ^ _775212) ^ [_1571844, _1571846, _1571848, _1571850, _1571852] : [class_Complete__Lattice_Ocomplete__lattice(_1571844), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571846), _1571848)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1571844), _1571850), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1571846, _1571844), _1571848), _1571852)) = hAPP(hAPP(c_Finite__Set_Ofold(_1571846, _1571844, hAPP(hAPP(c_COMBB(_1571844, tc_fun(_1571844, _1571844), _1571846), c_Lattices_Osemilattice__sup__class_Osup(_1571844)), _1571852)), _1571850), _1571848))], (48309 ^ _775212) ^ [_1741182, _1741184, _1741186] : [-(hAPP(c_List_Oset(_1741182), hAPP(c_List_Ofilter(_1741182, _1741184), _1741186)) = hAPP(c_Set_OCollect(_1741182), hAPP(hAPP(c_COMBS(_1741182, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1741182), c_fconj), hAPP(hAPP(c_COMBC(_1741182, tc_fun(_1741182, tc_HOL_Obool), tc_HOL_Obool), c_member(_1741182)), hAPP(c_List_Oset(_1741182), _1741186)))), _1741184)))], (24066 ^ _775212) ^ [_1193347, _1193349] : [-(_1193347 = _1193349), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193347), _1193349)), 24073 ^ _775212 : [(24076 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193349), _1193347))], (24074 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193347), _1193349)))]]], (27457 ^ _775212) ^ [_1259444, _1259446, _1259448, _1259450] : [class_Orderings_Olinorder(_1259444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259444), _1259446), _1259448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259444), _1259448), _1259450)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259444, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1259444, _1259446, _1259448)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1259444, _1259448, _1259450)) = c_SetInterval_Oord__class_OatLeastAtMost(_1259444, _1259446, _1259450))], (9393 ^ _775212) ^ [_927169, _927171, _927173] : [class_Orderings_Olinorder(_927169), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927169), _927171), _927173))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927169), _927173), _927171)))], (33889 ^ _775212) ^ [_1393826, _1393828, _1393830, _1393832, _1393834] : [c_Finite__Set_Ofolding__one__idem(_1393826, _1393828, _1393830), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393826), _1393832)), -(_1393832 = c_Orderings_Obot__class_Obot(tc_fun(_1393826, tc_HOL_Obool))), -(hAPP(_1393830, hAPP(hAPP(c_Set_Oinsert(_1393826), _1393834), _1393832)) = hAPP(hAPP(_1393828, _1393834), hAPP(_1393830, _1393832)))], (40411 ^ _775212) ^ [_1551472, _1551474, _1551476, _1551478] : [c_Finite__Set_Ofun__left__comm__idem(_1551472, _1551474, _1551476), -(hAPP(c_Fun_Ocomp(_1551474, _1551474, _1551474, hAPP(_1551476, _1551478)), hAPP(_1551476, _1551478)) = hAPP(_1551476, _1551478))], (33449 ^ _775212) ^ [_1383030, _1383032, _1383034, _1383036] : [c_Wellfounded_Omax__extp(_1383030, hAPP(hAPP(c_COMBC(_1383030, tc_fun(tc_prod(_1383030, _1383030), tc_HOL_Obool), tc_fun(_1383030, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383030, tc_fun(tc_fun(tc_prod(_1383030, _1383030), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1383030, _1383030), tc_HOL_Obool), tc_fun(_1383030, tc_HOL_Obool)), _1383030), c_COMBC(_1383030, tc_fun(tc_prod(_1383030, _1383030), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383030, tc_prod(_1383030, _1383030)), tc_fun(_1383030, tc_fun(tc_fun(tc_prod(_1383030, _1383030), tc_HOL_Obool), tc_HOL_Obool)), _1383030), hAPP(c_COMBB(tc_prod(_1383030, _1383030), tc_fun(tc_fun(tc_prod(_1383030, _1383030), tc_HOL_Obool), tc_HOL_Obool), _1383030), c_member(tc_prod(_1383030, _1383030)))), c_Product__Type_OPair(_1383030, _1383030)))), _1383032), _1383034, _1383036), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1383030, tc_HOL_Obool), tc_fun(_1383030, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1383030, tc_HOL_Obool), tc_fun(_1383030, tc_HOL_Obool)), _1383034), _1383036)), c_Wellfounded_Omax__ext(_1383030, _1383032))))], (5672 ^ _775212) ^ [_864646, _864648, _864650, _864652] : [c_Com_Ocom_OSemi(_864646, _864648) = c_Com_Ocom_OSemi(_864650, _864652), 5675 ^ _775212 : [(5678 ^ _775212) ^ [] : [-(_864648 = _864652)], (5676 ^ _775212) ^ [] : [-(_864646 = _864650)]]], (26248 ^ _775212) ^ [_1235464, _1235466, _1235468, _1235470] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235464), _1235466)), 26251 ^ _775212 : [(26252 ^ _775212) ^ [_1235618] : [26254 ^ _775212 : [(26260 ^ _775212) ^ [] : [-(_1235618 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26256 ^ [_1235464, _1235466, _1235468, _1235470, _1235618]), 26253 ^ [_1235464, _1235466, _1235468, _1235470, _1235618]))], (26258 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26256 ^ [_1235464, _1235466, _1235468, _1235470, _1235618]), _1235468)))], (26255 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26253 ^ [_1235464, _1235466, _1235468, _1235470, _1235618]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1235466))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235464), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1235618), _1235470))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235464), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1235618), _1235466)), _1235470))))]]], (45582 ^ _775212) ^ [_1680227, _1680229] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1680227, _1680229) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1680227), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1680229), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (9163 ^ _775212) ^ [_923601, _923603, _923605] : [class_Rings_Olinordered__idom(_923601), 9166 ^ _775212 : [(9173 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _923603), _923605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923601), hAPP(c_Int_Oring__1__class_Oof__int(_923601), _923603)), hAPP(c_Int_Oring__1__class_Oof__int(_923601), _923605))))], (9167 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923601), hAPP(c_Int_Oring__1__class_Oof__int(_923601), _923603)), hAPP(c_Int_Oring__1__class_Oof__int(_923601), _923605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _923603), _923605)))]]], (36387 ^ _775212) ^ [_1450821, _1450823] : [class_Groups_Oordered__ab__group__add(_1450821), -(c_Fun_Oinj__on(_1450821, _1450821, c_Groups_Ouminus__class_Ouminus(_1450821), _1450823))], (10043 ^ _775212) ^ [_938217, _938219, _938221] : [class_Groups_Oordered__comm__monoid__add(_938217), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938217), _938219), c_Groups_Ozero__class_Ozero(_938217))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938217), _938221), c_Groups_Ozero__class_Ozero(_938217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938217), _938219), _938221)), c_Groups_Ozero__class_Ozero(_938217))))], (22714 ^ _775212) ^ [_1167371, _1167373, _1167375, _1167377] : [class_Groups_Oordered__ab__group__add(_1167371), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1167371), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1167371), _1167373), _1167375)), _1167377) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1167371), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1167371), _1167373), _1167377)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1167371), _1167375), _1167377)))], (13360 ^ _775212) ^ [_996876, _996878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996878)), -(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), _996876), _996878))))], (5827 ^ _775212) ^ [_867336] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _867336)], (34112 ^ _775212) ^ [_1399532, _1399534, _1399536] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399532, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399532), _1399534), _1399536), -(_1399534 = c_Orderings_Obot__class_Obot(tc_fun(_1399532, tc_HOL_Obool)))], (26405 ^ _775212) ^ [_1238995, _1238997, _1238999] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1238995), _1238997), _1238999) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1238995), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1238995, tc_Int_Oint), _1238997), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238999))), class_Groups_Ocomm__monoid__add(_1238995), class_Groups_Ocomm__monoid__mult(_1238995)], (23336 ^ _775212) ^ [_1179923, _1179925] : [class_Orderings_Olinorder(_1179923), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179923), _1179925), _1179925) = _1179925)], (25703 ^ _775212) ^ [_1224531, _1224533, _1224535] : [class_Fields_Ofield(_1224531), -(_1224533 = c_Groups_Oone__class_Oone(_1224531)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1224531), hAPP(c_Power_Opower__class_Opower(_1224531), _1224533)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1224535)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1224531), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1224531), hAPP(hAPP(c_Power_Opower__class_Opower(_1224531), _1224533), _1224535)), c_Groups_Oone__class_Oone(_1224531))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1224531), _1224533), c_Groups_Oone__class_Oone(_1224531))))], (27441 ^ _775212) ^ [_1259084, _1259086, _1259088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1259084), _1259086)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1259084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1259086), _1259088)) = 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, _1259084), _1259086)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1259086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1259086), _1259088))))], (48637 ^ _775212) ^ [_1749004, _1749006, _1749008] : [class_Orderings_Olinorder(_1749004), c_List_Olinorder__class_Osorted(_1749004, _1749006), -(c_List_Olinorder__class_Osorted(_1749004, c_List_Olinorder__class_Oinsort__insert__key(_1749004, _1749004, c_COMBI(_1749004), _1749008, _1749006)))], (44604 ^ _775212) ^ [_1655064] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1655064)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1655064), tc_HOL_Obool))))], (38794 ^ _775212) ^ [_1504525, _1504527, _1504529, _1504531, _1504533] : [c_Finite__Set_Ofun__left__comm__idem(_1504525, _1504527, _1504529), -(hAPP(hAPP(_1504529, _1504531), hAPP(hAPP(_1504529, _1504531), _1504533)) = hAPP(hAPP(_1504529, _1504531), _1504533))], (39498 ^ _775212) ^ [_1527895, _1527897, _1527899, _1527901, _1527903, _1527905, _1527907] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527895, _1527897, _1527899), hAPP(hAPP(c_Relation_Orel__comp(_1527895, _1527901, _1527897), _1527903), _1527905)), _1527907) = hAPP(hAPP(c_Relation_Orel__comp(_1527895, _1527901, _1527899), _1527903), hAPP(hAPP(c_Relation_Orel__comp(_1527901, _1527897, _1527899), _1527905), _1527907)))], (52599 ^ _775212) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (39488 ^ _775212) ^ [_1527512, _1527514, _1527516, _1527518, _1527520] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1527512, _1527514)), hAPP(hAPP(c_Product__Type_OPair(_1527512, _1527514), _1527516), _1527518)), _1527520)), -(hBOOL(hAPP(hAPP(c_member(_1527514), _1527518), hAPP(c_Relation_ORange(_1527512, _1527514), _1527520))))], (31513 ^ _775212) ^ [_1345539, _1345541, _1345543] : [class_Orderings_Olinorder(_1345539), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345539), _1345541)), hBOOL(hAPP(hAPP(c_member(_1345539), _1345543), _1345541)), 31524 ^ _775212 : [(31531 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345539, tc_HOL_Obool)), _1345541), hAPP(hAPP(c_Set_Oinsert(_1345539), _1345543), c_Orderings_Obot__class_Obot(tc_fun(_1345539, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1345539, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1345539, _1345541) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345539), _1345543), c_Big__Operators_Olinorder__class_OMax(_1345539, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345539, tc_HOL_Obool)), _1345541), hAPP(hAPP(c_Set_Oinsert(_1345539), _1345543), c_Orderings_Obot__class_Obot(tc_fun(_1345539, tc_HOL_Obool)))))))], (31525 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345539, tc_HOL_Obool)), _1345541), hAPP(hAPP(c_Set_Oinsert(_1345539), _1345543), c_Orderings_Obot__class_Obot(tc_fun(_1345539, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1345539, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1345539, _1345541) = _1345543)]]], (32822 ^ _775212) ^ [_1370559, _1370561, _1370563, _1370565, _1370567] : [c_Fun_Ofun__upd(_1370559, _1370561, _1370563, _1370565, _1370567) = _1370563, -(hAPP(_1370563, _1370565) = _1370567)], (42858 ^ _775212) ^ [_1609960, _1609962, _1609964, _1609966, _1609968, _1609970, _1609972, _1609974] : [c_Fun_Oinj__on(_1609960, _1609962, _1609964, _1609966), 42864 ^ _775212 : [(42867 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1609960, tc_HOL_Obool)), hAPP(_1609972, 42863 ^ [_1609960, _1609962, _1609964, _1609966, _1609968, _1609970, _1609972, _1609974])), _1609966))], (42865 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1609968), 42863 ^ [_1609960, _1609962, _1609964, _1609966, _1609968, _1609970, _1609972, _1609974]), _1609970)))]], hBOOL(hAPP(hAPP(c_member(_1609968), _1609974), _1609970)), -(hAPP(c_Set_Oimage(_1609960, _1609962, _1609964), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609968, tc_fun(_1609960, tc_HOL_Obool)), _1609970), _1609972)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609968, tc_fun(_1609962, tc_HOL_Obool)), _1609970), hAPP(hAPP(c_COMBB(tc_fun(_1609960, tc_HOL_Obool), tc_fun(_1609962, tc_HOL_Obool), _1609968), c_Set_Oimage(_1609960, _1609962, _1609964)), _1609972)))], (8882 ^ _775212) ^ [_919240, _919242, _919244, _919246] : [class_Orderings_Oorder(_919240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919240), _919242), _919244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919240), _919246), _919242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919240), _919246), _919244)))], (34913 ^ _775212) ^ [_1416585, _1416587, _1416589, _1416591] : [class_Lattices_Osemilattice__inf(_1416585), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416585), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416585), _1416587), _1416589)), _1416591) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416585), _1416587), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416585), _1416589), _1416591)))], (7314 ^ _775212) ^ [_891412, _891414, _891416] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_891412, _891414, _891416)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _891416)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9185 ^ _775212) ^ [_923965, _923967, _923969] : [class_Rings_Olinordered__idom(_923965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923965), c_Groups_Ozero__class_Ozero(_923965)), _923967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923965), c_Groups_Ozero__class_Ozero(_923965)), _923969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923965), _923969), c_Groups_Oone__class_Oone(_923965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923965), _923969), _923967)), _923967)))], (37134 ^ _775212) ^ [_1466146, _1466148, _1466150, _1466152] : [class_Groups_Ocomm__monoid__add(_1466146), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466148), _1466150)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466148, _1466146), _1466152), _1466150) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1466146, _1466148, c_Groups_Oplus__class_Oplus(_1466146)), _1466152), c_Groups_Ozero__class_Ozero(_1466146)), _1466150))], (42810 ^ _775212) ^ [_1608793] : [-(hAPP(c_Relation_ODomain(_1608793, _1608793), c_Relation_OId(_1608793)) = c_Orderings_Otop__class_Otop(tc_fun(_1608793, tc_HOL_Obool)))], (4208 ^ _775212) ^ [_839102, _839104] : [_839104 = _839102, -(c_SetInterval_Oord__class_OlessThan(_839104) = c_SetInterval_Oord__class_OlessThan(_839102))], (45548 ^ _775212) ^ [_1679602, _1679604, _1679606, _1679608] : [class_Groups_Ocomm__monoid__add(_1679602), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1679602), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1679602), _1679604), c_List_Oupto(_1679606, _1679608))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1679602), _1679604), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1679606, _1679608))))], (52431 ^ _775212) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (31433 ^ _775212) ^ [_1344017, _1344019] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1344017, _1344019), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344017), _1344019)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344019), _1344017)))], (37634 ^ _775212) ^ [_1477431, _1477433, _1477435, _1477437] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1477431, _1477433, _1477435, _1477437, c_Orderings_Obot__class_Obot(tc_fun(_1477431, tc_HOL_Obool))), _1477437)))], (18105 ^ _775212) ^ [_1082611, _1082613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1082611)), c_Int_OBit0(_1082613))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1082611), _1082613)))], (2282 ^ _775212) ^ [_808449, _808451, _808453, _808455] : [-(c_Orderings_Oord_Omin(_808455, _808451) = c_Orderings_Oord_Omin(_808453, _808449)), _808455 = _808453, _808451 = _808449], (24746 ^ _775212) ^ [_1205021, _1205023, _1205025, _1205027] : [class_Rings_Ocomm__semiring__1(_1205021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1205023), _1205025)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205021), hAPP(hAPP(c_Power_Opower__class_Opower(_1205021), _1205027), _1205023)), hAPP(hAPP(c_Power_Opower__class_Opower(_1205021), _1205027), _1205025))))], (41602 ^ _775212) ^ [_1577151, _1577153] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1577151, _1577151)), c_Transitive__Closure_Otrancl(_1577151, _1577153))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1577151, _1577151)), _1577153)))], (27737 ^ _775212) ^ [_1265453, _1265455, _1265457, _1265459, _1265461, _1265463] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265453, tc_fun(_1265455, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265457, tc_fun(_1265453, tc_HOL_Obool)), _1265459), _1265461)), _1265463) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265457, tc_fun(_1265455, tc_HOL_Obool)), _1265459), hAPP(hAPP(c_COMBC(_1265457, tc_fun(_1265453, tc_fun(_1265455, tc_HOL_Obool)), tc_fun(_1265455, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1265453, tc_HOL_Obool), tc_fun(tc_fun(_1265453, tc_fun(_1265455, tc_HOL_Obool)), tc_fun(_1265455, tc_HOL_Obool)), _1265457), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265453, tc_fun(_1265455, tc_HOL_Obool))), _1265461)), _1265463)))], (33708 ^ _775212) ^ [_1389761, _1389763, _1389765, _1389767, _1389769] : [class_Groups_Ocomm__monoid__add(_1389761), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389763), _1389765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1389763, tc_HOL_Obool)), _1389767), _1389765)), 33722 ^ _775212 : [(33725 ^ _775212) ^ [] : [hAPP(_1389769, 33721 ^ [_1389761, _1389763, _1389765, _1389767, _1389769]) = c_Groups_Ozero__class_Ozero(_1389761)], (33723 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389763), 33721 ^ [_1389761, _1389763, _1389765, _1389767, _1389769]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1389763, tc_HOL_Obool)), _1389765), _1389767))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1389763, _1389761), _1389769), _1389767) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1389763, _1389761), _1389769), _1389765))], (38985 ^ _775212) ^ [_1508640, _1508642, _1508644, _1508646] : [hBOOL(hAPP(hAPP(c_member(_1508640), _1508642), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1508640, tc_HOL_Obool)), _1508644), hAPP(c_Set_OCollect(_1508640), _1508646)))), 38988 ^ _775212 : [(38991 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1508646, _1508642)))], (38989 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508640), _1508642), _1508644)))]]], (50879 ^ _775212) ^ [_1795302, _1795304, _1795306, _1795308] : [-(c_Predicate_Oconversep(_1795302, _1795304, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1795302, tc_fun(_1795304, tc_HOL_Obool))), _1795306), _1795308)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1795304, tc_fun(_1795302, tc_HOL_Obool))), c_Predicate_Oconversep(_1795302, _1795304, _1795306)), c_Predicate_Oconversep(_1795302, _1795304, _1795308)))], (38929 ^ _775212) ^ [_1507506, _1507508] : [-(hBOOL(hAPP(_1507508, 38930 ^ [_1507506, _1507508]))), -(hAPP(c_Set_OCollect(_1507506), _1507508) = c_Orderings_Obot__class_Obot(tc_fun(_1507506, tc_HOL_Obool)))], (35539 ^ _775212) ^ [_1431387, _1431389, _1431391, _1431393, _1431395] : [class_Groups_Ocomm__monoid__mult(_1431387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431389), _1431391)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431389), _1431393)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431389, tc_HOL_Obool)), _1431391), _1431393) = c_Orderings_Obot__class_Obot(tc_fun(_1431389, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1431389, _1431387), _1431395), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431389, tc_HOL_Obool)), _1431391), _1431393)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1431387), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1431389, _1431387), _1431395), _1431391)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1431389, _1431387), _1431395), _1431393)))], (41598 ^ _775212) ^ [_1577056, _1577058] : [-(hAPP(c_Relation_ODomain(_1577056, _1577056), c_Transitive__Closure_Otrancl(_1577056, _1577058)) = hAPP(c_Relation_ODomain(_1577056, _1577056), _1577058))], (10859 ^ _775212) ^ [_952649, _952651] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952649), _952651)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952649)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952651)))], (28359 ^ _775212) ^ [_1278119, _1278121, _1278123] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1278119), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278119, tc_HOL_Obool)), _1278121), _1278123)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278119), _1278121)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278119), _1278123))], (15731 ^ _775212) ^ [_1041335, _1041337, _1041339, _1041341, _1041343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041335), _1041337)), 15734 ^ _775212 : [(15741 ^ _775212) ^ [] : [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), _1041337), _1041335)), _1041339)), _1041341)), _1041343)), -(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), _1041337), _1041339)), _1041341)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1041335), _1041339)), _1041343))))], (15735 ^ _775212) ^ [] : [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), _1041337), _1041339)), _1041341)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1041335), _1041339)), _1041343))), -(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), _1041337), _1041335)), _1041339)), _1041341)), _1041343)))]]], (24054 ^ _775212) ^ [_1193150, _1193152] : [24061 ^ _775212 : [(24064 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193152), _1193150))], (24062 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193150), _1193152)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193150), _1193152)), -(_1193150 = _1193152)], (33990 ^ _775212) ^ [_1396009, _1396011, _1396013] : [-(hAPP(c_Relation_OImage(_1396009, _1396011, _1396013), c_Orderings_Obot__class_Obot(tc_fun(_1396009, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1396011, tc_HOL_Obool)))], (17811 ^ _775212) ^ [_1077652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1077652))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1077652)))], (49603 ^ _775212) ^ [_1768101, _1768103, _1768105] : [-(c_List_OdropWhile(_1768101, _1768103, _1768105) = hAPP(hAPP(c_List_Odrop(_1768101), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768101)), c_List_OtakeWhile(_1768101, _1768103, _1768105))), _1768105))], (46486 ^ _775212) ^ [_1701498, _1701500] : [hBOOL(hAPP(c_List_Odistinct(_1701498), _1701500)), -(hBOOL(hAPP(c_List_Odistinct(_1701498), hAPP(c_List_Otl(_1701498), _1701500))))], (4830 ^ _775212) ^ [_848773, _848775, _848777, _848779] : [-(c_List_Omap(_848779, _848775) = c_List_Omap(_848777, _848773)), _848779 = _848777, _848775 = _848773], (18699 ^ _775212) ^ [_1092839, _1092841] : [class_Rings_Oring__1__no__zero__divisors(_1092839), 18702 ^ _775212 : [(18703 ^ _775212) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1092839), _1092841), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1092839), -(_1092841 = c_Groups_Oone__class_Oone(_1092839)), -(_1092841 = hAPP(c_Groups_Ouminus__class_Ouminus(_1092839), c_Groups_Oone__class_Oone(_1092839)))], (18713 ^ _775212) ^ [] : [18714 ^ _775212 : [(18717 ^ _775212) ^ [] : [_1092841 = hAPP(c_Groups_Ouminus__class_Ouminus(_1092839), c_Groups_Oone__class_Oone(_1092839))], (18715 ^ _775212) ^ [] : [_1092841 = c_Groups_Oone__class_Oone(_1092839)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1092839), _1092841), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1092839))]]], (51361 ^ _775212) ^ [_1806745, _1806747, _1806749] : [hBOOL(hAPP(hAPP(c_member(_1806747), _1806745), c_Orderings_Obot__class_Obot(tc_fun(_1806747, tc_HOL_Obool)))), hBOOL(hAPP(_1806749, _1806745))], (28796 ^ _775212) ^ [_1287062, _1287064, _1287066] : [class_Lattices_Obounded__lattice__bot(_1287062), 28799 ^ _775212 : [(28808 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287062), _1287064), _1287066) = c_Orderings_Obot__class_Obot(_1287062)), _1287064 = c_Orderings_Obot__class_Obot(_1287062), _1287066 = c_Orderings_Obot__class_Obot(_1287062)], (28800 ^ _775212) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287062), _1287064), _1287066) = c_Orderings_Obot__class_Obot(_1287062), 28803 ^ _775212 : [(28806 ^ _775212) ^ [] : [-(_1287066 = c_Orderings_Obot__class_Obot(_1287062))], (28804 ^ _775212) ^ [] : [-(_1287064 = c_Orderings_Obot__class_Obot(_1287062))]]]]], (31255 ^ _775212) ^ [_1340608, _1340610, _1340612] : [hAPP(c_Finite__Set_Ocard(_1340608), _1340610) = hAPP(c_Nat_OSuc, _1340612), 31260 ^ _775212 : [(31263 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1340608), 31258 ^ [_1340608, _1340610, _1340612]), 31259 ^ [_1340608, _1340610, _1340612]))], (31265 ^ _775212) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1340608), 31259 ^ [_1340608, _1340610, _1340612]) = _1340612)], (31267 ^ _775212) ^ [] : [_1340612 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(31259 ^ [_1340608, _1340610, _1340612] = c_Orderings_Obot__class_Obot(tc_fun(_1340608, tc_HOL_Obool)))], (31261 ^ _775212) ^ [] : [-(_1340610 = hAPP(hAPP(c_Set_Oinsert(_1340608), 31258 ^ [_1340608, _1340610, _1340612]), 31259 ^ [_1340608, _1340610, _1340612]))]]], (25032 ^ _775212) ^ [_1210571, _1210573] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210571), _1210573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1210573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1210571), _1210573)))], (17183 ^ _775212) ^ [_1067605] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1067605))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067605)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (48890 ^ _775212) ^ [_1753194, _1753196, _1753198] : [class_Orderings_Olinorder(_1753194), 48893 ^ _775212 : [(48912 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1753194, hAPP(hAPP(c_List_Oappend(_1753194), _1753196), _1753198))), c_List_Olinorder__class_Osorted(_1753194, _1753196), c_List_Olinorder__class_Osorted(_1753194, _1753198), 48922 ^ _775212 : [(48928 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1753194), 48921 ^ [_1753194, _1753196, _1753198]), 48924 ^ [_1753194, _1753196, _1753198]))], (48926 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753194), 48924 ^ [_1753194, _1753196, _1753198]), hAPP(c_List_Oset(_1753194), _1753198))))], (48923 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753194), 48921 ^ [_1753194, _1753196, _1753198]), hAPP(c_List_Oset(_1753194), _1753196))))]]], (48894 ^ _775212) ^ [] : [c_List_Olinorder__class_Osorted(_1753194, hAPP(hAPP(c_List_Oappend(_1753194), _1753196), _1753198)), 48897 ^ _775212 : [(48902 ^ _775212) ^ [_1753430] : [hBOOL(hAPP(hAPP(c_member(_1753194), _1753430), hAPP(c_List_Oset(_1753194), _1753196))), 48905 ^ _775212 : [(48906 ^ _775212) ^ [_1753540] : [hBOOL(hAPP(hAPP(c_member(_1753194), _1753540), hAPP(c_List_Oset(_1753194), _1753198))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1753194), _1753430), _1753540)))]]], (48900 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1753194, _1753198))], (48898 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1753194, _1753196))]]]]], (9361 ^ _775212) ^ [_926751, _926753, _926755] : [class_Orderings_Oorder(_926751), 9364 ^ _775212 : [(9365 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926751), _926753), _926755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926751), _926753), _926755))), -(_926753 = _926755)], (9375 ^ _775212) ^ [] : [9376 ^ _775212 : [(9379 ^ _775212) ^ [] : [_926753 = _926755], (9377 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926751), _926753), _926755))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926751), _926753), _926755)))]]], (26268 ^ _775212) ^ [_1235928, _1235930, _1235932, _1235934] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235928), _1235930)), 26271 ^ _775212 : [(26272 ^ _775212) ^ [_1236082] : [26274 ^ _775212 : [(26280 ^ _775212) ^ [] : [-(_1236082 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26276 ^ [_1235928, _1235930, _1235932, _1235934, _1236082]), 26273 ^ [_1235928, _1235930, _1235932, _1235934, _1236082]))], (26278 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26276 ^ [_1235928, _1235930, _1235932, _1235934, _1236082]), _1235932)))], (26275 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26273 ^ [_1235928, _1235930, _1235932, _1235934, _1236082]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1235930))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236082), _1235934))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236082), _1235930)), _1235934))))]]], (39729 ^ _775212) ^ [_1535556, _1535558] : [-(c_Wellfounded_Owf(_1535556, hAPP(c_Wellfounded_Omeasure(_1535556), _1535558)))], (26170 ^ _775212) ^ [_1233954, _1233956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233954)), 26179 ^ _775212 : [(26182 ^ _775212) ^ [] : [hBOOL(hAPP(_1233956, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26175 ^ [_1233954, _1233956]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 26176 ^ [_1233954, _1233956]), _1233954))))], (26180 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1233956, 26175 ^ [_1233954, _1233956])))]], 26183 ^ _775212 : [(26186 ^ _775212) ^ [] : [hBOOL(hAPP(_1233956, 26175 ^ [_1233954, _1233956]))], (26184 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1233956, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26175 ^ [_1233954, _1233956]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 26176 ^ [_1233954, _1233956]), _1233954)))))]], 26187 ^ _775212 : [(26197 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1233956, 26204 ^ [_1233954, _1233956]))), 26198 ^ _775212 : [(26199 ^ _775212) ^ [_1234501] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1234501), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1233954))), hBOOL(hAPP(_1233956, _1234501))]]], (26188 ^ _775212) ^ [] : [26189 ^ _775212 : [(26190 ^ _775212) ^ [_1234386] : [hBOOL(hAPP(_1233956, _1234386))]], 26192 ^ _775212 : [(26195 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1233956, 26191 ^ [_1233954, _1233956])))], (26193 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26191 ^ [_1233954, _1233956]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1233954))))]]]]], (18227 ^ _775212) ^ [_1084694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1084694)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1084694))))], (48617 ^ _775212) ^ [_1748715] : [class_Orderings_Olinorder(_1748715), -(c_List_Olinorder__class_Osorted(_1748715, c_List_Olist_ONil(_1748715)))], (45371 ^ _775212) ^ [_1674774, _1674776, _1674778, _1674780] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1674774) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1674776), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1674774)), hAPP(hAPP(c_List_Olist_OCons(_1674776), _1674778), _1674780)) = c_List_Olist_ONil(_1674776))], (29794 ^ _775212) ^ [_1306083, _1306085, _1306087, _1306089] : [_1306083 = _1306085, hBOOL(hAPP(hAPP(c_member(_1306087), _1306085), _1306089)), -(hBOOL(hAPP(hAPP(c_member(_1306087), _1306083), _1306089)))], (11306 ^ _775212) ^ [_960858] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _960858)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _960858)) = _960858)], (48689 ^ _775212) ^ [_1749749, _1749751, _1749753] : [class_Orderings_Olinorder(_1749749), 48692 ^ _775212 : [(48699 ^ _775212) ^ [] : [c_List_Olinorder__class_Osorted(_1749749, _1749753), -(c_List_Olinorder__class_Osorted(_1749749, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1749749, _1749749, c_COMBI(_1749749)), _1749751), _1749753)))], (48693 ^ _775212) ^ [] : [c_List_Olinorder__class_Osorted(_1749749, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1749749, _1749749, c_COMBI(_1749749)), _1749751), _1749753)), -(c_List_Olinorder__class_Osorted(_1749749, _1749753))]]], (4708 ^ _775212) ^ [_846970, _846972] : [_846972 = _846970, -(c_Enum_Oenum__class_Oenum__all(_846972) = c_Enum_Oenum__class_Oenum__all(_846970))], (52683 ^ _775212) ^ [_1828318, _1828320, _1828322, _1828324, _1828326, _1828328] : [-(hAPP(hAPP(hAPP(c_COMBS(_1828318, _1828320, _1828322), _1828324), _1828326), _1828328) = hAPP(hAPP(_1828324, _1828328), hAPP(_1828326, _1828328)))], (44370 ^ _775212) ^ [_1648101, _1648103, _1648105, _1648107] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1648101), tc_List_Olist(_1648101), c_List_Olistrel(_1648101, _1648103)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1648101)), hAPP(hAPP(c_List_Olist_OCons(_1648101), _1648105), _1648107)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1648101), tc_HOL_Obool)))) = c_List_Oset__Cons(_1648101, hAPP(c_Relation_OImage(_1648101, _1648101, _1648103), hAPP(hAPP(c_Set_Oinsert(_1648101), _1648105), c_Orderings_Obot__class_Obot(tc_fun(_1648101, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1648101), tc_List_Olist(_1648101), c_List_Olistrel(_1648101, _1648103)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1648101)), _1648107), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1648101), tc_HOL_Obool))))))], (50174 ^ _775212) ^ [_1781166, _1781168, _1781170, _1781172, _1781174] : [hAPP(c_List_Ofilter(_1781166, _1781168), _1781170) = hAPP(hAPP(c_List_Olist_OCons(_1781166), _1781172), _1781174), 50179 ^ _775212 : [(50188 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1781168, _1781172)))], (50190 ^ _775212) ^ [] : [-(_1781174 = hAPP(c_List_Ofilter(_1781166, _1781168), 50178 ^ [_1781166, _1781168, _1781170, _1781172, _1781174]))], (50182 ^ _775212) ^ [_1781480] : [hBOOL(hAPP(hAPP(c_member(_1781166), _1781480), hAPP(c_List_Oset(_1781166), 50177 ^ [_1781166, _1781168, _1781170, _1781172, _1781174]))), hBOOL(hAPP(_1781168, _1781480))], (50180 ^ _775212) ^ [] : [-(_1781170 = hAPP(hAPP(c_List_Oappend(_1781166), 50177 ^ [_1781166, _1781168, _1781170, _1781172, _1781174]), hAPP(hAPP(c_List_Olist_OCons(_1781166), _1781172), 50178 ^ [_1781166, _1781168, _1781170, _1781172, _1781174])))]]], (27585 ^ _775212) ^ [_1261959, _1261961] : [-(hAPP(c_Set_Oimage(_1261959, _1261959, c_COMBI(_1261959)), _1261961) = _1261961)], (552 ^ _775212) ^ [_783726, _783728, _783730, _783732, _783734, _783736] : [-(c_Finite__Set_Ofolding__one(_783734, _783730, _783726)), c_Finite__Set_Ofolding__one(_783736, _783732, _783728), _783736 = _783734, _783732 = _783730, _783728 = _783726], (17049 ^ _775212) ^ [_1065375] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065375))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1065375) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44192 ^ _775212) ^ [_1642248, _1642250, _1642252, _1642254, _1642256, _1642258] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642248), tc_List_Olist(_1642248))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642248), tc_List_Olist(_1642248)), hAPP(hAPP(c_List_Olist_OCons(_1642248), _1642250), _1642252)), hAPP(hAPP(c_List_Olist_OCons(_1642248), _1642254), _1642256))), c_List_Olex(_1642248, _1642258)))), 44193 ^ _775212 : [(44200 ^ _775212) ^ [] : [_1642250 = _1642254, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642248), tc_List_Olist(_1642248))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642248), tc_List_Olist(_1642248)), _1642252), _1642256)), c_List_Olex(_1642248, _1642258)))], (44194 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1642248, _1642248)), hAPP(hAPP(c_Product__Type_OPair(_1642248, _1642248), _1642250), _1642254)), _1642258)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642248)), _1642252) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642248)), _1642256)]]], (10071 ^ _775212) ^ [_938725, _938727, _938729, _938731] : [class_Groups_Oordered__comm__monoid__add(_938725), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938725), c_Groups_Ozero__class_Ozero(_938725)), _938727)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938725), _938729), _938731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938725), _938729), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938725), _938727), _938731))))], (18913 ^ _775212) ^ [_1097084] : [-(_1097084 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 18916 ^ _775212 : [(18923 ^ _775212) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1097084, 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, _1097084) = 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), _1097084), 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)))], (18917 ^ _775212) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1097084, 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, _1097084) = 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), _1097084), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (52653 ^ _775212) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (47172 ^ _775212) ^ [_1715636, _1715638] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715636)), c_List_Obutlast(_1715636, _1715638)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715636)), _1715638)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (50665 ^ _775212) ^ [_1791397, _1791399] : [c_Wellfounded_Oacyclic(_1791397, hAPP(c_Set_OCollect(tc_prod(_1791397, _1791397)), hAPP(c_Product__Type_Oprod_Oprod__case(_1791397, _1791397, tc_HOL_Obool), c_Predicate_Oconversep(_1791397, _1791397, _1791399)))), -(c_Wellfounded_Oacyclic(_1791397, hAPP(c_Set_OCollect(tc_prod(_1791397, _1791397)), hAPP(c_Product__Type_Oprod_Oprod__case(_1791397, _1791397, tc_HOL_Obool), _1791399))))], (41193 ^ _775212) ^ [_1569277, _1569279] : [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), _1569277), _1569279)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1569277), _1569279)))], (44256 ^ _775212) ^ [_1644537, _1644539, _1644541, _1644543] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644537), tc_List_Olist(_1644537))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644537), tc_List_Olist(_1644537)), _1644539), _1644541)), c_List_Olex(_1644537, _1644543)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644537), tc_List_Olist(_1644537))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644537), tc_List_Olist(_1644537)), _1644539), _1644541)), c_List_Olexord(_1644537, _1644543))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644537)), _1644539) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644537)), _1644541)], (18633 ^ _775212) ^ [_1091827, _1091829] : [class_Rings_Olinordered__idom(_1091827), 18636 ^ _775212 : [(18643 ^ _775212) ^ [] : [-(_1091829 = c_Groups_Ozero__class_Ozero(_1091827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091827), c_Groups_Ozero__class_Ozero(_1091827)), hAPP(hAPP(c_Power_Opower__class_Opower(_1091827), _1091829), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (18637 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091827), c_Groups_Ozero__class_Ozero(_1091827)), hAPP(hAPP(c_Power_Opower__class_Opower(_1091827), _1091829), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1091829 = c_Groups_Ozero__class_Ozero(_1091827)]]], (42373 ^ _775212) ^ [_1596192, _1596194, _1596196, _1596198, _1596200] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596192, _1596194)), hAPP(hAPP(c_Product__Type_OPair(_1596192, _1596194), _1596196), _1596198)), _1596200)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596194, _1596192)), hAPP(hAPP(c_Product__Type_OPair(_1596194, _1596192), _1596198), _1596196)), hAPP(c_Relation_Oconverse(_1596192, _1596194), _1596200))))], (8219 ^ _775212) ^ [_907751, _907753] : [class_Groups_Oab__group__add(_907751), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907751), hAPP(c_Groups_Ouminus__class_Ouminus(_907751), _907753)), _907753) = c_Groups_Ozero__class_Ozero(_907751))], (45254 ^ _775212) ^ [_1671841, _1671843] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671841), tc_List_Olist(_1671841))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671841), tc_List_Olist(_1671841)), c_List_Olist_ONil(_1671841)), c_List_Olist_ONil(_1671841))), c_List_Olistrel(_1671841, _1671843))))], (914 ^ _775212) ^ [_789183, _789185, _789187, _789189] : [-(c_Wellfounded_Oacyclic(_789187, _789183)), c_Wellfounded_Oacyclic(_789189, _789185), _789189 = _789187, _789185 = _789183], (39033 ^ _775212) ^ [_1509715, _1509717, _1509719] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1509715, tc_HOL_Obool)), _1509717), _1509719) = hAPP(c_Set_OCollect(_1509715), hAPP(hAPP(c_COMBS(_1509715, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509715), c_fconj), hAPP(hAPP(c_COMBC(_1509715, tc_fun(_1509715, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509715)), _1509717))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1509715), c_fNot), hAPP(hAPP(c_COMBC(_1509715, tc_fun(_1509715, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509715)), _1509719)))))], (21233 ^ _775212) ^ [_1138815, _1138817] : [-(c_Divides_Opdivmod(_1138815, _1138817) = 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), _1138815)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1138817))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1138815), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1138817))))], (43553 ^ _775212) ^ [_1626247, _1626249, _1626251] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1626247, tc_HOL_Obool)), _1626249), _1626251) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1626247, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1626247, tc_HOL_Obool)), _1626249), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1626247, tc_HOL_Obool)), _1626251), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1626247, tc_HOL_Obool), tc_HOL_Obool))))))], (14829 ^ _775212) ^ [_1023619, _1023621, _1023623, _1023625] : [class_Rings_Ocomm__semiring__1(_1023619), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023619), hAPP(hAPP(c_Power_Opower__class_Opower(_1023619), _1023621), _1023623)), hAPP(hAPP(c_Power_Opower__class_Opower(_1023619), _1023621), _1023625)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1023619), _1023621), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1023623), _1023625)))], (46438 ^ _775212) ^ [_1700534, _1700536] : [-(_1700534 = c_List_Olist_ONil(_1700536)), -(hAPP(c_List_Orotate1(_1700536), _1700534) = hAPP(hAPP(c_List_Oappend(_1700536), hAPP(c_List_Otl(_1700536), _1700534)), hAPP(hAPP(c_List_Olist_OCons(_1700536), hAPP(c_List_Ohd(_1700536), _1700534)), c_List_Olist_ONil(_1700536))))], (47348 ^ _775212) ^ [_1719091, _1719093] : [-(c_List_Opartition(_1719091, _1719093, c_List_Olist_ONil(_1719091)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1719091), tc_List_Olist(_1719091)), c_List_Olist_ONil(_1719091)), c_List_Olist_ONil(_1719091)))], (11068 ^ _775212) ^ [_956526, _956528, _956530, _956532, _956534] : [class_Rings_Olinordered__semiring__strict(_956526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956526), _956528), _956530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956526), _956532), _956534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956526), c_Groups_Ozero__class_Ozero(_956526)), _956528)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956526), c_Groups_Ozero__class_Ozero(_956526)), _956532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956526), _956528), _956532)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956526), _956530), _956534))))], (16295 ^ _775212) ^ [_1051576, _1051578, _1051580, _1051582] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051576), hAPP(c_Int_Onumber__class_Onumber__of(_1051576), _1051578)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051576), _1051580), _1051582)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051576), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051576), hAPP(c_Int_Onumber__class_Onumber__of(_1051576), _1051578)), _1051580)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051576), hAPP(c_Int_Onumber__class_Onumber__of(_1051576), _1051578)), _1051582))), class_Int_Onumber(_1051576), class_Rings_Osemiring(_1051576)], (12807 ^ _775212) ^ [_986474, _986476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _986474), _986476)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _986474, _986476) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _986474), _986476))], (30644 ^ _775212) ^ [_1327917, _1327919, _1327921, _1327923] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327917), _1327919)), hBOOL(hAPP(hAPP(c_member(_1327917), _1327921), _1327919)), -(hBOOL(hAPP(hAPP(c_member(_1327917), _1327921), _1327923))), -(hAPP(c_Finite__Set_Ocard(_1327917), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327917, tc_HOL_Obool)), _1327919), hAPP(hAPP(c_Set_Oinsert(_1327917), _1327921), _1327923))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1327917), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327917, tc_HOL_Obool)), _1327919), _1327923))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (24672 ^ _775212) ^ [_1203526, _1203528, _1203530] : [class_Divides_Osemiring__div(_1203526), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1203526), _1203528), _1203530)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1203526), _1203528), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1203526), _1203530), _1203528)) = _1203530)], (23212 ^ _775212) ^ [_1177305, _1177307, _1177309, _1177311, _1177313, _1177315, _1177317] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1177305, _1177307, tc_fun(_1177309, tc_HOL_Obool)), _1177311), hAPP(hAPP(c_Product__Type_OPair(_1177305, _1177307), _1177313), _1177315)), _1177317)), -(hBOOL(hAPP(hAPP(hAPP(_1177311, _1177313), _1177315), _1177317)))], (18357 ^ _775212) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (12723 ^ _775212) ^ [_985085, _985087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _985085)), -(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, _985087, _985085))))], (47951 ^ _775212) ^ [_1732879, _1732881] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732879)), c_List_Oremdups(_1732879, _1732881))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732879)), _1732881))))], (7497 ^ _775212) ^ [_894797, _894799] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894797)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894799)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _894797), _894799)))], (44537 ^ _775212) ^ [_1653132, _1653134, _1653136, _1653138] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653132)), hAPP(hAPP(c_List_Olist_OCons(_1653132), _1653134), _1653136)), c_List_Olists(_1653132, _1653138)))), hBOOL(hAPP(hAPP(c_member(_1653132), _1653134), _1653138)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653132)), _1653136), c_List_Olists(_1653132, _1653138)))], (45895 ^ _775212) ^ [_1687169, _1687171, _1687173, _1687175] : [hAPP(hAPP(c_List_Oappend(_1687169), _1687171), _1687173) = hAPP(hAPP(c_List_Oappend(_1687169), _1687171), _1687175), -(_1687173 = _1687175)], (24446 ^ _775212) ^ [_1199616, _1199618, _1199620] : [class_Rings_Ocomm__ring__1(_1199616), 24449 ^ _775212 : [(24456 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199616), _1199618), _1199620)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199616), hAPP(c_Groups_Ouminus__class_Ouminus(_1199616), _1199618)), _1199620)))], (24450 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199616), hAPP(c_Groups_Ouminus__class_Ouminus(_1199616), _1199618)), _1199620)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199616), _1199618), _1199620)))]]], (40498 ^ _775212) ^ [_1553522, _1553524, _1553526, _1553528, _1553530] : [hAPP(c_Set_Oimage(_1553522, _1553524, _1553526), c_Orderings_Otop__class_Otop(tc_fun(_1553522, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1553524, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1553524, _1553528, _1553530), c_Orderings_Otop__class_Otop(tc_fun(_1553524, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1553528, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1553522, _1553528, hAPP(c_Fun_Ocomp(_1553524, _1553528, _1553522, _1553530), _1553526)), c_Orderings_Otop__class_Otop(tc_fun(_1553522, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1553528, tc_HOL_Obool)))], (52723 ^ _775212) ^ [_1828843, _1828845] : [hBOOL(hAPP(hAPP(c_fconj, _1828843), _1828845)), -(hBOOL(_1828843))], (50735 ^ _775212) ^ [_1792568, _1792570, _1792572, _1792574] : [-(hAPP(hAPP(c_List_Otake(_1792568), _1792570), c_List_Oreplicate(_1792568, _1792572, _1792574)) = c_List_Oreplicate(_1792568, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1792570), _1792572), _1792574))], (28726 ^ _775212) ^ [_1285557, _1285559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1285557, tc_HOL_Obool)), _1285559), c_Orderings_Obot__class_Obot(tc_fun(_1285557, tc_HOL_Obool))))], (18147 ^ _775212) ^ [_1083381, _1083383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083381), _1083383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1083381)), c_Int_OBit0(_1083383))))], (16741 ^ _775212) ^ [_1060783] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060783)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1060783)))], (24862 ^ _775212) ^ [_1207100, _1207102, _1207104, _1207106, _1207108] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1207100, _1207102, tc_HOL_Obool, _1207104), _1207106), _1207108)), -(hBOOL(hAPP(_1207104, hAPP(hAPP(c_Product__Type_OPair(_1207100, _1207102), _1207106), _1207108))))], (28998 ^ _775212) ^ [_1290437] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290437, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1290437, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1290437, tc_HOL_Obool)))], (34623 ^ _775212) ^ [_1411149, _1411151, _1411153] : [class_Lattices_Osemilattice__inf(_1411149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411149), _1411151), _1411153)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411149), _1411153), _1411151) = _1411151)], (35809 ^ _775212) ^ [_1436685, _1436687, _1436689, _1436691, _1436693, _1436695, _1436697, _1436699, _1436701, _1436703] : [c_Equiv__Relations_Ocongruent2(_1436685, _1436687, _1436689, _1436691, _1436693, _1436695), hBOOL(hAPP(hAPP(c_member(tc_prod(_1436685, _1436685)), hAPP(hAPP(c_Product__Type_OPair(_1436685, _1436685), _1436697), _1436699)), _1436691)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1436687, _1436687)), hAPP(hAPP(c_Product__Type_OPair(_1436687, _1436687), _1436701), _1436703)), _1436693)), -(hAPP(hAPP(_1436695, _1436697), _1436701) = hAPP(hAPP(_1436695, _1436699), _1436703))], (34653 ^ _775212) ^ [_1411650, _1411652, _1411654, _1411656] : [class_Lattices_Osemilattice__inf(_1411650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411650), _1411652), _1411654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411650), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411650), _1411652), _1411656)), _1411654)))], (42719 ^ _775212) ^ [_1605773, _1605775, _1605777] : [-(hAPP(c_Relation_Oconverse(_1605773, _1605775), _1605777) = hAPP(c_Set_OCollect(tc_prod(_1605775, _1605773)), hAPP(c_Product__Type_Oprod_Oprod__case(_1605775, _1605773, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1605775, tc_fun(tc_prod(_1605773, _1605775), tc_HOL_Obool), tc_fun(_1605773, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1605773, tc_fun(tc_fun(tc_prod(_1605773, _1605775), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1605773, _1605775), tc_HOL_Obool), tc_fun(_1605773, tc_HOL_Obool)), _1605775), c_COMBC(_1605773, tc_fun(tc_prod(_1605773, _1605775), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1605773, tc_prod(_1605773, _1605775)), tc_fun(_1605773, tc_fun(tc_fun(tc_prod(_1605773, _1605775), tc_HOL_Obool), tc_HOL_Obool)), _1605775), hAPP(c_COMBB(tc_prod(_1605773, _1605775), tc_fun(tc_fun(tc_prod(_1605773, _1605775), tc_HOL_Obool), tc_HOL_Obool), _1605773), c_member(tc_prod(_1605773, _1605775)))), hAPP(c_COMBC(_1605773, _1605775, tc_prod(_1605773, _1605775)), c_Product__Type_OPair(_1605773, _1605775))))), _1605777))))], (16005 ^ _775212) ^ [_1046353, _1046355] : [class_Rings_Olinordered__idom(_1046353), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046353), hAPP(c_Groups_Oabs__class_Oabs(_1046353), _1046355)), hAPP(c_Groups_Oabs__class_Oabs(_1046353), _1046355)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046353), _1046355), _1046355))], (13545 ^ _775212) ^ [_999874, _999876, _999878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _999874)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _999874), _999876)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _999874), _999878)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _999876), _999878))], (42875 ^ _775212) ^ [_1610449] : [-(c_Relation_Osingle__valued(_1610449, _1610449, c_Relation_OId(_1610449)))], (24576 ^ _775212) ^ [_1201936] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201936), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1201936 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (27027 ^ _775212) ^ [_1251034, _1251036] : [class_Lattices_Osemilattice__sup(_1251034), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251034), _1251036), _1251036) = _1251036)], (17755 ^ _775212) ^ [_1076709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1076709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1076709))))], (38983 ^ _775212) ^ [_1508526, _1508528, _1508530] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1508526, tc_HOL_Obool)), _1508528), _1508530) = hAPP(c_Set_OCollect(_1508526), hAPP(hAPP(c_COMBS(_1508526, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508526), c_fdisj), hAPP(hAPP(c_COMBC(_1508526, tc_fun(_1508526, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508526)), _1508528))), hAPP(hAPP(c_COMBC(_1508526, tc_fun(_1508526, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508526)), _1508530))))], (37054 ^ _775212) ^ [_1464409, _1464411, _1464413] : [-(c_Fun_Oinj__on(tc_prod(_1464409, _1464411), tc_prod(_1464411, _1464409), hAPP(c_Product__Type_Oprod_Oprod__case(_1464409, _1464411, tc_prod(_1464411, _1464409)), hAPP(c_COMBC(_1464411, _1464409, tc_prod(_1464411, _1464409)), c_Product__Type_OPair(_1464411, _1464409))), _1464413))], (32659 ^ _775212) ^ [_1367116, _1367118, _1367120] : [class_Orderings_Olinorder(_1367116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367116), _1367118)), hBOOL(hAPP(hAPP(c_member(_1367116), _1367120), _1367118)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1367116), _1367120), c_Big__Operators_Olattice_OInf__fin(_1367116, c_Orderings_Oord__class_Omin(_1367116), _1367118)) = _1367120)], (38961 ^ _775212) ^ [_1508033, _1508035, _1508037] : [hBOOL(hAPP(_1508037, _1508035)), -(hBOOL(hAPP(hAPP(c_member(_1508033), _1508035), hAPP(c_Set_OCollect(_1508033), _1508037))))], (52419 ^ _775212) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (37210 ^ _775212) ^ [_1467700, _1467702, _1467704, _1467706] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467700), _1467702)), -(hAPP(c_Set_Oimage(_1467700, _1467704, _1467706), _1467702) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1467704, tc_HOL_Obool), _1467700, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467704, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1467700, tc_fun(_1467704, tc_HOL_Obool), tc_fun(_1467704, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1467704, tc_fun(tc_fun(_1467704, tc_HOL_Obool), tc_fun(_1467704, tc_HOL_Obool)), _1467700), c_Set_Oinsert(_1467704)), _1467706)), c_Orderings_Obot__class_Obot(tc_fun(_1467704, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1467704, tc_HOL_Obool))), _1467702))], (52395 ^ _775212) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (47676 ^ _775212) ^ [_1726493, _1726495, _1726497, _1726499, _1726501, _1726503, _1726505] : [c_List_Olist__all2(_1726493, _1726495, _1726497, _1726499, _1726501), c_List_Olist__all2(_1726493, _1726495, _1726497, _1726503, _1726505), -(c_List_Olist__all2(_1726493, _1726495, _1726497, hAPP(hAPP(c_List_Oappend(_1726493), _1726499), _1726503), hAPP(hAPP(c_List_Oappend(_1726495), _1726501), _1726505)))], (27333 ^ _775212) ^ [_1256825, _1256827, _1256829, _1256831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256825, tc_HOL_Obool)), _1256827), _1256829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256825, tc_HOL_Obool)), _1256831), _1256829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256825, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256825, tc_HOL_Obool)), _1256827), _1256831)), _1256829)))], (52085 ^ _775212) ^ [_1821851, _1821853, _1821855, _1821857, _1821859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1821851, tc_HOL_Obool)), _1821853), hAPP(c_Set_Oimage(_1821855, _1821851, _1821857), _1821859))), -(c_Fun_Oinj__on(_1821851, _1821855, c_Hilbert__Choice_Oinv__into(_1821855, _1821851, _1821859, _1821857), _1821853))], (42804 ^ _775212) ^ [_1608670, _1608672, _1608674] : [_1608672 = _1608674, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608670, _1608670)), hAPP(hAPP(c_Product__Type_OPair(_1608670, _1608670), _1608672), _1608674)), c_Relation_OId(_1608670))))], (29136 ^ _775212) ^ [_1292778, _1292780, _1292782, _1292784, _1292786] : [-(_1292778 = c_Orderings_Obot__class_Obot(tc_fun(_1292780, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292782, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292780, tc_fun(_1292782, tc_HOL_Obool)), _1292778), _1292784)), _1292786) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1292780, tc_fun(_1292782, tc_HOL_Obool)), _1292778), hAPP(hAPP(c_COMBC(_1292780, tc_fun(_1292782, tc_HOL_Obool), tc_fun(_1292782, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1292782, tc_HOL_Obool), tc_fun(tc_fun(_1292782, tc_HOL_Obool), tc_fun(_1292782, tc_HOL_Obool)), _1292780), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292782, tc_HOL_Obool))), _1292784)), _1292786)))], (14329 ^ _775212) ^ [_1014271, _1014273, _1014275, _1014277] : [class_Rings_Ocomm__semiring__1(_1014271), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1014271), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014271), _1014273), _1014275)), _1014277) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014271), hAPP(hAPP(c_Power_Opower__class_Opower(_1014271), _1014273), _1014277)), hAPP(hAPP(c_Power_Opower__class_Opower(_1014271), _1014275), _1014277)))], (1214 ^ _775212) ^ [_793243, _793245] : [-(class_Rings_Oordered__ring(_793243)), _793245 = _793243, class_Rings_Oordered__ring(_793245)], (43322 ^ _775212) ^ [_1620789, _1620791, _1620793, _1620795] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620789, tc_HOL_Obool), hAPP(c_Set_Oimage(_1620791, tc_fun(_1620789, tc_HOL_Obool), _1620793), _1620795)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1620791, tc_fun(_1620789, tc_HOL_Obool)), _1620795), _1620793))], (52337 ^ _775212) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (17799 ^ _775212) ^ [_1077444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1077444)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1077444), c_Int_OMin)))], (19025 ^ _775212) ^ [_1099103, _1099105, _1099107, _1099109] : [class_Rings_Odivision__ring(_1099103), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099103), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099103), _1099105), _1099107)), _1099109) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099103), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099103), _1099105), _1099109)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099103), _1099107), _1099109)))], (48376 ^ _775212) ^ [_1743421, _1743423] : [-(c_List_Ofoldr(tc_List_Olist(_1743421), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1743421)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1743421))), c_List_Otranspose(_1743421, _1743423), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1743421))), hAPP(c_List_Ofilter(tc_List_Olist(_1743421), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1743421)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1743421), tc_List_Olist(_1743421), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1743421)))), _1743423)))], (4680 ^ _775212) ^ [_846528, _846530, _846532, _846534, _846536, _846538] : [-(c_List_OtakeWhile(_846538, _846534, _846530) = c_List_OtakeWhile(_846536, _846532, _846528)), _846538 = _846536, _846534 = _846532, _846530 = _846528], (15185 ^ _775212) ^ [_1030802, _1030804, _1030806, _1030808] : [class_Rings_Olinordered__semidom(_1030802), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030802), hAPP(hAPP(c_Power_Opower__class_Opower(_1030802), _1030804), _1030806)), hAPP(hAPP(c_Power_Opower__class_Opower(_1030802), _1030808), _1030806))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1030802), c_Groups_Ozero__class_Ozero(_1030802)), _1030808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030802), _1030804), _1030808)))], (6537 ^ _775212) ^ [_878804, _878806, _878808] : [_878804 = _878808, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878804), _878806) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878808), _878806))], (21863 ^ _775212) ^ [_1150138, _1150140] : [-(_1150138 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1150140, _1150138), c_Divides_Odivmod__int(_1150140, _1150138))))], (30800 ^ _775212) ^ [_1331348, _1331350] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1331348, _1331348)), hAPP(hAPP(c_Product__Type_OPair(_1331348, _1331348), 30801 ^ [_1331348, _1331350]), 30801 ^ [_1331348, _1331350])), _1331350)), -(c_Nitpick_Orefl_H(_1331348, _1331350))], (46192 ^ _775212) ^ [_1694858, _1694860, _1694862, _1694864, _1694866] : [-(hAPP(hAPP(c_List_Odrop(_1694858), _1694860), hAPP(hAPP(c_List_Omap(_1694862, _1694858), _1694864), _1694866)) = hAPP(hAPP(c_List_Omap(_1694862, _1694858), _1694864), hAPP(hAPP(c_List_Odrop(_1694862), _1694860), _1694866)))], (48408 ^ _775212) ^ [_1744335, _1744337, _1744339] : [-(c_List_Osublist(_1744335, _1744337, _1744339) = hAPP(hAPP(c_List_Omap(tc_prod(_1744335, tc_Nat_Onat), _1744335), c_Product__Type_Ofst(_1744335, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1744335, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1744335, 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(_1744335, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1744335, tc_Nat_Onat))), _1744339)), hAPP(hAPP(c_List_Ozip(_1744335, tc_Nat_Onat), _1744337), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744335)), _1744337))))))], (49275 ^ _775212) ^ [_1761142, _1761144] : [-(hAPP(c_List_Orev(_1761142), _1761144) = hAPP(c_List_Ofoldl(tc_List_Olist(_1761142), _1761142, hAPP(c_COMBC(_1761142, tc_List_Olist(_1761142), tc_List_Olist(_1761142)), c_List_Olist_OCons(_1761142)), c_List_Olist_ONil(_1761142)), _1761144))], (12705 ^ _775212) ^ [_984797, _984799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _984797)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984797), _984799)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _984797, _984799) = _984797)], (24230 ^ _775212) ^ [_1195935, _1195937] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195935), _1195937))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195935), _1195937)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195937), _1195935)))], (39363 ^ _775212) ^ [_1523113] : [-(c_Int_Oint__ge__less__than(_1523113) = 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), _1523113)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (11090 ^ _775212) ^ [_956949, _956951, _956953, _956955, _956957] : [class_Rings_Olinordered__semiring__strict(_956949), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956949), _956951), _956953)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956949), _956955), _956957)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956949), c_Groups_Ozero__class_Ozero(_956949)), _956951)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956949), c_Groups_Ozero__class_Ozero(_956949)), _956955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956949), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956949), _956951), _956955)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956949), _956953), _956957))))], (42410 ^ _775212) ^ [_1597127, _1597129, _1597131, _1597133, _1597135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597127, tc_HOL_Obool)), _1597129), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597131, tc_fun(_1597127, tc_HOL_Obool)), _1597133), _1597135))), 42413 ^ _775212 : [(42414 ^ _775212) ^ [_1597260] : [hBOOL(hAPP(hAPP(c_member(_1597131), _1597260), _1597133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597127, tc_HOL_Obool)), _1597129), hAPP(_1597135, _1597260))))]]], (6543 ^ _775212) ^ [_878909, _878911] : [class_Groups_Ocomm__monoid__add(_878909), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878909), _878911), c_Groups_Ozero__class_Ozero(_878909)) = _878911)], (36207 ^ _775212) ^ [_1446950, _1446952, _1446954] : [class_Lattices_Olattice(_1446950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446950), _1446952)), -(_1446954 = c_Orderings_Obot__class_Obot(tc_fun(_1446950, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1446950, tc_HOL_Obool)), _1446954), _1446952)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1446950), c_Big__Operators_Olattice__class_OInf__fin(_1446950, _1446954)), c_Big__Operators_Olattice__class_OInf__fin(_1446950, _1446952)) = c_Big__Operators_Olattice__class_OInf__fin(_1446950, _1446952))], (11714 ^ _775212) ^ [_967517, _967519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967517), hAPP(c_Nat_OSuc, _967519))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967517), _967519))), -(_967517 = hAPP(c_Nat_OSuc, _967519))], (2648 ^ _775212) ^ [_814266, _814268] : [_814268 = _814266, -(c_DSequence_Ounion(_814268) = c_DSequence_Ounion(_814266))], (21033 ^ _775212) ^ [_1135248, _1135250, _1135252, _1135254] : [class_Fields_Olinordered__field__inverse__zero(_1135248), class_Int_Onumber(_1135248), 21040 ^ _775212 : [(21041 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135248), hAPP(c_Int_Onumber__class_Onumber__of(_1135248), _1135250)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135248), _1135252), _1135254))), 21044 ^ _775212 : [(21051 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135248), c_Groups_Ozero__class_Ozero(_1135248)), _1135254))), 21054 ^ _775212 : [(21061 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135248), _1135254), c_Groups_Ozero__class_Ozero(_1135248)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135248), hAPP(c_Int_Onumber__class_Onumber__of(_1135248), _1135250)), c_Groups_Ozero__class_Ozero(_1135248))))], (21055 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135248), _1135254), c_Groups_Ozero__class_Ozero(_1135248))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135248), _1135252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135248), hAPP(c_Int_Onumber__class_Onumber__of(_1135248), _1135250)), _1135254))))]]], (21045 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135248), c_Groups_Ozero__class_Ozero(_1135248)), _1135254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135248), hAPP(c_Int_Onumber__class_Onumber__of(_1135248), _1135250)), _1135254)), _1135252)))]]], (21067 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135248), hAPP(c_Int_Onumber__class_Onumber__of(_1135248), _1135250)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135248), _1135252), _1135254)))), 21070 ^ _775212 : [(21073 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135248), hAPP(c_Int_Onumber__class_Onumber__of(_1135248), _1135250)), _1135254)), _1135252))], (21071 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135248), c_Groups_Ozero__class_Ozero(_1135248)), _1135254)))]], 21074 ^ _775212 : [(21077 ^ _775212) ^ [] : [21078 ^ _775212 : [(21081 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135248), _1135252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135248), hAPP(c_Int_Onumber__class_Onumber__of(_1135248), _1135250)), _1135254)))], (21079 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135248), _1135254), c_Groups_Ozero__class_Ozero(_1135248))))]], 21082 ^ _775212 : [(21085 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135248), hAPP(c_Int_Onumber__class_Onumber__of(_1135248), _1135250)), c_Groups_Ozero__class_Ozero(_1135248)))], (21083 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135248), _1135254), c_Groups_Ozero__class_Ozero(_1135248)))]]], (21075 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135248), c_Groups_Ozero__class_Ozero(_1135248)), _1135254))]]]]], (38343 ^ _775212) ^ [_1496100, _1496102] : [class_Lattices_Olattice(_1496100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496100), _1496102)), -(c_Big__Operators_Olattice__class_OInf__fin(_1496100, _1496102) = hAPP(c_Finite__Set_Ofold1(_1496100, c_Lattices_Osemilattice__inf__class_Oinf(_1496100)), _1496102))], (28087 ^ _775212) ^ [] : [-(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)))], (21635 ^ _775212) ^ [_1145681, _1145683] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1145681, _1145683) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1145681, _1145683)))], (46708 ^ _775212) ^ [_1706287, _1706289] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1706287), _1706289))), -(c_Nitpick_Ocard_H(_1706287, _1706289) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18197 ^ _775212) ^ [_1084195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1084195)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084195), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27315 ^ _775212) ^ [_1256460, _1256462, _1256464] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256460, tc_HOL_Obool)), _1256462), _1256464) = _1256464, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256460, tc_HOL_Obool)), _1256462), _1256464)))], (17737 ^ _775212) ^ [_1076418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1076418)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076418), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9245 ^ _775212) ^ [_925033, _925035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _925033), c_Groups_Oone__class_Oone(tc_Int_Oint))), _925035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _925033), _925035)))], (36817 ^ _775212) ^ [_1459073, _1459075, _1459077, _1459079] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1459073), _1459075)), 36820 ^ _775212 : [(36827 ^ _775212) ^ [] : [hAPP(c_Finite__Set_Ocard(_1459077), hAPP(c_Set_Oimage(_1459073, _1459077, _1459079), _1459075)) = hAPP(c_Finite__Set_Ocard(_1459073), _1459075), -(c_Fun_Oinj__on(_1459073, _1459077, _1459079, _1459075))], (36821 ^ _775212) ^ [] : [c_Fun_Oinj__on(_1459073, _1459077, _1459079, _1459075), -(hAPP(c_Finite__Set_Ocard(_1459077), hAPP(c_Set_Oimage(_1459073, _1459077, _1459079), _1459075)) = hAPP(c_Finite__Set_Ocard(_1459073), _1459075))]]], (27539 ^ _775212) ^ [_1261044, _1261046, _1261048, _1261050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1261044, _1261046)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1261048, _1261050))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1261044), _1261046)), 27546 ^ _775212 : [(27549 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1261046), _1261050)))], (27547 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1261048), _1261044)))]]], (23798 ^ _775212) ^ [_1188806] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1188806)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1188806))], (36193 ^ _775212) ^ [_1446742, _1446744, _1446746] : [class_Lattices_Olattice(_1446742), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446742), _1446744)), -(_1446744 = c_Orderings_Obot__class_Obot(tc_fun(_1446742, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1446742, hAPP(hAPP(c_Set_Oinsert(_1446742), _1446746), _1446744)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1446742), _1446746), c_Big__Operators_Olattice__class_OInf__fin(_1446742, _1446744)))], (47432 ^ _775212) ^ [_1721309, _1721311, _1721313, _1721315, _1721317] : [class_Orderings_Olinorder(_1721309), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721311)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1721311, _1721309, _1721313), _1721315), _1721317)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721311)), _1721317)))], (45694 ^ _775212) ^ [_1682797, _1682799, _1682801, _1682803, _1682805] : [-(hAPP(hAPP(c_List_Olist__update(_1682797, hAPP(hAPP(c_List_Oappend(_1682797), _1682799), hAPP(hAPP(c_List_Olist_OCons(_1682797), _1682801), _1682803))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682797)), _1682799)), _1682805) = hAPP(hAPP(c_List_Oappend(_1682797), _1682799), hAPP(hAPP(c_List_Olist_OCons(_1682797), _1682805), _1682803)))], (25797 ^ _775212) ^ [_1226280] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1226280) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1226280))], (42525 ^ _775212) ^ [_1600506, _1600508, _1600510, _1600512, _1600514] : [-(hAPP(c_Relation_Oconverse(_1600506, _1600508), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1600510, tc_fun(tc_prod(_1600506, _1600508), tc_HOL_Obool)), _1600512), _1600514)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1600510, tc_fun(tc_prod(_1600508, _1600506), tc_HOL_Obool)), _1600512), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1600506, _1600508), tc_HOL_Obool), tc_fun(tc_prod(_1600508, _1600506), tc_HOL_Obool), _1600510), c_Relation_Oconverse(_1600506, _1600508)), _1600514)))], (40037 ^ _775212) ^ [_1542657, _1542659] : [c_Wellfounded_Owf(_1542657, _1542659), -(c_Wellfounded_Owf(tc_List_Olist(_1542657), c_List_Olenlex(_1542657, _1542659)))], (8749 ^ _775212) ^ [_917134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _917134), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_917134 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 8752 ^ [_917134]))))], (18269 ^ _775212) ^ [_1085425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1085425)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085425), c_Int_OPls)))], (23710 ^ _775212) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (38321 ^ _775212) ^ [_1495706, _1495708, _1495710, _1495712, _1495714] : [c_Relation_Orefl__on(_1495706, _1495708, _1495710), c_Relation_Orefl__on(_1495706, _1495712, _1495714), -(c_Relation_Orefl__on(_1495706, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1495706, tc_HOL_Obool)), _1495708), _1495712), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1495706, _1495706), tc_HOL_Obool)), _1495710), _1495714)))], (12243 ^ _775212) ^ [_976530, _976532, _976534] : [12244 ^ _775212 : [(12247 ^ _775212) ^ [] : [_976532 = _976534], (12245 ^ _775212) ^ [] : [_976530 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _976530), _976532) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _976530), _976534))], (39520 ^ _775212) ^ [_1528563, _1528565, _1528567, _1528569] : [hAPP(hAPP(c_Relation_Orel__comp(_1528563, _1528563, _1528563), _1528565), _1528567) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528563, _1528563), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1528563, _1528563, _1528563), _1528569), _1528567) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528563, _1528563), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1528563, _1528563, _1528563), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528563, _1528563), tc_HOL_Obool)), _1528565), _1528569)), _1528567) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528563, _1528563), tc_HOL_Obool)))], (40786 ^ _775212) ^ [_1559876, _1559878, _1559880, _1559882, _1559884, _1559886] : [c_Finite__Set_Ofolding(_1559876, _1559878, _1559880, _1559882), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559876), _1559884)), -(hAPP(_1559882, hAPP(hAPP(c_Set_Oinsert(_1559876), _1559886), _1559884)) = hAPP(c_Fun_Ocomp(_1559878, _1559878, _1559878, hAPP(_1559882, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1559876, tc_HOL_Obool)), _1559884), hAPP(hAPP(c_Set_Oinsert(_1559876), _1559886), c_Orderings_Obot__class_Obot(tc_fun(_1559876, tc_HOL_Obool)))))), hAPP(_1559880, _1559886)))], (42465 ^ _775212) ^ [_1599214, _1599216, _1599218, _1599220, _1599222] : [hBOOL(hAPP(hAPP(c_member(_1599214), _1599216), _1599218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1599220, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599214, tc_fun(_1599220, tc_HOL_Obool)), _1599218), _1599222)), hAPP(_1599222, _1599216))))], (47877 ^ _775212) ^ [_1731115, _1731117] : [hBOOL(hAPP(c_List_Odistinct(_1731115), _1731117)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1731115, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731115), tc_fun(_1731115, tc_HOL_Obool)), c_List_Oset(_1731115)), c_Enum_Osublists(_1731115, _1731117)))))], (31021 ^ _775212) ^ [_1335628, _1335630] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335630), _1335628)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1335628), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335630))))], (36343 ^ _775212) ^ [_1449331, _1449333] : [class_Lattices_Olattice(_1449331), hBOOL(hAPP(c_Finite__Set_Ofinite(_1449331), _1449333)), -(_1449333 = c_Orderings_Obot__class_Obot(tc_fun(_1449331, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1449331), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1449331), 36356 ^ [_1449331, _1449333]), 36357 ^ [_1449331, _1449333])), hAPP(hAPP(c_Set_Oinsert(_1449331), 36356 ^ [_1449331, _1449333]), hAPP(hAPP(c_Set_Oinsert(_1449331), 36357 ^ [_1449331, _1449333]), c_Orderings_Obot__class_Obot(tc_fun(_1449331, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1449331), c_Big__Operators_Olattice__class_OInf__fin(_1449331, _1449333)), _1449333)))], (46970 ^ _775212) ^ [_1711909, _1711911, _1711913, _1711915] : [-(_1711909 = c_List_Olist_ONil(_1711911)), -(c_List_Olast(_1711913, hAPP(hAPP(c_List_Omap(_1711911, _1711913), _1711915), _1711909)) = hAPP(_1711915, c_List_Olast(_1711911, _1711909)))], (11895 ^ _775212) ^ [_970557, _970559, _970561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970557), _970559)), _970561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970557), _970561)))], (1734 ^ _775212) ^ [_799743, _799745] : [-(class_Rings_Ozero__neq__one(_799743)), _799745 = _799743, class_Rings_Ozero__neq__one(_799745)], (48414 ^ _775212) ^ [_1744680, _1744682] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1744680), _1744682) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1744680, _1744682)))], (13340 ^ _775212) ^ [_996618, _996620, _996622] : [-(_996618 = 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), _996618), _996620)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996618), _996622)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _996620), _996622))], (16915 ^ _775212) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (52605 ^ _775212) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (6809 ^ _775212) ^ [_883744, _883746, _883748] : [class_Groups_Oordered__comm__monoid__add(_883744), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883744), _883746), c_Groups_Ozero__class_Ozero(_883744))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883744), _883748), c_Groups_Ozero__class_Ozero(_883744))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883744), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883744), _883746), _883748)), c_Groups_Ozero__class_Ozero(_883744))))], (33296 ^ _775212) ^ [_1379982, _1379984, _1379986] : [class_Orderings_Olinorder(_1379982), hAPP(_1379984, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1379982), 33301 ^ [_1379982, _1379984, _1379986]), 33302 ^ [_1379982, _1379984, _1379986])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1379982), hAPP(_1379984, 33301 ^ [_1379982, _1379984, _1379986])), hAPP(_1379984, 33302 ^ [_1379982, _1379984, _1379986])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379982), _1379986)), -(_1379986 = c_Orderings_Obot__class_Obot(tc_fun(_1379982, tc_HOL_Obool))), -(hAPP(_1379984, c_Big__Operators_Olattice_OInf__fin(_1379982, c_Orderings_Oord__class_Omin(_1379982), _1379986)) = c_Big__Operators_Olattice_OInf__fin(_1379982, c_Orderings_Oord__class_Omin(_1379982), hAPP(c_Set_Oimage(_1379982, _1379982, _1379984), _1379986)))], (31451 ^ _775212) ^ [_1344341, _1344343] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1344341, _1344343), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344341), _1344343)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344343), _1344341)))], (26444 ^ _775212) ^ [_1239746, _1239748, _1239750, _1239752, _1239754, _1239756, _1239758, _1239760] : [class_Groups_Ocomm__monoid__add(_1239746), class_Orderings_Oord(_1239748), _1239750 = _1239752, _1239754 = _1239756, 26462 ^ _775212 : [(26467 ^ _775212) ^ [] : [hAPP(_1239758, 26461 ^ [_1239746, _1239748, _1239750, _1239752, _1239754, _1239756, _1239758, _1239760]) = hAPP(_1239760, 26461 ^ [_1239746, _1239748, _1239750, _1239752, _1239754, _1239756, _1239758, _1239760])], (26465 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239748), 26461 ^ [_1239746, _1239748, _1239750, _1239752, _1239754, _1239756, _1239758, _1239760]), _1239756)))], (26463 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239748), _1239752), 26461 ^ [_1239746, _1239748, _1239750, _1239752, _1239754, _1239756, _1239758, _1239760])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1239748, _1239746), _1239758), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1239748, _1239750), _1239754)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1239748, _1239746), _1239760), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1239748, _1239752), _1239756)))], (43565 ^ _775212) ^ [_1626671, _1626673, _1626675] : [class_Complete__Lattice_Ocomplete__lattice(_1626671), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626671), _1626673)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1626671), _1626675), c_Complete__Lattice_OSup__class_OSup(_1626671, _1626673)) = hAPP(hAPP(c_Finite__Set_Ofold(_1626671, _1626671, c_Lattices_Osemilattice__sup__class_Osup(_1626671)), _1626675), _1626673))], (47915 ^ _775212) ^ [_1731940, _1731942, _1731944, _1731946, _1731948] : [47917 ^ _775212 : [(47920 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1731940, _1731942, tc_HOL_Obool), _1731948), 47916 ^ [_1731940, _1731942, _1731944, _1731946, _1731948]))], (47918 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1731940, _1731942)), 47916 ^ [_1731940, _1731942, _1731944, _1731946, _1731948]), hAPP(c_List_Oset(tc_prod(_1731940, _1731942)), hAPP(hAPP(c_List_Ozip(_1731940, _1731942), _1731944), _1731946)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731940)), _1731944) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731942)), _1731946), -(c_List_Olist__all2(_1731940, _1731942, _1731948, _1731944, _1731946))], (28712 ^ _775212) ^ [_1285252, _1285254, _1285256] : [-(hAPP(c_Set_Oimage(_1285252, _1285254, _1285256), c_Orderings_Obot__class_Obot(tc_fun(_1285252, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1285254, tc_HOL_Obool)))], (23044 ^ _775212) ^ [_1174126, _1174128, _1174130] : [class_Orderings_Olinorder(_1174126), 23047 ^ _775212 : [(23054 ^ _775212) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174126), _1174128), _1174130) = _1174130, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174126), _1174128), _1174130)))], (23048 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174126), _1174128), _1174130)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174126), _1174128), _1174130) = _1174130)]]], (41971 ^ _775212) ^ [_1585838, _1585840, _1585842, _1585844, _1585846] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585838, _1585838)), hAPP(hAPP(c_Product__Type_OPair(_1585838, _1585838), _1585840), _1585842)), c_Transitive__Closure_Ortrancl(_1585838, _1585844))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585838, _1585838)), hAPP(hAPP(c_Product__Type_OPair(_1585838, _1585838), _1585842), _1585846)), _1585844)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585838, _1585838)), hAPP(hAPP(c_Product__Type_OPair(_1585838, _1585838), _1585840), _1585846)), c_Transitive__Closure_Otrancl(_1585838, _1585844))))], (48416 ^ _775212) ^ [_1744717, _1744719] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1744717, _1744719)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1744717), _1744719))], (37936 ^ _775212) ^ [_1485323, _1485325, _1485327] : [c_Equiv__Relations_Oequiv(_1485323, _1485325, _1485327), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1485323, _1485323), tc_HOL_Obool)), _1485327), hAPP(hAPP(c_Product__Type_OSigma(_1485323, _1485323), _1485325), hAPP(c_COMBK(tc_fun(_1485323, tc_HOL_Obool), _1485323), _1485325)))))], (9291 ^ _775212) ^ [_925731, _925733, _925735] : [class_Orderings_Olinorder(_925731), 9294 ^ _775212 : [(9301 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925731), _925735), _925733)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925731), _925733), _925735))], (9295 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925731), _925733), _925735))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925731), _925735), _925733)))]]], (31132 ^ _775212) ^ [_1338020, _1338022, _1338024, _1338026, _1338028, _1338030] : [c_Finite__Set_Ofolding__image__simple(_1338020, _1338022, _1338024, _1338026, _1338028, _1338030), -(hAPP(_1338030, c_Orderings_Obot__class_Obot(tc_fun(_1338022, tc_HOL_Obool))) = _1338026)], (33735 ^ _775212) ^ [_1390339, _1390341, _1390343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1390339, tc_HOL_Obool)), _1390341), _1390343)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1390339, tc_HOL_Obool)), _1390341), hAPP(c_Set_OPow(_1390339), _1390343))))], (27944 ^ _775212) ^ [_1270261] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1270261)), 27948 ^ _775212 : [(27949 ^ _775212) ^ [_1270341] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1270341), _1270261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1270341), 27947 ^ [_1270261])))]]], (30100 ^ _775212) ^ [_1314681, _1314683, _1314685, _1314687] : [hBOOL(hAPP(hAPP(c_member(_1314681), _1314683), _1314685)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314681, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1314681), _1314683), _1314687)), _1314685) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314681, tc_HOL_Obool)), _1314687), _1314685))], (41428 ^ _775212) ^ [_1573901, _1573903, _1573905] : [class_Orderings_Olinorder(_1573901), hBOOL(hAPP(c_Finite__Set_Ofinite(_1573901), _1573903)), -(c_Big__Operators_Olinorder__class_OMin(_1573901, hAPP(hAPP(c_Set_Oinsert(_1573901), _1573905), _1573903)) = hAPP(hAPP(c_Finite__Set_Ofold(_1573901, _1573901, c_Orderings_Oord__class_Omin(_1573901)), _1573905), _1573903))], (27295 ^ _775212) ^ [_1256050, _1256052, _1256054, _1256056] : [class_Lattices_Osemilattice__sup(_1256050), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256050), _1256052), _1256054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256050), _1256052), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256050), _1256054), _1256056))))], (20977 ^ _775212) ^ [_1134179, _1134181, _1134183, _1134185] : [class_Fields_Olinordered__field__inverse__zero(_1134179), class_Int_Onumber(_1134179), 20984 ^ _775212 : [(20985 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134179), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134179), _1134181), _1134183)), hAPP(c_Int_Onumber__class_Onumber__of(_1134179), _1134185))), 20988 ^ _775212 : [(20995 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134179), c_Groups_Ozero__class_Ozero(_1134179)), _1134183))), 20998 ^ _775212 : [(21005 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134179), _1134183), c_Groups_Ozero__class_Ozero(_1134179)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134179), c_Groups_Ozero__class_Ozero(_1134179)), hAPP(c_Int_Onumber__class_Onumber__of(_1134179), _1134185))))], (20999 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134179), _1134183), c_Groups_Ozero__class_Ozero(_1134179))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134179), hAPP(c_Int_Onumber__class_Onumber__of(_1134179), _1134185)), _1134183)), _1134181)))]]], (20989 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134179), c_Groups_Ozero__class_Ozero(_1134179)), _1134183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134179), _1134181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134179), hAPP(c_Int_Onumber__class_Onumber__of(_1134179), _1134185)), _1134183))))]]], (21011 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134179), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134179), _1134181), _1134183)), hAPP(c_Int_Onumber__class_Onumber__of(_1134179), _1134185)))), 21014 ^ _775212 : [(21017 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134179), _1134181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134179), hAPP(c_Int_Onumber__class_Onumber__of(_1134179), _1134185)), _1134183)))], (21015 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134179), c_Groups_Ozero__class_Ozero(_1134179)), _1134183)))]], 21018 ^ _775212 : [(21021 ^ _775212) ^ [] : [21022 ^ _775212 : [(21025 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134179), hAPP(c_Int_Onumber__class_Onumber__of(_1134179), _1134185)), _1134183)), _1134181))], (21023 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134179), _1134183), c_Groups_Ozero__class_Ozero(_1134179))))]], 21026 ^ _775212 : [(21029 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134179), c_Groups_Ozero__class_Ozero(_1134179)), hAPP(c_Int_Onumber__class_Onumber__of(_1134179), _1134185)))], (21027 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134179), _1134183), c_Groups_Ozero__class_Ozero(_1134179)))]]], (21019 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134179), c_Groups_Ozero__class_Ozero(_1134179)), _1134183))]]]]], (39605 ^ _775212) ^ [_1531329, _1531331, _1531333, _1531335] : [hBOOL(hAPP(c_Predicate_ORangeP(_1531329, _1531331, hAPP(hAPP(c_COMBC(_1531329, tc_fun(tc_prod(_1531329, _1531331), tc_HOL_Obool), tc_fun(_1531331, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531331, tc_fun(tc_fun(tc_prod(_1531329, _1531331), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1531329, _1531331), tc_HOL_Obool), tc_fun(_1531331, tc_HOL_Obool)), _1531329), c_COMBC(_1531331, tc_fun(tc_prod(_1531329, _1531331), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531331, tc_prod(_1531329, _1531331)), tc_fun(_1531331, tc_fun(tc_fun(tc_prod(_1531329, _1531331), tc_HOL_Obool), tc_HOL_Obool)), _1531329), hAPP(c_COMBB(tc_prod(_1531329, _1531331), tc_fun(tc_fun(tc_prod(_1531329, _1531331), tc_HOL_Obool), tc_HOL_Obool), _1531331), c_member(tc_prod(_1531329, _1531331)))), c_Product__Type_OPair(_1531329, _1531331)))), _1531333)), _1531335)), -(hBOOL(hAPP(hAPP(c_member(_1531331), _1531335), hAPP(c_Relation_ORange(_1531329, _1531331), _1531333))))], (13561 ^ _775212) ^ [_1000179, _1000181] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1000179), _1000181) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1000181 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13570 ^ _775212 : [(13573 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1000179), _1000181)))], (13571 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000179)))]], 13574 ^ _775212 : [(13577 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1000181), _1000179)))], (13575 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1000179), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (49051 ^ _775212) ^ [_1756370, _1756372, _1756374, _1756376, _1756378] : [class_Orderings_Olinorder(_1756370), c_Fun_Oinj__on(_1756372, _1756370, _1756374, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1756372, tc_HOL_Obool)), hAPP(c_List_Oset(_1756372), _1756376)), hAPP(c_List_Oset(_1756372), _1756378))), c_List_Olinorder__class_Osorted(_1756370, hAPP(hAPP(c_List_Omap(_1756372, _1756370), _1756374), _1756376)), hBOOL(hAPP(c_List_Odistinct(_1756370), hAPP(hAPP(c_List_Omap(_1756372, _1756370), _1756374), _1756376))), c_List_Olinorder__class_Osorted(_1756370, hAPP(hAPP(c_List_Omap(_1756372, _1756370), _1756374), _1756378)), hBOOL(hAPP(c_List_Odistinct(_1756370), hAPP(hAPP(c_List_Omap(_1756372, _1756370), _1756374), _1756378))), hAPP(c_List_Oset(_1756372), _1756376) = hAPP(c_List_Oset(_1756372), _1756378), -(_1756376 = _1756378)], (43774 ^ _775212) ^ [_1631827, _1631829, _1631831, _1631833, _1631835] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631827, _1631827)), hAPP(hAPP(c_Product__Type_OPair(_1631827, _1631827), _1631829), _1631831)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631827, _1631827), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1631833)), _1631835))), 43778 ^ _775212 : [(43781 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631827, _1631827)), hAPP(hAPP(c_Product__Type_OPair(_1631827, _1631827), 43777 ^ [_1631827, _1631829, _1631831, _1631833, _1631835]), _1631831)), _1631835)))], (43779 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631827, _1631827)), hAPP(hAPP(c_Product__Type_OPair(_1631827, _1631827), _1631829), 43777 ^ [_1631827, _1631829, _1631831, _1631833, _1631835])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631827, _1631827), tc_HOL_Obool), _1631833), _1631835))))]]], (43499 ^ _775212) ^ [_1625179] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625179, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1625179, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1625179, tc_HOL_Obool)))], (28101 ^ _775212) ^ [_1273010, _1273012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1273010), hAPP(c_Nat_OSuc, _1273012))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1273010, hAPP(c_Nat_OSuc, _1273012)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1273012)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1273010, _1273012)))], (15955 ^ _775212) ^ [_1045464, _1045466] : [class_Groups_Oordered__ab__group__add__abs(_1045464), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045464), _1045466), hAPP(c_Groups_Oabs__class_Oabs(_1045464), _1045466))))], (21647 ^ _775212) ^ [_1145919, _1145921, _1145923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1145919, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1145919, tc_HOL_Obool)), _1145921)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1145919, tc_HOL_Obool)), _1145923))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1145919, tc_HOL_Obool)), _1145923), _1145921)))], (22862 ^ _775212) ^ [_1170685, _1170687, _1170689, _1170691, _1170693] : [hBOOL(hAPP(hAPP(_1170685, _1170687), _1170689)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1170691, _1170693, tc_HOL_Obool), _1170685), hAPP(hAPP(c_Product__Type_OPair(_1170691, _1170693), _1170687), _1170689))))], (21473 ^ _775212) ^ [_1142950, _1142952, _1142954, _1142956] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1142950, _1142952), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1142954), _1142956))), -(_1142952 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1142950, _1142952) = _1142956)], (23496 ^ _775212) ^ [_1183020, _1183022] : [-(c_Nitpick_Oinverse__frac(_1183020, _1183022) = hAPP(hAPP(c_Nitpick_Ofrac(_1183020), hAPP(c_Nitpick_Odenom(_1183020), _1183022)), hAPP(c_Nitpick_Onum(_1183020), _1183022)))], (25128 ^ _775212) ^ [_1212430, _1212432] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212430), _1212432)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212430), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1212432))))], (51389 ^ _775212) ^ [_1807182, _1807184] : [-(c_Relation_Otrans(_1807182, c_Relation_OId__on(_1807182, _1807184)))], (31385 ^ _775212) ^ [_1343156, _1343158] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343156), _1343158)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1343158, _1343156) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (23226 ^ _775212) ^ [_1177694, _1177696, _1177698, _1177700, _1177702, _1177704] : [hAPP(_1177700, hAPP(c_Product__Type_Ofst(_1177694, _1177698), _1177702)) = hAPP(_1177704, hAPP(c_Product__Type_Ofst(_1177694, _1177698), _1177702)), -(hAPP(c_Product__Type_Oapfst(_1177694, _1177696, _1177698, _1177700), _1177702) = hAPP(c_Product__Type_Oapfst(_1177694, _1177696, _1177698, _1177704), _1177702))], (15943 ^ _775212) ^ [_1045258, _1045260] : [class_Groups_Oordered__ab__group__add__abs(_1045258), -(hAPP(c_Groups_Oabs__class_Oabs(_1045258), hAPP(c_Groups_Oabs__class_Oabs(_1045258), _1045260)) = hAPP(c_Groups_Oabs__class_Oabs(_1045258), _1045260))], (29854 ^ _775212) ^ [_1307100, _1307102] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1307100)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1307102))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1307100), _1307102)))], (13925 ^ _775212) ^ [_1006707, _1006709, _1006711] : [-(hBOOL(hAPP(_1006707, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1006709, _1006711)))), 13928 ^ _775212 : [(13931 ^ _775212) ^ [] : [hBOOL(hAPP(_1006707, _1006709))], (13929 ^ _775212) ^ [] : [-(_1006711 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 13932 ^ _775212 : [(13937 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13935 ^ [_1006707, _1006709, _1006711]), _1006711)))], (13939 ^ _775212) ^ [] : [-(_1006709 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1006711), 13934 ^ [_1006707, _1006709, _1006711])), 13935 ^ [_1006707, _1006709, _1006711]))], (13941 ^ _775212) ^ [] : [hBOOL(hAPP(_1006707, 13935 ^ [_1006707, _1006709, _1006711]))], (13933 ^ _775212) ^ [] : [_1006711 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (44144 ^ _775212) ^ [_1641160, _1641162, _1641164, _1641166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641160)), _1641162)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641160)), _1641164))), _1641162 = hAPP(hAPP(c_List_Olist_OCons(_1641160), _1641166), _1641164)], (52413 ^ _775212) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (50625 ^ _775212) ^ [_1790471, _1790473, _1790475] : [c_List_Olist__ex1(_1790471, _1790473, _1790475), 50629 ^ _775212 : [(50634 ^ _775212) ^ [_1790717] : [-(_1790717 = 50628 ^ [_1790471, _1790473, _1790475]), hBOOL(hAPP(hAPP(c_member(_1790471), _1790717), hAPP(c_List_Oset(_1790471), _1790475))), hBOOL(hAPP(_1790473, _1790717))], (50632 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1790473, 50628 ^ [_1790471, _1790473, _1790475])))], (50630 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790471), 50628 ^ [_1790471, _1790473, _1790475]), hAPP(c_List_Oset(_1790471), _1790475))))]]], (15291 ^ _775212) ^ [_1032737, _1032739, _1032741, _1032743] : [class_Rings_Olinordered__semidom(_1032737), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1032739), _1032741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032737), c_Groups_Oone__class_Oone(_1032737)), _1032743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032737), hAPP(hAPP(c_Power_Opower__class_Opower(_1032737), _1032743), _1032739)), hAPP(hAPP(c_Power_Opower__class_Opower(_1032737), _1032743), _1032741))))], (18171 ^ _775212) ^ [_1083743] : [c_Int_OPls = _1083743, -(c_Int_OPls = c_Int_OBit0(_1083743))], (23542 ^ _775212) ^ [_1183876, _1183878] : [-(_1183876 = _1183878), -(c_Random_Oinc__shift(_1183876, _1183878) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1183878), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (32199 ^ _775212) ^ [_1357586, _1357588] : [-(hBOOL(hAPP(hAPP(c_member(_1357586), _1357588), c_Orderings_Otop__class_Otop(tc_fun(_1357586, tc_HOL_Obool)))))], (27814 ^ _775212) ^ [_1267444, _1267446, _1267448, _1267450, _1267452, _1267454] : [-(hAPP(c_Set_Oimage(_1267444, _1267446, _1267448), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267450, tc_fun(_1267444, tc_HOL_Obool)), _1267452), _1267454)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267450, tc_fun(_1267446, tc_HOL_Obool)), _1267452), hAPP(hAPP(c_COMBB(tc_fun(_1267444, tc_HOL_Obool), tc_fun(_1267446, tc_HOL_Obool), _1267450), c_Set_Oimage(_1267444, _1267446, _1267448)), _1267454)))], (22954 ^ _775212) ^ [_1172568, _1172570, _1172572, _1172574] : [class_Orderings_Olinorder(_1172568), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172568), _1172570), _1172572)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172568), _1172574), _1172572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172568), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1172568), _1172570), _1172574)), _1172572)))], (37654 ^ _775212) ^ [_1477865, _1477867, _1477869, _1477871, _1477873] : [class_Groups_Oab__semigroup__mult(_1477865), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1477865, _1477865, c_Groups_Otimes__class_Otimes(_1477865), _1477867, _1477869), _1477871)), -(hBOOL(hAPP(hAPP(c_member(_1477865), _1477867), _1477869))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1477865, _1477865, c_Groups_Otimes__class_Otimes(_1477865), _1477873, hAPP(hAPP(c_Set_Oinsert(_1477865), _1477867), _1477869)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1477865), _1477873), _1477871))))], (6697 ^ _775212) ^ [_881608, _881610] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881608), hAPP(c_Nat_OSuc, _881610)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881608), _881610)))], (6939 ^ _775212) ^ [_885758, _885760, _885762] : [class_Rings_Olinordered__semidom(_885758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885758), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_885758), _885760)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_885758), _885762))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885760), _885762)))], (9981 ^ _775212) ^ [_936997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _936997)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _936997)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _936997)))], (44142 ^ _775212) ^ [_1640869, _1640871, _1640873] : [-(hAPP(c_List_Olexn(_1640869, _1640871), hAPP(c_Nat_OSuc, _1640873)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1640869), tc_List_Olist(_1640869)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1640869, tc_List_Olist(_1640869)), tc_prod(_1640869, tc_List_Olist(_1640869))), tc_prod(tc_List_Olist(_1640869), tc_List_Olist(_1640869)), c_Product__Type_Omap__pair(tc_prod(_1640869, tc_List_Olist(_1640869)), tc_List_Olist(_1640869), tc_prod(_1640869, tc_List_Olist(_1640869)), tc_List_Olist(_1640869), hAPP(c_Product__Type_Oprod_Oprod__case(_1640869, tc_List_Olist(_1640869), tc_List_Olist(_1640869)), c_List_Olist_OCons(_1640869)), hAPP(c_Product__Type_Oprod_Oprod__case(_1640869, tc_List_Olist(_1640869), tc_List_Olist(_1640869)), c_List_Olist_OCons(_1640869)))), c_Wellfounded_Olex__prod(_1640869, tc_List_Olist(_1640869), _1640871, hAPP(c_List_Olexn(_1640869, _1640871), _1640873)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1640869), tc_List_Olist(_1640869))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1640869), tc_List_Olist(_1640869), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1640869), tc_fun(tc_List_Olist(_1640869), tc_HOL_Obool), tc_fun(tc_List_Olist(_1640869), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1640869), tc_HOL_Obool), tc_fun(tc_List_Olist(_1640869), tc_HOL_Obool)), tc_List_Olist(_1640869)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1640869))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1640869)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1640869), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1640869)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1640869)))), hAPP(c_Nat_OSuc, _1640873))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1640869), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1640869)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1640869)))), hAPP(c_Nat_OSuc, _1640873)))))))], (45262 ^ _775212) ^ [_1672140, _1672142, _1672144] : [_1672140 = _1672142, 45265 ^ _775212 : [(45268 ^ _775212) ^ [_1672296] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1672144, _1672144)), _1672296), hAPP(c_List_Oset(tc_prod(_1672144, _1672144)), hAPP(hAPP(c_List_Ozip(_1672144, _1672144), _1672140), _1672142)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1672144, _1672144, tc_HOL_Obool), c_fequal), _1672296)))], (45266 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672144)), _1672140) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672144)), _1672142))]]], (44547 ^ _775212) ^ [_1653349, _1653351, _1653353] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653349)), _1653351), c_List_Olists(_1653349, c_Wellfounded_Oacc(_1653349, _1653353)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653349)), _1653351), c_Wellfounded_Oacc(tc_List_Olist(_1653349), c_List_Olistrel1(_1653349, _1653353)))))], (9269 ^ _775212) ^ [_925440] : [class_Rings_Ozero__neq__one(_925440), c_Groups_Ozero__class_Ozero(_925440) = c_Groups_Oone__class_Oone(_925440)], (14285 ^ _775212) ^ [_1013275, _1013277, _1013279, _1013281, _1013283, _1013285] : [class_Divides_Oring__div(_1013275), c_Divides_Odiv__class_Omod(_1013275, _1013277, _1013279) = c_Divides_Odiv__class_Omod(_1013275, _1013281, _1013279), c_Divides_Odiv__class_Omod(_1013275, _1013283, _1013279) = c_Divides_Odiv__class_Omod(_1013275, _1013285, _1013279), -(c_Divides_Odiv__class_Omod(_1013275, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1013275), _1013277), _1013283), _1013279) = c_Divides_Odiv__class_Omod(_1013275, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1013275), _1013281), _1013285), _1013279))], (52483 ^ _775212) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (23360 ^ _775212) ^ [_1180292, _1180294] : [-(_1180292 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1180294, _1180292) = c_Nitpick_Onat__gcd(_1180292, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1180294, _1180292)))], (43278 ^ _775212) ^ [_1619867] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619867, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1619867, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1619867, tc_HOL_Obool)))], (26557 ^ _775212) ^ [_1242099, _1242101] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1242099, _1242101)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1242101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242099), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (46612 ^ _775212) ^ [_1704155, _1704157, _1704159, _1704161] : [hBOOL(hAPP(c_List_Odistinct(_1704155), hAPP(hAPP(c_List_Omap(_1704157, _1704155), _1704159), _1704161))), 46615 ^ _775212 : [(46618 ^ _775212) ^ [] : [-(c_Fun_Oinj__on(_1704157, _1704155, _1704159, hAPP(c_List_Oset(_1704157), _1704161)))], (46616 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1704157), _1704161)))]]], (12061 ^ _775212) ^ [_973389, _973391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973389), hAPP(c_Nat_OSuc, _973391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973389), _973391)))], (9203 ^ _775212) ^ [_924288, _924290, _924292] : [class_Rings_Olinordered__idom(_924288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924288), c_Groups_Ozero__class_Ozero(_924288)), _924290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924288), c_Groups_Ozero__class_Ozero(_924288)), _924292)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924288), _924292), c_Groups_Oone__class_Oone(_924288))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924288), _924290), _924292)), _924290)))], (37399 ^ _775212) ^ [_1471463, _1471465, _1471467, _1471469, _1471471] : [hBOOL(hAPP(hAPP(c_member(_1471463), _1471465), hAPP(c_Set_Ovimage(_1471463, _1471467, _1471469), _1471471))), -(hBOOL(hAPP(hAPP(c_member(_1471467), hAPP(_1471469, _1471465)), _1471471)))], (3124 ^ _775212) ^ [_822110, _822112, _822114, _822116, _822118, _822120, _822122, _822124] : [-(c_Sum__Type_OPlus(_822124, _822120, _822116, _822112) = c_Sum__Type_OPlus(_822122, _822118, _822114, _822110)), _822124 = _822122, _822120 = _822118, _822116 = _822114, _822112 = _822110], (51633 ^ _775212) ^ [_1813319, _1813321] : [c_Relation_Otrans(_1813319, _1813321), c_Relation_Oantisym(_1813319, _1813321), -(c_Relation_Otrans(_1813319, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1813319, _1813319), tc_HOL_Obool)), _1813321), c_Relation_OId(_1813319))))], (15923 ^ _775212) ^ [_1044963, _1044965, _1044967] : [class_Int_Onumber__ring(_1044963), class_Int_Oring__char__0(_1044963), 15930 ^ _775212 : [(15937 ^ _775212) ^ [] : [_1044965 = _1044967, -(hAPP(c_Int_Onumber__class_Onumber__of(_1044963), _1044965) = hAPP(c_Int_Onumber__class_Onumber__of(_1044963), _1044967))], (15931 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1044963), _1044965) = hAPP(c_Int_Onumber__class_Onumber__of(_1044963), _1044967), -(_1044965 = _1044967)]]], (43073 ^ _775212) ^ [_1615211, _1615213, _1615215, _1615217] : [-(hAPP(hAPP(c_Nat_Ocompow(_1615211, _1615211), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1615213), _1615215)), _1615217) = hAPP(c_Fun_Ocomp(_1615211, _1615211, _1615211, hAPP(hAPP(c_Nat_Ocompow(_1615211, _1615211), _1615213), _1615217)), hAPP(hAPP(c_Nat_Ocompow(_1615211, _1615211), _1615215), _1615217)))], (44379 ^ _775212) ^ [_1648398, _1648400, _1648402] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648398), tc_List_Olist(_1648398))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648398), tc_List_Olist(_1648398)), _1648400), _1648400)), c_List_Olistrel(_1648398, c_Transitive__Closure_Ortrancl(_1648398, _1648402)))))], (13304 ^ _775212) ^ [_995972, _995974] : [class_Divides_Osemiring__div(_995972), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_995972), _995974), c_Groups_Oone__class_Oone(_995972)) = _995974)], (22218 ^ _775212) ^ [_1157120, _1157122, _1157124, _1157126] : [-(c_Nat_Onat_Onat__case(_1157120, _1157122, _1157124, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157126)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1157120), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1157126))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1157120, _1157120), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1157120, tc_fun(_1157120, _1157120)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1157120, tc_fun(_1157120, _1157120)), tc_Int_Oint), c_If(_1157120)), c_Nat__Numeral_Oneg)), _1157122)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1157120, tc_Int_Oint), _1157124), c_Int_Onat))))], (23822 ^ _775212) ^ [_1189261, _1189263] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1189261), _1189263) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1189261)), hAPP(c_Code__Numeral_Onat__of, _1189263))))], (49514 ^ _775212) ^ [_1766370, _1766372, _1766374] : [-(hAPP(hAPP(c_List_Oappend(_1766370), c_List_OtakeWhile(_1766370, _1766372, _1766374)), c_List_OdropWhile(_1766370, _1766372, _1766374)) = _1766374)], (5088 ^ _775212) ^ [_852810, _852812, _852814, _852816] : [-(c_List_Oupto(_852816, _852812) = c_List_Oupto(_852814, _852810)), _852816 = _852814, _852812 = _852810], (32850 ^ _775212) ^ [_1371022, _1371024, _1371026, _1371028, _1371030, _1371032, _1371034] : [-(_1371022 = _1371024), -(c_Fun_Ofun__upd(_1371026, _1371028, c_Fun_Ofun__upd(_1371026, _1371028, _1371030, _1371022, _1371032), _1371024, _1371034) = c_Fun_Ofun__upd(_1371026, _1371028, c_Fun_Ofun__upd(_1371026, _1371028, _1371030, _1371024, _1371034), _1371022, _1371032))], (14143 ^ _775212) ^ [_1010764, _1010766] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1010764)), _1010766) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1010764), _1010766)))], (46937 ^ _775212) ^ [_1711199, _1711201, _1711203, _1711205] : [-(_1711199 = c_List_Olist_ONil(_1711201)), 46940 ^ _775212 : [(46947 ^ _775212) ^ [] : [-(_1711203 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711201)), _1711199)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1711201, hAPP(hAPP(c_List_Olist__update(_1711201, _1711199), _1711203), _1711205)) = c_List_Olast(_1711201, _1711199))], (46941 ^ _775212) ^ [] : [_1711203 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711201)), _1711199)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1711201, hAPP(hAPP(c_List_Olist__update(_1711201, _1711199), _1711203), _1711205)) = _1711205)]]], (34967 ^ _775212) ^ [_1417704, _1417706, _1417708, _1417710] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417704, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417704, tc_HOL_Obool)), _1417706), _1417708)), _1417710) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417704, tc_HOL_Obool)), _1417706), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417704, tc_HOL_Obool)), _1417708), _1417710)))], (20013 ^ _775212) ^ [_1116557, _1116559, _1116561, _1116563] : [class_Fields_Olinordered__field(_1116557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116557), _1116559), _1116561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116557), c_Groups_Ozero__class_Ozero(_1116557)), _1116563)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116557), c_Groups_Ozero__class_Ozero(_1116557)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116557), _1116561), _1116559))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116557), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116557), _1116563), _1116561)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116557), _1116563), _1116559))))], (30088 ^ _775212) ^ [_1314384, _1314386, _1314388, _1314390, _1314392] : [_1314384 = hAPP(_1314386, _1314388), -(hBOOL(hAPP(hAPP(c_member(_1314390), _1314384), hAPP(c_Set_Oimage(_1314392, _1314390, _1314386), c_Orderings_Otop__class_Otop(tc_fun(_1314392, tc_HOL_Obool))))))], (26501 ^ _775212) ^ [_1240935, _1240937, _1240939] : [-(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)), _1240935)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1240937, _1240939)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1240937), _1240935), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1240939), _1240935)))], (40150 ^ _775212) ^ [_1544895, _1544897] : [c_Wellfounded_Owf(_1544895, _1544897), -(c_Wellfounded_OwfP(_1544895, c_FunDef_Oin__rel(_1544895, _1544895, _1544897)))], (26982 ^ _775212) ^ [_1250057, _1250059, _1250061, _1250063] : [26984 ^ _775212 : [(26987 ^ _775212) ^ [] : [hBOOL(hAPP(_1250063, 26983 ^ [_1250057, _1250059, _1250061, _1250063]))], (26985 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1250057), 26983 ^ [_1250057, _1250059, _1250061, _1250063]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1250057, tc_HOL_Obool)), _1250059), _1250061))))]], 26988 ^ _775212 : [(26995 ^ _775212) ^ [_1250374] : [hBOOL(hAPP(hAPP(c_member(_1250057), _1250374), _1250061)), -(hBOOL(hAPP(_1250063, _1250374)))], (26989 ^ _775212) ^ [_1250277] : [hBOOL(hAPP(hAPP(c_member(_1250057), _1250277), _1250059)), -(hBOOL(hAPP(_1250063, _1250277)))]]], (41696 ^ _775212) ^ [_1579518, _1579520, _1579522, _1579524, _1579526, _1579528] : [c_Finite__Set_Ofun__left__comm(_1579518, _1579520, _1579522), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579518), _1579524)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1579518, _1579520, _1579522), _1579526), hAPP(hAPP(c_Set_Oinsert(_1579518), _1579528), _1579524)) = hAPP(hAPP(_1579522, _1579528), hAPP(hAPP(c_Finite__Set_Ofold(_1579518, _1579520, _1579522), _1579526), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1579518, tc_HOL_Obool)), _1579524), hAPP(hAPP(c_Set_Oinsert(_1579518), _1579528), c_Orderings_Obot__class_Obot(tc_fun(_1579518, tc_HOL_Obool)))))))], (25392 ^ _775212) ^ [_1217090, _1217092] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217090), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217092))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1217090))), _1217092)))], (47641 ^ _775212) ^ [_1725730, _1725732, _1725734, _1725736, _1725738] : [-(c_List_Olist__all2(_1725730, _1725732, _1725734, _1725736, _1725738)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725730)), _1725736) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725732)), _1725738), 47647 ^ _775212 : [(47650 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1725730, _1725732, tc_HOL_Obool), _1725734), 47646 ^ [_1725730, _1725732, _1725734, _1725736, _1725738]))], (47648 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1725730, _1725732)), 47646 ^ [_1725730, _1725732, _1725734, _1725736, _1725738]), hAPP(c_List_Oset(tc_prod(_1725730, _1725732)), hAPP(hAPP(c_List_Ozip(_1725730, _1725732), _1725736), _1725738)))))]]], (29432 ^ _775212) ^ [_1299142, _1299144, _1299146, _1299148] : [_1299142 = _1299144, 29437 ^ _775212 : [(29440 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1299146), _1299148), _1299144)))], (29438 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1299146), _1299148), _1299142)))]], 29441 ^ _775212 : [(29444 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1299146), _1299148), _1299144))], (29442 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1299146), _1299148), _1299142))]]], (51181 ^ _775212) ^ [_1802752, _1802754, _1802756] : [c_List_Olist__all(tc_Int_Oint, _1802752, c_List_Oupto(_1802754, _1802756)), -(c_List_Oall__interval__int(_1802752, _1802754, _1802756))], (43724 ^ _775212) ^ [_1630089, _1630091, _1630093, _1630095, _1630097] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630089, _1630089)), hAPP(hAPP(c_Product__Type_OPair(_1630089, _1630089), _1630091), _1630093)), c_Transitive__Closure_Ortrancl(_1630089, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1630089, _1630089), tc_HOL_Obool)), _1630095), _1630097)))), 43730 ^ _775212 : [(43736 ^ _775212) ^ [] : [43732 ^ [_1630089, _1630091, _1630093, _1630095, _1630097] = 43729 ^ [_1630089, _1630091, _1630093, _1630095, _1630097]], (43734 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630089, _1630089)), hAPP(hAPP(c_Product__Type_OPair(_1630089, _1630089), 43732 ^ [_1630089, _1630091, _1630093, _1630095, _1630097]), 43729 ^ [_1630089, _1630091, _1630093, _1630095, _1630097])), _1630097)))], (43731 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630089, _1630089)), hAPP(hAPP(c_Product__Type_OPair(_1630089, _1630089), 43729 ^ [_1630089, _1630091, _1630093, _1630095, _1630097]), _1630093)), c_Transitive__Closure_Ortrancl(_1630089, _1630095))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630089, _1630089)), hAPP(hAPP(c_Product__Type_OPair(_1630089, _1630089), _1630091), _1630093)), c_Transitive__Closure_Ortrancl(_1630089, _1630095))))], (8924 ^ _775212) ^ [_919919, _919921, _919923] : [class_Orderings_Oorder(_919919), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919919), _919921), _919923)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919919), _919923), _919921)), -(_919921 = _919923)], (7887 ^ _775212) ^ [_901791, _901793, _901795] : [class_Groups_Oordered__ab__group__add(_901791), 7890 ^ _775212 : [(7897 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901791), _901795), _901793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901791), hAPP(c_Groups_Ouminus__class_Ouminus(_901791), _901793)), hAPP(c_Groups_Ouminus__class_Ouminus(_901791), _901795))))], (7891 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901791), hAPP(c_Groups_Ouminus__class_Ouminus(_901791), _901793)), hAPP(c_Groups_Ouminus__class_Ouminus(_901791), _901795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901791), _901795), _901793)))]]], (16907 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (47843 ^ _775212) ^ [_1730285, _1730287, _1730289, _1730291, _1730293, _1730295, _1730297, _1730299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730285), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730287)), _1730289))), c_List_Olist__all2(_1730287, _1730291, _1730293, _1730289, _1730295), hBOOL(hAPP(hAPP(_1730293, _1730297), _1730299)), -(c_List_Olist__all2(_1730287, _1730291, _1730293, hAPP(hAPP(c_List_Olist__update(_1730287, _1730289), _1730285), _1730297), hAPP(hAPP(c_List_Olist__update(_1730291, _1730295), _1730285), _1730299)))], (26391 ^ _775212) ^ [_1238669, _1238671] : [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)), _1238669)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238671))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1238669), _1238671)))], (43933 ^ _775212) ^ [_1635776, _1635778] : [-(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)))), _1635776)) = 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)))), _1635778))), 43935 ^ _775212 : [(43938 ^ _775212) ^ [] : [43939 ^ _775212 : [(43942 ^ _775212) ^ [] : [hBOOL(hAPP(_1635778, 43934 ^ [_1635776, _1635778]))], (43940 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1635776, 43934 ^ [_1635776, _1635778])))]], 43943 ^ _775212 : [(43946 ^ _775212) ^ [] : [hBOOL(hAPP(_1635776, 43934 ^ [_1635776, _1635778]))], (43944 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1635778, 43934 ^ [_1635776, _1635778])))]]], (43936 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 43934 ^ [_1635776, _1635778])))]]], (12681 ^ _775212) ^ [_984386, _984388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _984386), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984388), _984386)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _984386, _984388) = _984386)], (2420 ^ _775212) ^ [_810554, _810556, _810558, _810560, _810562, _810564] : [-(c_Nitpick_Oof__frac(_810564, _810560, _810556) = c_Nitpick_Oof__frac(_810562, _810558, _810554)), _810564 = _810562, _810560 = _810558, _810556 = _810554], (32273 ^ _775212) ^ [_1359564, _1359566, _1359568, _1359570] : [32274 ^ _775212 : [(32277 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1359568), _1359570)))], (32275 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1359564), _1359566)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1359564, _1359568)), c_Sum__Type_OPlus(_1359564, _1359568, _1359566, _1359570)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20139 ^ _775212) ^ [_1118823, _1118825, _1118827, _1118829] : [class_Fields_Ofield(_1118823), -(_1118825 = c_Groups_Ozero__class_Ozero(_1118823)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118823), _1118827), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118823), _1118829), _1118825)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118823), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118823), _1118825), _1118827)), _1118829)), _1118825))], (29722 ^ _775212) ^ [_1304698, _1304700, _1304702, _1304704] : [hBOOL(hAPP(hAPP(c_member(_1304698), _1304700), _1304702)), -(hBOOL(hAPP(hAPP(c_member(_1304698), _1304700), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304698, tc_HOL_Obool)), _1304704), _1304702))))], (14805 ^ _775212) ^ [_1023167, _1023169, _1023171] : [class_Power_Opower(_1023167), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1023167), _1023169), hAPP(c_Nat_OSuc, _1023171)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023167), _1023169), hAPP(hAPP(c_Power_Opower__class_Opower(_1023167), _1023169), _1023171)))], (38403 ^ _775212) ^ [_1497092, _1497094, _1497096, _1497098, _1497100] : [c_Relation_Orefl__on(_1497092, _1497094, _1497096), hBOOL(hAPP(hAPP(c_member(tc_prod(_1497092, _1497092)), hAPP(hAPP(c_Product__Type_OPair(_1497092, _1497092), _1497098), _1497100)), _1497096)), -(hBOOL(hAPP(hAPP(c_member(_1497092), _1497098), _1497094)))], (34771 ^ _775212) ^ [_1413872, _1413874] : [class_Lattices_Obounded__lattice__top(_1413872), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1413872), _1413874), c_Orderings_Otop__class_Otop(_1413872)) = _1413874)], (35063 ^ _775212) ^ [_1420236, _1420238, _1420240, _1420242] : [hBOOL(hAPP(hAPP(c_member(_1420236), _1420238), _1420240)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420236, tc_HOL_Obool)), _1420240), hAPP(hAPP(c_Set_Oinsert(_1420236), _1420238), _1420242)) = hAPP(hAPP(c_Set_Oinsert(_1420236), _1420238), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420236, tc_HOL_Obool)), _1420240), _1420242)))], (38642 ^ _775212) ^ [_1501435, _1501437, _1501439] : [class_Groups_Oab__semigroup__mult(_1501435), -(_1501437 = c_Orderings_Obot__class_Obot(tc_fun(_1501435, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1501435), _1501437)), -(hBOOL(hAPP(hAPP(c_member(_1501435), _1501439), _1501437))), -(hAPP(c_Finite__Set_Ofold1(_1501435, c_Groups_Otimes__class_Otimes(_1501435)), hAPP(hAPP(c_Set_Oinsert(_1501435), _1501439), _1501437)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1501435), _1501439), hAPP(c_Finite__Set_Ofold1(_1501435, c_Groups_Otimes__class_Otimes(_1501435)), _1501437)))], (27087 ^ _775212) ^ [_1252256, _1252258, _1252260, _1252262] : [class_Lattices_Osemilattice__sup(_1252256), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252256), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252256), _1252258), _1252260)), _1252262) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252256), _1252258), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252256), _1252260), _1252262)))], (30310 ^ _775212) ^ [_1320524, _1320526, _1320528] : [hBOOL(hAPP(hAPP(c_member(_1320524), _1320526), _1320528)), -(hAPP(hAPP(c_Set_Oinsert(_1320524), _1320526), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320524, tc_HOL_Obool)), _1320528), hAPP(hAPP(c_Set_Oinsert(_1320524), _1320526), c_Orderings_Obot__class_Obot(tc_fun(_1320524, tc_HOL_Obool))))) = _1320528)], (13215 ^ _775212) ^ [_994161, _994163, _994165] : [hBOOL(hAPP(_994161, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _994163), _994165))), 13220 ^ _775212 : [(13223 ^ _775212) ^ [] : [-(hBOOL(hAPP(_994161, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (13221 ^ _775212) ^ [] : [-(_994165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 13225 ^ _775212 : [(13230 ^ _775212) ^ [] : [-(hBOOL(hAPP(_994161, 13224 ^ [_994161, _994163, _994165])))], (13228 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994165), hAPP(c_Nat_OSuc, 13224 ^ [_994161, _994163, _994165])))))], (13226 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994165), 13224 ^ [_994161, _994163, _994165])), _994163)))]]], (24354 ^ _775212) ^ [_1197978, _1197980, _1197982, _1197984] : [class_Divides_Osemiring__div(_1197978), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197978), _1197980), _1197982)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197978), _1197980), _1197984)), 24365 ^ _775212 : [(24372 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197978), _1197982), _1197984)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197978), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1197978), _1197982), _1197980)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1197978), _1197984), _1197980))))], (24366 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197978), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1197978), _1197982), _1197980)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1197978), _1197984), _1197980))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197978), _1197982), _1197984)))]]], (37008 ^ _775212) ^ [_1463476, _1463478, _1463480, _1463482, _1463484, _1463486] : [c_Fun_Oinj__on(_1463476, _1463478, _1463480, _1463482), hBOOL(hAPP(hAPP(c_member(_1463478), _1463484), hAPP(c_Set_Oimage(_1463476, _1463478, _1463480), _1463482))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1463476, tc_HOL_Obool)), _1463482), _1463486)), -(hBOOL(hAPP(hAPP(c_member(_1463476), hAPP(c_Fun_Othe__inv__into(_1463476, _1463478, _1463482, _1463480), _1463484)), _1463486)))], (34761 ^ _775212) ^ [_1413695, _1413697] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413695, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1413695, tc_HOL_Obool))), _1413697) = _1413697)], (24134 ^ _775212) ^ [_1194400, _1194402, _1194404] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194400), _1194402)), _1194402 = _1194404, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194400), _1194404)))], (44266 ^ _775212) ^ [_1644824, _1644826, _1644828, _1644830, _1644832, _1644834] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644824, _1644824)), hAPP(hAPP(c_Product__Type_OPair(_1644824, _1644824), _1644826), _1644828)), c_Transitive__Closure_Ortrancl(_1644824, _1644830))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644824), tc_List_Olist(_1644824))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644824), tc_List_Olist(_1644824)), _1644832), _1644834)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1644824), c_List_Olistrel1(_1644824, _1644830)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644824), tc_List_Olist(_1644824))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644824), tc_List_Olist(_1644824)), hAPP(hAPP(c_List_Olist_OCons(_1644824), _1644826), _1644832)), hAPP(hAPP(c_List_Olist_OCons(_1644824), _1644828), _1644834))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1644824), c_List_Olistrel1(_1644824, _1644830)))))], (14090 ^ _775212) ^ [_1009705, _1009707, _1009709] : [class_Fields_Olinordered__field__inverse__zero(_1009705), 14096 ^ _775212 : [(14101 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009705), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009705), 14095 ^ [_1009705, _1009707, _1009709]), _1009707)), _1009709))], (14099 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009705), 14095 ^ [_1009705, _1009707, _1009709]), c_Groups_Oone__class_Oone(_1009705))))], (14097 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009705), c_Groups_Ozero__class_Ozero(_1009705)), 14095 ^ [_1009705, _1009707, _1009709])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009705), _1009707), _1009709)))], (4044 ^ _775212) ^ [_836598, _836600] : [_836600 = _836598, -(c_Set_OPow(_836600) = c_Set_OPow(_836598))], (18299 ^ _775212) ^ [_1085960, _1085962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085960), _1085962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1085960)), c_Int_OBit0(_1085962))))], (44827 ^ _775212) ^ [_1660834, _1660836, _1660838, _1660840] : [-(hBOOL(hAPP(hAPP(c_member(_1660834), _1660836), hAPP(c_List_Oset(_1660834), _1660838)))), hBOOL(hAPP(hAPP(c_member(_1660834), _1660836), hAPP(c_List_Oset(_1660834), c_List_Osublist(_1660834, _1660838, _1660840))))], (8159 ^ _775212) ^ [_906749, _906751] : [class_Groups_Olinordered__ab__group__add(_906749), 8162 ^ _775212 : [(8169 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906749), c_Groups_Ozero__class_Ozero(_906749)), _906751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906749), hAPP(c_Groups_Ouminus__class_Ouminus(_906749), _906751)), _906751)))], (8163 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906749), hAPP(c_Groups_Ouminus__class_Ouminus(_906749), _906751)), _906751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906749), c_Groups_Ozero__class_Ozero(_906749)), _906751)))]]], (35009 ^ _775212) ^ [_1419175, _1419177, _1419179] : [class_Lattices_Oboolean__algebra(_1419175), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1419175), _1419177), _1419179) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419175), _1419177), hAPP(c_Groups_Ouminus__class_Ouminus(_1419175), _1419179)))], (51442 ^ _775212) ^ [_1808539, _1808541, _1808543] : [c_Relation_Otrans(_1808539, _1808541), c_Relation_Otrans(_1808539, _1808543), -(c_Relation_Otrans(_1808539, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1808539, _1808539), tc_HOL_Obool)), _1808541), _1808543)))], (25593 ^ _775212) ^ [_1221312, _1221314, _1221316, _1221318, _1221320] : [class_Groups_Ocomm__monoid__add(_1221312), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221314, _1221312), hAPP(hAPP(c_COMBS(_1221314, _1221312, _1221312), hAPP(hAPP(c_COMBB(_1221312, tc_fun(_1221312, _1221312), _1221314), c_Groups_Oplus__class_Oplus(_1221312)), _1221316)), _1221318)), _1221320) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221312), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221314, _1221312), _1221316), _1221320)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221314, _1221312), _1221318), _1221320)))], (22982 ^ _775212) ^ [_1173066, _1173068, _1173070] : [class_Orderings_Olinorder(_1173066), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173066), _1173068), _1173070)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173066), _1173070), _1173068) = _1173070)], (30106 ^ _775212) ^ [_1314830, _1314832, _1314834, _1314836] : [-(hBOOL(hAPP(hAPP(c_member(_1314830), _1314832), _1314834))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314830, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1314830), _1314832), _1314836)), _1314834) = hAPP(hAPP(c_Set_Oinsert(_1314830), _1314832), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314830, tc_HOL_Obool)), _1314836), _1314834)))], (18593 ^ _775212) ^ [_1091113] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091113), _1091113)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1091113)], (37096 ^ _775212) ^ [_1465217, _1465219, _1465221, _1465223] : [c_Fun_Oinj__on(_1465217, _1465219, _1465221, _1465223), -(hAPP(c_Set_Oimage(_1465219, _1465217, c_Fun_Othe__inv__into(_1465217, _1465219, _1465223, _1465221)), hAPP(c_Set_Oimage(_1465217, _1465219, _1465221), _1465223)) = _1465223)], (36619 ^ _775212) ^ [_1455093, _1455095, _1455097, _1455099, _1455101] : [c_Fun_Oinj__on(_1455093, _1455095, _1455097, c_Orderings_Otop__class_Otop(tc_fun(_1455093, tc_HOL_Obool))), 36622 ^ _775212 : [(36629 ^ _775212) ^ [] : [_1455099 = _1455101, -(hAPP(c_Set_Oimage(_1455093, _1455095, _1455097), _1455099) = hAPP(c_Set_Oimage(_1455093, _1455095, _1455097), _1455101))], (36623 ^ _775212) ^ [] : [hAPP(c_Set_Oimage(_1455093, _1455095, _1455097), _1455099) = hAPP(c_Set_Oimage(_1455093, _1455095, _1455097), _1455101), -(_1455099 = _1455101)]]], (18573 ^ _775212) ^ [_1090728, _1090730] : [class_Rings_Olinordered__idom(_1090728), -(hAPP(c_Groups_Oabs__class_Oabs(_1090728), hAPP(hAPP(c_Power_Opower__class_Opower(_1090728), _1090730), 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(_1090728), _1090730), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19565 ^ _775212) ^ [_1108536, _1108538, _1108540] : [class_Rings_Odivision__ring(_1108536), -(_1108538 = c_Groups_Ozero__class_Ozero(_1108536)), 19572 ^ _775212 : [(19579 ^ _775212) ^ [] : [_1108540 = _1108538, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108536), _1108540), _1108538) = c_Groups_Oone__class_Oone(_1108536))], (19573 ^ _775212) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108536), _1108540), _1108538) = c_Groups_Oone__class_Oone(_1108536), -(_1108540 = _1108538)]]], (44429 ^ _775212) ^ [_1649844, _1649846, _1649848, _1649850, _1649852, _1649854] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649844, _1649844)), hAPP(hAPP(c_Product__Type_OPair(_1649844, _1649844), _1649846), _1649848)), _1649850)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649844), tc_List_Olist(_1649844))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649844), tc_List_Olist(_1649844)), _1649852), _1649854)), c_List_Olistrel(_1649844, _1649850))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649844), tc_List_Olist(_1649844))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649844), tc_List_Olist(_1649844)), hAPP(hAPP(c_List_Olist_OCons(_1649844), _1649846), _1649852)), hAPP(hAPP(c_List_Olist_OCons(_1649844), _1649848), _1649854))), c_List_Olistrel(_1649844, _1649850))))], (27662 ^ _775212) ^ [_1263439, _1263441, _1263443] : [class_Orderings_Olinorder(_1263439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263439), _1263441), _1263443)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263439, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1263439, _1263441), _1263443)), hAPP(c_SetInterval_Oord__class_OatLeast(_1263439), _1263443)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1263439), _1263441))], (13270 ^ _775212) ^ [_995333] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _995333) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7526 ^ _775212) ^ [_895271, _895273] : [class_Rings_Olinordered__idom(_895271), 7529 ^ _775212 : [(7536 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _895273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_895271), c_Groups_Ozero__class_Ozero(_895271)), hAPP(c_Int_Oring__1__class_Oof__int(_895271), _895273))))], (7530 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_895271), c_Groups_Ozero__class_Ozero(_895271)), hAPP(c_Int_Oring__1__class_Oof__int(_895271), _895273))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _895273)))]]], (26435 ^ _775212) ^ [_1239564, _1239566, _1239568, _1239570] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1239564, tc_Nat_Onat), _1239566), _1239568) = hAPP(c_Nat_OSuc, _1239570), 26439 ^ _775212 : [(26442 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1239566, 26438 ^ [_1239564, _1239566, _1239568, _1239570]))))], (26440 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1239564), 26438 ^ [_1239564, _1239566, _1239568, _1239570]), _1239568)))]]], (27321 ^ _775212) ^ [_1256583, _1256585, _1256587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256583, tc_HOL_Obool)), _1256585), _1256587)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256583, tc_HOL_Obool)), _1256585), _1256587) = _1256587)], (34421 ^ _775212) ^ [_1406554, _1406556, _1406558, _1406560] : [hBOOL(hAPP(hAPP(c_member(_1406554), _1406556), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406554, tc_HOL_Obool)), _1406558), _1406560))), 34424 ^ _775212 : [(34427 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406554), _1406556), _1406560)))], (34425 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406554), _1406556), _1406558)))]]], (22560 ^ _775212) ^ [_1164632, _1164634, _1164636, _1164638] : [class_Orderings_Olinorder(_1164632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164632), _1164634), _1164636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164632), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1164632), _1164638), _1164634)), _1164636)))], (26817 ^ _775212) ^ [_1246597, _1246599, _1246601, _1246603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246597, _1246599)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246601, _1246603))), 26820 ^ _775212 : [(26821 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246597), _1246599)), 26824 ^ _775212 : [(26829 ^ _775212) ^ [] : [26830 ^ _775212 : [(26833 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246597), _1246601))], (26831 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246601), _1246597)))]], 26834 ^ _775212 : [(26837 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246603), _1246599))], (26835 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246599), _1246603)))]]], (26827 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246599), _1246603)))], (26825 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246601), _1246597)))]]], (26839 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246601), _1246603)))]]], (39566 ^ _775212) ^ [_1529834, _1529836, _1529838] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1529834, _1529836)), _1529838)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1529836), hAPP(c_Relation_ORange(_1529834, _1529836), _1529838))))], (38238 ^ _775212) ^ [_1493940, _1493942, _1493944] : [c_Relation_Orefl__on(_1493940, _1493942, _1493944), 38241 ^ _775212 : [(38244 ^ _775212) ^ [_1494122] : [hBOOL(hAPP(hAPP(c_member(_1493940), _1494122), _1493942)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1493940, _1493940)), hAPP(hAPP(c_Product__Type_OPair(_1493940, _1493940), _1494122), _1494122)), _1493944)))], (38242 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1493940, _1493940), tc_HOL_Obool)), _1493944), hAPP(hAPP(c_Product__Type_OSigma(_1493940, _1493940), _1493942), hAPP(c_COMBK(tc_fun(_1493940, tc_HOL_Obool), _1493940), _1493942)))))]]], (44680 ^ _775212) ^ [_1656932, _1656934, _1656936, _1656938] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656932), tc_List_Olist(_1656932))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656932), tc_List_Olist(_1656932)), _1656934), _1656936)), c_List_Olexord(_1656932, _1656938)))), 44681 ^ _775212 : [(44688 ^ _775212) ^ [_1657239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657239), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656932)), _1656934)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656932)), _1656936)))), hAPP(hAPP(c_List_Otake(_1656932), _1657239), _1656934) = hAPP(hAPP(c_List_Otake(_1656932), _1657239), _1656936), hBOOL(hAPP(hAPP(c_member(tc_prod(_1656932, _1656932)), hAPP(hAPP(c_Product__Type_OPair(_1656932, _1656932), hAPP(hAPP(c_List_Onth(_1656932), _1656934), _1657239)), hAPP(hAPP(c_List_Onth(_1656932), _1656936), _1657239))), _1656938))], (44682 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656932)), _1656934)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656932)), _1656936))), hAPP(hAPP(c_List_Otake(_1656932), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656932)), _1656934)), _1656936) = _1656934]]], (47006 ^ _775212) ^ [_1712398, _1712400, _1712402] : [-(_1712398 = c_List_Olist_ONil(_1712400)), -(c_List_Olast(_1712400, hAPP(hAPP(c_List_Oappend(_1712400), _1712402), _1712398)) = c_List_Olast(_1712400, _1712398))], (34059 ^ _775212) ^ [_1397894, _1397896] : [-(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), _1397894), _1397896)), 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), _1397896), _1397894)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (39591 ^ _775212) ^ [_1530484, _1530486, _1530488, _1530490] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1530484, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1530484, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1530486, _1530484), _1530488)), hAPP(c_Relation_ORange(_1530486, _1530484), _1530490))), hAPP(c_Relation_ORange(_1530486, _1530484), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1530486, _1530484), tc_HOL_Obool)), _1530488), _1530490)))))], (36097 ^ _775212) ^ [_1444805, _1444807, _1444809, _1444811, _1444813] : [class_Groups_Ocomm__monoid__add(_1444805), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444807), _1444809)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444807), _1444811)), 36111 ^ _775212 : [(36114 ^ _775212) ^ [] : [hAPP(_1444813, 36110 ^ [_1444805, _1444807, _1444809, _1444811, _1444813]) = c_Groups_Ozero__class_Ozero(_1444805)], (36112 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1444807), 36110 ^ [_1444805, _1444807, _1444809, _1444811, _1444813]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444807, tc_HOL_Obool)), _1444809), _1444811))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444807, _1444805), _1444813), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1444807, tc_HOL_Obool)), _1444809), _1444811)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1444805), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444807, _1444805), _1444813), _1444809)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444807, _1444805), _1444813), _1444811)))], (50153 ^ _775212) ^ [_1780616, _1780618, _1780620, _1780622, _1780624] : [-(hAPP(hAPP(c_List_Olist_OCons(_1780616), _1780618), _1780620) = hAPP(c_List_Ofilter(_1780616, _1780622), _1780624)), 50154 ^ _775212 : [(50155 ^ _775212) ^ [_1780744, _1780746] : [_1780624 = hAPP(hAPP(c_List_Oappend(_1780616), _1780746), hAPP(hAPP(c_List_Olist_OCons(_1780616), _1780618), _1780744)), 50161 ^ _775212 : [(50164 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1780622, 50160 ^ [_1780616, _1780618, _1780620, _1780622, _1780624, _1780744, _1780746])))], (50162 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1780616), 50160 ^ [_1780616, _1780618, _1780620, _1780622, _1780624, _1780744, _1780746]), hAPP(c_List_Oset(_1780616), _1780746))))]], hBOOL(hAPP(_1780622, _1780618)), _1780620 = hAPP(c_List_Ofilter(_1780616, _1780622), _1780744)]]], (44491 ^ _775212) ^ [_1651925, _1651927, _1651929, _1651931, _1651933] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651925), tc_List_Olist(_1651925))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651925), tc_List_Olist(_1651925)), hAPP(hAPP(c_List_Olist_OCons(_1651925), _1651927), _1651929)), _1651931)), c_List_Olistrel(_1651925, _1651933))), 44496 ^ _775212 : [(44501 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651925), tc_List_Olist(_1651925))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651925), tc_List_Olist(_1651925)), _1651929), 44495 ^ [_1651925, _1651927, _1651929, _1651931, _1651933])), c_List_Olistrel(_1651925, _1651933))))], (44499 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651925, _1651925)), hAPP(hAPP(c_Product__Type_OPair(_1651925, _1651925), _1651927), 44494 ^ [_1651925, _1651927, _1651929, _1651931, _1651933])), _1651933)))], (44497 ^ _775212) ^ [] : [-(_1651931 = hAPP(hAPP(c_List_Olist_OCons(_1651925), 44494 ^ [_1651925, _1651927, _1651929, _1651931, _1651933]), 44495 ^ [_1651925, _1651927, _1651929, _1651931, _1651933]))]]], (35091 ^ _775212) ^ [_1421055, _1421057, _1421059, _1421061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1421055, tc_HOL_Obool)), _1421061), _1421057)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421055, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421055, tc_HOL_Obool)), _1421057), _1421059)), _1421061) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421055, tc_HOL_Obool)), _1421057), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421055, tc_HOL_Obool)), _1421059), _1421061)))], (11794 ^ _775212) ^ [_968762, _968764] : [11795 ^ _775212 : [(11798 ^ _775212) ^ [] : [_968762 = _968764], (11796 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968762), _968764))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968762), _968764)))], (10888 ^ _775212) ^ [_953151, _953153] : [10889 ^ _775212 : [(10890 ^ _775212) ^ [_953204] : [_953153 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _953151), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _953204))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _953151), _953153)))], (38014 ^ _775212) ^ [_1487552, _1487554, _1487556, _1487558] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1487552, _1487554)), hAPP(hAPP(c_Product__Type_OSigma(_1487552, _1487554), _1487556), hAPP(c_COMBK(tc_fun(_1487554, tc_HOL_Obool), _1487552), _1487558)))), -(_1487556 = c_Orderings_Obot__class_Obot(tc_fun(_1487552, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1487554), _1487558)))], (7312 ^ _775212) ^ [_891371, _891373, _891375] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_891371, _891373, _891375)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_891375)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23442 ^ _775212) ^ [_1181973, _1181975, _1181977, _1181979, _1181981, _1181983, _1181985] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1181973, _1181975, _1181977, _1181979), _1181981), _1181983), _1181985) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1181975, _1181977, _1181979), _1181983), hAPP(_1181981, _1181985)))], (33819 ^ _775212) ^ [_1392457, _1392459, _1392461] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1392457), _1392459)), hBOOL(hAPP(_1392461, _1392459)), 33830 ^ _775212 : [(33833 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1392457), 33828 ^ [_1392457, _1392459, _1392461]), 33829 ^ [_1392457, _1392459, _1392461])))], (33835 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1392461, 33829 ^ [_1392457, _1392459, _1392461])))], (33837 ^ _775212) ^ [] : [hBOOL(hAPP(_1392461, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1392457, tc_HOL_Obool)), 33829 ^ [_1392457, _1392459, _1392461]), hAPP(hAPP(c_Set_Oinsert(_1392457), 33828 ^ [_1392457, _1392459, _1392461]), c_Orderings_Obot__class_Obot(tc_fun(_1392457, tc_HOL_Obool))))))], (33831 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1392457), 33829 ^ [_1392457, _1392459, _1392461])))]], -(hBOOL(hAPP(_1392461, c_Orderings_Obot__class_Obot(tc_fun(_1392457, tc_HOL_Obool)))))], (6703 ^ _775212) ^ [_881749, _881751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881749), _881751)), _881749))], (23440 ^ _775212) ^ [_1181922, _1181924, _1181926, _1181928, _1181930] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1181922, _1181924, _1181922, _1181926), hAPP(c_Product__Type_OPair(_1181924, _1181922), _1181928)), _1181930) = hAPP(_1181930, _1181928))], (39759 ^ _775212) ^ [_1536099, _1536101] : [c_Wellfounded_Owf(_1536099, _1536101), -(c_Wellfounded_Owf(tc_fun(_1536099, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1536099, _1536101)))], (50263 ^ _775212) ^ [_1783139, _1783141] : [class_Enum_Oenum(_1783139), 50266 ^ _775212 : [(50274 ^ _775212) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1783139), _1783141)), 50277 ^ _775212 : [(50278 ^ _775212) ^ [_1783357] : [-(hBOOL(hAPP(_1783141, _1783357)))]]], (50267 ^ _775212) ^ [] : [hBOOL(hAPP(_1783141, 50268 ^ [_1783139, _1783141])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1783139), _1783141)))]]], (34509 ^ _775212) ^ [_1408602, _1408604, _1408606, _1408608] : [class_Lattices_Odistrib__lattice(_1408602), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408602), _1408604), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408602), _1408606), _1408608)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408602), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408602), _1408604), _1408606)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408602), _1408604), _1408608)))], (12699 ^ _775212) ^ [_984692, _984694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984692), 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, _984694, _984692)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21603 ^ _775212) ^ [_1145140, _1145142] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145140))), 21606 ^ _775212 : [(21613 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145142))), -(c_Divides_Odivmod__int(_1145140, _1145142) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1145140), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1145142))))], (21607 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145142)), -(c_Divides_Odivmod__int(_1145140, _1145142) = c_Divides_OnegDivAlg(_1145140, _1145142))]]], (29064 ^ _775212) ^ [_1291466, _1291468, _1291470, _1291472] : [-(_1291466 = c_Orderings_Obot__class_Obot(tc_fun(_1291468, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1291468, _1291470, hAPP(c_COMBK(_1291470, _1291468), _1291472)), _1291466) = hAPP(hAPP(c_Set_Oinsert(_1291470), _1291472), c_Orderings_Obot__class_Obot(tc_fun(_1291470, tc_HOL_Obool))))], (46794 ^ _775212) ^ [_1708020, _1708022, _1708024] : [-(hAPP(c_List_Orotate(_1708020, hAPP(c_Nat_OSuc, _1708022)), _1708024) = hAPP(c_List_Orotate1(_1708020), hAPP(c_List_Orotate(_1708020, _1708022), _1708024)))], (23330 ^ _775212) ^ [_1179836] : [class_Orderings_Oord(_1179836), -(c_Orderings_Oord__class_Omax(_1179836) = c_Orderings_Oord_Omax(_1179836, c_Orderings_Oord__class_Oless__eq(_1179836)))], (42447 ^ _775212) ^ [_1598576, _1598578, _1598580, _1598582, _1598584] : [hBOOL(hAPP(hAPP(c_member(_1598576), _1598578), _1598580)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1598582, tc_HOL_Obool)), hAPP(_1598584, _1598578)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598576, tc_fun(_1598582, tc_HOL_Obool)), _1598580), _1598584)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598576, tc_fun(_1598582, tc_HOL_Obool)), _1598580), _1598584))], (30873 ^ _775212) ^ [_1332759, _1332761, _1332763, _1332765] : [hBOOL(hAPP(hAPP(_1332763, _1332765), _1332761)), -(hBOOL(hAPP(hAPP(c_member(_1332759), _1332761), c_SetInterval_Oord_OgreaterThan(_1332759, _1332763, _1332765))))], (42557 ^ _775212) ^ [_1601604, _1601606, _1601608] : [-(hAPP(c_Relation_ODomain(_1601604, _1601606), hAPP(c_Relation_Oconverse(_1601606, _1601604), _1601608)) = hAPP(c_Relation_ORange(_1601606, _1601604), _1601608))], (47488 ^ _775212) ^ [_1722501, _1722503, _1722505, _1722507] : [hBOOL(hAPP(c_List_Olistsp(_1722501, _1722503), _1722505)), hBOOL(hAPP(c_List_Olistsp(_1722501, _1722507), _1722505)), -(hBOOL(hAPP(c_List_Olistsp(_1722501, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1722501, tc_HOL_Obool)), _1722503), _1722507)), _1722505)))], (52451 ^ _775212) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (34130 ^ _775212) ^ [_1399907, _1399909, _1399911] : [_1399909 = c_Orderings_Obot__class_Obot(tc_fun(_1399907, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399907), _1399909), _1399911) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399907, tc_HOL_Obool), tc_HOL_Obool)))], (16419 ^ _775212) ^ [_1054225, _1054227, _1054229] : [class_Int_Onumber__ring(_1054225), -(hAPP(c_Int_Onumber__class_Onumber__of(_1054225), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1054227), _1054229)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054225), hAPP(c_Int_Onumber__class_Onumber__of(_1054225), _1054227)), hAPP(c_Int_Onumber__class_Onumber__of(_1054225), _1054229)))], (51252 ^ _775212) ^ [_1804153, _1804155, _1804157] : [c_List_Olist__ex(_1804153, _1804155, _1804157), 51256 ^ _775212 : [(51259 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1804155, 51255 ^ [_1804153, _1804155, _1804157])))], (51257 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804153), 51255 ^ [_1804153, _1804155, _1804157]), hAPP(c_List_Oset(_1804153), _1804157))))]]], (47694 ^ _775212) ^ [_1726885, _1726887, _1726889, _1726891, _1726893, _1726895, _1726897] : [-(c_List_Olist__all2(_1726885, _1726887, _1726889, hAPP(hAPP(c_List_Olist_OCons(_1726885), _1726891), _1726893), hAPP(hAPP(c_List_Olist_OCons(_1726887), _1726895), _1726897))), hBOOL(hAPP(hAPP(_1726889, _1726891), _1726895)), c_List_Olist__all2(_1726885, _1726887, _1726889, _1726893, _1726897)], (34595 ^ _775212) ^ [_1410651, _1410653, _1410655, _1410657] : [class_Lattices_Osemilattice__inf(_1410651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410651), _1410653), _1410655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410651), _1410653), _1410657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410651), _1410653), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1410651), _1410655), _1410657))))], (41915 ^ _775212) ^ [_1584563, _1584565] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1584563, _1584563, _1584563), _1584565), c_Transitive__Closure_Ortrancl(_1584563, _1584565)) = hAPP(hAPP(c_Relation_Orel__comp(_1584563, _1584563, _1584563), c_Transitive__Closure_Ortrancl(_1584563, _1584565)), _1584565))], (43535 ^ _775212) ^ [_1625926, _1625928] : [class_Complete__Lattice_Ocomplete__lattice(_1625926), -(c_Complete__Lattice_OSup__class_OSup(_1625926, hAPP(hAPP(c_Set_Oinsert(_1625926), _1625928), c_Orderings_Obot__class_Obot(tc_fun(_1625926, tc_HOL_Obool)))) = _1625928)], (45483 ^ _775212) ^ [_1678180] : [45485 ^ _775212 : [(45488 ^ _775212) ^ [] : [45484 ^ [_1678180] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45486 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 45484 ^ [_1678180]), hAPP(c_List_Oset(tc_Nat_Onat), _1678180))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1678180) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5915 ^ _775212) ^ [_868909, _868911, _868913, _868915, _868917, _868919] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_868909, _868911, _868913), _868915, _868917, _868919)), 5916 ^ _775212 : [(5923 ^ _775212) ^ [] : [-(hBOOL(hAPP(_868909, _868915))), c_Natural_Oevaln(_868913, _868915, _868917, _868919)], (5917 ^ _775212) ^ [] : [hBOOL(hAPP(_868909, _868915)), c_Natural_Oevaln(_868911, _868915, _868917, _868919)]]], (27593 ^ _775212) ^ [_1262140, _1262142, _1262144, _1262146, _1262148] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1262140, tc_fun(_1262142, tc_HOL_Obool)), _1262144), _1262146), _1262148)), 27597 ^ _775212 : [(27600 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1262146, 27596 ^ [_1262140, _1262142, _1262144, _1262146, _1262148]), _1262148)))], (27598 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1262140), 27596 ^ [_1262140, _1262142, _1262144, _1262146, _1262148]), _1262144)))]]], (10547 ^ _775212) ^ [_947283, _947285] : [class_Groups_Olinordered__ab__group__add(_947283), 10550 ^ _775212 : [(10557 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947283), _947285), c_Groups_Ozero__class_Ozero(_947283))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947283), _947285), hAPP(c_Groups_Ouminus__class_Ouminus(_947283), _947285))))], (10551 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947283), _947285), hAPP(c_Groups_Ouminus__class_Ouminus(_947283), _947285))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947283), _947285), c_Groups_Ozero__class_Ozero(_947283))))]]], (41011 ^ _775212) ^ [_1565223, _1565225, _1565227, _1565229] : [class_Groups_Ocomm__monoid__mult(_1565223), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565225), _1565227)), 41021 ^ _775212 : [(41024 ^ _775212) ^ [] : [hAPP(_1565229, 41020 ^ [_1565223, _1565225, _1565227, _1565229]) = c_Groups_Oone__class_Oone(_1565223)], (41022 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565225), 41020 ^ [_1565223, _1565225, _1565227, _1565229]), _1565227)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1565223, _1565225, c_Groups_Otimes__class_Otimes(_1565223)), _1565229), c_Groups_Oone__class_Oone(_1565223)), _1565227) = c_Groups_Oone__class_Oone(_1565223))], (18821 ^ _775212) ^ [_1095230, _1095232, _1095234] : [class_Rings_Ocomm__semiring__1(_1095230), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1095230), _1095232), 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)))), _1095234))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095230), _1095232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095230), hAPP(hAPP(c_Power_Opower__class_Opower(_1095230), _1095232), _1095234)), hAPP(hAPP(c_Power_Opower__class_Opower(_1095230), _1095232), _1095234))))], (21303 ^ _775212) ^ [_1140129, _1140131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1140129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1140131)), -(c_Divides_OposDivAlg(_1140129, _1140131) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1140129), _1140131)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1140129, _1140131)))], (51781 ^ _775212) ^ [_1816196, _1816198, _1816200] : [c_Relation_Osym(_1816196, _1816198), c_Relation_Osym(_1816196, _1816200), -(c_Relation_Osym(_1816196, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1816196, _1816196), tc_HOL_Obool)), _1816198), _1816200)))], (48623 ^ _775212) ^ [_1748792, _1748794] : [class_Orderings_Olinorder(_1748792), -(c_List_Olinorder__class_Osorted(_1748792, hAPP(hAPP(c_List_Olist_OCons(_1748792), _1748794), c_List_Olist_ONil(_1748792))))], (6707 ^ _775212) ^ [_881851, _881853, _881855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881851), _881853)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881851), _881855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _881853), _881855)))], (18209 ^ _775212) ^ [_1084403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1084403)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084403), c_Int_OPls)))], (27069 ^ _775212) ^ [_1251827, _1251829, _1251831, _1251833] : [class_Lattices_Osemilattice__sup(_1251827), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251827), _1251829), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251827), _1251831), _1251833)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251827), _1251831), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251827), _1251829), _1251833)))], (26551 ^ _775212) ^ [_1241976, _1241978] : [class_Groups_Oordered__ab__group__add(_1241976), -(hAPP(c_Set_Oimage(_1241976, _1241976, c_Groups_Ouminus__class_Ouminus(_1241976)), hAPP(c_SetInterval_Oord__class_OlessThan(_1241976), _1241978)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1241976), hAPP(c_Groups_Ouminus__class_Ouminus(_1241976), _1241978)))], (19011 ^ _775212) ^ [] : [-(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))], (52139 ^ _775212) ^ [_1822691, _1822693] : [class_Lattices_Odistrib__lattice(_1822691), -(class_Lattices_Odistrib__lattice(tc_fun(_1822693, _1822691)))], (6725 ^ _775212) ^ [_882206, _882208, _882210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882206), _882208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882210), _882208))))], (49798 ^ _775212) ^ [_1772114, _1772116, _1772118] : [hBOOL(hAPP(c_List_Odistinct(_1772114), _1772116)), -(hBOOL(hAPP(c_List_Odistinct(_1772114), c_List_Oinsert(_1772114, _1772118, _1772116))))], (29901 ^ _775212) ^ [_1308085, _1308087, _1308089] : [hBOOL(hAPP(hAPP(c_member(_1308085), _1308087), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308085, tc_HOL_Obool)), _1308089))), hBOOL(hAPP(hAPP(c_member(_1308085), _1308087), _1308089))], (534 ^ _775212) ^ [_783457, _783459, _783461, _783463, _783465, _783467] : [-(c_Finite__Set_Ofolding__one__idem(_783465, _783461, _783457)), c_Finite__Set_Ofolding__one__idem(_783467, _783463, _783459), _783467 = _783465, _783463 = _783461, _783459 = _783457], (24682 ^ _775212) ^ [_1203703, _1203705, _1203707, _1203709] : [class_Divides_Osemiring__div(_1203703), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1203703), _1203705), _1203707)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1203703), _1203709), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1203703), _1203707), _1203705)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1203703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1203703), _1203709), _1203707)), _1203705))], (45411 ^ _775212) ^ [_1675803, _1675805, _1675807, _1675809, _1675811] : [class_Groups_Ocomm__monoid__add(_1675803), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1675803), hAPP(hAPP(c_List_Omap(_1675805, _1675803), hAPP(hAPP(c_COMBS(_1675805, _1675803, _1675803), hAPP(hAPP(c_COMBB(_1675803, tc_fun(_1675803, _1675803), _1675805), c_Groups_Oplus__class_Oplus(_1675803)), _1675807)), _1675809)), _1675811)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1675803), hAPP(c_List_Omonoid__add__class_Olistsum(_1675803), hAPP(hAPP(c_List_Omap(_1675805, _1675803), _1675807), _1675811))), hAPP(c_List_Omonoid__add__class_Olistsum(_1675803), hAPP(hAPP(c_List_Omap(_1675805, _1675803), _1675809), _1675811))))], (5765 ^ _775212) ^ [_866156, _866158, _866160, _866162, _866164, _866166] : [c_Com_Ocom_OCond(_866156, _866158, _866160) = c_Com_Ocom_OCond(_866162, _866164, _866166), 5768 ^ _775212 : [(5773 ^ _775212) ^ [] : [-(_866160 = _866166)], (5771 ^ _775212) ^ [] : [-(_866158 = _866164)], (5769 ^ _775212) ^ [] : [-(_866156 = _866162)]]], (3178 ^ _775212) ^ [_822951, _822953, _822955, _822957, _822959, _822961, _822963, _822965] : [-(c_Nitpick_Oprod(_822965, _822961, _822957, _822953) = c_Nitpick_Oprod(_822963, _822959, _822955, _822951)), _822965 = _822963, _822961 = _822959, _822957 = _822955, _822953 = _822951], (42027 ^ _775212) ^ [_1587167, _1587169, _1587171, _1587173] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587167, _1587167)), hAPP(hAPP(c_Product__Type_OPair(_1587167, _1587167), _1587169), _1587171)), c_Transitive__Closure_Ortrancl(_1587167, _1587173))), hBOOL(hAPP(hAPP(c_member(_1587167), _1587171), c_Wellfounded_Oacc(_1587167, _1587173))), -(hBOOL(hAPP(hAPP(c_member(_1587167), _1587169), c_Wellfounded_Oacc(_1587167, _1587173))))], (39436 ^ _775212) ^ [_1525948, _1525950, _1525952, _1525954] : [-(c_Product__Type_Oapfst(_1525948, _1525950, _1525952, _1525954) = c_Product__Type_Omap__pair(_1525948, _1525950, _1525952, _1525952, _1525954, c_Fun_Oid(_1525952)))], (46468 ^ _775212) ^ [_1701153, _1701155, _1701157, _1701159] : [hBOOL(hAPP(c_List_Odistinct(_1701153), _1701155)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1701153, _1701157)), hAPP(hAPP(c_List_Ozip(_1701153, _1701157), _1701155), _1701159))))], (47150 ^ _775212) ^ [_1715158, _1715160, _1715162] : [-(_1715158 = c_List_Olist_ONil(_1715160)), -(c_List_Obutlast(_1715160, hAPP(hAPP(c_List_Oappend(_1715160), _1715162), _1715158)) = hAPP(hAPP(c_List_Oappend(_1715160), _1715162), c_List_Obutlast(_1715160, _1715158)))], (3882 ^ _775212) ^ [_834123, _834125, _834127, _834129] : [-(c_Finite__Set_Ofold1(_834129, _834125) = c_Finite__Set_Ofold1(_834127, _834123)), _834129 = _834127, _834125 = _834123], (50799 ^ _775212) ^ [_1793819, _1793821, _1793823, _1793825] : [-(c_Predicate_Oconversep(_1793819, _1793821, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793819, tc_fun(_1793821, tc_HOL_Obool))), _1793823), _1793825)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793821, tc_fun(_1793819, tc_HOL_Obool))), c_Predicate_Oconversep(_1793819, _1793821, _1793823)), c_Predicate_Oconversep(_1793819, _1793821, _1793825)))], (6299 ^ _775212) ^ [_874672, _874674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874672), hAPP(c_Nat_OSuc, _874674))), -(_874672 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6307 ^ _775212 : [(6310 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 6306 ^ [_874672, _874674]), _874674)))], (6308 ^ _775212) ^ [] : [-(_874672 = hAPP(c_Nat_OSuc, 6306 ^ [_874672, _874674]))]]], (42645 ^ _775212) ^ [_1603998, _1604000, _1604002, _1604004] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603998, _1603998)), hAPP(hAPP(c_Product__Type_OPair(_1603998, _1603998), _1604000), _1604002)), c_Transitive__Closure_Otrancl(_1603998, hAPP(c_Relation_Oconverse(_1603998, _1603998), _1604004)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603998, _1603998)), hAPP(hAPP(c_Product__Type_OPair(_1603998, _1603998), _1604000), _1604002)), hAPP(c_Relation_Oconverse(_1603998, _1603998), c_Transitive__Closure_Otrancl(_1603998, _1604004)))))], (13597 ^ _775212) ^ [_1000705, _1000707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000705)), 13600 ^ _775212 : [(13607 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000707)), -(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), _1000707), _1000705))))], (13601 ^ _775212) ^ [] : [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), _1000707), _1000705))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000707)))]]], (22194 ^ _775212) ^ [_1156601, _1156603] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156601) = hAPP(c_Nat_OSuc, _1156603), -(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(_1156601))), 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)), _1156603))))))], (28263 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (29030 ^ _775212) ^ [_1290930, _1290932, _1290934] : [class_Orderings_Oorder(_1290930), 29033 ^ _775212 : [(29040 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290930), _1290932), _1290934))), -(c_Orderings_Obot__class_Obot(tc_fun(_1290930, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1290930, _1290932, _1290934))], (29034 ^ _775212) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1290930, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1290930, _1290932, _1290934), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290930), _1290932), _1290934))]]], (9099 ^ _775212) ^ [_922646, _922648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _922646), _922648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _922648), _922646)), -(_922646 = _922648)], (404 ^ _775212) ^ [_781442, _781444, _781446, _781448, _781450, _781452, _781454, _781456] : [-(c_Equiv__Relations_Ocongruent(_781454, _781450, _781446, _781442)), c_Equiv__Relations_Ocongruent(_781456, _781452, _781448, _781444), _781456 = _781454, _781452 = _781450, _781448 = _781446, _781444 = _781442], (18463 ^ _775212) ^ [_1088832] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1088832)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1088832)))], (42970 ^ _775212) ^ [_1612585, _1612587, _1612589] : [c_Relation_Ototal__on(_1612585, _1612587, _1612589), -(c_Relation_Ototal__on(_1612585, _1612587, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1612585, _1612585), tc_HOL_Obool)), _1612589), c_Relation_OId(_1612585))))], (17837 ^ _775212) ^ [_1078067, _1078069] : [c_Int_Oiszero(_1078067, hAPP(c_Int_Onumber__class_Onumber__of(_1078067), c_Int_OBit1(_1078069))), class_Int_Onumber__ring(_1078067), class_Int_Oring__char__0(_1078067)], (46384 ^ _775212) ^ [_1699700, _1699702, _1699704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1699700), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699702)), _1699704))), -(hAPP(hAPP(c_List_Oappend(_1699702), hAPP(hAPP(c_List_Otake(_1699702), _1699700), _1699704)), hAPP(hAPP(c_List_Olist_OCons(_1699702), hAPP(c_List_Ohd(_1699702), hAPP(hAPP(c_List_Odrop(_1699702), _1699700), _1699704))), c_List_Olist_ONil(_1699702))) = hAPP(hAPP(c_List_Otake(_1699702), hAPP(c_Nat_OSuc, _1699700)), _1699704))], (27678 ^ _775212) ^ [_1263761, _1263763, _1263765, _1263767, _1263769] : [class_Complete__Lattice_Ocomplete__lattice(_1263761), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263763, tc_HOL_Obool)), _1263765), _1263767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263761), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1263763, _1263761), _1263765), _1263769)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1263763, _1263761), _1263767), _1263769))))], (28720 ^ _775212) ^ [_1285428, _1285430, _1285432, _1285434] : [_1285434 = c_Orderings_Obot__class_Obot(tc_fun(_1285428, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1285428, _1285430, _1285432), _1285434) = c_Orderings_Obot__class_Obot(tc_fun(_1285430, tc_HOL_Obool)))], (6990 ^ _775212) ^ [_886554, _886556, _886558, _886560] : [class_Orderings_Oorder(_886554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886554), _886556), _886558)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886554), _886560), _886556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_886554), _886560), _886558)))], (11967 ^ _775212) ^ [_971865, _971867] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971865), _971867), 11970 ^ _775212 : [(11973 ^ _775212) ^ [] : [-(_971867 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11971 ^ _775212) ^ [] : [-(_971865 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (47591 ^ _775212) ^ [_1724641, _1724643, _1724645, _1724647, _1724649] : [class_Orderings_Olinorder(_1724641), hBOOL(hAPP(c_List_Odistinct(_1724643), _1724645)), -(hBOOL(hAPP(c_List_Odistinct(_1724643), c_List_Olinorder__class_Oinsort__insert__key(_1724643, _1724641, _1724647, _1724649, _1724645))))], (42836 ^ _775212) ^ [_1609418, _1609420] : [-(c_Relation_Oirrefl(_1609418, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1609418, _1609418), tc_HOL_Obool)), _1609420), c_Relation_OId(_1609418))))], (52641 ^ _775212) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (52447 ^ _775212) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (23878 ^ _775212) ^ [_1190224, _1190226, _1190228, _1190230, _1190232] : [hBOOL(hAPP(_1190224, hAPP(hAPP(c_Product__Type_OPair(_1190226, _1190228), _1190230), _1190232))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1190226, _1190228, tc_HOL_Obool, _1190224), _1190230), _1190232)))], (34919 ^ _775212) ^ [_1416728, _1416730, _1416732, _1416734, _1416736] : [class_Lattices_Olattice(_1416728), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416730, _1416728)), _1416732), _1416734), _1416736) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416728), hAPP(_1416732, _1416736)), hAPP(_1416734, _1416736)))], (17659 ^ _775212) ^ [_1075107, _1075109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1075107)), c_Int_OBit1(_1075109))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1075107), _1075109)))], (21901 ^ _775212) ^ [_1150798, _1150800, _1150802, _1150804, _1150806, _1150808] : [hBOOL(hAPP(_1150798, _1150800)), hBOOL(hAPP(_1150802, _1150804)), 21908 ^ _775212 : [(21911 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1150802, hAPP(c_Product__Type_Osnd(_1150806, _1150808), hAPP(hAPP(c_Product__Type_OPair(_1150806, _1150808), _1150800), _1150804)))))], (21909 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1150798, hAPP(c_Product__Type_Ofst(_1150806, _1150808), hAPP(hAPP(c_Product__Type_OPair(_1150806, _1150808), _1150800), _1150804)))))]]], (28520 ^ _775212) ^ [_1281230, _1281232, _1281234] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1281230), _1281232)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1281230, tc_HOL_Obool)), _1281234), _1281232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1281230), _1281234)), hAPP(c_Finite__Set_Ocard(_1281230), _1281232))))], (40900 ^ _775212) ^ [_1562622, _1562624, _1562626, _1562628, _1562630, _1562632] : [c_Finite__Set_Ofolding__idem(_1562622, _1562624, _1562626, _1562628), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562622), _1562630)), hBOOL(hAPP(hAPP(c_member(_1562622), _1562632), _1562630)), -(hAPP(c_Fun_Ocomp(_1562624, _1562624, _1562624, hAPP(_1562628, _1562630)), hAPP(_1562626, _1562632)) = hAPP(_1562628, _1562630))], (29600 ^ _775212) ^ [_1302301, _1302303] : [_1302303 = c_Orderings_Obot__class_Obot(tc_fun(_1302301, tc_HOL_Obool)), 29603 ^ _775212 : [(29604 ^ _775212) ^ [_1302381] : [hBOOL(hAPP(hAPP(c_member(_1302301), _1302381), _1302303))]]], (11744 ^ _775212) ^ [_968015, _968017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968015), _968017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968015), hAPP(c_Nat_OSuc, _968017))))], (49732 ^ _775212) ^ [_1771048, _1771050, _1771052, _1771054] : [-(hAPP(c_List_OremoveAll(_1771048, _1771050), hAPP(hAPP(c_List_Oappend(_1771048), _1771052), _1771054)) = hAPP(hAPP(c_List_Oappend(_1771048), hAPP(c_List_OremoveAll(_1771048, _1771050), _1771052)), hAPP(c_List_OremoveAll(_1771048, _1771050), _1771054)))], (19171 ^ _775212) ^ [_1101793, _1101795, _1101797] : [class_Fields_Olinordered__field__inverse__zero(_1101793), 19174 ^ _775212 : [(19189 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101793), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101793), _1101795), _1101797)), c_Groups_Ozero__class_Ozero(_1101793)))), 19190 ^ _775212 : [(19197 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101793), _1101795), c_Groups_Ozero__class_Ozero(_1101793))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101793), c_Groups_Ozero__class_Ozero(_1101793)), _1101797))], (19191 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101793), c_Groups_Ozero__class_Ozero(_1101793)), _1101795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101793), _1101797), c_Groups_Ozero__class_Ozero(_1101793)))]]], (19175 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101793), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101793), _1101795), _1101797)), c_Groups_Ozero__class_Ozero(_1101793))), 19180 ^ _775212 : [(19183 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101793), _1101797), c_Groups_Ozero__class_Ozero(_1101793))))], (19181 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101793), c_Groups_Ozero__class_Ozero(_1101793)), _1101795)))]], 19184 ^ _775212 : [(19187 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101793), c_Groups_Ozero__class_Ozero(_1101793)), _1101797)))], (19185 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101793), _1101795), c_Groups_Ozero__class_Ozero(_1101793))))]]]]], (14335 ^ _775212) ^ [_1014430, _1014432] : [class_Groups_Omonoid__mult(_1014430), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1014430), c_Groups_Oone__class_Oone(_1014430)), _1014432) = c_Groups_Oone__class_Oone(_1014430))], (17491 ^ _775212) ^ [_1072230, _1072232] : [class_Int_Onumber__ring(_1072230), class_Rings_Olinordered__idom(_1072230), 17498 ^ _775212 : [(17505 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1072232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072230), c_Groups_Ozero__class_Ozero(_1072230)), hAPP(c_Int_Onumber__class_Onumber__of(_1072230), _1072232))))], (17499 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072230), c_Groups_Ozero__class_Ozero(_1072230)), hAPP(c_Int_Onumber__class_Onumber__of(_1072230), _1072232))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1072232)))]]], (50709 ^ _775212) ^ [_1792170, _1792172, _1792174] : [c_List_Olist_ONil(_1792170) = c_List_Oreplicate(_1792170, _1792172, _1792174), -(_1792172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48185 ^ _775212) ^ [_1738100, _1738102, _1738104] : [-(c_Enum_On__lists(_1738100, hAPP(c_Nat_OSuc, _1738102), _1738104) = c_List_Oconcat(tc_List_Olist(_1738100), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1738100), tc_List_Olist(tc_List_Olist(_1738100))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1738100), tc_List_Olist(_1738100), tc_List_Olist(tc_List_Olist(_1738100))), hAPP(hAPP(c_COMBB(tc_fun(_1738100, tc_List_Olist(_1738100)), tc_fun(tc_List_Olist(_1738100), tc_List_Olist(tc_List_Olist(_1738100))), tc_List_Olist(_1738100)), c_List_Omap(_1738100, tc_List_Olist(_1738100))), hAPP(c_COMBC(_1738100, tc_List_Olist(_1738100), tc_List_Olist(_1738100)), c_List_Olist_OCons(_1738100)))), _1738104)), c_Enum_On__lists(_1738100, _1738102, _1738104))))], (40480 ^ _775212) ^ [_1552944, _1552946, _1552948, _1552950, _1552952, _1552954, _1552956] : [hAPP(c_Fun_Ocomp(_1552944, _1552946, _1552948, _1552950), _1552952) = _1552954, -(hAPP(_1552950, hAPP(_1552952, _1552956)) = hAPP(_1552954, _1552956))], (37429 ^ _775212) ^ [_1472181, _1472183, _1472185, _1472187] : [-(hAPP(c_Set_Ovimage(_1472181, _1472183, _1472185), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1472183, tc_HOL_Obool)), _1472187)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1472181, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1472181, _1472183, _1472185), _1472187)))], (11366 ^ _775212) ^ [_961712, _961714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _961712)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _961714)))), 11369 ^ _775212 : [(11372 ^ _775212) ^ [] : [-(_961714 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11370 ^ _775212) ^ [] : [-(_961712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7973 ^ _775212) ^ [_903328, _903330, _903332] : [class_Rings_Ono__zero__divisors(_903328), -(_903330 = c_Groups_Ozero__class_Ozero(_903328)), -(_903332 = c_Groups_Ozero__class_Ozero(_903328)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903328), _903330), _903332) = c_Groups_Ozero__class_Ozero(_903328)], (51657 ^ _775212) ^ [_1813707, _1813709] : [c_Relation_Oantisym(_1813707, hAPP(c_Relation_Oconverse(_1813707, _1813707), _1813709)), -(c_Relation_Oantisym(_1813707, _1813709))], (3208 ^ _775212) ^ [_823422, _823424, _823426, _823428] : [-(c_Wellfounded_Omin__ext(_823428, _823424) = c_Wellfounded_Omin__ext(_823426, _823422)), _823428 = _823426, _823424 = _823422], (21289 ^ _775212) ^ [_1139964, _1139966] : [_1139964 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1139966, _1139964) = 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), _1139966)))], (17315 ^ _775212) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (14571 ^ _775212) ^ [_1018754, _1018756, _1018758] : [-(hBOOL(hAPP(_1018754, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1018756), _1018758))))), 14574 ^ _775212 : [(14577 ^ _775212) ^ [] : [hBOOL(hAPP(_1018754, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1018756)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1018758))))], (14575 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1018758), _1018756)))]], 14578 ^ _775212 : [(14581 ^ _775212) ^ [] : [hBOOL(hAPP(_1018754, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14579 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1018756), _1018758)))]]], (47000 ^ _775212) ^ [_1712291, _1712293, _1712295] : [_1712291 = c_List_Olist_ONil(_1712293), -(c_List_Olast(_1712293, hAPP(hAPP(c_List_Oappend(_1712293), _1712295), _1712291)) = c_List_Olast(_1712293, _1712295))], (27818 ^ _775212) ^ [_1267605, _1267607, _1267609, _1267611, _1267613] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267605, tc_fun(_1267607, tc_HOL_Obool)), _1267609), hAPP(hAPP(c_COMBS(_1267605, tc_fun(_1267607, tc_HOL_Obool), tc_fun(_1267607, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1267607, tc_HOL_Obool), tc_fun(tc_fun(_1267607, tc_HOL_Obool), tc_fun(_1267607, tc_HOL_Obool)), _1267605), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267607, tc_HOL_Obool))), _1267611)), _1267613)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267607, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267605, tc_fun(_1267607, tc_HOL_Obool)), _1267609), _1267611)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267605, tc_fun(_1267607, tc_HOL_Obool)), _1267609), _1267613)))], (42830 ^ _775212) ^ [_1609185, _1609187] : [-(c_Transitive__Closure_Ortrancl(_1609185, _1609187) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1609185, _1609185), tc_HOL_Obool)), c_Relation_OId(_1609185)), hAPP(hAPP(c_Relation_Orel__comp(_1609185, _1609185, _1609185), c_Transitive__Closure_Ortrancl(_1609185, _1609187)), _1609187)))], (1704 ^ _775212) ^ [_799368, _799370] : [-(class_Divides_Osemiring__div(_799368)), _799370 = _799368, class_Divides_Osemiring__div(_799370)], (5811 ^ _775212) ^ [_866949, _866951, _866953, _866955] : [c_Com_Ocom_OWhile(_866949, _866951) = c_Com_Ocom_OSemi(_866953, _866955)], (37912 ^ _775212) ^ [_1484466, _1484468, _1484470, _1484472, _1484474, _1484476] : [class_Groups_Ocomm__monoid__mult(_1484466), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1484468, _1484466), hAPP(hAPP(c_COMBC(_1484468, tc_fun(_1484470, tc_HOL_Obool), _1484466), hAPP(hAPP(c_COMBB(tc_fun(_1484470, _1484466), tc_fun(tc_fun(_1484470, tc_HOL_Obool), _1484466), _1484468), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1484470, _1484466)), _1484472)), _1484474)), _1484476) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1484468, _1484470), _1484466), hAPP(c_Product__Type_Oprod_Oprod__case(_1484468, _1484470, _1484466), _1484472)), hAPP(hAPP(c_Product__Type_OSigma(_1484468, _1484470), _1484476), hAPP(c_COMBK(tc_fun(_1484470, tc_HOL_Obool), _1484468), _1484474))))], (35285 ^ _775212) ^ [_1425608, _1425610, _1425612] : [class_Orderings_Oorder(_1425608), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425608, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1425608), _1425610)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1425608, _1425610, _1425612)) = c_Orderings_Obot__class_Obot(tc_fun(_1425608, tc_HOL_Obool)))], (14459 ^ _775212) ^ [_1016642, _1016644, _1016646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016642), _1016644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016642), _1016646)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016644), _1016642)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016646), _1016642)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016644), _1016646))], (45742 ^ _775212) ^ [_1683937, _1683939, _1683941] : [-(hAPP(hAPP(c_List_Olist__update(_1683937, c_List_Olist_ONil(_1683937)), _1683939), _1683941) = c_List_Olist_ONil(_1683937))], (16905 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (45678 ^ _775212) ^ [_1682405, _1682407, _1682409, _1682411, _1682413, _1682415] : [hAPP(hAPP(c_List_Olist_OCons(_1682405), _1682407), _1682409) = _1682411, _1682413 = hAPP(hAPP(c_List_Oappend(_1682405), _1682409), _1682415), -(hAPP(hAPP(c_List_Olist_OCons(_1682405), _1682407), _1682413) = hAPP(hAPP(c_List_Oappend(_1682405), _1682411), _1682415))], (44481 ^ _775212) ^ [_1651728, _1651730, _1651732, _1651734, _1651736, _1651738] : [-(c_List_Olistrelp(_1651728, _1651730, hAPP(hAPP(c_List_Olist_OCons(_1651728), _1651732), _1651734), hAPP(hAPP(c_List_Olist_OCons(_1651728), _1651736), _1651738))), hBOOL(hAPP(hAPP(_1651730, _1651732), _1651736)), c_List_Olistrelp(_1651728, _1651730, _1651734, _1651738)], (39325 ^ _775212) ^ [_1521370, _1521372, _1521374] : [class_Orderings_Olinorder(_1521370), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521370), _1521372)), -(_1521372 = c_Orderings_Obot__class_Obot(tc_fun(_1521370, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521370), _1521374)), -(_1521374 = c_Orderings_Obot__class_Obot(tc_fun(_1521370, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1521370), c_Big__Operators_Olattice_OSup__fin(_1521370, c_Orderings_Oord__class_Omax(_1521370), _1521372)), c_Big__Operators_Olattice_OSup__fin(_1521370, c_Orderings_Oord__class_Omax(_1521370), _1521374)) = c_Big__Operators_Olattice_OSup__fin(_1521370, c_Orderings_Oord__class_Omax(_1521370), hAPP(c_Set_OCollect(_1521370), hAPP(hAPP(c_COMBB(tc_fun(_1521370, tc_HOL_Obool), tc_HOL_Obool, _1521370), c_HOL_OEx(_1521370)), hAPP(hAPP(c_COMBB(tc_fun(_1521370, tc_fun(_1521370, tc_HOL_Obool)), tc_fun(_1521370, tc_HOL_Obool), _1521370), hAPP(c_COMBB(tc_fun(_1521370, tc_HOL_Obool), tc_HOL_Obool, _1521370), c_HOL_OEx(_1521370))), hAPP(hAPP(c_COMBC(_1521370, tc_fun(_1521370, tc_fun(_1521370, tc_HOL_Obool)), tc_fun(_1521370, tc_fun(_1521370, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1521370, tc_fun(tc_fun(_1521370, tc_HOL_Obool), tc_fun(_1521370, tc_HOL_Obool))), tc_fun(tc_fun(_1521370, tc_fun(_1521370, tc_HOL_Obool)), tc_fun(_1521370, tc_fun(_1521370, tc_HOL_Obool))), _1521370), c_COMBS(_1521370, tc_fun(_1521370, tc_HOL_Obool), tc_fun(_1521370, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1521370, tc_fun(_1521370, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1521370, tc_fun(tc_fun(_1521370, tc_HOL_Obool), tc_fun(_1521370, tc_HOL_Obool))), _1521370), hAPP(c_COMBB(tc_fun(_1521370, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1521370, tc_HOL_Obool), tc_fun(_1521370, tc_HOL_Obool)), _1521370), c_COMBS(_1521370, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1521370, tc_fun(_1521370, tc_HOL_Obool)), tc_fun(_1521370, tc_fun(_1521370, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1521370), hAPP(c_COMBB(tc_fun(_1521370, tc_HOL_Obool), tc_fun(_1521370, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1521370), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521370), c_fconj))), hAPP(hAPP(c_COMBC(_1521370, tc_fun(_1521370, tc_fun(_1521370, _1521370)), tc_fun(_1521370, tc_fun(_1521370, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1521370, _1521370), tc_fun(_1521370, tc_HOL_Obool)), tc_fun(tc_fun(_1521370, tc_fun(_1521370, _1521370)), tc_fun(_1521370, tc_fun(_1521370, tc_HOL_Obool))), _1521370), c_COMBB(tc_fun(_1521370, _1521370), tc_fun(_1521370, tc_HOL_Obool), _1521370)), hAPP(hAPP(c_COMBB(tc_fun(_1521370, tc_HOL_Obool), tc_fun(tc_fun(_1521370, _1521370), tc_fun(_1521370, tc_HOL_Obool)), _1521370), c_COMBB(_1521370, tc_HOL_Obool, _1521370)), c_fequal))), c_Orderings_Oord__class_Omin(_1521370)))))), hAPP(hAPP(c_COMBC(_1521370, tc_fun(_1521370, tc_HOL_Obool), tc_fun(_1521370, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1521370, tc_HOL_Obool), tc_fun(_1521370, tc_HOL_Obool)), _1521370), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1521370)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521370), c_fconj), hAPP(hAPP(c_COMBC(_1521370, tc_fun(_1521370, tc_HOL_Obool), tc_HOL_Obool), c_member(_1521370)), _1521372)))), hAPP(hAPP(c_COMBC(_1521370, tc_fun(_1521370, tc_HOL_Obool), tc_HOL_Obool), c_member(_1521370)), _1521374))))))))], (5296 ^ _775212) ^ [_856046, _856048, _856050, _856052] : [-(c_Relation_OId__on(_856052, _856048) = c_Relation_OId__on(_856050, _856046)), _856052 = _856050, _856048 = _856046], (52459 ^ _775212) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (45520 ^ _775212) ^ [_1678879, _1678881, _1678883, _1678885, _1678887] : [_1678879 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1678881, _1678883, _1678885), _1678879), _1678887) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1678883), _1678881), c_List_Olist_ONil(_1678883)), _1678887))], (51805 ^ _775212) ^ [_1816566, _1816568] : [c_Relation_Osym(_1816566, _1816568), 51808 ^ _775212 : [(51809 ^ _775212) ^ [_1816672, _1816674] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1816566, _1816566)), hAPP(hAPP(c_Product__Type_OPair(_1816566, _1816566), _1816674), _1816672)), _1816568)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1816566, _1816566)), hAPP(hAPP(c_Product__Type_OPair(_1816566, _1816566), _1816672), _1816674)), _1816568)))]]], (33473 ^ _775212) ^ [_1384058, _1384060, _1384062, _1384064] : [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), _1384058), _1384060)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1384062), _1384064))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1384058), _1384064) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1384062), _1384060))], (7433 ^ _775212) ^ [_893521, _893523, _893525, _893527] : [class_Rings_Ocomm__semiring__1(_893521), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893521), _893523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893521), _893525), _893527)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893521), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893521), _893523), _893525)), _893527))], (37393 ^ _775212) ^ [_1471332, _1471334, _1471336, _1471338, _1471340] : [hBOOL(hAPP(hAPP(c_member(_1471332), hAPP(_1471334, _1471336)), _1471338)), -(hBOOL(hAPP(hAPP(c_member(_1471340), _1471336), hAPP(c_Set_Ovimage(_1471340, _1471332, _1471334), _1471338))))], (38228 ^ _775212) ^ [_1493589, _1493591, _1493593, _1493595, _1493597, _1493599, _1493601, _1493603] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1493589, _1493591)), _1493593), hAPP(c_Set_Oimage(tc_prod(_1493595, _1493597), tc_prod(_1493589, _1493591), c_Product__Type_Omap__pair(_1493595, _1493589, _1493597, _1493591, _1493599, _1493601)), _1493603))), 38233 ^ _775212 : [(38236 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1493595, _1493597)), hAPP(hAPP(c_Product__Type_OPair(_1493595, _1493597), 38231 ^ [_1493589, _1493591, _1493593, _1493595, _1493597, _1493599, _1493601, _1493603]), 38232 ^ [_1493589, _1493591, _1493593, _1493595, _1493597, _1493599, _1493601, _1493603])), _1493603)))], (38234 ^ _775212) ^ [] : [-(_1493593 = hAPP(hAPP(c_Product__Type_OPair(_1493589, _1493591), hAPP(_1493599, 38231 ^ [_1493589, _1493591, _1493593, _1493595, _1493597, _1493599, _1493601, _1493603])), hAPP(_1493601, 38232 ^ [_1493589, _1493591, _1493593, _1493595, _1493597, _1493599, _1493601, _1493603])))]]], (19399 ^ _775212) ^ [_1105889, _1105891, _1105893, _1105895] : [class_Rings_Odivision__ring(_1105889), -(_1105891 = c_Groups_Ozero__class_Ozero(_1105889)), _1105893 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105889), _1105895), _1105891), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105889), _1105893), _1105891) = _1105895)], (18419 ^ _775212) ^ [_1088063, _1088065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088063), _1088065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1088063)), c_Int_OBit1(_1088065))))], (45576 ^ _775212) ^ [_1680169, _1680171] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1680169)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1680171)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1680169), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1680171)) = c_List_Olist_ONil(tc_Int_Oint))], (43700 ^ _775212) ^ [_1629695, _1629697, _1629699, _1629701, _1629703, _1629705, _1629707] : [c_Finite__Set_Ofun__left__comm(_1629695, _1629697, _1629699), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1629695, _1629697, _1629699, _1629701, hAPP(hAPP(c_Set_Oinsert(_1629695), _1629703), _1629705)), _1629707)), -(hBOOL(hAPP(hAPP(c_member(_1629695), _1629703), _1629705))), 43712 ^ _775212 : [(43715 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1629695, _1629697, _1629699, _1629701, _1629705), 43711 ^ [_1629695, _1629697, _1629699, _1629701, _1629703, _1629705, _1629707])))], (43713 ^ _775212) ^ [] : [-(_1629707 = hAPP(hAPP(_1629699, _1629703), 43711 ^ [_1629695, _1629697, _1629699, _1629701, _1629703, _1629705, _1629707]))]]], (7268 ^ _775212) ^ [_890699, _890701] : [class_Groups_Olinordered__ab__group__add(_890699), 7271 ^ _775212 : [(7278 ^ _775212) ^ [] : [_890701 = c_Groups_Ozero__class_Ozero(_890699), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_890699), _890701), _890701) = c_Groups_Ozero__class_Ozero(_890699))], (7272 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_890699), _890701), _890701) = c_Groups_Ozero__class_Ozero(_890699), -(_890701 = c_Groups_Ozero__class_Ozero(_890699))]]], (45114 ^ _775212) ^ [_1668390, _1668392, _1668394, _1668396] : [c_List_Olist_ONil(_1668390) = hAPP(hAPP(c_List_Omap(_1668392, _1668390), _1668394), _1668396), -(_1668396 = c_List_Olist_ONil(_1668392))], (18257 ^ _775212) ^ [_1085241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1085241))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1085241)))], (31003 ^ _775212) ^ [_1335212, _1335214, _1335216, _1335218] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1335212, _1335212)), hAPP(hAPP(c_Product__Type_OPair(_1335212, _1335212), _1335214), _1335216)), hAPP(c_Wellfounded_Omeasure(_1335212), _1335218))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1335218, _1335214)), hAPP(_1335218, _1335216))))], (16567 ^ _775212) ^ [_1057062, _1057064, _1057066, _1057068] : [class_Int_Onumber__ring(_1057062), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057062), hAPP(c_Int_Onumber__class_Onumber__of(_1057062), _1057064)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057062), hAPP(c_Int_Onumber__class_Onumber__of(_1057062), _1057066)), _1057068)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057062), hAPP(c_Int_Onumber__class_Onumber__of(_1057062), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1057064), _1057066))), _1057068))], (22874 ^ _775212) ^ [_1170957, _1170959, _1170961, _1170963] : [class_Orderings_Olinorder(_1170957), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1170957), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1170957), _1170959), _1170961)), _1170963) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1170957), _1170959), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1170957), _1170961), _1170963)))], (30548 ^ _775212) ^ [_1325655, _1325657, _1325659, _1325661, _1325663] : [class_Groups_Ocomm__monoid__add(_1325655), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325657), _1325659)), hBOOL(hAPP(hAPP(c_member(_1325657), _1325661), _1325659)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1325657, _1325655), _1325663), _1325659) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325655), hAPP(_1325663, _1325661)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1325657, _1325655), _1325663), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325657, tc_HOL_Obool)), _1325659), hAPP(hAPP(c_Set_Oinsert(_1325657), _1325661), c_Orderings_Obot__class_Obot(tc_fun(_1325657, tc_HOL_Obool)))))))], (52309 ^ _775212) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (50689 ^ _775212) ^ [_1791860, _1791862, _1791864, _1791866] : [-(hBOOL(hAPP(_1791860, _1791862))), -(hAPP(c_List_Ofilter(_1791864, _1791860), c_List_Oreplicate(_1791864, _1791866, _1791862)) = c_List_Olist_ONil(_1791864))], (52275 ^ _775212) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (23986 ^ _775212) ^ [_1192025, _1192027, _1192029, _1192031] : [class_Rings_Ocomm__semiring__1(_1192025), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1192025), _1192027), _1192029)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1192025), _1192029), _1192031)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1192025), _1192027), _1192031)))], (3710 ^ _775212) ^ [_831397, _831399, _831401, _831403] : [-(c_List_Olexn(_831403, _831399) = c_List_Olexn(_831401, _831397)), _831403 = _831401, _831399 = _831397], (38800 ^ _775212) ^ [_1504646, _1504648, _1504650, _1504652, _1504654] : [c_Finite__Set_Ofun__left__comm__idem(_1504646, _1504648, _1504650), -(c_Finite__Set_Ofun__left__comm__idem(_1504652, _1504648, hAPP(hAPP(c_COMBB(_1504646, tc_fun(_1504648, _1504648), _1504652), _1504650), _1504654)))], (34825 ^ _775212) ^ [_1414695, _1414697] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414695, tc_HOL_Obool)), _1414697), _1414697) = _1414697)], (36879 ^ _775212) ^ [_1460336] : [-(c_Fun_Oinj__on(_1460336, tc_fun(_1460336, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1460336, tc_fun(_1460336, tc_HOL_Obool), tc_fun(_1460336, tc_HOL_Obool)), c_Set_Oinsert(_1460336)), c_Orderings_Obot__class_Obot(tc_fun(_1460336, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1460336, tc_HOL_Obool))))], (50725 ^ _775212) ^ [_1792436, _1792438, _1792440, _1792442, _1792444] : [-(hAPP(hAPP(c_List_Omap(_1792436, _1792438), _1792440), c_List_Oreplicate(_1792436, _1792442, _1792444)) = c_List_Oreplicate(_1792438, _1792442, hAPP(_1792440, _1792444)))], (51373 ^ _775212) ^ [_1806951, _1806953] : [c_Relation_Otrans(_1806951, _1806953), -(c_Relation_Otrans(_1806951, hAPP(c_Relation_Oconverse(_1806951, _1806951), _1806953)))], (49681 ^ _775212) ^ [_1769933, _1769935] : [class_Orderings_Olinorder(_1769933), 49684 ^ _775212 : [(49705 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1769933, _1769935)), 49706 ^ _775212 : [(49709 ^ _775212) ^ [_1770493, _1770495] : [_1769935 = hAPP(hAPP(c_List_Olist_OCons(_1769933), _1770493), _1770495), 49715 ^ _775212 : [(49718 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1769933), _1770493), 49714 ^ [_1769933, _1769935, _1770493, _1770495]))], (49716 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769933), 49714 ^ [_1769933, _1769935, _1770493, _1770495]), hAPP(c_List_Oset(_1769933), _1770495))))]], c_List_Olinorder__class_Osorted(_1769933, _1770495)], (49707 ^ _775212) ^ [] : [_1769935 = c_List_Olist_ONil(_1769933)]]], (49685 ^ _775212) ^ [] : [c_List_Olinorder__class_Osorted(_1769933, _1769935), -(_1769935 = c_List_Olist_ONil(_1769933)), 49694 ^ _775212 : [(49697 ^ _775212) ^ [_1770267] : [hBOOL(hAPP(hAPP(c_member(_1769933), _1770267), hAPP(c_List_Oset(_1769933), 49692 ^ [_1769933, _1769935]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1769933), 49693 ^ [_1769933, _1769935]), _1770267)))], (49703 ^ _775212) ^ [] : [-(c_List_Olinorder__class_Osorted(_1769933, 49692 ^ [_1769933, _1769935]))], (49695 ^ _775212) ^ [] : [-(_1769935 = hAPP(hAPP(c_List_Olist_OCons(_1769933), 49693 ^ [_1769933, _1769935]), 49692 ^ [_1769933, _1769935]))]]]]], (35109 ^ _775212) ^ [_1421609, _1421611] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1421609), _1421611) = 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)), _1421609)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1421611))))], (41408 ^ _775212) ^ [_1573531, _1573533, _1573535] : [class_Lattices_Olattice(_1573531), hBOOL(hAPP(c_Finite__Set_Ofinite(_1573531), _1573533)), -(c_Big__Operators_Olattice__class_OSup__fin(_1573531, hAPP(hAPP(c_Set_Oinsert(_1573531), _1573535), _1573533)) = hAPP(hAPP(c_Finite__Set_Ofold(_1573531, _1573531, c_Lattices_Osemilattice__sup__class_Osup(_1573531)), _1573535), _1573533))], (36683 ^ _775212) ^ [_1456310, _1456312, _1456314, _1456316] : [c_Fun_Oinj__on(_1456310, _1456312, _1456314, c_Orderings_Otop__class_Otop(tc_fun(_1456310, tc_HOL_Obool))), 36686 ^ _775212 : [(36700 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456312), _1456316), hAPP(c_Set_Oimage(_1456310, _1456312, _1456314), c_Orderings_Otop__class_Otop(tc_fun(_1456310, tc_HOL_Obool)))))), 36701 ^ _775212 : [(36702 ^ _775212) ^ [_1456713] : [_1456316 = hAPP(_1456314, _1456713), 36706 ^ _775212 : [(36709 ^ _775212) ^ [] : [36705 ^ [_1456310, _1456312, _1456314, _1456316, _1456713] = _1456713], (36707 ^ _775212) ^ [] : [-(_1456316 = hAPP(_1456314, 36705 ^ [_1456310, _1456312, _1456314, _1456316, _1456713]))]]]]], (36687 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1456312), _1456316), hAPP(c_Set_Oimage(_1456310, _1456312, _1456314), c_Orderings_Otop__class_Otop(tc_fun(_1456310, tc_HOL_Obool))))), 36691 ^ _775212 : [(36694 ^ _775212) ^ [_1456575] : [_1456316 = hAPP(_1456314, _1456575), -(_1456575 = 36690 ^ [_1456310, _1456312, _1456314, _1456316])], (36692 ^ _775212) ^ [] : [-(_1456316 = hAPP(_1456314, 36690 ^ [_1456310, _1456312, _1456314, _1456316]))]]]]], (25879 ^ _775212) ^ [_1228066, _1228068, _1228070, _1228072, _1228074] : [class_Groups_Ocomm__monoid__add(_1228066), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1228068), _1228070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1228070), _1228072)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228066), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228066), _1228074), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1228068), _1228070))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228066), _1228074), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1228070), _1228072))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228066), _1228074), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1228068), _1228072)))], (21743 ^ _775212) ^ [_1147774, _1147776, _1147778] : [21744 ^ _775212 : [(21747 ^ _775212) ^ [] : [_1147776 = _1147778], (21745 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1147774, tc_HOL_Obool)), _1147776), _1147778))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1147774, tc_HOL_Obool)), _1147776), _1147778)))], (41917 ^ _775212) ^ [_1584614, _1584616] : [-(c_Transitive__Closure_Otrancl(_1584614, _1584616) = hAPP(hAPP(c_Relation_Orel__comp(_1584614, _1584614, _1584614), _1584616), c_Transitive__Closure_Ortrancl(_1584614, _1584616)))], (39771 ^ _775212) ^ [_1536306, _1536308, _1536310, _1536312] : [c_Wellfounded_Owf(_1536306, _1536308), hBOOL(hAPP(hAPP(c_member(tc_prod(_1536306, _1536306)), hAPP(hAPP(c_Product__Type_OPair(_1536306, _1536306), _1536310), _1536312)), _1536308)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1536306, _1536306)), hAPP(hAPP(c_Product__Type_OPair(_1536306, _1536306), _1536312), _1536310)), _1536308))], (2070 ^ _775212) ^ [_805095, _805097, _805099, _805101, _805103, _805105] : [-(c_Power_Opower_Opower(_805105, _805101, _805097) = c_Power_Opower_Opower(_805103, _805099, _805095)), _805105 = _805103, _805101 = _805099, _805097 = _805095], (51415 ^ _775212) ^ [_1807806, _1807808] : [51418 ^ _775212 : [(51424 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1807806, _1807806)), hAPP(hAPP(c_Product__Type_OPair(_1807806, _1807806), 51416 ^ [_1807806, _1807808]), 51420 ^ [_1807806, _1807808])), _1807808))], (51422 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1807806, _1807806)), hAPP(hAPP(c_Product__Type_OPair(_1807806, _1807806), 51417 ^ [_1807806, _1807808]), 51420 ^ [_1807806, _1807808])), _1807808)))], (51419 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1807806, _1807806)), hAPP(hAPP(c_Product__Type_OPair(_1807806, _1807806), 51416 ^ [_1807806, _1807808]), 51417 ^ [_1807806, _1807808])), _1807808)))]], -(c_Relation_Otrans(_1807806, _1807808))], (45566 ^ _775212) ^ [_1679917, _1679919] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1679917), _1679919) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1679917, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1679919), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (38891 ^ _775212) ^ [_1506492, _1506494, _1506496, _1506498] : [-(hAPP(c_Set_OCollect(tc_prod(_1506492, _1506494)), hAPP(c_Product__Type_Oprod_Oprod__case(_1506492, _1506494, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1506492, tc_fun(_1506494, tc_HOL_Obool), tc_fun(_1506494, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1506494, tc_HOL_Obool), tc_fun(_1506494, tc_HOL_Obool)), _1506492), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1506494)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506492), c_fconj), _1506496))), _1506498))) = hAPP(hAPP(c_Product__Type_OSigma(_1506492, _1506494), hAPP(c_Set_OCollect(_1506492), _1506496)), hAPP(hAPP(c_COMBB(tc_fun(_1506494, tc_HOL_Obool), tc_fun(_1506494, tc_HOL_Obool), _1506492), c_Set_OCollect(_1506494)), _1506498)))], (18425 ^ _775212) ^ [_1088185, _1088187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1088185)), c_Int_OBit1(_1088187))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088185), _1088187)))], (16909 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (5516 ^ _775212) ^ [_859366, _859368] : [_859368 = _859366, -(c_COMBI(_859368) = c_COMBI(_859366))], (45260 ^ _775212) ^ [_1672063, _1672065, _1672067] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1672063), tc_List_Olist(_1672063))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1672063), tc_List_Olist(_1672063)), c_List_Olist_ONil(_1672063)), _1672065)), c_List_Olex(_1672063, _1672067)))], (24500 ^ _775212) ^ [_1200545, _1200547, _1200549, _1200551] : [class_Rings_Ocomm__semiring__1(_1200545), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1200545), _1200547), _1200549)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1200545), _1200547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200545), _1200551), _1200549))))], (13807 ^ _775212) ^ [_1004318, _1004320, _1004322] : [class_Divides_Osemiring__div(_1004318), -(_1004320 = c_Groups_Ozero__class_Ozero(_1004318)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1004318), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004318), _1004320), _1004322)), _1004320) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004318), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1004318), _1004322), _1004320)), c_Groups_Oone__class_Oone(_1004318)))], (41123 ^ _775212) ^ [_1567825, _1567827, _1567829] : [class_Orderings_Olinorder(_1567825), hBOOL(hAPP(c_Finite__Set_Ofinite(_1567825), _1567827)), 41133 ^ _775212 : [(41136 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1567825), 41132 ^ [_1567825, _1567827, _1567829]), _1567829))], (41134 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1567825), 41132 ^ [_1567825, _1567827, _1567829]), _1567827)))]], hBOOL(hAPP(hAPP(c_member(_1567825), _1567829), _1567827)), -(c_Big__Operators_Olinorder__class_OMax(_1567825, _1567827) = _1567829)], (46240 ^ _775212) ^ [_1696026, _1696028, _1696030] : [hAPP(hAPP(c_List_Odrop(_1696026), _1696028), _1696030) = c_List_Olist_ONil(_1696026), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696026)), _1696030)), _1696028)))], (44178 ^ _775212) ^ [_1641850, _1641852, _1641854, _1641856, _1641858, _1641860] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641850), tc_List_Olist(_1641850))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641850), tc_List_Olist(_1641850)), hAPP(hAPP(c_List_Olist_OCons(_1641850), _1641852), _1641854)), hAPP(hAPP(c_List_Olist_OCons(_1641850), _1641856), _1641858))), c_List_Olex(_1641850, _1641860))), 44183 ^ _775212 : [(44186 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641850)), _1641854) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641850)), _1641858))], (44184 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641850, _1641850)), hAPP(hAPP(c_Product__Type_OPair(_1641850, _1641850), _1641852), _1641856)), _1641860)))]], 44187 ^ _775212 : [(44190 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641850), tc_List_Olist(_1641850))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641850), tc_List_Olist(_1641850)), _1641854), _1641858)), c_List_Olex(_1641850, _1641860))))], (44188 ^ _775212) ^ [] : [-(_1641852 = _1641856)]]], (18099 ^ _775212) ^ [_1082509, _1082511] : [_1082509 = _1082511, -(c_Int_OBit0(_1082509) = c_Int_OBit0(_1082511))], (28898 ^ _775212) ^ [_1288698, _1288700, _1288702, _1288704] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288698, tc_HOL_Obool)), _1288700), hAPP(hAPP(c_Set_Oinsert(_1288698), _1288702), _1288704)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288698, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288698, tc_HOL_Obool)), _1288700), hAPP(hAPP(c_Set_Oinsert(_1288698), _1288702), c_Orderings_Obot__class_Obot(tc_fun(_1288698, tc_HOL_Obool))))), _1288704))], (2946 ^ _775212) ^ [_819221, _819223] : [_819223 = _819221, -(c_Int_OBit1(_819223) = c_Int_OBit1(_819221))], (29782 ^ _775212) ^ [_1305907, _1305909] : [hAPP(c_Int_ORep__Integ, _1305907) = hAPP(c_Int_ORep__Integ, _1305909), -(_1305907 = _1305909)], (44290 ^ _775212) ^ [_1645542, _1645544] : [-(c_List_Olistrel1(_1645542, hAPP(c_Relation_Oconverse(_1645542, _1645542), _1645544)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1645542), tc_List_Olist(_1645542)), c_List_Olistrel1(_1645542, _1645544)))], (42621 ^ _775212) ^ [_1603395, _1603397, _1603399, _1603401, _1603403] : [_1603395 = c_Orderings_Obot__class_Obot(tc_fun(_1603397, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1603399, tc_HOL_Obool)), _1603401), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1603397, tc_fun(_1603399, tc_HOL_Obool)), _1603395), _1603403)) = _1603401)], (24712 ^ _775212) ^ [_1204306, _1204308, _1204310, _1204312, _1204314] : [class_Divides_Osemiring__div(_1204306), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204306), _1204308), _1204310)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204306), _1204312), _1204314)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204306), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204306), _1204310), _1204308)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204306), _1204314), _1204312)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204306), _1204310), _1204314)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204306), _1204308), _1204312)))], (16767 ^ _775212) ^ [_1061135] : [class_Rings_Osemiring__1(_1061135), c_Int_Oiszero(_1061135, c_Groups_Oone__class_Oone(_1061135))], (17211 ^ _775212) ^ [_1068007, _1068009] : [class_Int_Onumber__ring(_1068007), 17214 ^ _775212 : [(17221 ^ _775212) ^ [] : [c_Int_Oiszero(_1068007, hAPP(c_Int_Onumber__class_Onumber__of(_1068007), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068009)))), -(c_Groups_Ozero__class_Ozero(_1068007) = hAPP(c_Int_Onumber__class_Onumber__of(_1068007), _1068009))], (17215 ^ _775212) ^ [] : [c_Groups_Ozero__class_Ozero(_1068007) = hAPP(c_Int_Onumber__class_Onumber__of(_1068007), _1068009), -(c_Int_Oiszero(_1068007, hAPP(c_Int_Onumber__class_Onumber__of(_1068007), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068009)))))]]], (15895 ^ _775212) ^ [_1044482, _1044484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1044482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044482), _1044484)), -(c_Divides_Odivmod__nat(_1044484, _1044482) = 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), _1044484), _1044482)), _1044482))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044484), _1044482), _1044482)))], (36403 ^ _775212) ^ [_1451079, _1451081, _1451083, _1451085, _1451087] : [c_Fun_Oinj__on(_1451079, _1451081, _1451083, c_Orderings_Otop__class_Otop(tc_fun(_1451079, tc_HOL_Obool))), 36406 ^ _775212 : [(36413 ^ _775212) ^ [] : [_1451085 = _1451087, -(hAPP(_1451083, _1451085) = hAPP(_1451083, _1451087))], (36407 ^ _775212) ^ [] : [hAPP(_1451083, _1451085) = hAPP(_1451083, _1451087), -(_1451085 = _1451087)]]], (52333 ^ _775212) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (33266 ^ _775212) ^ [_1379364, _1379366, _1379368, _1379370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1379364), _1379366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379368), _1379370)), -(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), _1379364), _1379368)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1379366), _1379370))), c_FunDef_Opair__less)))], (8085 ^ _775212) ^ [_905403, _905405, _905407, _905409, _905411] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_905403), 8088 ^ _775212 : [(8089 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905403), _905405), _905409)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905403), _905407), _905411)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905403), _905405), _905411)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905403), _905407), _905409)), -(_905405 = _905407), -(_905409 = _905411)], (8099 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905403), _905405), _905409)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905403), _905407), _905411)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905403), _905405), _905411)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905403), _905407), _905409))), 8102 ^ _775212 : [(8105 ^ _775212) ^ [] : [_905409 = _905411], (8103 ^ _775212) ^ [] : [_905405 = _905407]]]]], (50336 ^ _775212) ^ [_1784567, _1784569] : [c_List_Olist__ex(_1784567, _1784569, c_List_Olist_ONil(_1784567))], (48166 ^ _775212) ^ [_1737372, _1737374, _1737376] : [c_List_Oconcat(_1737372, _1737374) = c_List_Oconcat(_1737372, _1737376), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1737372))), _1737374) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1737372))), _1737376), 48176 ^ _775212 : [(48179 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1737372), tc_List_Olist(_1737372), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1737372), tc_fun(tc_List_Olist(_1737372), tc_Nat_Onat), tc_fun(tc_List_Olist(_1737372), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1737372), tc_Nat_Onat), tc_fun(tc_List_Olist(_1737372), tc_HOL_Obool)), tc_List_Olist(_1737372)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1737372))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1737372)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1737372))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1737372)))), 48175 ^ [_1737372, _1737374, _1737376]))], (48177 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1737372), tc_List_Olist(_1737372))), 48175 ^ [_1737372, _1737374, _1737376]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1737372), tc_List_Olist(_1737372))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1737372), tc_List_Olist(_1737372)), _1737374), _1737376)))))]], -(_1737374 = _1737376)], (21577 ^ _775212) ^ [_1144770, _1144772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144770)), 21580 ^ _775212 : [(21587 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144772))), 21590 ^ _775212 : [(21597 ^ _775212) ^ [] : [-(_1144770 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1144770, _1144772) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1144770), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1144772))))], (21591 ^ _775212) ^ [] : [_1144770 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1144770, _1144772) = 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)))]]], (21581 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144772)), -(c_Divides_Odivmod__int(_1144770, _1144772) = c_Divides_OposDivAlg(_1144770, _1144772))]]], (39959 ^ _775212) ^ [_1540156, _1540158, _1540160, _1540162] : [39960 ^ _775212 : [(39961 ^ _775212) ^ [_1540231] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540156, _1540160)), hAPP(hAPP(c_Product__Type_OPair(_1540156, _1540160), _1540158), _1540231)), _1540162))]], -(hBOOL(hAPP(hAPP(c_member(_1540156), _1540158), hAPP(c_Relation_ODomain(_1540156, _1540160), _1540162))))], (38580 ^ _775212) ^ [_1500307, _1500309, _1500311] : [class_Orderings_Olinorder(_1500307), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500307), _1500309)), -(_1500309 = c_Orderings_Obot__class_Obot(tc_fun(_1500307, tc_HOL_Obool))), 38591 ^ _775212 : [(38592 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500307), _1500311), hAPP(c_Finite__Set_Ofold1(_1500307, c_Orderings_Oord__class_Omin(_1500307)), _1500309))), 38595 ^ _775212 : [(38596 ^ _775212) ^ [_1500600] : [hBOOL(hAPP(hAPP(c_member(_1500307), _1500600), _1500309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500307), _1500311), _1500600)))]]], (38602 ^ _775212) ^ [] : [38604 ^ _775212 : [(38607 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500307), _1500311), 38603 ^ [_1500307, _1500309, _1500311]))], (38605 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1500307), 38603 ^ [_1500307, _1500309, _1500311]), _1500309)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500307), _1500311), hAPP(c_Finite__Set_Ofold1(_1500307, c_Orderings_Oord__class_Omin(_1500307)), _1500309))))]]], (11300 ^ _775212) ^ [_960743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _960743), 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)), _960743)), _960743)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52233 ^ _775212) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (40085 ^ _775212) ^ [_1543518, _1543520] : [-(hAPP(c_List_Olexn(_1543518, _1543520), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1543518), tc_List_Olist(_1543518)), tc_HOL_Obool)))], (16431 ^ _775212) ^ [_1054471, _1054473] : [class_Int_Onumber__ring(_1054471), -(hAPP(c_Int_Onumber__class_Onumber__of(_1054471), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1054473)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1054471), hAPP(c_Int_Onumber__class_Onumber__of(_1054471), _1054473)))], (1144 ^ _775212) ^ [_792368, _792370] : [-(class_Rings_Oring__no__zero__divisors(_792368)), _792370 = _792368, class_Rings_Oring__no__zero__divisors(_792370)], (51468 ^ _775212) ^ [_1809742, _1809744, _1809746, _1809748] : [class_Complete__Lattice_Ocomplete__lattice(_1809742), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1809744, _1809742), _1809746), _1809748) = c_Complete__Lattice_OInf__class_OInf(_1809742, hAPP(c_Set_OCollect(_1809742), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1809744, _1809742), tc_HOL_Obool), tc_HOL_Obool, _1809742), c_HOL_OEx(tc_fun(_1809744, _1809742))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1809744, _1809742), tc_HOL_Obool), tc_fun(tc_fun(_1809744, _1809742), tc_HOL_Obool), _1809742), hAPP(c_COMBS(tc_fun(_1809744, _1809742), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1809744, _1809742)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1809744, _1809742), tc_fun(tc_fun(_1809744, _1809742), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1809744, _1809742))), _1809746)))), hAPP(hAPP(c_COMBC(_1809742, tc_fun(tc_fun(_1809744, _1809742), _1809742), tc_fun(tc_fun(_1809744, _1809742), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1809742, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1809744, _1809742), _1809742), tc_fun(tc_fun(_1809744, _1809742), tc_HOL_Obool)), _1809742), c_COMBB(_1809742, tc_HOL_Obool, tc_fun(_1809744, _1809742))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1809744, _1809742), _1809744, _1809742), c_COMBI(tc_fun(_1809744, _1809742))), _1809748)))))))], (48392 ^ _775212) ^ [_1743955, _1743957, _1743959, _1743961, _1743963, _1743965, _1743967] : [-(c_List_Ofoldr(_1743955, _1743957, _1743959, hAPP(hAPP(c_List_Omap(_1743961, _1743955), _1743963), _1743965), _1743967) = c_List_Ofoldr(_1743961, _1743957, hAPP(c_Fun_Ocomp(_1743955, tc_fun(_1743957, _1743957), _1743961, _1743959), _1743963), _1743965, _1743967))], (16889 ^ _775212) ^ [_1063138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1063138)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1063138) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1063138), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35143 ^ _775212) ^ [_1422439, _1422441, _1422443, _1422445, _1422447, _1422449, _1422451, _1422453] : [c_Equiv__Relations_Oequiv(_1422439, _1422441, _1422443), c_Equiv__Relations_Ocongruent2(_1422439, _1422445, _1422447, _1422443, _1422449, _1422451), hBOOL(hAPP(hAPP(c_member(_1422439), _1422453), _1422441)), -(c_Equiv__Relations_Ocongruent(_1422445, _1422447, _1422449, hAPP(_1422451, _1422453)))], (15905 ^ _775212) ^ [_1044693] : [-(c_Divides_Odivmod__nat(_1044693, 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)), _1044693))], (46378 ^ _775212) ^ [_1699511, _1699513, _1699515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1699511), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699513)), _1699515))), -(_1699515 = hAPP(hAPP(c_List_Oappend(_1699513), hAPP(hAPP(c_List_Otake(_1699513), _1699511), _1699515)), hAPP(hAPP(c_List_Olist_OCons(_1699513), hAPP(hAPP(c_List_Onth(_1699513), _1699515), _1699511)), hAPP(hAPP(c_List_Odrop(_1699513), hAPP(c_Nat_OSuc, _1699511)), _1699515))))], (29578 ^ _775212) ^ [_1302023, _1302025] : [hBOOL(hAPP(hAPP(c_member(_1302023), _1302025), c_Orderings_Obot__class_Obot(tc_fun(_1302023, tc_HOL_Obool))))], (18965 ^ _775212) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (16959 ^ _775212) ^ [_1064093] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1064093))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1064093)) = _1064093)], (47782 ^ _775212) ^ [_1728813, _1728815, _1728817] : [-(c_Enum_Oproduct(_1728813, _1728815, c_List_Olist_ONil(_1728813), _1728817) = c_List_Olist_ONil(tc_prod(_1728813, _1728815)))], (40013 ^ _775212) ^ [_1541684, _1541686] : [-(hAPP(c_Relation_OField(_1541684), _1541686) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1541684, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1541684, _1541684), _1541686)), hAPP(c_Relation_ORange(_1541684, _1541684), _1541686)))], (52345 ^ _775212) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (2110 ^ _775212) ^ [_805699, _805701, _805703, _805705] : [-(c_Divides_OposDivAlg(_805705, _805701) = c_Divides_OposDivAlg(_805703, _805699)), _805705 = _805703, _805701 = _805699], (27793 ^ _775212) ^ [_1266846, _1266848, _1266850, _1266852, _1266854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1266846, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1266848, tc_fun(_1266846, tc_HOL_Obool)), _1266850), _1266852)), _1266854)), 27796 ^ _775212 : [(27797 ^ _775212) ^ [_1266979] : [hBOOL(hAPP(hAPP(c_member(_1266848), _1266979), _1266850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1266846, tc_HOL_Obool)), hAPP(_1266852, _1266979)), _1266854)))]]], (16103 ^ _775212) ^ [_1048056, _1048058] : [class_Groups_Oordered__ab__group__add__abs(_1048056), 16106 ^ _775212 : [(16113 ^ _775212) ^ [] : [_1048058 = c_Groups_Ozero__class_Ozero(_1048056), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048056), hAPP(c_Groups_Oabs__class_Oabs(_1048056), _1048058)), c_Groups_Ozero__class_Ozero(_1048056))))], (16107 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048056), hAPP(c_Groups_Oabs__class_Oabs(_1048056), _1048058)), c_Groups_Ozero__class_Ozero(_1048056))), -(_1048058 = c_Groups_Ozero__class_Ozero(_1048056))]]], (29416 ^ _775212) ^ [_1298778, _1298780, _1298782] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1298778), _1298780)), 29419 ^ _775212 : [(29426 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298778), _1298782), _1298780))), -(hAPP(c_Finite__Set_Ocard(_1298778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1298778, tc_HOL_Obool)), _1298780), hAPP(hAPP(c_Set_Oinsert(_1298778), _1298782), c_Orderings_Obot__class_Obot(tc_fun(_1298778, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1298778), _1298780))], (29420 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1298778), _1298782), _1298780)), -(hAPP(c_Finite__Set_Ocard(_1298778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1298778, tc_HOL_Obool)), _1298780), hAPP(hAPP(c_Set_Oinsert(_1298778), _1298782), c_Orderings_Obot__class_Obot(tc_fun(_1298778, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1298778), _1298780)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (28219 ^ _775212) ^ [_1275528, _1275530, _1275532] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1275528), _1275530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1275528, tc_HOL_Obool)), _1275530), _1275532)), -(hAPP(c_Finite__Set_Ocard(_1275528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1275528, tc_HOL_Obool)), _1275532), _1275530)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1275528), _1275532)), hAPP(c_Finite__Set_Ocard(_1275528), _1275530)))], (42927 ^ _775212) ^ [_1611513, _1611515, _1611517] : [42930 ^ _775212 : [(42936 ^ _775212) ^ [] : [42929 ^ [_1611513, _1611515, _1611517] = 42932 ^ [_1611513, _1611515, _1611517]], (42934 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611513, _1611515)), hAPP(hAPP(c_Product__Type_OPair(_1611513, _1611515), 42928 ^ [_1611513, _1611515, _1611517]), 42932 ^ [_1611513, _1611515, _1611517])), _1611517)))], (42931 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611513, _1611515)), hAPP(hAPP(c_Product__Type_OPair(_1611513, _1611515), 42928 ^ [_1611513, _1611515, _1611517]), 42929 ^ [_1611513, _1611515, _1611517])), _1611517)))]], -(c_Relation_Osingle__valued(_1611513, _1611515, _1611517))], (42597 ^ _775212) ^ [_1602733, _1602735, _1602737, _1602739, _1602741] : [_1602733 = c_Orderings_Obot__class_Obot(tc_fun(_1602735, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602735, tc_fun(_1602737, tc_HOL_Obool)), _1602733), hAPP(hAPP(c_COMBC(_1602735, tc_fun(_1602737, tc_HOL_Obool), tc_fun(_1602737, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602737, tc_HOL_Obool), tc_fun(tc_fun(_1602737, tc_HOL_Obool), tc_fun(_1602737, tc_HOL_Obool)), _1602735), c_Groups_Ominus__class_Ominus(tc_fun(_1602737, tc_HOL_Obool))), _1602739)), _1602741)) = c_Orderings_Otop__class_Otop(tc_fun(_1602737, tc_HOL_Obool)))], (41596 ^ _775212) ^ [_1577014] : [-(c_Transitive__Closure_Otrancl(_1577014, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1577014, _1577014), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1577014, _1577014), tc_HOL_Obool)))], (29961 ^ _775212) ^ [_1310378, _1310380, _1310382, _1310384] : [hAPP(hAPP(c_COMBC(_1310378, tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_fun(_1310380, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1310380, tc_fun(tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_fun(_1310380, tc_HOL_Obool)), _1310378), c_COMBC(_1310380, tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1310380, tc_prod(_1310378, _1310380)), tc_fun(_1310380, tc_fun(tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_HOL_Obool)), _1310378), hAPP(c_COMBB(tc_prod(_1310378, _1310380), tc_fun(tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_HOL_Obool), _1310380), c_member(tc_prod(_1310378, _1310380)))), c_Product__Type_OPair(_1310378, _1310380)))), _1310382) = hAPP(hAPP(c_COMBC(_1310378, tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_fun(_1310380, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1310380, tc_fun(tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_fun(_1310380, tc_HOL_Obool)), _1310378), c_COMBC(_1310380, tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1310380, tc_prod(_1310378, _1310380)), tc_fun(_1310380, tc_fun(tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_HOL_Obool)), _1310378), hAPP(c_COMBB(tc_prod(_1310378, _1310380), tc_fun(tc_fun(tc_prod(_1310378, _1310380), tc_HOL_Obool), tc_HOL_Obool), _1310380), c_member(tc_prod(_1310378, _1310380)))), c_Product__Type_OPair(_1310378, _1310380)))), _1310384), -(_1310382 = _1310384)], (33666 ^ _775212) ^ [_1388859, _1388861, _1388863, _1388865, _1388867] : [class_Groups_Ocomm__monoid__mult(_1388859), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388861), _1388863)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388861, tc_HOL_Obool)), _1388865), _1388863)), 33680 ^ _775212 : [(33683 ^ _775212) ^ [] : [hAPP(_1388867, 33679 ^ [_1388859, _1388861, _1388863, _1388865, _1388867]) = c_Groups_Oone__class_Oone(_1388859)], (33681 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388861), 33679 ^ [_1388859, _1388861, _1388863, _1388865, _1388867]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388861, tc_HOL_Obool)), _1388863), _1388865))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388861, _1388859), _1388867), _1388863) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388861, _1388859), _1388867), _1388865))], (52757 ^ _775212) ^ [_1829285, _1829287] : [-(hBOOL(_1829285)), -(hBOOL(hAPP(hAPP(c_fimplies, _1829285), _1829287)))], (36118 ^ _775212) ^ [_1445300, _1445302, _1445304] : [class_Lattices_Olattice(_1445300), hBOOL(hAPP(c_Finite__Set_Ofinite(_1445300), _1445302)), hBOOL(hAPP(hAPP(c_member(_1445300), _1445304), _1445302)), 36129 ^ _775212 : [(36136 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1445300, tc_HOL_Obool)), _1445302), hAPP(hAPP(c_Set_Oinsert(_1445300), _1445304), c_Orderings_Obot__class_Obot(tc_fun(_1445300, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1445300, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1445300, _1445302) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445300), _1445304), c_Big__Operators_Olattice__class_OInf__fin(_1445300, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1445300, tc_HOL_Obool)), _1445302), hAPP(hAPP(c_Set_Oinsert(_1445300), _1445304), c_Orderings_Obot__class_Obot(tc_fun(_1445300, tc_HOL_Obool)))))))], (36130 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1445300, tc_HOL_Obool)), _1445302), hAPP(hAPP(c_Set_Oinsert(_1445300), _1445304), c_Orderings_Obot__class_Obot(tc_fun(_1445300, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1445300, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1445300, _1445302) = _1445304)]]], (30286 ^ _775212) ^ [_1318897, _1318899, _1318901, _1318903] : [hBOOL(hAPP(hAPP(c_member(_1318899), _1318903), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318897, tc_fun(_1318899, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1318897, tc_HOL_Obool))), _1318901))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318897, tc_fun(_1318899, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1318897, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1318899, tc_HOL_Obool), tc_fun(_1318899, tc_HOL_Obool), _1318897), hAPP(c_COMBC(_1318899, tc_fun(_1318899, tc_HOL_Obool), tc_HOL_Obool), c_member(_1318899))), _1318901)), _1318903)))], (33747 ^ _775212) ^ [_1390588, _1390590] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1390588), _1390590)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1390588, tc_HOL_Obool)), hAPP(c_Set_OPow(_1390588), _1390590))))], (1904 ^ _775212) ^ [_801868, _801870] : [-(class_Nat_Osize(_801868)), _801870 = _801868, class_Nat_Osize(_801870)], (25535 ^ _775212) ^ [_1219930, _1219932, _1219934, _1219936] : [class_Groups_Oordered__ab__group__add__abs(_1219930), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219930), hAPP(c_Groups_Oabs__class_Oabs(_1219930), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1219932, _1219930), _1219934), _1219936))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1219932, _1219930), hAPP(hAPP(c_COMBB(_1219930, _1219930, _1219932), c_Groups_Oabs__class_Oabs(_1219930)), _1219934)), _1219936))))], (1224 ^ _775212) ^ [_793368, _793370] : [-(class_Rings_Ocomm__ring__1(_793368)), _793370 = _793368, class_Rings_Ocomm__ring__1(_793370)], (30378 ^ _775212) ^ [_1322092] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1322092), 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, _1322092)) = _1322092)], (13827 ^ _775212) ^ [_1004646, _1004648, _1004650, _1004652] : [class_Divides_Osemiring__div(_1004646), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004646), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004646), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1004646), _1004648), _1004650)), _1004650)), c_Divides_Odiv__class_Omod(_1004646, _1004648, _1004650))), _1004652) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004646), _1004648), _1004652))], (48803 ^ _775212) ^ [_1751527, _1751529, _1751531, _1751533, _1751535] : [class_Orderings_Olinorder(_1751527), 48806 ^ _775212 : [(48813 ^ _775212) ^ [] : [c_List_Olinorder__class_Osorted(_1751527, hAPP(hAPP(c_List_Omap(_1751529, _1751527), _1751531), _1751535)), -(c_List_Olinorder__class_Osorted(_1751527, hAPP(hAPP(c_List_Omap(_1751529, _1751527), _1751531), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1751529, _1751527, _1751531), _1751533), _1751535))))], (48807 ^ _775212) ^ [] : [c_List_Olinorder__class_Osorted(_1751527, hAPP(hAPP(c_List_Omap(_1751529, _1751527), _1751531), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1751529, _1751527, _1751531), _1751533), _1751535))), -(c_List_Olinorder__class_Osorted(_1751527, hAPP(hAPP(c_List_Omap(_1751529, _1751527), _1751531), _1751535)))]]], (28818 ^ _775212) ^ [_1287389, _1287391] : [class_Lattices_Obounded__lattice__bot(_1287389), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287389), _1287391), c_Orderings_Obot__class_Obot(_1287389)) = _1287391)], (42834 ^ _775212) ^ [_1609289] : [-(c_Relation_OId(_1609289) = hAPP(c_Set_OCollect(tc_prod(_1609289, _1609289)), hAPP(hAPP(c_COMBB(tc_fun(_1609289, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1609289, _1609289)), c_HOL_OEx(_1609289)), hAPP(hAPP(c_COMBC(tc_prod(_1609289, _1609289), tc_fun(_1609289, tc_prod(_1609289, _1609289)), tc_fun(_1609289, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1609289, _1609289), tc_HOL_Obool), tc_fun(tc_fun(_1609289, tc_prod(_1609289, _1609289)), tc_fun(_1609289, tc_HOL_Obool)), tc_prod(_1609289, _1609289)), c_COMBB(tc_prod(_1609289, _1609289), tc_HOL_Obool, _1609289)), c_fequal)), hAPP(hAPP(c_COMBS(_1609289, _1609289, tc_prod(_1609289, _1609289)), c_Product__Type_OPair(_1609289, _1609289)), c_COMBI(_1609289))))))], (11134 ^ _775212) ^ [_957795, _957797, _957799, _957801, _957803] : [class_Rings_Olinordered__semiring__strict(_957795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957795), _957797), _957799)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957795), _957801), _957803)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957795), c_Groups_Ozero__class_Ozero(_957795)), _957799)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957795), c_Groups_Ozero__class_Ozero(_957795)), _957801)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957795), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_957795), _957797), _957801)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_957795), _957799), _957803))))], (44786 ^ _775212) ^ [_1659782, _1659784] : [-(hAPP(hAPP(c_List_Omap(_1659782, _1659782), c_COMBI(_1659782)), _1659784) = _1659784)], (602 ^ _775212) ^ [_784457, _784459, _784461, _784463, _784465, _784467] : [-(c_Relation_Ototal__on(_784465, _784461, _784457)), c_Relation_Ototal__on(_784467, _784463, _784459), _784467 = _784465, _784463 = _784461, _784459 = _784457], (34991 ^ _775212) ^ [_1418792, _1418794, _1418796, _1418798] : [class_Lattices_Olattice(_1418792), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1418792), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1418792), _1418794), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418792), _1418796), _1418798))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418792), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1418792), _1418794), _1418796)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1418792), _1418794), _1418798)))))], (16645 ^ _775212) ^ [_1058863, _1058865, _1058867] : [16647 ^ _775212 : [(16650 ^ _775212) ^ [] : [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(_1058865, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 16646 ^ [_1058863, _1058865, _1058867]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1058865, 16646 ^ [_1058863, _1058865, _1058867])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (16648 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16646 ^ [_1058863, _1058865, _1058867]), _1058863)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1058865, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1058867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1058867), hAPP(_1058865, _1058863))), 16660 ^ _775212 : [(16663 ^ _775212) ^ [] : [-(hAPP(_1058865, 16659 ^ [_1058863, _1058865, _1058867]) = _1058867)], (16661 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 16659 ^ [_1058863, _1058865, _1058867]), _1058863)))]]], (44407 ^ _775212) ^ [_1649209, _1649211, _1649213, _1649215] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649209), tc_List_Olist(_1649209))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649209), tc_List_Olist(_1649209)), _1649211), _1649213)), c_List_Olistrel1(_1649209, _1649215))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649209), tc_List_Olist(_1649209))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649209), tc_List_Olist(_1649209)), _1649211), _1649213)), c_List_Olistrel(_1649209, c_Transitive__Closure_Ortrancl(_1649209, _1649215)))))], (23512 ^ _775212) ^ [_1183316, _1183318, _1183320] : [c_Nitpick_Oless__frac(_1183316, _1183318, _1183320), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1183316), c_Nitpick_Oplus__frac(_1183316, _1183318, c_Nitpick_Ouminus__frac(_1183316, _1183320)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (48027 ^ _775212) ^ [_1734259, _1734261, _1734263] : [-(hBOOL(hAPP(hAPP(c_member(_1734259), _1734261), hAPP(c_List_Oset(_1734259), _1734263)))), -(c_List_Oremdups(_1734259, hAPP(hAPP(c_List_Olist_OCons(_1734259), _1734261), _1734263)) = hAPP(hAPP(c_List_Olist_OCons(_1734259), _1734261), c_List_Oremdups(_1734259, _1734263)))], (52015 ^ _775212) ^ [_1820326, _1820328, _1820330, _1820332] : [c_Equiv__Relations_Opart__equivp(_1820326, _1820328), hBOOL(hAPP(hAPP(_1820328, _1820330), _1820332)), -(hBOOL(hAPP(hAPP(_1820328, _1820332), _1820330)))], (11224 ^ _775212) ^ [_959519, _959521] : [class_Rings_Osemiring__1(_959519), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_959519), hAPP(c_Nat_OSuc, _959521)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959519), c_Groups_Oone__class_Oone(_959519)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_959519), _959521)))], (8125 ^ _775212) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15769 ^ _775212) ^ [_1042209, _1042211] : [-(_1042209 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042209), _1042211) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042209), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1042211)))], (12215 ^ _775212) ^ [_976099, _976101] : [12216 ^ _775212 : [(12219 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _976101))], (12217 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _976099))]], 12220 ^ _775212 : [(12227 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _976099), _976101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _976099)), hAPP(c_Int_Onat, _976101))))], (12221 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _976099)), hAPP(c_Int_Onat, _976101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _976099), _976101)))]]], (37186 ^ _775212) ^ [_1467080, _1467082, _1467084, _1467086, _1467088] : [c_Fun_Oinj__on(_1467080, _1467082, _1467084, _1467086), hBOOL(hAPP(hAPP(c_member(_1467082), _1467088), hAPP(c_Set_Oimage(_1467080, _1467082, _1467084), _1467086))), -(hAPP(_1467084, hAPP(c_Fun_Othe__inv__into(_1467080, _1467082, _1467086, _1467084), _1467088)) = _1467088)], (23698 ^ _775212) ^ [_1187091, _1187093] : [_1187091 = _1187093, -(hAPP(c_Code__Numeral_Oof__nat, _1187091) = hAPP(c_Code__Numeral_Oof__nat, _1187093))], (28044 ^ _775212) ^ [_1271862] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1271862)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1271862), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1271862)))], (6324 ^ _775212) ^ [_875074, _875076] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_875074, _875076)) = 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), _875074)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _875076))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21089 ^ _775212) ^ [_1136317, _1136319, _1136321, _1136323] : [class_Fields_Olinordered__field__inverse__zero(_1136317), class_Int_Onumber(_1136317), 21096 ^ _775212 : [(21097 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136317), _1136319), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136317), _1136321), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323)))), 21100 ^ _775212 : [(21107 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136317), c_Groups_Ozero__class_Ozero(_1136317)), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323)))), 21110 ^ _775212 : [(21117 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136317), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323)), c_Groups_Ozero__class_Ozero(_1136317)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136317), _1136319), c_Groups_Ozero__class_Ozero(_1136317))))], (21111 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136317), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323)), c_Groups_Ozero__class_Ozero(_1136317))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136317), _1136321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136317), _1136319), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323)))))]]], (21101 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136317), c_Groups_Ozero__class_Ozero(_1136317)), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136317), _1136319), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323))), _1136321)))]]], (21123 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136317), _1136319), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136317), _1136321), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323))))), 21126 ^ _775212 : [(21129 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136317), _1136319), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323))), _1136321))], (21127 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136317), c_Groups_Ozero__class_Ozero(_1136317)), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323))))]], 21130 ^ _775212 : [(21133 ^ _775212) ^ [] : [21134 ^ _775212 : [(21137 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136317), _1136321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136317), _1136319), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323))))], (21135 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136317), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323)), c_Groups_Ozero__class_Ozero(_1136317))))]], 21138 ^ _775212 : [(21141 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136317), _1136319), c_Groups_Ozero__class_Ozero(_1136317)))], (21139 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136317), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323)), c_Groups_Ozero__class_Ozero(_1136317)))]]], (21131 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136317), c_Groups_Ozero__class_Ozero(_1136317)), hAPP(c_Int_Onumber__class_Onumber__of(_1136317), _1136323)))]]]]], (48855 ^ _775212) ^ [_1752554, _1752556, _1752558] : [class_Orderings_Olinorder(_1752554), -(c_List_Olinorder__class_Osorted(_1752554, hAPP(c_List_Ofilter(_1752554, hAPP(hAPP(c_COMBC(_1752554, _1752554, tc_HOL_Obool), c_fequal), hAPP(_1752556, _1752558))), _1752558)))], (41041 ^ _775212) ^ [_1565785, _1565787, _1565789, _1565791] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1565785, tc_HOL_Obool), tc_fun(_1565785, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1565785, tc_HOL_Obool), tc_fun(_1565785, tc_HOL_Obool)), _1565787), _1565789)), c_Wellfounded_Omax__ext(_1565785, _1565791))), 41044 ^ _775212 : [(41047 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1565785), _1565789)))], (41049 ^ _775212) ^ [] : [_1565789 = c_Orderings_Obot__class_Obot(tc_fun(_1565785, tc_HOL_Obool))], (41051 ^ _775212) ^ [_1566079] : [hBOOL(hAPP(hAPP(c_member(_1565785), _1566079), _1565787)), 41055 ^ _775212 : [(41058 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565785, _1565785)), hAPP(hAPP(c_Product__Type_OPair(_1565785, _1565785), _1566079), 41054 ^ [_1565785, _1565787, _1565789, _1565791, _1566079])), _1565791)))], (41056 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565785), 41054 ^ [_1565785, _1565787, _1565789, _1565791, _1566079]), _1565789)))]]], (41045 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1565785), _1565787)))]]], (49185 ^ _775212) ^ [_1759408, _1759410, _1759412, _1759414, _1759416] : [c_List_Olist__all2(_1759408, _1759410, _1759412, hAPP(c_List_Orev(_1759408), _1759414), _1759416), -(c_List_Olist__all2(_1759408, _1759410, _1759412, _1759414, hAPP(c_List_Orev(_1759410), _1759416)))], (7262 ^ _775212) ^ [_890608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _890608)), -(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), _890608))))], (10057 ^ _775212) ^ [_938472, _938474, _938476, _938478] : [class_Groups_Oordered__comm__monoid__add(_938472), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938472), c_Groups_Ozero__class_Ozero(_938472)), _938474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938472), _938476), _938478)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938472), _938476), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938472), _938478), _938474))))], (30146 ^ _775212) ^ [_1315545, _1315547] : [c_Nat__Transfer_Ois__nat(_1315545), c_Nat__Transfer_Onat__set(_1315547), 30153 ^ _775212 : [(30160 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1315545)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1315547))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1315545), _1315547)))], (30154 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1315545), _1315547)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1315545)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1315547))))]]], (16849 ^ _775212) ^ [_1062500, _1062502] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062500)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062500)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062502)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062500)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062502))))], (48199 ^ _775212) ^ [_1738769, _1738771, _1738773] : [hBOOL(hAPP(c_List_Odistinct(_1738769), _1738771)), -(hBOOL(hAPP(c_List_Odistinct(_1738769), hAPP(c_List_Ofilter(_1738769, _1738773), _1738771))))], (41165 ^ _775212) ^ [_1568569, _1568571, _1568573] : [c_Wellfounded_Owf(_1568569, _1568571), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568569, _1568569)), hAPP(hAPP(c_Product__Type_OPair(_1568569, _1568569), hAPP(_1568573, hAPP(c_Nat_OSuc, 41168 ^ [_1568569, _1568571, _1568573]))), hAPP(_1568573, 41168 ^ [_1568569, _1568571, _1568573]))), _1568571))], (50445 ^ _775212) ^ [_1786840, _1786842, _1786844] : [hBOOL(hAPP(hAPP(c_member(_1786840), _1786842), hAPP(c_List_Oset(_1786840), _1786844))), -(_1786844 = hAPP(hAPP(c_List_Oappend(_1786840), 50448 ^ [_1786840, _1786842, _1786844]), hAPP(hAPP(c_List_Olist_OCons(_1786840), _1786842), 50449 ^ [_1786840, _1786842, _1786844])))], (7508 ^ _775212) ^ [_894973] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _894973)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_894973)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34663 ^ _775212) ^ [_1411829, _1411831, _1411833, _1411835] : [class_Lattices_Osemilattice__inf(_1411829), 34666 ^ _775212 : [(34675 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411829), _1411831), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411829), _1411833), _1411835)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411829), _1411831), _1411833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411829), _1411831), _1411835))], (34667 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411829), _1411831), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411829), _1411833), _1411835))), 34670 ^ _775212 : [(34673 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411829), _1411831), _1411835)))], (34671 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411829), _1411831), _1411833)))]]]]], (43517 ^ _775212) ^ [_1625611, _1625613, _1625615, _1625617] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1625611, tc_fun(_1625613, tc_HOL_Obool)), _1625615), _1625617) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625613, tc_HOL_Obool), hAPP(c_Set_Oimage(_1625611, tc_fun(_1625613, tc_HOL_Obool), _1625617), _1625615)))], (39182 ^ _775212) ^ [_1515529, _1515531] : [-(hAPP(c_Set_OPow(_1515529), _1515531) = hAPP(c_Set_OCollect(tc_fun(_1515529, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1515529, tc_HOL_Obool), tc_fun(_1515529, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1515529, tc_HOL_Obool))), _1515531)))], (25282 ^ _775212) ^ [_1215156, _1215158, _1215160] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215156, _1215158) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215160, _1215158), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1215158), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1215156), _1215160))))], (22792 ^ _775212) ^ [_1169372, _1169374] : [_1169372 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1169372, _1169374) = 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)))], (22084 ^ _775212) ^ [_1154300, _1154302, _1154304, _1154306, _1154308] : [hAPP(c_Product__Type_Osnd(_1154300, _1154302), hAPP(hAPP(c_Product__Type_OPair(_1154300, _1154302), _1154304), _1154306)) = _1154308, -(_1154306 = _1154308)], (50737 ^ _775212) ^ [_1792615, _1792617, _1792619] : [-(_1792615 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1792617), c_List_Oreplicate(_1792617, _1792615, _1792619)) = _1792619)], (6100 ^ _775212) ^ [_871907, _871909] : [-(_871907 = _871909), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871907), _871909))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871909), _871907)))], (49333 ^ _775212) ^ [_1762429, _1762431] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1762429), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1762429))), _1762431))), 49336 ^ _775212 : [(49343 ^ _775212) ^ [] : [-(_1762431 = c_List_Olist_ONil(tc_List_Olist(_1762429))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1762429))), c_List_Otranspose(_1762429, _1762431)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762429)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1762429)), _1762431), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49337 ^ _775212) ^ [] : [_1762431 = c_List_Olist_ONil(tc_List_Olist(_1762429)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1762429))), c_List_Otranspose(_1762429, _1762431)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7403 ^ _775212) ^ [_893057, _893059, _893061] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_893057, _893059, _893061)], (4734 ^ _775212) ^ [_847361, _847363, _847365, _847367] : [-(c_List_Oconcat(_847367, _847363) = c_List_Oconcat(_847365, _847361)), _847367 = _847365, _847363 = _847361], (7192 ^ _775212) ^ [_889499, _889501, _889503] : [class_Orderings_Olinorder(_889499), 7195 ^ _775212 : [(7196 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889499), _889501), _889503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889499), _889503), _889501))), -(_889501 = _889503)], (7206 ^ _775212) ^ [] : [7207 ^ _775212 : [(7210 ^ _775212) ^ [] : [_889501 = _889503], (7208 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889499), _889503), _889501))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_889499), _889501), _889503))]]], (2808 ^ _775212) ^ [_816872, _816874, _816876, _816878, _816880, _816882, _816884, _816886, _816888, _816890, _816892, _816894, _816896, _816898] : [-(c_New__Random__Sequence_Oneg__decr__bind(_816898, _816894, _816890, _816886, _816882, _816878, _816874) = c_New__Random__Sequence_Oneg__decr__bind(_816896, _816892, _816888, _816884, _816880, _816876, _816872)), _816898 = _816896, _816894 = _816892, _816890 = _816888, _816886 = _816884, _816882 = _816880, _816878 = _816876, _816874 = _816872], (22708 ^ _775212) ^ [_1167212, _1167214, _1167216, _1167218] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1167212), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167212), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1167212), _1167214), _1167216)), _1167218) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1167212), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167212), _1167214), _1167218)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167212), _1167216), _1167218)))], (13193 ^ _775212) ^ [_993759, _993761, _993763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993759)), 13196 ^ _775212 : [(13197 ^ _775212) ^ [] : [-(_993761 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _993763), _993759)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993759), _993761)), _993763)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993759), hAPP(c_Nat_OSuc, _993761))))], (13207 ^ _775212) ^ [] : [_993761 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _993763), _993759), 13210 ^ _775212 : [(13213 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993759), hAPP(c_Nat_OSuc, _993761)))))], (13211 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993759), _993761)), _993763)))]]]]], (22880 ^ _775212) ^ [_1171100, _1171102, _1171104, _1171106] : [class_Orderings_Olinorder(_1171100), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171100), _1171102), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171100), _1171104), _1171106)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171100), _1171104), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171100), _1171102), _1171106)))], (19641 ^ _775212) ^ [_1109648, _1109650, _1109652] : [class_Fields_Olinordered__field(_1109648), -(_1109650 = c_Groups_Ozero__class_Ozero(_1109648)), -(hAPP(c_Groups_Oabs__class_Oabs(_1109648), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109648), _1109652), _1109650)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109648), hAPP(c_Groups_Oabs__class_Oabs(_1109648), _1109652)), hAPP(c_Groups_Oabs__class_Oabs(_1109648), _1109650)))], (46780 ^ _775212) ^ [_1707664, _1707666, _1707668, _1707670] : [-(hAPP(c_List_Ofoldl(_1707664, _1707666, _1707668, _1707670), c_List_Olist_ONil(_1707666)) = _1707670)], (30680 ^ _775212) ^ [_1328726, _1328728, _1328730] : [30682 ^ _775212 : [(30685 ^ _775212) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1328730, 30681 ^ [_1328726, _1328728, _1328730]))], (30683 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1328726), 30681 ^ [_1328726, _1328728, _1328730]), _1328728)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1328726, tc_Int_Oint), _1328730), _1328728) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1328726, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1328726), c_Int_Onat), _1328730)), _1328728)))], (48412 ^ _775212) ^ [_1744643, _1744645] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1744643, _1744645)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1744645), _1744643))], (25635 ^ _775212) ^ [_1222731, _1222733, _1222735, _1222737] : [class_Groups_Oordered__ab__group__add__abs(_1222731), -(hAPP(c_Groups_Oabs__class_Oabs(_1222731), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222733, _1222731), hAPP(hAPP(c_COMBB(_1222731, _1222731, _1222733), c_Groups_Oabs__class_Oabs(_1222731)), _1222735)), _1222737)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222733, _1222731), hAPP(hAPP(c_COMBB(_1222731, _1222731, _1222733), c_Groups_Oabs__class_Oabs(_1222731)), _1222735)), _1222737))], (52453 ^ _775212) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (19099 ^ _775212) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25498 ^ _775212) ^ [_1219094, _1219096] : [class_Orderings_Oorder(_1219094), 25505 ^ _775212 : [(25508 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219094), hAPP(_1219096, 25503 ^ [_1219094, _1219096])), hAPP(_1219096, 25504 ^ [_1219094, _1219096])))], (25506 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 25503 ^ [_1219094, _1219096]), 25504 ^ [_1219094, _1219096])))]], -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1219094, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219096))], (6555 ^ _775212) ^ [_879099, _879101] : [class_Groups_Olinordered__ab__group__add(_879099), 6558 ^ _775212 : [(6565 ^ _775212) ^ [] : [_879101 = c_Groups_Ozero__class_Ozero(_879099), -(c_Groups_Ozero__class_Ozero(_879099) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879099), _879101), _879101))], (6559 ^ _775212) ^ [] : [c_Groups_Ozero__class_Ozero(_879099) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879099), _879101), _879101), -(_879101 = c_Groups_Ozero__class_Ozero(_879099))]]], (34055 ^ _775212) ^ [_1397740, _1397742, _1397744, _1397746] : [-(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), _1397740), _1397742)), 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), _1397744), _1397746)), 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), _1397740), _1397744)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1397742), _1397746))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1397740), _1397746)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1397742), _1397744)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (52741 ^ _775212) ^ [_1829104, _1829106] : [hBOOL(_1829104), -(hBOOL(hAPP(hAPP(c_fdisj, _1829106), _1829104)))], (47012 ^ _775212) ^ [_1712464, _1712466, _1712468] : [_1712464 = c_List_Olist_ONil(_1712466), -(c_List_Olast(_1712466, hAPP(hAPP(c_List_Oappend(_1712466), _1712468), _1712464)) = c_List_Olast(_1712466, _1712468))], (51179 ^ _775212) ^ [_1802703, _1802705] : [-(c_Lazy__Sequence_Oappend(_1802703, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1802703), _1802705) = _1802705)], (1774 ^ _775212) ^ [_800243, _800245] : [-(class_Groups_Omonoid__add(_800243)), _800245 = _800243, class_Groups_Omonoid__add(_800245)], (8035 ^ _775212) ^ [_904260] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _904260)), _904260) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6865 ^ _775212) ^ [_884630, _884632] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884630), _884632), 6870 ^ _775212 : [(6873 ^ _775212) ^ [] : [-(_884632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6871 ^ _775212) ^ [] : [-(_884630 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6874 ^ _775212 : [(6877 ^ _775212) ^ [] : [-(_884632 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6875 ^ _775212) ^ [] : [-(_884630 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (40107 ^ _775212) ^ [_1544172, _1544174] : [c_Wellfounded_OwfP(_1544172, _1544174), -(c_Wellfounded_Owf(_1544172, hAPP(c_Set_OCollect(tc_prod(_1544172, _1544172)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544172, _1544172, tc_HOL_Obool), _1544174))))], (34489 ^ _775212) ^ [_1408086, _1408088, _1408090, _1408092] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408086, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408086, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408086, tc_HOL_Obool)), _1408088), _1408090)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408086, tc_HOL_Obool)), _1408090), _1408092))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408086, tc_HOL_Obool)), _1408092), _1408088)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408086, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408086, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408086, tc_HOL_Obool)), _1408088), _1408090)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408086, tc_HOL_Obool)), _1408090), _1408092))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408086, tc_HOL_Obool)), _1408092), _1408088)))], (47138 ^ _775212) ^ [_1714977, _1714979, _1714981] : [-(_1714977 = c_List_Olist_ONil(_1714979)), -(c_List_Obutlast(_1714979, hAPP(hAPP(c_List_Olist_OCons(_1714979), _1714981), _1714977)) = hAPP(hAPP(c_List_Olist_OCons(_1714979), _1714981), c_List_Obutlast(_1714979, _1714977)))], (52109 ^ _775212) ^ [_1822296, _1822298] : [class_Complete__Lattice_Ocomplete__lattice(_1822296), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1822298, _1822296)))], (16941 ^ _775212) ^ [_1063836] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1063836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1063836), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10375 ^ _775212) ^ [_944179, _944181, _944183, _944185, _944187] : [class_Rings_Oordered__semiring(_944179), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944179), _944181), _944183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944179), _944185), _944187)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944179), c_Groups_Ozero__class_Ozero(_944179)), _944181)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944179), c_Groups_Ozero__class_Ozero(_944179)), _944185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944179), _944181), _944185)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944179), _944183), _944187))))], (23812 ^ _775212) ^ [_1189069] : [-(hAPP(c_Code__Numeral_Onat__of, _1189069) = c_Code__Numeral_Onat__of__aux(_1189069, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (43599 ^ _775212) ^ [_1627196, _1627198, _1627200, _1627202] : [-(_1627196 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1627198, tc_HOL_Obool), tc_HOL_Obool))), 43605 ^ _775212 : [(43608 ^ _775212) ^ [] : [c_Fun_Oinj__on(_1627198, _1627200, _1627202, 43604 ^ [_1627196, _1627198, _1627200, _1627202])], (43606 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1627198, tc_HOL_Obool)), 43604 ^ [_1627196, _1627198, _1627200, _1627202]), _1627196)))]], -(c_Fun_Oinj__on(_1627198, _1627200, _1627202, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1627198, tc_HOL_Obool), _1627196)))], (6150 ^ _775212) ^ [_872388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _872388)), _872388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46861 ^ _775212) ^ [_1709303, _1709305, _1709307] : [class_Lattices_Olattice(_1709303), -(c_Big__Operators_Olattice__class_OSup__fin(_1709303, hAPP(c_List_Oset(_1709303), hAPP(hAPP(c_List_Olist_OCons(_1709303), _1709305), _1709307))) = hAPP(c_List_Ofoldl(_1709303, _1709303, c_Lattices_Osemilattice__sup__class_Osup(_1709303), _1709305), _1709307))], (16327 ^ _775212) ^ [_1052341, _1052343, _1052345, _1052347] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052341), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1052341), _1052343), _1052345)), hAPP(c_Int_Onumber__class_Onumber__of(_1052341), _1052347)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1052341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052341), _1052343), hAPP(c_Int_Onumber__class_Onumber__of(_1052341), _1052347))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052341), _1052345), hAPP(c_Int_Onumber__class_Onumber__of(_1052341), _1052347)))), class_Int_Onumber(_1052341), class_Rings_Oring(_1052341)], (51932 ^ _775212) ^ [_1818781, _1818783] : [51933 ^ _775212 : [(51934 ^ _775212) ^ [_1818837] : [hBOOL(hAPP(hAPP(_1818781, _1818837), _1818837))]], c_Predicate_Osymp(_1818783, _1818781), c_Predicate_Otransp(_1818783, _1818781), -(c_Equiv__Relations_Opart__equivp(_1818783, _1818781))], (43008 ^ _775212) ^ [_1613560, _1613562, _1613564, _1613566] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613560, _1613560)), _1613562), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1613560, _1613560), tc_HOL_Obool), _1613564), _1613566))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613560, _1613560)), _1613562), c_Transitive__Closure_Ortrancl(_1613560, _1613566))))], (36525 ^ _775212) ^ [_1453338, _1453340, _1453342, _1453344] : [36527 ^ _775212 : [(36531 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1453338), 36529 ^ [_1453338, _1453340, _1453342, _1453344]), _1453344)))], (36533 ^ _775212) ^ [] : [-(hAPP(_1453342, 36526 ^ [_1453338, _1453340, _1453342, _1453344]) = hAPP(_1453342, 36529 ^ [_1453338, _1453340, _1453342, _1453344]))], (36535 ^ _775212) ^ [] : [36526 ^ [_1453338, _1453340, _1453342, _1453344] = 36529 ^ [_1453338, _1453340, _1453342, _1453344]], (36528 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1453338), 36526 ^ [_1453338, _1453340, _1453342, _1453344]), _1453344)))]], -(c_Fun_Oinj__on(_1453338, _1453340, _1453342, _1453344))], (25434 ^ _775212) ^ [_1217789, _1217791, _1217793, _1217795] : [-(c_New__Random__Sequence_Opos__empty(_1217789, _1217791, _1217793, _1217795) = c_New__DSequence_Opos__empty(_1217789))], (86 ^ _775212) ^ [_776393, _776395] : [-(class_Rings_Oinverse(_776393)), _776395 = _776393, class_Rings_Oinverse(_776395)], (18445 ^ _775212) ^ [_1088547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088547), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1088547)), c_Int_OMin)))], (51399 ^ _775212) ^ [_1807321, _1807323] : [-(c_Relation_Otrans(_1807321, c_Transitive__Closure_Ortrancl(_1807321, _1807323)))], (27309 ^ _775212) ^ [_1256343, _1256345, _1256347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256343, tc_HOL_Obool)), _1256345), _1256347)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256343, tc_HOL_Obool)), _1256345), _1256347) = _1256347)], (26351 ^ _775212) ^ [_1237882, _1237884, _1237886, _1237888, _1237890] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1237882, tc_HOL_Obool)), _1237884), hAPP(c_Set_Oimage(_1237886, _1237882, _1237888), _1237890)))), 26352 ^ _775212 : [(26353 ^ _775212) ^ [_1237962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1237886, tc_HOL_Obool)), _1237962), _1237890)), _1237884 = hAPP(c_Set_Oimage(_1237886, _1237882, _1237888), _1237962)]]], (40393 ^ _775212) ^ [_1551134, _1551136, _1551138] : [-(hAPP(c_Fun_Ocomp(_1551134, _1551136, _1551134, _1551138), c_Fun_Oid(_1551134)) = _1551138)], (49998 ^ _775212) ^ [_1777219, _1777221, _1777223] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1777219, _1777221), _1777223) = c_Lazy__Sequence_Oproduct(_1777219, _1777221, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1777219, _1777223), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1777221, _1777223))), class_Lazy__Sequence_Osmall__lazy(_1777219), class_Lazy__Sequence_Osmall__lazy(_1777221)], (18141 ^ _775212) ^ [_1083280, _1083282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1083280)), c_Int_OBit0(_1083282))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083280), _1083282)))], (9127 ^ _775212) ^ [_923028] : [class_Rings_Olinordered__semidom(_923028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923028), c_Groups_Oone__class_Oone(_923028)), c_Groups_Ozero__class_Ozero(_923028)))], (47304 ^ _775212) ^ [_1718170, _1718172, _1718174] : [-(hBOOL(hAPP(hAPP(c_member(_1718170), _1718172), hAPP(c_List_Oset(_1718170), _1718174)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718170)), c_List_Oremove1(_1718170, _1718172, _1718174)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718170)), _1718174))], (7635 ^ _775212) ^ [_897353, _897355, _897357, _897359] : [class_Rings_Ocomm__semiring__1(_897353), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897353), _897355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897353), _897357), _897359)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897353), _897357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897353), _897355), _897359)))], (16837 ^ _775212) ^ [_1062310, _1062312] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062310)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062310)), _1062312) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062310)), _1062312)))], (44054 ^ _775212) ^ [_1638498, _1638500, _1638502, _1638504] : [class_Rings_Olinordered__semidom(_1638498), 44060 ^ _775212 : [(44063 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1638498), c_Groups_Ozero__class_Ozero(_1638498)), hAPP(_1638504, 44059 ^ [_1638498, _1638500, _1638502, _1638504])))], (44061 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1638500), 44059 ^ [_1638498, _1638500, _1638502, _1638504]), _1638502)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1638498), c_Groups_Ozero__class_Ozero(_1638498)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1638500, _1638498), _1638504), _1638502))))], (23762 ^ _775212) ^ [_1188206, _1188208] : [_1188206 = _1188208, -(hAPP(c_Code__Numeral_Onat__of, _1188206) = hAPP(c_Code__Numeral_Onat__of, _1188208))], (5068 ^ _775212) ^ [_852504, _852506, _852508, _852510, _852512, _852514] : [-(c_Lazy__Sequence_Oappend(_852514, _852510, _852506) = c_Lazy__Sequence_Oappend(_852512, _852508, _852504)), _852514 = _852512, _852510 = _852508, _852506 = _852504], (6962 ^ _775212) ^ [_886181, _886183] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886181), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886183), _886181)))))], (46802 ^ _775212) ^ [_1708177, _1708179] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1708177), _1708179) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 46805 ^ _775212 : [(46808 ^ _775212) ^ [_1708291] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1708291), hAPP(c_List_Oset(tc_Nat_Onat), _1708179))), -(_1708291 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46806 ^ _775212) ^ [] : [-(_1708177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (46033 ^ _775212) ^ [_1690339, _1690341, _1690343, _1690345, _1690347] : [-(hAPP(hAPP(c_List_Olist__update(_1690339, hAPP(hAPP(c_List_Olist_OCons(_1690339), _1690341), _1690343)), _1690345), _1690347) = c_Nat_Onat_Onat__case(tc_List_Olist(_1690339), hAPP(hAPP(c_List_Olist_OCons(_1690339), _1690347), _1690343), hAPP(hAPP(c_COMBB(tc_List_Olist(_1690339), tc_List_Olist(_1690339), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1690339), _1690341)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1690339, tc_List_Olist(_1690339)), c_List_Olist__update(_1690339, _1690343)), _1690347)), _1690345))], (50762 ^ _775212) ^ [_1793069, _1793071, _1793073, _1793075] : [50763 ^ _775212 : [(50766 ^ _775212) ^ [] : [_1793071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50764 ^ _775212) ^ [] : [hBOOL(hAPP(_1793075, _1793073))]], 50767 ^ _775212 : [(50768 ^ _775212) ^ [_1793194] : [hBOOL(hAPP(hAPP(c_member(_1793069), _1793194), hAPP(c_List_Oset(_1793069), c_List_Oreplicate(_1793069, _1793071, _1793073)))), -(hBOOL(hAPP(_1793075, _1793194)))]]], (48380 ^ _775212) ^ [_1743687, _1743689, _1743691, _1743693] : [-(c_List_Ofoldr(_1743687, _1743689, _1743691, c_List_Olist_ONil(_1743687), _1743693) = _1743693)], (21667 ^ _775212) ^ [_1146423, _1146425, _1146427] : [_1146423 = _1146425, 21670 ^ _775212 : [(21673 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146427, tc_HOL_Obool)), _1146425), _1146423)))], (21671 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146427, tc_HOL_Obool)), _1146423), _1146425)))]]], (16555 ^ _775212) ^ [_1056882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1056882)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1056882 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31301 ^ _775212) ^ [_1341628, _1341630, _1341632, _1341634, _1341636, _1341638] : [-(hBOOL(hAPP(hAPP(c_member(_1341628), _1341630), c_SetInterval_Oord_OgreaterThanAtMost(_1341628, _1341632, _1341634, _1341636, _1341638)))), hBOOL(hAPP(hAPP(_1341634, _1341636), _1341630)), hBOOL(hAPP(hAPP(_1341632, _1341630), _1341638))], (44152 ^ _775212) ^ [_1641361, _1641363, _1641365] : [hAPP(hAPP(c_List_Olist_OCons(_1641361), _1641363), _1641365) = _1641365], (45029 ^ _775212) ^ [_1665773, _1665775, _1665777, _1665779] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1665773), tc_List_Olist(_1665773))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1665773), tc_List_Olist(_1665773)), _1665775), _1665777)), c_List_Olistrel(_1665773, _1665779))), 45032 ^ _775212 : [(45035 ^ _775212) ^ [_1666109] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1665773, _1665773)), _1666109), hAPP(c_List_Oset(tc_prod(_1665773, _1665773)), hAPP(hAPP(c_List_Ozip(_1665773, _1665773), _1665775), _1665777)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1665773, _1665773, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1665773, tc_fun(tc_prod(_1665773, _1665773), tc_HOL_Obool), tc_fun(_1665773, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1665773, tc_fun(tc_fun(tc_prod(_1665773, _1665773), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1665773, _1665773), tc_HOL_Obool), tc_fun(_1665773, tc_HOL_Obool)), _1665773), c_COMBC(_1665773, tc_fun(tc_prod(_1665773, _1665773), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1665773, tc_prod(_1665773, _1665773)), tc_fun(_1665773, tc_fun(tc_fun(tc_prod(_1665773, _1665773), tc_HOL_Obool), tc_HOL_Obool)), _1665773), hAPP(c_COMBB(tc_prod(_1665773, _1665773), tc_fun(tc_fun(tc_prod(_1665773, _1665773), tc_HOL_Obool), tc_HOL_Obool), _1665773), c_member(tc_prod(_1665773, _1665773)))), c_Product__Type_OPair(_1665773, _1665773)))), _1665779)), _1666109)))], (45033 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665773)), _1665775) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665773)), _1665777))]]], (42549 ^ _775212) ^ [_1601446, _1601448, _1601450] : [c_Equiv__Relations_Oequiv(_1601446, _1601448, _1601450), -(hAPP(hAPP(c_Relation_Orel__comp(_1601446, _1601446, _1601446), hAPP(c_Relation_Oconverse(_1601446, _1601446), _1601450)), _1601450) = _1601450)], (26342 ^ _775212) ^ [_1237678, _1237680, _1237682, _1237684, _1237686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1237678, tc_HOL_Obool)), _1237680), hAPP(c_Set_Oimage(_1237682, _1237678, _1237684), _1237686))), 26346 ^ _775212 : [(26349 ^ _775212) ^ [] : [-(_1237680 = hAPP(c_Set_Oimage(_1237682, _1237678, _1237684), 26345 ^ [_1237678, _1237680, _1237682, _1237684, _1237686]))], (26347 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1237682, tc_HOL_Obool)), 26345 ^ [_1237678, _1237680, _1237682, _1237684, _1237686]), _1237686)))]]], (50839 ^ _775212) ^ [_1794661, _1794663, _1794665, _1794667, _1794669] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1794661, _1794663, _1794665), _1794667), _1794669)), -(hBOOL(hAPP(hAPP(_1794665, _1794669), _1794667)))], (34979 ^ _775212) ^ [_1418330, _1418332, _1418334, _1418336, _1418338] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418330, tc_HOL_Obool)), _1418332), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418334, tc_fun(_1418330, tc_HOL_Obool)), _1418336), _1418338)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418334, tc_fun(_1418330, tc_HOL_Obool)), _1418336), hAPP(hAPP(c_COMBB(tc_fun(_1418330, tc_HOL_Obool), tc_fun(_1418330, tc_HOL_Obool), _1418334), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418330, tc_HOL_Obool)), _1418332)), _1418338)))], (21913 ^ _775212) ^ [_1151045, _1151047, _1151049, _1151051, _1151053] : [hBOOL(hAPP(hAPP(_1151045, _1151047), _1151049)), -(hBOOL(hAPP(hAPP(_1151045, hAPP(c_Product__Type_Osnd(_1151051, _1151053), hAPP(hAPP(c_Product__Type_OPair(_1151051, _1151053), _1151049), _1151047))), hAPP(c_Product__Type_Ofst(_1151051, _1151053), hAPP(hAPP(c_Product__Type_OPair(_1151051, _1151053), _1151049), _1151047)))))], (37616 ^ _775212) ^ [_1476866, _1476868, _1476870] : [hBOOL(hAPP(hAPP(c_member(_1476866), _1476870), c_Wellfounded_Oacc(_1476866, _1476868))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1476866, hAPP(hAPP(c_COMBC(_1476866, tc_fun(tc_prod(_1476866, _1476866), tc_HOL_Obool), tc_fun(_1476866, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476866, tc_fun(tc_fun(tc_prod(_1476866, _1476866), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1476866, _1476866), tc_HOL_Obool), tc_fun(_1476866, tc_HOL_Obool)), _1476866), c_COMBC(_1476866, tc_fun(tc_prod(_1476866, _1476866), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476866, tc_prod(_1476866, _1476866)), tc_fun(_1476866, tc_fun(tc_fun(tc_prod(_1476866, _1476866), tc_HOL_Obool), tc_HOL_Obool)), _1476866), hAPP(c_COMBB(tc_prod(_1476866, _1476866), tc_fun(tc_fun(tc_prod(_1476866, _1476866), tc_HOL_Obool), tc_HOL_Obool), _1476866), c_member(tc_prod(_1476866, _1476866)))), c_Product__Type_OPair(_1476866, _1476866)))), _1476868)), _1476870)))], (39892 ^ _775212) ^ [_1538720, _1538722, _1538724] : [_1538724 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1538720, _1538722), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1538720, _1538722), _1538724) = c_Orderings_Obot__class_Obot(tc_fun(_1538720, tc_HOL_Obool)))], (26746 ^ _775212) ^ [_1245214, _1245216] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1245214), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1245216) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1245214, _1245216))], (40510 ^ _775212) ^ [_1553843, _1553845, _1553847, _1553849, _1553851] : [c_Fun_Oinj__on(_1553843, _1553845, _1553847, c_Orderings_Otop__class_Otop(tc_fun(_1553843, tc_HOL_Obool))), c_Fun_Oinj__on(_1553849, _1553843, _1553851, c_Orderings_Otop__class_Otop(tc_fun(_1553849, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1553849, _1553845, hAPP(c_Fun_Ocomp(_1553843, _1553845, _1553849, _1553847), _1553851), c_Orderings_Otop__class_Otop(tc_fun(_1553849, tc_HOL_Obool))))], (7046 ^ _775212) ^ [_887458, _887460, _887462, _887464] : [class_Orderings_Oorder(_887458), _887460 = _887462, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887458), _887464), _887462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887458), _887464), _887460)))], (16713 ^ _775212) ^ [_1060244, _1060246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060244)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1060244), _1060246)))], (45393 ^ _775212) ^ [_1675458] : [class_Groups_Omonoid__add(_1675458), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1675458), c_List_Olist_ONil(_1675458)) = c_Groups_Ozero__class_Ozero(_1675458))], (14167 ^ _775212) ^ [_1011268, _1011270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1011268), _1011270)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1011270)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1011268)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1011270), _1011268)))], (34167 ^ _775212) ^ [_1400869, _1400871, _1400873, _1400875, _1400877] : [c_Equiv__Relations_Oequiv(_1400869, _1400871, _1400873), hBOOL(hAPP(hAPP(c_member(_1400869), _1400875), _1400871)), hBOOL(hAPP(hAPP(c_member(_1400869), _1400877), _1400871)), 34178 ^ _775212 : [(34185 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1400869, _1400869)), hAPP(hAPP(c_Product__Type_OPair(_1400869, _1400869), _1400875), _1400877)), _1400873)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400869), hAPP(hAPP(c_Set_Oinsert(_1400869), _1400875), c_Orderings_Obot__class_Obot(tc_fun(_1400869, tc_HOL_Obool)))), _1400873) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400869), hAPP(hAPP(c_Set_Oinsert(_1400869), _1400877), c_Orderings_Obot__class_Obot(tc_fun(_1400869, tc_HOL_Obool)))), _1400873))], (34179 ^ _775212) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400869), hAPP(hAPP(c_Set_Oinsert(_1400869), _1400875), c_Orderings_Obot__class_Obot(tc_fun(_1400869, tc_HOL_Obool)))), _1400873) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400869), hAPP(hAPP(c_Set_Oinsert(_1400869), _1400877), c_Orderings_Obot__class_Obot(tc_fun(_1400869, tc_HOL_Obool)))), _1400873), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1400869, _1400869)), hAPP(hAPP(c_Product__Type_OPair(_1400869, _1400869), _1400875), _1400877)), _1400873)))]]], (26095 ^ _775212) ^ [_1232359, _1232361] : [26097 ^ _775212 : [(26100 ^ _775212) ^ [] : [hBOOL(hAPP(_1232361, 26096 ^ [_1232359, _1232361]))], (26098 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26096 ^ [_1232359, _1232361]), _1232359)))]], 26101 ^ _775212 : [(26102 ^ _775212) ^ [_1232509] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1232509), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232359))), -(hBOOL(hAPP(_1232361, _1232509)))]]], (41526 ^ _775212) ^ [_1575795, _1575797, _1575799] : [class_Lattices_Olattice(_1575795), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575795), _1575797)), -(hBOOL(hAPP(hAPP(c_member(_1575795), _1575799), _1575797))), -(c_Big__Operators_Olattice__class_OInf__fin(_1575795, hAPP(hAPP(c_Set_Oinsert(_1575795), _1575799), _1575797)) = hAPP(hAPP(c_Finite__Set_Ofold(_1575795, _1575795, c_Lattices_Osemilattice__inf__class_Oinf(_1575795)), _1575799), _1575797))], (28754 ^ _775212) ^ [_1286074, _1286076, _1286078, _1286080] : [28756 ^ _775212 : [(28759 ^ _775212) ^ [] : [hAPP(_1286080, 28755 ^ [_1286074, _1286076, _1286078, _1286080]) = c_Orderings_Obot__class_Obot(tc_fun(_1286076, tc_HOL_Obool))], (28757 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1286074), 28755 ^ [_1286074, _1286076, _1286078, _1286080]), _1286078)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1286074, tc_fun(_1286076, tc_HOL_Obool)), _1286078), _1286080) = c_Orderings_Obot__class_Obot(tc_fun(_1286076, tc_HOL_Obool)))], (11230 ^ _775212) ^ [_959640, _959642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _959640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _959642)), -(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), _959642), _959640))))], (28265 ^ _775212) ^ [] : [-(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))))], (3934 ^ _775212) ^ [_834889, _834891, _834893, _834895] : [-(c_Big__Operators_Olinorder__class_OMin(_834895, _834891) = c_Big__Operators_Olinorder__class_OMin(_834893, _834889)), _834895 = _834893, _834891 = _834889], (13857 ^ _775212) ^ [_1005397, _1005399, _1005401] : [hBOOL(hAPP(_1005397, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1005399), _1005401))), 13860 ^ _775212 : [(13867 ^ _775212) ^ [] : [-(_1005401 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 13870 ^ _775212 : [(13871 ^ _775212) ^ [_1005649, _1005651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1005649), _1005401)), _1005399 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005401), _1005651)), _1005649), -(hBOOL(hAPP(_1005397, _1005651)))]]], (13861 ^ _775212) ^ [] : [_1005401 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1005397, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (29967 ^ _775212) ^ [_1310927, _1310929, _1310931, _1310933] : [_1310931 = _1310933, -(hAPP(hAPP(c_COMBC(_1310927, tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_fun(_1310929, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1310929, tc_fun(tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_fun(_1310929, tc_HOL_Obool)), _1310927), c_COMBC(_1310929, tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1310929, tc_prod(_1310927, _1310929)), tc_fun(_1310929, tc_fun(tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_HOL_Obool)), _1310927), hAPP(c_COMBB(tc_prod(_1310927, _1310929), tc_fun(tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_HOL_Obool), _1310929), c_member(tc_prod(_1310927, _1310929)))), c_Product__Type_OPair(_1310927, _1310929)))), _1310931) = hAPP(hAPP(c_COMBC(_1310927, tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_fun(_1310929, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1310929, tc_fun(tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_fun(_1310929, tc_HOL_Obool)), _1310927), c_COMBC(_1310929, tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1310929, tc_prod(_1310927, _1310929)), tc_fun(_1310929, tc_fun(tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_HOL_Obool)), _1310927), hAPP(c_COMBB(tc_prod(_1310927, _1310929), tc_fun(tc_fun(tc_prod(_1310927, _1310929), tc_HOL_Obool), tc_HOL_Obool), _1310929), c_member(tc_prod(_1310927, _1310929)))), c_Product__Type_OPair(_1310927, _1310929)))), _1310933))], (28428 ^ _775212) ^ [_1279444, _1279446, _1279448, _1279450] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279444), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279444, tc_HOL_Obool)), _1279446), hAPP(hAPP(c_Set_Oinsert(_1279444), _1279448), _1279450)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279444), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279444, tc_HOL_Obool)), _1279446), _1279450))))], (44885 ^ _775212) ^ [_1661991, _1661993, _1661995] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1661991, tc_HOL_Obool)), hAPP(c_List_Oset(_1661991), _1661993)), hAPP(c_List_Oset(_1661991), hAPP(hAPP(c_List_Olist_OCons(_1661991), _1661995), _1661993)))))], (11374 ^ _775212) ^ [_961839, _961841] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _961839)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _961841))))), _961839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _961841 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47085 ^ _775212) ^ [_1713828, _1713830, _1713832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1713828), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713830)), _1713832))), -(c_List_Obutlast(_1713830, hAPP(hAPP(c_List_Otake(_1713830), _1713828), _1713832)) = hAPP(hAPP(c_List_Otake(_1713830), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1713828), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1713832))], (30166 ^ _775212) ^ [_1315848, _1315850, _1315852] : [class_Orderings_Oord(_1315848), 30169 ^ _775212 : [(30176 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315848), _1315850), _1315852)), -(hBOOL(hAPP(hAPP(c_member(_1315848), _1315850), hAPP(c_SetInterval_Oord__class_OatMost(_1315848), _1315852))))], (30170 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1315848), _1315850), hAPP(c_SetInterval_Oord__class_OatMost(_1315848), _1315852))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315848), _1315850), _1315852)))]]], (51261 ^ _775212) ^ [_1804307, _1804309, _1804311] : [-(c_List_Olist__ex(_1804307, _1804309, _1804311)), 51262 ^ _775212 : [(51263 ^ _775212) ^ [_1804364] : [hBOOL(hAPP(hAPP(c_member(_1804307), _1804364), hAPP(c_List_Oset(_1804307), _1804311))), hBOOL(hAPP(_1804309, _1804364))]]], (47132 ^ _775212) ^ [_1714874, _1714876, _1714878] : [_1714874 = c_List_Olist_ONil(_1714876), -(c_List_Obutlast(_1714876, hAPP(hAPP(c_List_Olist_OCons(_1714876), _1714878), _1714874)) = c_List_Olist_ONil(_1714876))], (22200 ^ _775212) ^ [_1156724, _1156726] : [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(_1156724))), 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)), _1156726))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156724) = hAPP(c_Nat_OSuc, _1156726))], (31755 ^ _775212) ^ [_1349706, _1349708, _1349710] : [class_Lattices_Olattice(_1349706), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349706), _1349708)), hBOOL(hAPP(hAPP(c_member(_1349706), _1349710), _1349708)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1349706), _1349710), c_Big__Operators_Olattice__class_OSup__fin(_1349706, _1349708)) = c_Big__Operators_Olattice__class_OSup__fin(_1349706, _1349708))], (46620 ^ _775212) ^ [_1704306, _1704308, _1704310, _1704312] : [-(hBOOL(hAPP(c_List_Odistinct(_1704306), hAPP(hAPP(c_List_Omap(_1704308, _1704306), _1704310), _1704312)))), hBOOL(hAPP(c_List_Odistinct(_1704308), _1704312)), c_Fun_Oinj__on(_1704308, _1704306, _1704310, hAPP(c_List_Oset(_1704308), _1704312))], (52191 ^ _775212) ^ [_1823373, _1823375] : [class_Orderings_Obot(_1823373), -(class_Orderings_Obot(tc_fun(_1823375, _1823373)))], (50280 ^ _775212) ^ [_1783392, _1783394, _1783396] : [class_Enum_Oenum(_1783392), class_Enum_Oenum(_1783394), 50287 ^ _775212 : [(50294 ^ _775212) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1783394), hAPP(hAPP(c_COMBB(tc_fun(_1783392, tc_HOL_Obool), tc_HOL_Obool, _1783394), c_Enum_Oenum__class_Oenum__all(_1783392)), hAPP(hAPP(c_COMBB(tc_fun(_1783392, tc_prod(_1783394, _1783392)), tc_fun(_1783392, tc_HOL_Obool), _1783394), hAPP(c_COMBB(tc_prod(_1783394, _1783392), tc_HOL_Obool, _1783392), _1783396)), c_Product__Type_OPair(_1783394, _1783392))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1783394, _1783392)), _1783396)))], (50288 ^ _775212) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1783394, _1783392)), _1783396)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1783394), hAPP(hAPP(c_COMBB(tc_fun(_1783392, tc_HOL_Obool), tc_HOL_Obool, _1783394), c_Enum_Oenum__class_Oenum__all(_1783392)), hAPP(hAPP(c_COMBB(tc_fun(_1783392, tc_prod(_1783394, _1783392)), tc_fun(_1783392, tc_HOL_Obool), _1783394), hAPP(c_COMBB(tc_prod(_1783394, _1783392), tc_HOL_Obool, _1783392), _1783396)), c_Product__Type_OPair(_1783394, _1783392))))))]]], (27820 ^ _775212) ^ [_1267726, _1267728, _1267730, _1267732, _1267734] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267726, tc_fun(_1267728, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267726, tc_HOL_Obool)), _1267730), _1267732)), _1267734) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267728, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267726, tc_fun(_1267728, tc_HOL_Obool)), _1267730), _1267734)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267726, tc_fun(_1267728, tc_HOL_Obool)), _1267732), _1267734)))], (40888 ^ _775212) ^ [_1562344, _1562346, _1562348, _1562350, _1562352, _1562354, _1562356] : [c_Finite__Set_Ofolding__idem(_1562344, _1562346, _1562348, _1562350), -(hAPP(c_Fun_Ocomp(_1562346, _1562346, _1562352, hAPP(_1562348, _1562354)), hAPP(c_Fun_Ocomp(_1562346, _1562346, _1562352, hAPP(_1562348, _1562354)), _1562356)) = hAPP(c_Fun_Ocomp(_1562346, _1562346, _1562352, hAPP(_1562348, _1562354)), _1562356))], (14793 ^ _775212) ^ [_1022905, _1022907, _1022909] : [class_Rings_Ocomm__semiring__1(_1022905), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022905), _1022907), hAPP(hAPP(c_Power_Opower__class_Opower(_1022905), _1022907), _1022909)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1022905), _1022907), hAPP(c_Nat_OSuc, _1022909)))], (37761 ^ _775212) ^ [_1480176, _1480178, _1480180, _1480182] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1480176), _1480178)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480176), _1480180)), -(_1480180 = c_Orderings_Obot__class_Obot(tc_fun(_1480176, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1480176, tc_HOL_Obool), tc_fun(_1480176, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1480176, tc_HOL_Obool), tc_fun(_1480176, tc_HOL_Obool)), _1480178), _1480180)), c_Wellfounded_Omax__ext(_1480176, _1480182)))), 37775 ^ _775212 : [(37778 ^ _775212) ^ [_1480581] : [hBOOL(hAPP(hAPP(c_member(_1480176), _1480581), _1480180)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1480176, _1480176)), hAPP(hAPP(c_Product__Type_OPair(_1480176, _1480176), 37774 ^ [_1480176, _1480178, _1480180, _1480182]), _1480581)), _1480182))], (37776 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1480176), 37774 ^ [_1480176, _1480178, _1480180, _1480182]), _1480178)))]]], (4050 ^ _775212) ^ [_836683, _836685, _836687, _836689] : [-(c_HOL_OLet(_836689, _836685) = c_HOL_OLet(_836687, _836683)), _836689 = _836687, _836685 = _836683], (1274 ^ _775212) ^ [_793993, _793995] : [-(class_Int_Onumber__ring(_793993)), _793995 = _793993, class_Int_Onumber__ring(_793995)], (9659 ^ _775212) ^ [_931282, _931284, _931286, _931288] : [class_Groups_Oordered__ab__semigroup__add(_931282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931282), _931284), _931286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931282), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931282), _931288), _931284)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931282), _931288), _931286))))], (46550 ^ _775212) ^ [_1702673, _1702675] : [hBOOL(hAPP(c_List_Odistinct(_1702673), _1702675)), -(hAPP(c_Finite__Set_Ocard(_1702673), hAPP(c_List_Oset(_1702673), _1702675)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702673)), _1702675))], (37363 ^ _775212) ^ [_1470736, _1470738, _1470740] : [class_Lattices_Olattice(_1470736), hAPP(_1470738, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1470736), 37368 ^ [_1470736, _1470738, _1470740]), 37369 ^ [_1470736, _1470738, _1470740])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1470736), hAPP(_1470738, 37368 ^ [_1470736, _1470738, _1470740])), hAPP(_1470738, 37369 ^ [_1470736, _1470738, _1470740])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470736), _1470740)), -(_1470740 = c_Orderings_Obot__class_Obot(tc_fun(_1470736, tc_HOL_Obool))), -(hAPP(_1470738, c_Big__Operators_Olattice__class_OInf__fin(_1470736, _1470740)) = c_Big__Operators_Olattice__class_OInf__fin(_1470736, hAPP(c_Set_Oimage(_1470736, _1470736, _1470738), _1470740)))], (50213 ^ _775212) ^ [_1782210, _1782212, _1782214, _1782216] : [class_Orderings_Oorder(_1782210), class_Enum_Oenum(_1782212), 50220 ^ _775212 : [(50227 ^ _775212) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1782212), hAPP(hAPP(c_COMBS(_1782212, _1782210, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1782210, tc_fun(_1782210, tc_HOL_Obool), _1782212), c_Orderings_Oord__class_Oless__eq(_1782210)), _1782214)), _1782216))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1782212, _1782210)), _1782214), _1782216)))], (50221 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1782212, _1782210)), _1782214), _1782216)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1782212), hAPP(hAPP(c_COMBS(_1782212, _1782210, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1782210, tc_fun(_1782210, tc_HOL_Obool), _1782212), c_Orderings_Oord__class_Oless__eq(_1782210)), _1782214)), _1782216))))]]], (27051 ^ _775212) ^ [_1251452, _1251454, _1251456] : [class_Lattices_Osemilattice__sup(_1251452), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251452), _1251454), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251452), _1251454), _1251456)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251452), _1251454), _1251456))], (51175 ^ _775212) ^ [_1802622, _1802624, _1802626] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1802622) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1802622, _1802624, _1802626)], (2998 ^ _775212) ^ [_820057, _820059, _820061, _820063, _820065, _820067] : [-(c_SetInterval_Oord_OgreaterThan(_820067, _820063, _820059) = c_SetInterval_Oord_OgreaterThan(_820065, _820061, _820057)), _820067 = _820065, _820063 = _820061, _820059 = _820057], (18123 ^ _775212) ^ [_1082935, _1082937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1082935), _1082937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1082935)), c_Int_OBit0(_1082937))))], (35115 ^ _775212) ^ [_1421753, _1421755, _1421757, _1421759, _1421761] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1421753, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1421755, _1421753, _1421757), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421755, tc_HOL_Obool)), _1421759), _1421761))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421753, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1421755, _1421753, _1421757), _1421759)), hAPP(c_Relation_OImage(_1421755, _1421753, _1421757), _1421761)))))], (45858 ^ _775212) ^ [_1686179, _1686181, _1686183, _1686185, _1686187, _1686189] : [-(hAPP(hAPP(c_List_Omap(_1686179, _1686181), _1686183), hAPP(hAPP(c_List_Olist__update(_1686179, _1686185), _1686187), _1686189)) = hAPP(hAPP(c_List_Olist__update(_1686181, hAPP(hAPP(c_List_Omap(_1686179, _1686181), _1686183), _1686185)), _1686187), hAPP(_1686183, _1686189)))], (38678 ^ _775212) ^ [_1502060, _1502062, _1502064, _1502066] : [c_Big__Operators_Osemilattice__big(_1502060, _1502062, _1502064), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502060), _1502066)), -(hAPP(_1502064, _1502066) = hAPP(c_Finite__Set_Ofold1(_1502060, _1502062), _1502066))], (10733 ^ _775212) ^ [_950604] : [-(hBOOL(hAPP(_950604, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 10740 ^ [_950604])))), 10734 ^ _775212 : [(10735 ^ _775212) ^ [_950656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950656)), hBOOL(hAPP(_950604, _950656))]]], (15408 ^ _775212) ^ [_1034996, _1034998, _1035000] : [hBOOL(hAPP(_1034996, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034998), _1035000))), 15411 ^ _775212 : [(15418 ^ _775212) ^ [_1035181] : [_1034998 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035000), _1035181), -(hBOOL(hAPP(_1034996, _1035181)))], (15412 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034998), _1035000)), -(hBOOL(hAPP(_1034996, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (23606 ^ _775212) ^ [_1185162, _1185164, _1185166, _1185168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1185162, tc_HOL_Obool)), _1185164), _1185166)), hBOOL(hAPP(_1185164, _1185168)), -(hBOOL(hAPP(_1185166, _1185168)))], (22206 ^ _775212) ^ [_1156868, _1156870] : [hAPP(c_Nat_OSuc, _1156868) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156870), -(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(_1156870))), 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)), _1156868))))))], (16483 ^ _775212) ^ [_1055613, _1055615, _1055617] : [class_Groups_Oordered__ab__group__add__abs(_1055613), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055613), hAPP(c_Groups_Oabs__class_Oabs(_1055613), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1055613), _1055615), _1055617))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055613), hAPP(c_Groups_Oabs__class_Oabs(_1055613), _1055615)), hAPP(c_Groups_Oabs__class_Oabs(_1055613), _1055617)))))], (40156 ^ _775212) ^ [_1544995, _1544997] : [c_Wellfounded_OwfP(_1544995, hAPP(hAPP(c_COMBC(_1544995, tc_fun(tc_prod(_1544995, _1544995), tc_HOL_Obool), tc_fun(_1544995, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544995, tc_fun(tc_fun(tc_prod(_1544995, _1544995), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1544995, _1544995), tc_HOL_Obool), tc_fun(_1544995, tc_HOL_Obool)), _1544995), c_COMBC(_1544995, tc_fun(tc_prod(_1544995, _1544995), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544995, tc_prod(_1544995, _1544995)), tc_fun(_1544995, tc_fun(tc_fun(tc_prod(_1544995, _1544995), tc_HOL_Obool), tc_HOL_Obool)), _1544995), hAPP(c_COMBB(tc_prod(_1544995, _1544995), tc_fun(tc_fun(tc_prod(_1544995, _1544995), tc_HOL_Obool), tc_HOL_Obool), _1544995), c_member(tc_prod(_1544995, _1544995)))), c_Product__Type_OPair(_1544995, _1544995)))), _1544997)), -(c_Wellfounded_Owf(_1544995, _1544997))], (8741 ^ _775212) ^ [_917006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _917006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _917006))))], (15041 ^ _775212) ^ [_1027429, _1027431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027429), _1027431)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027431), _1027429)), _1027429) = _1027431)], (46982 ^ _775212) ^ [_1712080, _1712082, _1712084] : [-(_1712080 = c_List_Olist_ONil(_1712082)), -(c_List_Olast(_1712082, hAPP(hAPP(c_List_Olist_OCons(_1712082), _1712084), _1712080)) = c_List_Olast(_1712082, _1712080))], (5574 ^ _775212) ^ [_860259, _860261, _860263, _860265] : [-(hAPP(_860265, _860261) = hAPP(_860263, _860259)), _860265 = _860263, _860261 = _860259], (23382 ^ _775212) ^ [_1180558, _1180560] : [-(c_Nitpick_Onat__lcm(_1180558, _1180560) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1180558), _1180560)), c_Nitpick_Onat__gcd(_1180558, _1180560)))], (33410 ^ _775212) ^ [_1382149, _1382151, _1382153] : [33412 ^ _775212 : [(33415 ^ _775212) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1382153, 33411 ^ [_1382149, _1382151, _1382153]))], (33413 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1382149), 33411 ^ [_1382149, _1382151, _1382153]), _1382151)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382149, tc_Int_Oint), _1382153), _1382151) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382149, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1382149), c_Int_Onat), _1382153)), _1382151)))], (41468 ^ _775212) ^ [_1574653, _1574655, _1574657] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1574653), _1574655)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1574653, tc_HOL_Obool)), _1574657), _1574655) = hAPP(hAPP(c_Finite__Set_Ofold(_1574653, tc_fun(_1574653, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1574653, tc_HOL_Obool), tc_fun(tc_fun(_1574653, tc_HOL_Obool), tc_fun(_1574653, tc_HOL_Obool)), _1574653), hAPP(c_COMBC(tc_fun(_1574653, tc_HOL_Obool), tc_fun(_1574653, tc_HOL_Obool), tc_fun(_1574653, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1574653, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1574653, tc_fun(_1574653, tc_HOL_Obool), tc_fun(_1574653, tc_HOL_Obool)), c_Set_Oinsert(_1574653)), c_Orderings_Obot__class_Obot(tc_fun(_1574653, tc_HOL_Obool))))), _1574657), _1574655))], (15281 ^ _775212) ^ [_1032548, _1032550, _1032552] : [class_Rings_Olinordered__semidom(_1032548), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032548), c_Groups_Oone__class_Oone(_1032548)), _1032550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032548), c_Groups_Oone__class_Oone(_1032548)), hAPP(hAPP(c_Power_Opower__class_Opower(_1032548), _1032550), hAPP(c_Nat_OSuc, _1032552)))))], (48081 ^ _775212) ^ [_1735379, _1735381, _1735383] : [-(c_List_Oconcat(_1735379, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1735379)), _1735381), _1735383)) = hAPP(hAPP(c_List_Oappend(_1735379), _1735381), c_List_Oconcat(_1735379, _1735383)))], (33523 ^ _775212) ^ [_1385687, _1385689, _1385691, _1385693, _1385695, _1385697] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1385693, _1385693)), hAPP(hAPP(c_Product__Type_OPair(_1385693, _1385693), hAPP(_1385697, _1385689)), hAPP(_1385697, _1385691))), _1385695)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1385687, _1385687)), hAPP(hAPP(c_Product__Type_OPair(_1385687, _1385687), _1385689), _1385691)), hAPP(hAPP(c_Relation_Oinv__image(_1385693, _1385687), _1385695), _1385697))))], (46464 ^ _775212) ^ [_1701040, _1701042, _1701044] : [-(hAPP(hAPP(c_List_Otake(_1701040), _1701042), hAPP(c_List_Otl(_1701040), _1701044)) = hAPP(c_List_Otl(_1701040), hAPP(hAPP(c_List_Otake(_1701040), hAPP(c_Nat_OSuc, _1701042)), _1701044)))], (15857 ^ _775212) ^ [_1043727, _1043729, _1043731] : [15859 ^ _775212 : [(15864 ^ _775212) ^ [] : [hBOOL(hAPP(_1043729, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 15858 ^ [_1043727, _1043729, _1043731]), _1043727)))], (15862 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1043729, 15858 ^ [_1043727, _1043729, _1043731])))], (15860 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15858 ^ [_1043727, _1043729, _1043731]), _1043727)))]], hBOOL(hAPP(_1043729, _1043731)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043731), _1043727)), -(hBOOL(hAPP(_1043729, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42663 ^ _775212) ^ [_1604599, _1604601, _1604603, _1604605, _1604607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1604601, tc_HOL_Obool)), _1604605), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1604601, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1604599, _1604601, hAPP(c_Relation_Oconverse(_1604601, _1604599), _1604603)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1604599, tc_HOL_Obool)), _1604607))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1604599, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1604601, _1604599, _1604603), _1604605)), _1604607)))], (29274 ^ _775212) ^ [_1295608, _1295610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1295608), _1295610)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1295608), hAPP(c_Nat_OSuc, _1295610)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1295610), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1295608), _1295610)))], (42309 ^ _775212) ^ [_1594336, _1594338] : [-(hAPP(c_Relation_OField(_1594336), hAPP(c_Relation_Oconverse(_1594336, _1594336), _1594338)) = hAPP(c_Relation_OField(_1594336), _1594338))], (35357 ^ _775212) ^ [_1427172, _1427174, _1427176, _1427178, _1427180] : [class_Groups_Ocomm__monoid__mult(_1427172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427174), _1427176)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427174), _1427178)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427172), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1427174, _1427172), _1427180), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427174, tc_HOL_Obool)), _1427176), _1427178))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1427174, _1427172), _1427180), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427174, tc_HOL_Obool)), _1427176), _1427178))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427172), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1427174, _1427172), _1427180), _1427176)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1427174, _1427172), _1427180), _1427178)))], (41672 ^ _775212) ^ [_1578918, _1578920, _1578922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578918, _1578918), tc_HOL_Obool)), _1578920), _1578922)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578918, _1578918), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1578918, _1578918, _1578918), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1578918, _1578918), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1578918, _1578920)), _1578922)), _1578920)), _1578922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578918, _1578918), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1578918, _1578920)), _1578922)))], (18503 ^ _775212) ^ [_1089607, _1089609] : [class_Rings_Oring__1__no__zero__divisors(_1089607), 18506 ^ _775212 : [(18513 ^ _775212) ^ [] : [_1089609 = c_Groups_Ozero__class_Ozero(_1089607), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1089607), _1089609), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1089607))], (18507 ^ _775212) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1089607), _1089609), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1089607), -(_1089609 = c_Groups_Ozero__class_Ozero(_1089607))]]], (46420 ^ _775212) ^ [_1700380, _1700382, _1700384] : [-(_1700380 = c_List_Olist_ONil(_1700382)), -(hAPP(c_List_Ohd(_1700382), hAPP(hAPP(c_List_Oappend(_1700382), _1700380), _1700384)) = hAPP(c_List_Ohd(_1700382), _1700380))], (19853 ^ _775212) ^ [_1113542, _1113544, _1113546, _1113548] : [class_Fields_Olinordered__field__inverse__zero(_1113542), 19856 ^ _775212 : [(19857 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113542), _1113544), _1113546)), _1113548)), 19860 ^ _775212 : [(19867 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), c_Groups_Ozero__class_Ozero(_1113542)), _1113546))), 19870 ^ _775212 : [(19877 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), _1113546), c_Groups_Ozero__class_Ozero(_1113542)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), c_Groups_Ozero__class_Ozero(_1113542)), _1113548)))], (19871 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), _1113546), c_Groups_Ozero__class_Ozero(_1113542))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113542), _1113548), _1113546)), _1113544)))]]], (19861 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), c_Groups_Ozero__class_Ozero(_1113542)), _1113546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), _1113544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113542), _1113548), _1113546))))]]], (19883 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113542), _1113544), _1113546)), _1113548))), 19886 ^ _775212 : [(19889 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), _1113544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113542), _1113548), _1113546)))], (19887 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), c_Groups_Ozero__class_Ozero(_1113542)), _1113546)))]], 19890 ^ _775212 : [(19893 ^ _775212) ^ [] : [19894 ^ _775212 : [(19897 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113542), _1113548), _1113546)), _1113544))], (19895 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), _1113546), c_Groups_Ozero__class_Ozero(_1113542))))]], 19898 ^ _775212 : [(19901 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), c_Groups_Ozero__class_Ozero(_1113542)), _1113548))], (19899 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), _1113546), c_Groups_Ozero__class_Ozero(_1113542)))]]], (19891 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113542), c_Groups_Ozero__class_Ozero(_1113542)), _1113546))]]]]], (17713 ^ _775212) ^ [_1076082] : [c_Int_OMin = c_Int_OBit1(_1076082), -(c_Int_OMin = _1076082)], (46400 ^ _775212) ^ [_1700101, _1700103, _1700105] : [-(hAPP(c_List_Ohd(_1700101), hAPP(hAPP(c_List_Olist_OCons(_1700101), _1700103), _1700105)) = _1700103)], (36325 ^ _775212) ^ [_1448983, _1448985, _1448987] : [class_Lattices_Olattice(_1448983), hBOOL(hAPP(c_Finite__Set_Ofinite(_1448983), _1448985)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1448983), _1448987)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448983, tc_HOL_Obool)), _1448985), _1448987) = c_Orderings_Obot__class_Obot(tc_fun(_1448983, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1448983), c_Big__Operators_Olattice__class_OInf__fin(_1448983, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448983, tc_HOL_Obool)), _1448985), _1448987))), c_Big__Operators_Olattice__class_OInf__fin(_1448983, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448983, tc_HOL_Obool)), _1448985), _1448987))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1448983), c_Big__Operators_Olattice__class_OInf__fin(_1448983, _1448985)), c_Big__Operators_Olattice__class_OInf__fin(_1448983, _1448987)))], (45349 ^ _775212) ^ [_1674356, _1674358, _1674360, _1674362] : [_1674356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1674358), _1674356), hAPP(hAPP(c_List_Olist_OCons(_1674358), _1674360), _1674362)) = c_List_Olist_ONil(_1674358))], (10587 ^ _775212) ^ [_947951, _947953] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _947951), _947953) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _947951 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _947953 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30064 ^ _775212) ^ [_1313878, _1313880, _1313882, _1313884] : [-(hBOOL(hAPP(hAPP(c_member(_1313878), _1313880), _1313882))), 30067 ^ _775212 : [(30074 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313878, tc_HOL_Obool)), _1313882), _1313884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313878, tc_HOL_Obool)), _1313882), hAPP(hAPP(c_Set_Oinsert(_1313878), _1313880), _1313884))))], (30068 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313878, tc_HOL_Obool)), _1313882), hAPP(hAPP(c_Set_Oinsert(_1313878), _1313880), _1313884))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313878, tc_HOL_Obool)), _1313882), _1313884)))]]], (9014 ^ _775212) ^ [_921308, _921310, _921312, _921314, _921316] : [class_Orderings_Oord(_921308), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921310, _921308)), _921312), _921314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921308), hAPP(_921312, _921316)), hAPP(_921314, _921316))))], (18579 ^ _775212) ^ [_1090845, _1090847] : [class_Rings_Olinordered__idom(_1090845), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1090845), hAPP(c_Groups_Oabs__class_Oabs(_1090845), _1090847)), 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(_1090845), _1090847), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (9781 ^ _775212) ^ [_933375, _933377, _933379] : [class_Groups_Oordered__ab__group__add(_933375), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933375), _933377), _933379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933375), hAPP(c_Groups_Ouminus__class_Ouminus(_933375), _933379)), hAPP(c_Groups_Ouminus__class_Ouminus(_933375), _933377))))], (5963 ^ _775212) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39965 ^ _775212) ^ [_1540316] : [class_Orderings_Owellorder(_1540316), -(c_Wellfounded_Owf(_1540316, hAPP(c_Set_OCollect(tc_prod(_1540316, _1540316)), hAPP(c_Product__Type_Oprod_Oprod__case(_1540316, _1540316, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1540316)))))], (26471 ^ _775212) ^ [_1240375, _1240377] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1240375, _1240377)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1240377), _1240375)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (2530 ^ _775212) ^ [_812287, _812289, _812291, _812293] : [-(c_Divides_Odivmod__nat(_812293, _812289) = c_Divides_Odivmod__nat(_812291, _812287)), _812293 = _812291, _812289 = _812287], (12628 ^ _775212) ^ [_983522, _983524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _983522)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _983524)), -(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, _983522, _983524))))], (14105 ^ _775212) ^ [_1010054, _1010056, _1010058] : [class_Rings_Oring__1(_1010054), -(hAPP(c_Int_Oring__1__class_Oof__int(_1010054), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1010056), _1010058)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1010054), hAPP(c_Int_Oring__1__class_Oof__int(_1010054), _1010056)), hAPP(c_Int_Oring__1__class_Oof__int(_1010054), _1010058)))], (13783 ^ _775212) ^ [_1003842, _1003844, _1003846] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003842), _1003844)), _1003846) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003842), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1003844), _1003846))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003842), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1003844, _1003846))), _1003846)))], (29991 ^ _775212) ^ [_1312016, _1312018, _1312020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1312016, tc_HOL_Obool)), _1312018), _1312020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1312016, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1312016, tc_fun(_1312016, tc_HOL_Obool), tc_HOL_Obool), c_member(_1312016)), _1312018)), hAPP(hAPP(c_COMBC(_1312016, tc_fun(_1312016, tc_HOL_Obool), tc_HOL_Obool), c_member(_1312016)), _1312020))))], (25985 ^ _775212) ^ [_1230188, _1230190, _1230192, _1230194] : [class_Groups_Ocomm__monoid__add(_1230188), 25988 ^ _775212 : [(25995 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1230190), _1230192))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1230188), _1230194), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1230192), hAPP(c_Nat_OSuc, _1230190))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230188), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1230188), _1230194), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1230192), _1230190))), hAPP(_1230194, _1230190)))], (25989 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1230190), _1230192)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1230188), _1230194), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1230192), hAPP(c_Nat_OSuc, _1230190))) = c_Groups_Ozero__class_Ozero(_1230188))]]], (39831 ^ _775212) ^ [_1537365] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1537365)))], (16163 ^ _775212) ^ [_1049039, _1049041, _1049043, _1049045, _1049047] : [class_Rings_Olinordered__idom(_1049039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049039), hAPP(c_Groups_Oabs__class_Oabs(_1049039), _1049041)), _1049043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049039), hAPP(c_Groups_Oabs__class_Oabs(_1049039), _1049045)), _1049047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049039), hAPP(c_Groups_Oabs__class_Oabs(_1049039), _1049041)), hAPP(c_Groups_Oabs__class_Oabs(_1049039), _1049045))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049039), _1049043), _1049047))))], (22126 ^ _775212) ^ [] : [-(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))], (22570 ^ _775212) ^ [_1164811, _1164813, _1164815] : [class_Orderings_Olinorder(_1164811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164811), _1164813), _1164815)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1164811), _1164813), _1164815) = _1164813)], (30620 ^ _775212) ^ [_1327329, _1327331, _1327333] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327329), _1327331)), hBOOL(hAPP(hAPP(c_member(_1327329), _1327333), _1327331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1327329), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327329, tc_HOL_Obool)), _1327331), hAPP(hAPP(c_Set_Oinsert(_1327329), _1327333), c_Orderings_Obot__class_Obot(tc_fun(_1327329, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1327329), _1327331))))], (27836 ^ _775212) ^ [_1268124, _1268126, _1268128, _1268130, _1268132] : [class_Groups_Oab__group__add(_1268124), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268126), _1268128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1268126, tc_HOL_Obool)), _1268130), _1268128)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1268126, _1268124), _1268132), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1268126, tc_HOL_Obool)), _1268128), _1268130)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1268124), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1268126, _1268124), _1268132), _1268128)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1268126, _1268124), _1268132), _1268130)))], (29308 ^ _775212) ^ [_1296372, _1296374, _1296376] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1296372), _1296374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1296372), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1296372, tc_HOL_Obool)), _1296374), hAPP(hAPP(c_Set_Oinsert(_1296372), _1296376), c_Orderings_Obot__class_Obot(tc_fun(_1296372, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1296372), _1296374))))], (1094 ^ _775212) ^ [_791743, _791745] : [-(class_Rings_Olinordered__semiring__1__strict(_791743)), _791745 = _791743, class_Rings_Olinordered__semiring__1__strict(_791745)], (14517 ^ _775212) ^ [_1017772, _1017774, _1017776] : [-(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, _1017772, _1017774)), _1017776), _1017774) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1017772), _1017776), _1017774))], (13487 ^ _775212) ^ [_998940, _998942, _998944, _998946] : [class_Divides_Osemiring__div(_998940), -(_998942 = c_Groups_Ozero__class_Ozero(_998940)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_998940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998940), _998944), _998942)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998940), _998946), _998942)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_998940), _998944), _998946))], (34859 ^ _775212) ^ [_1415386, _1415388, _1415390] : [class_Lattices_Osemilattice__inf(_1415386), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415386), _1415388), _1415390) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415386), _1415390), _1415388))], (11196 ^ _775212) ^ [_958980, _958982, _958984] : [class_Rings_Olinordered__ring__strict(_958980), 11199 ^ _775212 : [(11208 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958980), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958980), _958982), _958982)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958980), _958984), _958984))), c_Groups_Ozero__class_Ozero(_958980)))), _958982 = c_Groups_Ozero__class_Ozero(_958980), _958984 = c_Groups_Ozero__class_Ozero(_958980)], (11200 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958980), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958980), _958982), _958982)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958980), _958984), _958984))), c_Groups_Ozero__class_Ozero(_958980))), 11203 ^ _775212 : [(11206 ^ _775212) ^ [] : [-(_958984 = c_Groups_Ozero__class_Ozero(_958980))], (11204 ^ _775212) ^ [] : [-(_958982 = c_Groups_Ozero__class_Ozero(_958980))]]]]], (13711 ^ _775212) ^ [_1002504, _1002506, _1002508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002504), 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)), _1002506)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002506), _1002508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1002504), _1002506)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1002504), _1002508))))], (49133 ^ _775212) ^ [_1758205, _1758207] : [hAPP(c_List_Orev(_1758205), _1758207) = c_List_Olist_ONil(_1758205), -(_1758207 = c_List_Olist_ONil(_1758205))], (34931 ^ _775212) ^ [_1416956, _1416958, _1416960, _1416962] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416956, tc_HOL_Obool)), _1416958), _1416960), _1416962)), -(hBOOL(hAPP(_1416958, _1416962)))], (30332 ^ _775212) ^ [_1320895, _1320897, _1320899, _1320901, _1320903] : [class_Groups_Ocomm__monoid__add(_1320895), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320897), _1320899)), 30339 ^ _775212 : [(30346 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1320897), _1320901), _1320899))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320897, _1320895), hAPP(hAPP(c_COMBC(_1320897, _1320895, _1320895), hAPP(hAPP(c_COMBS(_1320897, _1320895, tc_fun(_1320895, _1320895)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1320895, tc_fun(_1320895, _1320895)), _1320897), c_If(_1320895)), hAPP(c_fequal, _1320901))), _1320903)), c_Groups_Ozero__class_Ozero(_1320895))), _1320899) = c_Groups_Ozero__class_Ozero(_1320895))], (30340 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1320897), _1320901), _1320899)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320897, _1320895), hAPP(hAPP(c_COMBC(_1320897, _1320895, _1320895), hAPP(hAPP(c_COMBS(_1320897, _1320895, tc_fun(_1320895, _1320895)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1320895, tc_fun(_1320895, _1320895)), _1320897), c_If(_1320895)), hAPP(c_fequal, _1320901))), _1320903)), c_Groups_Ozero__class_Ozero(_1320895))), _1320899) = hAPP(_1320903, _1320901))]]], (50905 ^ _775212) ^ [_1795919, _1795921, _1795923, _1795925] : [-(hBOOL(hAPP(hAPP(c_member(_1795919), _1795921), hAPP(c_List_Oset(_1795919), c_List_Oreplicate(_1795919, _1795923, _1795925))))), _1795921 = _1795925, -(_1795923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11026 ^ _775212) ^ [_955719, _955721, _955723, _955725] : [class_Rings_Olinordered__semiring(_955719), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955719), _955721), _955723)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955719), _955721), _955725))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955719), c_Groups_Ozero__class_Ozero(_955719)), _955721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955719), _955723), _955725)))], (29869 ^ _775212) ^ [_1307419, _1307421, _1307423, _1307425, _1307427] : [-(hBOOL(hAPP(hAPP(c_member(_1307419), _1307421), hAPP(c_Set_Oimage(_1307423, _1307419, _1307425), _1307427)))), 29870 ^ _775212 : [(29871 ^ _775212) ^ [_1307489] : [hBOOL(hAPP(hAPP(c_member(_1307423), _1307489), _1307427)), _1307421 = hAPP(_1307425, _1307489)]]], (42459 ^ _775212) ^ [_1598989, _1598991, _1598993, _1598995] : [hBOOL(hAPP(hAPP(c_member(_1598991), _1598995), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598989, tc_fun(_1598991, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1598989, tc_HOL_Obool))), _1598993))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598989, tc_fun(_1598991, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1598989, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1598991, tc_HOL_Obool), tc_fun(_1598991, tc_HOL_Obool), _1598989), hAPP(c_COMBC(_1598991, tc_fun(_1598991, tc_HOL_Obool), tc_HOL_Obool), c_member(_1598991))), _1598993)), _1598995)))], (40486 ^ _775212) ^ [_1553065, _1553067, _1553069, _1553071, _1553073, _1553075] : [-(hAPP(hAPP(c_Fun_Ocomp(_1553065, _1553067, _1553069, hAPP(c_COMBK(_1553067, _1553065), _1553071)), _1553073), _1553075) = _1553071)], (51857 ^ _775212) ^ [_1817650, _1817652, _1817654] : [c_Relation_Orefl__on(_1817650, _1817652, _1817654), c_Relation_Osym(_1817650, _1817654), c_Relation_Otrans(_1817650, _1817654), -(c_Equiv__Relations_Oequiv(_1817650, _1817652, _1817654))], (46686 ^ _775212) ^ [_1705653, _1705655, _1705657, _1705659] : [class_Groups_Ocomm__monoid__add(_1705653), 46689 ^ _775212 : [(46696 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1705655), _1705657))), -(c_Nitpick_Osetsum_H(_1705655, _1705653, _1705659, _1705657) = c_Groups_Ozero__class_Ozero(_1705653))], (46690 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1705655), _1705657)), -(c_Nitpick_Osetsum_H(_1705655, _1705653, _1705659, _1705657) = hAPP(c_List_Omonoid__add__class_Olistsum(_1705653), hAPP(hAPP(c_List_Omap(_1705655, _1705653), _1705659), c_Hilbert__Choice_OEps(tc_List_Olist(_1705655), hAPP(hAPP(c_COMBS(tc_List_Olist(_1705655), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1705655)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1705655), tc_fun(_1705655, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1705655, tc_HOL_Obool), tc_fun(tc_fun(_1705655, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1705655)), c_fequal), c_List_Oset(_1705655))), _1705657))), c_List_Odistinct(_1705655))))))]]], (27612 ^ _775212) ^ [_1262552, _1262554, _1262556] : [class_Orderings_Olinorder(_1262552), 27615 ^ _775212 : [(27622 ^ _775212) ^ [] : [_1262554 = _1262556, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1262552), _1262554) = hAPP(c_SetInterval_Oord__class_OatLeast(_1262552), _1262556))], (27616 ^ _775212) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1262552), _1262554) = hAPP(c_SetInterval_Oord__class_OatLeast(_1262552), _1262556), -(_1262554 = _1262556)]]], (23742 ^ _775212) ^ [_1187862, _1187864, _1187866] : [-(c_Random__Sequence_Oempty(_1187862, _1187864, _1187866) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1187862)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1187862)))], (17313 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24524 ^ _775212) ^ [_1200995, _1200997, _1200999, _1201001] : [class_Rings_Odvd(_1200995), _1200997 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200995), _1200999), _1201001), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1200995), _1200999), _1200997)))], (40121 ^ _775212) ^ [_1544422, _1544424, _1544426] : [c_Wellfounded_OwfP(_1544422, _1544424), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1544422, _1544424), _1544426)))], (22922 ^ _775212) ^ [_1171945, _1171947, _1171949, _1171951, _1171953] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1171945, _1171947, tc_HOL_Obool), _1171949), hAPP(hAPP(c_Product__Type_OPair(_1171945, _1171947), _1171951), _1171953))), -(hBOOL(hAPP(hAPP(_1171949, _1171951), _1171953)))], (28042 ^ _775212) ^ [_1271813, _1271815] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271813, tc_HOL_Obool)), _1271815), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1271813, tc_HOL_Obool)), _1271815)) = c_Orderings_Otop__class_Otop(tc_fun(_1271813, tc_HOL_Obool)))], (18413 ^ _775212) ^ [_1087962, _1087964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1087962)), c_Int_OBit1(_1087964))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1087962), _1087964)))], (44559 ^ _775212) ^ [_1653656, _1653658, _1653660, _1653662] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653656), tc_List_Olist(_1653656))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653656), tc_List_Olist(_1653656)), _1653658), _1653660)), c_List_Olistrel(_1653656, _1653662))), 44562 ^ _775212 : [(44565 ^ _775212) ^ [_1653885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653885), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653656)), _1653658))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1653656, _1653656)), hAPP(hAPP(c_Product__Type_OPair(_1653656, _1653656), hAPP(hAPP(c_List_Onth(_1653656), _1653658), _1653885)), hAPP(hAPP(c_List_Onth(_1653656), _1653660), _1653885))), _1653662)))], (44563 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653656)), _1653658) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653656)), _1653660))]]], (21927 ^ _775212) ^ [_1151368, _1151370, _1151372] : [_1151370 = _1151372, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151368, tc_HOL_Obool)), _1151370) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151368, tc_HOL_Obool)), _1151372))], (6268 ^ _775212) ^ [_874168, _874170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874170), hAPP(c_Nat_OSuc, _874168))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874168), _874170))], (17273 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (12123 ^ _775212) ^ [_974507, _974509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974507)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974507), _974509)))], (48286 ^ _775212) ^ [_1740587, _1740589, _1740591] : [48288 ^ _775212 : [(48291 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1740589, 48287 ^ [_1740587, _1740589, _1740591])))], (48289 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740587), 48287 ^ [_1740587, _1740589, _1740591]), hAPP(c_List_Oset(_1740587), _1740591))))]], -(hAPP(c_List_Ofilter(_1740587, _1740589), _1740591) = c_List_Olist_ONil(_1740587))], (52355 ^ _775212) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (15227 ^ _775212) ^ [_1031583, _1031585, _1031587, _1031589] : [class_Rings_Olinordered__semidom(_1031583), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1031583), hAPP(hAPP(c_Power_Opower__class_Opower(_1031583), _1031585), hAPP(c_Nat_OSuc, _1031587))), hAPP(hAPP(c_Power_Opower__class_Opower(_1031583), _1031589), hAPP(c_Nat_OSuc, _1031587)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1031583), c_Groups_Ozero__class_Ozero(_1031583)), _1031589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1031583), _1031585), _1031589)))], (13955 ^ _775212) ^ [_1007321, _1007323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1007321)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1007321), _1007323)), _1007321) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (22666 ^ _775212) ^ [_1166474, _1166476, _1166478, _1166480] : [class_Orderings_Olinorder(_1166474), 22669 ^ _775212 : [(22678 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166474), _1166476), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166474), _1166478), _1166480)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166474), _1166476), _1166478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166474), _1166476), _1166480))], (22670 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166474), _1166476), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166474), _1166478), _1166480))), 22673 ^ _775212 : [(22676 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166474), _1166476), _1166480)))], (22674 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166474), _1166476), _1166478)))]]]]], (22500 ^ _775212) ^ [_1163603, _1163605, _1163607] : [class_Orderings_Olinorder(_1163603), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163603), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1163603), _1163605), _1163607)), _1163605)))], (45198 ^ _775212) ^ [_1670156, _1670158] : [-(hAPP(hAPP(c_List_Otake(_1670156), _1670158), c_List_Olist_ONil(_1670156)) = c_List_Olist_ONil(_1670156))], (27155 ^ _775212) ^ [_1253629, _1253631, _1253633, _1253635] : [class_Lattices_Osemilattice__sup(_1253629), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253629), _1253631), _1253633)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253629), _1253635), _1253633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253629), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1253629), _1253631), _1253635)), _1253633)))], (31469 ^ _775212) ^ [_1344650, _1344652] : [class_Rings_Olinordered__idom(_1344650), hBOOL(hAPP(hAPP(c_member(_1344650), _1344652), c_Int_Oring__1__class_OInts(_1344650))), 31476 ^ _775212 : [(31483 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344650), _1344652), c_Groups_Ozero__class_Ozero(_1344650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344650), c_Groups_Oone__class_Oone(_1344650)), _1344652)), _1344652)), c_Groups_Ozero__class_Ozero(_1344650))))], (31477 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344650), c_Groups_Oone__class_Oone(_1344650)), _1344652)), _1344652)), c_Groups_Ozero__class_Ozero(_1344650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344650), _1344652), c_Groups_Ozero__class_Ozero(_1344650))))]]], (46184 ^ _775212) ^ [_1694658, _1694660, _1694662, _1694664] : [hBOOL(hAPP(hAPP(c_member(_1694658), _1694660), hAPP(c_List_Oset(_1694658), hAPP(hAPP(c_List_Odrop(_1694658), _1694662), _1694664)))), -(hBOOL(hAPP(hAPP(c_member(_1694658), _1694660), hAPP(c_List_Oset(_1694658), _1694664))))], (2382 ^ _775212) ^ [_809963, _809965, _809967, _809969] : [-(c_Nitpick_Oint__lcm(_809969, _809965) = c_Nitpick_Oint__lcm(_809967, _809963)), _809969 = _809967, _809965 = _809963], (15445 ^ _775212) ^ [_1035685, _1035687] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1035685), _1035687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1035685), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1035687), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (18519 ^ _775212) ^ [_1089848] : [class_Rings_Osemiring__1(_1089848), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1089848), c_Groups_Ozero__class_Ozero(_1089848)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1089848))], (11272 ^ _775212) ^ [_960315] : [hAPP(c_Int_Onat, _960315) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _960315), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39572 ^ _775212) ^ [_1529947, _1529949, _1529951] : [-(hAPP(c_Set_Oimage(tc_prod(_1529947, _1529949), _1529949, c_Product__Type_Osnd(_1529947, _1529949)), _1529951) = hAPP(c_Relation_ORange(_1529947, _1529949), _1529951))], (5599 ^ _775212) ^ [_863368] : [hAPP(c_Nat_OSuc, _863368) = _863368], (24018 ^ _775212) ^ [_1192558, _1192560] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192558), _1192560)), 24023 ^ _775212 : [(24026 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192560), _1192558))], (24024 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192558), _1192560)))]], -(_1192558 = _1192560)], (39093 ^ _775212) ^ [_1511811, _1511813, _1511815, _1511817, _1511819, _1511821] : [class_Groups_Ocomm__monoid__add(_1511811), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511813), _1511815)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511813, _1511811), _1511817), _1511815) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511819, _1511811), hAPP(hAPP(c_COMBB(tc_fun(_1511813, tc_HOL_Obool), _1511811, _1511819), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511813, _1511811), _1511817)), hAPP(hAPP(c_COMBB(tc_fun(_1511813, tc_HOL_Obool), tc_fun(_1511813, tc_HOL_Obool), _1511819), c_Set_OCollect(_1511813)), hAPP(hAPP(c_COMBB(tc_fun(_1511813, tc_HOL_Obool), tc_fun(_1511813, tc_HOL_Obool), _1511819), hAPP(c_COMBS(_1511813, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511813), c_fconj), hAPP(hAPP(c_COMBC(_1511813, tc_fun(_1511813, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511813)), _1511815)))), hAPP(c_COMBC(_1511813, _1511819, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1511819, tc_fun(_1511819, tc_HOL_Obool), _1511813), c_fequal), _1511821)))))), hAPP(c_Set_Oimage(_1511813, _1511819, _1511821), _1511815)))], (26379 ^ _775212) ^ [_1238458, _1238460] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238458) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238460), -(_1238458 = _1238460)], (4406 ^ _775212) ^ [_842227, _842229] : [_842229 = _842227, -(c_List_Oembed__list(_842229) = c_List_Oembed__list(_842227))], (8772 ^ _775212) ^ [_917518] : [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, _917518))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _917518)))], (2464 ^ _775212) ^ [_811230, _811232, _811234, _811236] : [-(c_Nitpick_OAbs__Frac(_811236, _811232) = c_Nitpick_OAbs__Frac(_811234, _811230)), _811236 = _811234, _811232 = _811230], (8695 ^ _775212) ^ [_916199, _916201, _916203] : [class_Rings_Olinordered__ring__strict(_916199), 8698 ^ _775212 : [(8699 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916199), c_Groups_Ozero__class_Ozero(_916199)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916199), _916201), _916201)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916199), _916203), _916203)))), _916201 = c_Groups_Ozero__class_Ozero(_916199), _916203 = c_Groups_Ozero__class_Ozero(_916199)], (8709 ^ _775212) ^ [] : [8710 ^ _775212 : [(8713 ^ _775212) ^ [] : [-(_916203 = c_Groups_Ozero__class_Ozero(_916199))], (8711 ^ _775212) ^ [] : [-(_916201 = c_Groups_Ozero__class_Ozero(_916199))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916199), c_Groups_Ozero__class_Ozero(_916199)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916199), _916201), _916201)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916199), _916203), _916203)))))]]], (26871 ^ _775212) ^ [_1247602, _1247604, _1247606] : [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), _1247602), _1247604))), -(hBOOL(hAPP(hAPP(_1247606, _1247602), _1247604))), 26878 ^ _775212 : [(26881 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 26876 ^ [_1247602, _1247604, _1247606]), 26877 ^ [_1247602, _1247604, _1247606])), -(hBOOL(hAPP(hAPP(_1247606, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26876 ^ [_1247602, _1247604, _1247606]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 26877 ^ [_1247602, _1247604, _1247606])))], (26887 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1247606, 26876 ^ [_1247602, _1247604, _1247606]), 26877 ^ [_1247602, _1247604, _1247606]))], (26879 ^ _775212) ^ [] : [-(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), 26876 ^ [_1247602, _1247604, _1247606]), 26877 ^ [_1247602, _1247604, _1247606]))))]]], (26720 ^ _775212) ^ [_1244726, _1244728] : [class_Orderings_Olinorder(_1244726), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1244726, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1244726), _1244728)) = hAPP(c_SetInterval_Oord__class_OatMost(_1244726), _1244728))], (44124 ^ _775212) ^ [_1639967, _1639969, _1639971, _1639973, _1639975] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639967), tc_List_Olist(_1639967))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639967), tc_List_Olist(_1639967)), _1639969), _1639971)), hAPP(c_List_Olexn(_1639967, _1639973), _1639975))), 44127 ^ _775212 : [(44130 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639967)), _1639971) = _1639975)], (44128 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639967)), _1639969) = _1639975)]]], (3488 ^ _775212) ^ [_827908, _827910, _827912, _827914, _827916, _827918, _827920, _827922] : [-(c_New__Random__Sequence_Opos__bind(_827922, _827918, _827914, _827910) = c_New__Random__Sequence_Opos__bind(_827920, _827916, _827912, _827908)), _827922 = _827920, _827918 = _827916, _827914 = _827912, _827910 = _827908], (51462 ^ _775212) ^ [_1809299, _1809301, _1809303, _1809305] : [class_Complete__Lattice_Ocomplete__lattice(_1809299), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1809301, _1809299), _1809303), _1809305) = c_Complete__Lattice_OSup__class_OSup(_1809299, hAPP(c_Set_OCollect(_1809299), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1809301, _1809299), tc_HOL_Obool), tc_HOL_Obool, _1809299), c_HOL_OEx(tc_fun(_1809301, _1809299))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1809301, _1809299), tc_HOL_Obool), tc_fun(tc_fun(_1809301, _1809299), tc_HOL_Obool), _1809299), hAPP(c_COMBS(tc_fun(_1809301, _1809299), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1809301, _1809299)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1809301, _1809299), tc_fun(tc_fun(_1809301, _1809299), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1809301, _1809299))), _1809303)))), hAPP(hAPP(c_COMBC(_1809299, tc_fun(tc_fun(_1809301, _1809299), _1809299), tc_fun(tc_fun(_1809301, _1809299), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1809299, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1809301, _1809299), _1809299), tc_fun(tc_fun(_1809301, _1809299), tc_HOL_Obool)), _1809299), c_COMBB(_1809299, tc_HOL_Obool, tc_fun(_1809301, _1809299))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1809301, _1809299), _1809301, _1809299), c_COMBI(tc_fun(_1809301, _1809299))), _1809305)))))))], (29476 ^ _775212) ^ [_1299982, _1299984, _1299986, _1299988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1299982, tc_HOL_Obool)), _1299984), _1299986)), hBOOL(hAPP(hAPP(c_member(_1299982), _1299988), _1299984)), -(hBOOL(hAPP(hAPP(c_member(_1299982), _1299988), _1299986)))], (49561 ^ _775212) ^ [_1767267, _1767269] : [-(c_List_OdropWhile(_1767267, _1767269, c_List_Olist_ONil(_1767267)) = c_List_Olist_ONil(_1767267))], (7589 ^ _775212) ^ [_896375, _896377, _896379] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896375), _896377)), _896379) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _896375), _896379)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _896377), _896379)))], (52197 ^ _775212) ^ [_1823452, _1823454] : [class_Groups_Ouminus(_1823452), -(class_Groups_Ouminus(tc_fun(_1823454, _1823452)))], (23806 ^ _775212) ^ [_1188958, _1188960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1188958)), hAPP(c_Code__Numeral_Onat__of, _1188960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1188958), _1188960)))], (3196 ^ _775212) ^ [_823252, _823254] : [_823254 = _823252, -(c_Int_Oring__1__class_Oof__int(_823254) = c_Int_Oring__1__class_Oof__int(_823252))], (2874 ^ _775212) ^ [_818063, _818065] : [_818065 = _818063, -(c_Divides_Odiv__class_Odiv(_818065) = c_Divides_Odiv__class_Odiv(_818063))], (19905 ^ _775212) ^ [_1114495, _1114497, _1114499, _1114501] : [class_Fields_Olinordered__field(_1114495), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114495), c_Groups_Ozero__class_Ozero(_1114495)), _1114497)), 19912 ^ _775212 : [(19919 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114495), _1114499), _1114497)), _1114501)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114495), _1114499), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114495), _1114501), _1114497))))], (19913 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114495), _1114499), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114495), _1114501), _1114497))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114495), _1114499), _1114497)), _1114501)))]]], (46714 ^ _775212) ^ [_1706332, _1706334] : [class_Lattices_Oab__semigroup__idem__mult(_1706332), -(_1706334 = c_List_Olist_ONil(_1706332)), -(hAPP(c_Finite__Set_Ofold1(_1706332, c_Groups_Otimes__class_Otimes(_1706332)), hAPP(c_List_Oset(_1706332), _1706334)) = hAPP(c_List_Ofoldl(_1706332, _1706332, c_Groups_Otimes__class_Otimes(_1706332), hAPP(c_List_Ohd(_1706332), _1706334)), hAPP(c_List_Otl(_1706332), _1706334)))], (31210 ^ _775212) ^ [_1339566, _1339568, _1339570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1339566, tc_HOL_Obool)), _1339568), hAPP(hAPP(c_Set_Oinsert(_1339566), _1339570), c_Orderings_Obot__class_Obot(tc_fun(_1339566, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1339566, _1339570, _1339568) = _1339570)], (21897 ^ _775212) ^ [_1150702, _1150704, _1150706] : [-(_1150702 = hAPP(hAPP(c_Product__Type_OPair(_1150704, _1150706), hAPP(c_Product__Type_Ofst(_1150704, _1150706), _1150702)), hAPP(c_Product__Type_Osnd(_1150704, _1150706), _1150702)))], (34609 ^ _775212) ^ [_1410900, _1410902, _1410904, _1410906] : [class_Lattices_Osemilattice__inf(_1410900), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410900), _1410902), _1410904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410900), _1410902), _1410906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410900), _1410902), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1410900), _1410904), _1410906))))], (52351 ^ _775212) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (24784 ^ _775212) ^ [_1205746, _1205748, _1205750, _1205752] : [class_Divides_Osemiring__div(_1205746), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205746), _1205748), _1205750)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1205746), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1205746), _1205750), _1205748)), _1205752) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1205746), hAPP(hAPP(c_Power_Opower__class_Opower(_1205746), _1205750), _1205752)), hAPP(hAPP(c_Power_Opower__class_Opower(_1205746), _1205748), _1205752)))], (28323 ^ _775212) ^ [_1277418, _1277420] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1277418, _1277420)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1277418, _1277420), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277418), c_Orderings_Otop__class_Otop(tc_fun(_1277418, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277420), c_Orderings_Otop__class_Otop(tc_fun(_1277420, tc_HOL_Obool))))], (14059 ^ _775212) ^ [_1009120, _1009122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009120)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009122)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1009120)), hAPP(c_Int_Onat, _1009122)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1009120, _1009122)))], (51799 ^ _775212) ^ [_1816468, _1816470] : [c_Relation_Osym(_1816468, _1816470), -(c_Relation_Osym(_1816468, c_Transitive__Closure_Ortrancl(_1816468, _1816470)))], (4572 ^ _775212) ^ [_844814, _844816, _844818, _844820, _844822, _844824] : [-(c_List_OdropWhile(_844824, _844820, _844816) = c_List_OdropWhile(_844822, _844818, _844814)), _844824 = _844822, _844820 = _844818, _844816 = _844814], (44172 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18649 ^ _775212) ^ [_1092051, _1092053] : [class_Rings_Olinordered__idom(_1092051), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092051), hAPP(hAPP(c_Power_Opower__class_Opower(_1092051), _1092053), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1092051)))], (1294 ^ _775212) ^ [_794243, _794245] : [-(class_Groups_Oabs__if(_794243)), _794245 = _794243, class_Groups_Oabs__if(_794245)], (13449 ^ _775212) ^ [_998336, _998338] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _998336), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _998338)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _998336, _998338)))], (28484 ^ _775212) ^ [_1280528, _1280530, _1280532] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1280528), _1280530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1280528), _1280530)), hAPP(c_Finite__Set_Ocard(_1280528), hAPP(hAPP(c_Set_Oinsert(_1280528), _1280532), _1280530)))))], (47617 ^ _775212) ^ [_1725108, _1725110, _1725112, _1725114, _1725116] : [class_Orderings_Olinorder(_1725108), hBOOL(hAPP(hAPP(c_member(_1725108), hAPP(_1725110, _1725112)), hAPP(c_Set_Oimage(_1725114, _1725108, _1725110), hAPP(c_List_Oset(_1725114), _1725116)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1725114, _1725108, _1725110, _1725112, _1725116) = _1725116)], (34581 ^ _775212) ^ [_1410380, _1410382, _1410384, _1410386, _1410388] : [class_Lattices_Osemilattice__inf(_1410380), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410380), _1410382), _1410384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410380), _1410386), _1410388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410380), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1410380), _1410382), _1410386)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1410380), _1410384), _1410388))))], (23194 ^ _775212) ^ [_1176928, _1176930, _1176932, _1176934] : [class_Orderings_Olinorder(_1176928), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176928), _1176930), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176928), _1176932), _1176934)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176928), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176928), _1176930), _1176932)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176928), _1176930), _1176934)))], (52677 ^ _775212) ^ [_1828176, _1828178, _1828180, _1828182] : [-(hAPP(hAPP(c_COMBK(_1828176, _1828178), _1828180), _1828182) = _1828180)], (44584 ^ _775212) ^ [_1654508, _1654510, _1654512, _1654514] : [44587 ^ _775212 : [(44592 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1654508, _1654508)), hAPP(hAPP(c_Product__Type_OPair(_1654508, _1654508), 44586 ^ [_1654508, _1654510, _1654512, _1654514]), 44585 ^ [_1654508, _1654510, _1654512, _1654514])), _1654510))], (44590 ^ _775212) ^ [] : [44585 ^ [_1654508, _1654510, _1654512, _1654514] = 44586 ^ [_1654508, _1654510, _1654512, _1654514]], (44588 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1654508, _1654508)), hAPP(hAPP(c_Product__Type_OPair(_1654508, _1654508), 44585 ^ [_1654508, _1654510, _1654512, _1654514]), 44586 ^ [_1654508, _1654510, _1654512, _1654514])), _1654510))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654508), tc_List_Olist(_1654508))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654508), tc_List_Olist(_1654508)), _1654512), _1654514)), c_List_Olexord(_1654508, _1654510)))), -(_1654512 = _1654514), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654508), tc_List_Olist(_1654508))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654508), tc_List_Olist(_1654508)), _1654514), _1654512)), c_List_Olexord(_1654508, _1654510))))], (33687 ^ _775212) ^ [_1389310, _1389312, _1389314, _1389316, _1389318] : [class_Groups_Ocomm__monoid__add(_1389310), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389312), _1389314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1389312, tc_HOL_Obool)), _1389316), _1389314)), 33701 ^ _775212 : [(33704 ^ _775212) ^ [] : [hAPP(_1389318, 33700 ^ [_1389310, _1389312, _1389314, _1389316, _1389318]) = c_Groups_Ozero__class_Ozero(_1389310)], (33702 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389312), 33700 ^ [_1389310, _1389312, _1389314, _1389316, _1389318]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1389312, tc_HOL_Obool)), _1389314), _1389316))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1389312, _1389310), _1389318), _1389314) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1389312, _1389310), _1389318), _1389316))], (22506 ^ _775212) ^ [_1163710, _1163712, _1163714] : [class_Orderings_Olinorder(_1163710), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163710), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1163710), _1163712), _1163714)), _1163714)))], (24216 ^ _775212) ^ [_1195705, _1195707] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195705), _1195707)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195707), _1195705))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195707), _1195705)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1195705), _1195707)))], (46843 ^ _775212) ^ [_1708928, _1708930, _1708932, _1708934, _1708936] : [c_Finite__Set_Ofun__left__comm__idem(_1708928, _1708930, _1708932), -(hAPP(hAPP(c_Finite__Set_Ofold(_1708928, _1708930, _1708932), _1708934), hAPP(c_List_Oset(_1708928), _1708936)) = hAPP(c_List_Ofoldl(_1708930, _1708928, hAPP(c_COMBC(_1708928, _1708930, _1708930), _1708932), _1708934), _1708936))], (8862 ^ _775212) ^ [_918935, _918937, _918939] : [class_Orderings_Olinorder(_918935), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918935), _918937), _918939))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918935), _918939), _918937)))], (26559 ^ _775212) ^ [_1242146, _1242148, _1242150] : [class_Groups_Ocomm__monoid__add(_1242146), class_Groups_Ocomm__monoid__mult(_1242146), c_Nat__Transfer_Onat__set(_1242148), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1242146), _1242150), _1242148) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1242146), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1242146, tc_Nat_Onat), _1242150), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1242148)))], (8896 ^ _775212) ^ [_919473, _919475, _919477] : [class_Orderings_Oorder(_919473), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919473), _919475), _919477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919473), _919477), _919475)), -(_919477 = _919475)], (48232 ^ _775212) ^ [_1739522, _1739524, _1739526] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1739522), tc_List_Olist(_1739522)), c_List_Opartition(_1739522, _1739524, _1739526)) = hAPP(c_List_Ofilter(_1739522, _1739524), _1739526))], (49021 ^ _775212) ^ [_1755646, _1755648] : [class_Orderings_Olinorder(_1755646), 49024 ^ _775212 : [(49025 ^ _775212) ^ [] : [c_List_Olinorder__class_Osorted(_1755646, _1755648), 49028 ^ _775212 : [(49029 ^ _775212) ^ [_1755817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755817), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755646)), _1755648))), 49032 ^ _775212 : [(49033 ^ _775212) ^ [_1755934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1755934), _1755817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1755646), hAPP(hAPP(c_List_Onth(_1755646), _1755648), _1755934)), hAPP(hAPP(c_List_Onth(_1755646), _1755648), _1755817))))]]]]], (49039 ^ _775212) ^ [] : [49041 ^ _775212 : [(49047 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1755646), hAPP(hAPP(c_List_Onth(_1755646), _1755648), 49043 ^ [_1755646, _1755648])), hAPP(hAPP(c_List_Onth(_1755646), _1755648), 49040 ^ [_1755646, _1755648])))], (49045 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 49043 ^ [_1755646, _1755648]), 49040 ^ [_1755646, _1755648])))], (49042 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49040 ^ [_1755646, _1755648]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755646)), _1755648))))]], -(c_List_Olinorder__class_Osorted(_1755646, _1755648))]]], (36507 ^ _775212) ^ [_1452953, _1452955, _1452957, _1452959] : [c_Fun_Oinj__on(_1452953, _1452955, _1452957, _1452959), 36510 ^ _775212 : [(36511 ^ _775212) ^ [_1453061] : [hBOOL(hAPP(hAPP(c_member(_1452953), _1453061), _1452959)), 36514 ^ _775212 : [(36515 ^ _775212) ^ [_1453163] : [hBOOL(hAPP(hAPP(c_member(_1452953), _1453163), _1452959)), hAPP(_1452957, _1453061) = hAPP(_1452957, _1453163), -(_1453061 = _1453163)]]]]], (28676 ^ _775212) ^ [_1284577, _1284579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284577, tc_HOL_Obool)), _1284579), c_Orderings_Obot__class_Obot(tc_fun(_1284577, tc_HOL_Obool)))), -(_1284579 = c_Orderings_Obot__class_Obot(tc_fun(_1284577, tc_HOL_Obool)))], (38897 ^ _775212) ^ [_1506726, _1506728, _1506730] : [-(hAPP(c_Set_OCollect(_1506726), hAPP(hAPP(c_COMBS(_1506726, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506726), c_fconj), _1506728)), _1506730)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506726, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1506726), _1506728)), hAPP(c_Set_OCollect(_1506726), _1506730)))], (52629 ^ _775212) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (46414 ^ _775212) ^ [_1700267, _1700269, _1700271] : [_1700267 = c_List_Olist_ONil(_1700269), -(hAPP(c_List_Ohd(_1700269), hAPP(hAPP(c_List_Oappend(_1700269), _1700267), _1700271)) = hAPP(c_List_Ohd(_1700269), _1700271))], (23288 ^ _775212) ^ [] : [-(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)))))], (39031 ^ _775212) ^ [_1509669, _1509671] : [-(hAPP(c_Set_OCollect(_1509669), hAPP(c_fequal, _1509671)) = hAPP(hAPP(c_Set_Oinsert(_1509669), _1509671), c_Orderings_Obot__class_Obot(tc_fun(_1509669, tc_HOL_Obool))))], (29648 ^ _775212) ^ [_1303315, _1303317, _1303319, _1303321] : [-(hBOOL(hAPP(hAPP(c_member(_1303315), _1303317), _1303319))), -(hBOOL(hAPP(hAPP(c_member(_1303315), _1303317), _1303321))), 29655 ^ _775212 : [(29662 ^ _775212) ^ [] : [_1303319 = _1303321, -(hAPP(hAPP(c_Set_Oinsert(_1303315), _1303317), _1303319) = hAPP(hAPP(c_Set_Oinsert(_1303315), _1303317), _1303321))], (29656 ^ _775212) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_1303315), _1303317), _1303319) = hAPP(hAPP(c_Set_Oinsert(_1303315), _1303317), _1303321), -(_1303319 = _1303321)]]], (28700 ^ _775212) ^ [_1285024, _1285026, _1285028, _1285030] : [c_Orderings_Obot__class_Obot(tc_fun(_1285024, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1285026, _1285024, _1285028), _1285030), -(_1285030 = c_Orderings_Obot__class_Obot(tc_fun(_1285026, tc_HOL_Obool)))], (28279 ^ _775212) ^ [_1276580, _1276582, _1276584] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276580), _1276582)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276580, tc_HOL_Obool)), _1276584), _1276582)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1276580), _1276584)))], (4528 ^ _775212) ^ [_844122, _844124] : [_844124 = _844122, -(c_Enum_Oenum__class_Oenum__ex(_844124) = c_Enum_Oenum__class_Oenum__ex(_844122))], (51749 ^ _775212) ^ [_1815702, _1815704] : [c_Relation_Osym(_1815702, _1815704), -(c_Relation_Osym(tc_List_Olist(_1815702), c_List_Olistrel(_1815702, _1815704)))], (14997 ^ _775212) ^ [_1026572, _1026574, _1026576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026572), _1026574)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026576), _1026572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026572), _1026576)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026574), _1026576))))], (26531 ^ _775212) ^ [_1241539] : [-(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)), _1241539)) = hAPP(c_Int_Onat, _1241539))], (64 ^ _775212) ^ [_776040, _776042, _776044, _776046, _776048, _776050, _776052, _776054] : [-(c_Nat__Transfer_Otransfer__morphism(_776052, _776048, _776044, _776040)), c_Nat__Transfer_Otransfer__morphism(_776054, _776050, _776046, _776042), _776054 = _776052, _776050 = _776048, _776046 = _776044, _776042 = _776040], (6332 ^ _775212) ^ [_875270, _875272] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_875270, _875272)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _875272)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9491 ^ _775212) ^ [_928599, _928601, _928603] : [class_Orderings_Oorder(_928599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928599), _928601), _928603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928599), _928601), _928603))), -(_928601 = _928603)], (4332 ^ _775212) ^ [_841072, _841074, _841076, _841078, _841080, _841082, _841084, _841086, _841088, _841090] : [-(c_List_Ofoldr(_841090, _841086, _841082, _841078, _841074) = c_List_Ofoldr(_841088, _841084, _841080, _841076, _841072)), _841090 = _841088, _841086 = _841084, _841082 = _841080, _841078 = _841076, _841074 = _841072], (25611 ^ _775212) ^ [_1221859, _1221861, _1221863, _1221865, _1221867, _1221869, _1221871] : [class_Rings_Osemiring__0(_1221859), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221859), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221861, _1221859), _1221863), _1221865)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221867, _1221859), _1221869), _1221871)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221861, _1221859), hAPP(hAPP(c_COMBC(_1221861, tc_fun(_1221867, tc_HOL_Obool), _1221859), hAPP(hAPP(c_COMBB(tc_fun(_1221867, _1221859), tc_fun(tc_fun(_1221867, tc_HOL_Obool), _1221859), _1221861), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221867, _1221859)), hAPP(hAPP(c_COMBC(_1221861, tc_fun(_1221867, _1221859), tc_fun(_1221867, _1221859)), hAPP(hAPP(c_COMBB(tc_fun(_1221859, _1221859), tc_fun(tc_fun(_1221867, _1221859), tc_fun(_1221867, _1221859)), _1221861), c_COMBB(_1221859, _1221859, _1221867)), hAPP(hAPP(c_COMBB(_1221859, tc_fun(_1221859, _1221859), _1221861), c_Groups_Otimes__class_Otimes(_1221859)), _1221863))), _1221869))), _1221871)), _1221865))], (35077 ^ _775212) ^ [_1420662, _1420664, _1420666] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420662, tc_HOL_Obool)), _1420664), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1420662, tc_HOL_Obool)), _1420666), _1420664)) = c_Orderings_Obot__class_Obot(tc_fun(_1420662, tc_HOL_Obool)))], (24124 ^ _775212) ^ [_1194247, _1194249, _1194251] : [_1194247 = _1194249, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194249), _1194251)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194247), _1194251)))], (10697 ^ _775212) ^ [_949987, _949989] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _949987)), _949989) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _949989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949987), _949989)))], (25042 ^ _775212) ^ [_1210724, _1210726, _1210728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1210724)), 25045 ^ _775212 : [(25052 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210726), _1210728)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210724), _1210726)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210724), _1210728))))], (25046 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210724), _1210726)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210724), _1210728))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210726), _1210728)))]]], (33179 ^ _775212) ^ [_1377459, _1377461, _1377463, _1377465, _1377467] : [class_Groups_Ocomm__monoid__mult(_1377459), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377461), _1377463)), -(hBOOL(hAPP(hAPP(c_member(_1377461), _1377465), _1377463))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377461, _1377459), _1377467), hAPP(hAPP(c_Set_Oinsert(_1377461), _1377465), _1377463)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377459), hAPP(_1377467, _1377465)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377461, _1377459), _1377467), _1377463)))], (45806 ^ _775212) ^ [_1685101, _1685103, _1685105] : [_1685105 = c_List_Olist_ONil(_1685103), -(_1685101 = hAPP(hAPP(c_List_Oappend(_1685103), _1685105), _1685101))], (39023 ^ _775212) ^ [_1509541, _1509543, _1509545] : [-(hBOOL(hAPP(_1509541, _1509543))), -(hAPP(c_Set_OCollect(_1509545), hAPP(hAPP(c_COMBS(_1509545, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509545), c_fconj), hAPP(c_fequal, _1509543))), _1509541)) = c_Orderings_Obot__class_Obot(tc_fun(_1509545, tc_HOL_Obool)))], (11688 ^ _775212) ^ [_967134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967134), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_967134 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11836 ^ _775212) ^ [_969427, _969429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969427), _969429)), -(_969429 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969427), 11839 ^ [_969427, _969429]))], (21313 ^ _775212) ^ [_1140304, _1140306] : [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), _1140304), _1140306))), 21316 ^ _775212 : [(21325 ^ _775212) ^ [] : [-(c_Divides_OposDivAlg(_1140304, _1140306) = hAPP(c_Divides_Oadjust(_1140306), c_Divides_OposDivAlg(_1140304, 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)))), _1140306)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140304), _1140306))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1140306), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21317 ^ _775212) ^ [] : [21318 ^ _775212 : [(21321 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1140306), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21319 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140304), _1140306))]], -(c_Divides_OposDivAlg(_1140304, _1140306) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1140304))]]], (4760 ^ _775212) ^ [_847744, _847746] : [_847746 = _847744, -(c_List_Otake(_847746) = c_List_Otake(_847744))], (23548 ^ _775212) ^ [_1183923, _1183925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1183923)), -(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(_1183923), _1183925))), _1183923)))], (12773 ^ _775212) ^ [_985896, _985898, _985900] : [class_Lattices_Oab__semigroup__idem__mult(_985896), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985896), _985898), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985896), _985898), _985900)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985896), _985898), _985900))], (5815 ^ _775212) ^ [_867049, _867051] : [c_Com_Ocom_OWhile(_867049, _867051) = c_Com_Ocom_OSKIP], (32179 ^ _775212) ^ [_1357142, _1357144] : [class_Lattices_Olattice(_1357142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357142), _1357144)), -(_1357144 = c_Orderings_Obot__class_Obot(tc_fun(_1357142, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1357142), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1357142), 32192 ^ [_1357142, _1357144]), 32193 ^ [_1357142, _1357144])), hAPP(hAPP(c_Set_Oinsert(_1357142), 32192 ^ [_1357142, _1357144]), hAPP(hAPP(c_Set_Oinsert(_1357142), 32193 ^ [_1357142, _1357144]), c_Orderings_Obot__class_Obot(tc_fun(_1357142, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1357142), c_Big__Operators_Olattice__class_OSup__fin(_1357142, _1357144)), _1357144)))], (10855 ^ _775212) ^ [_952571] : [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)), _952571)), _952571) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (52661 ^ _775212) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (48224 ^ _775212) ^ [_1739286, _1739288, _1739290] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1739286, tc_HOL_Obool)), hAPP(c_List_Oset(_1739286), hAPP(c_List_Ofilter(_1739286, _1739288), _1739290))), hAPP(c_List_Oset(_1739286), _1739290))))], (27057 ^ _775212) ^ [_1251577, _1251579, _1251581] : [class_Lattices_Olattice(_1251577), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251577), _1251579), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251577), _1251579), _1251581)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251577), _1251579), _1251581))], (23554 ^ _775212) ^ [_1184030, _1184032] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1184030), _1184032) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1184030), _1184032))], (49575 ^ _775212) ^ [_1767508, _1767510, _1767512, _1767514, _1767516] : [hBOOL(hAPP(hAPP(c_member(_1767508), _1767510), hAPP(c_List_Oset(_1767508), _1767512))), -(hBOOL(hAPP(_1767514, _1767510))), -(c_List_OdropWhile(_1767508, _1767514, hAPP(hAPP(c_List_Oappend(_1767508), _1767512), _1767516)) = hAPP(hAPP(c_List_Oappend(_1767508), c_List_OdropWhile(_1767508, _1767514, _1767512)), _1767516))], (41712 ^ _775212) ^ [_1579930, _1579932, _1579934, _1579936, _1579938, _1579940, _1579942] : [c_Finite__Set_Ofun__left__comm(_1579930, _1579932, _1579934), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1579930, _1579932, _1579934, _1579936, _1579938), _1579940)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1579930, _1579932, _1579934, _1579936, _1579938), _1579942)), -(_1579942 = _1579940)], (25134 ^ _775212) ^ [_1212529, _1212531] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212529), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1212531))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212529), _1212531)))], (23768 ^ _775212) ^ [_1188312, _1188314] : [hAPP(c_Code__Numeral_Onat__of, _1188312) = hAPP(c_Code__Numeral_Onat__of, _1188314), -(_1188312 = _1188314)], (15019 ^ _775212) ^ [_1027033, _1027035, _1027037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027033), _1027035)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027037), _1027035)), _1027033) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027037), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027035), _1027033)))], (22928 ^ _775212) ^ [_1172074, _1172076, _1172078, _1172080] : [class_Orderings_Olinorder(_1172074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172074), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1172074), _1172076), _1172078)), _1172080)), 22935 ^ _775212 : [(22938 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172074), _1172078), _1172080)))], (22936 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1172074), _1172076), _1172080)))]]], (45607 ^ _775212) ^ [_1680839, _1680841, _1680843, _1680845, _1680847] : [-(hAPP(hAPP(c_List_Oappend(_1680839), _1680841), _1680843) = hAPP(hAPP(c_List_Olist_OCons(_1680839), _1680845), _1680847)), 45608 ^ _775212 : [(45615 ^ _775212) ^ [_1681022] : [_1680841 = hAPP(hAPP(c_List_Olist_OCons(_1680839), _1680845), _1681022), hAPP(hAPP(c_List_Oappend(_1680839), _1681022), _1680843) = _1680847], (45609 ^ _775212) ^ [] : [_1680841 = c_List_Olist_ONil(_1680839), _1680843 = hAPP(hAPP(c_List_Olist_OCons(_1680839), _1680845), _1680847)]]], (9721 ^ _775212) ^ [_932416, _932418, _932420] : [9722 ^ _775212 : [(9725 ^ _775212) ^ [] : [_932418 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9723 ^ _775212) ^ [] : [_932416 = _932420]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932416), _932418) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932420), _932418))], (45536 ^ _775212) ^ [_1679366, _1679368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1679366), _1679368)), -(c_List_Oupto(_1679368, _1679366) = c_List_Olist_ONil(tc_Int_Oint))], (18541 ^ _775212) ^ [] : [-(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))))))], (15121 ^ _775212) ^ [_1029046, _1029048, _1029050, _1029052, _1029054, _1029056] : [class_Rings_Oordered__ring(_1029046), 15124 ^ _775212 : [(15131 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029046), _1029052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029046), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029046), _1029054), _1029048)), _1029050)), _1029056))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029046), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029046), _1029048), _1029050)), _1029052)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029046), _1029054), _1029050)), _1029056))))], (15125 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029046), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029046), _1029048), _1029050)), _1029052)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029046), _1029054), _1029050)), _1029056))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029046), _1029052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029046), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029046), _1029054), _1029048)), _1029050)), _1029056))))]]], (45017 ^ _775212) ^ [_1665101, _1665103] : [-(c_List_Olists(_1665101, _1665103) = hAPP(c_Set_OCollect(tc_List_Olist(_1665101)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1665101), tc_fun(_1665101, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1665101, tc_HOL_Obool), tc_fun(tc_fun(_1665101, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1665101)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1665101, tc_HOL_Obool))), c_List_Oset(_1665101))), _1665103)))], (39518 ^ _775212) ^ [_1528529, _1528531] : [-(hAPP(c_Relation_ORange(_1528529, _1528529), c_Relation_OId__on(_1528529, _1528531)) = _1528531)], (50743 ^ _775212) ^ [_1792662, _1792664, _1792666, _1792668] : [-(hAPP(hAPP(c_List_Odrop(_1792662), _1792664), c_List_Oreplicate(_1792662, _1792666, _1792668)) = c_List_Oreplicate(_1792662, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1792666), _1792664), _1792668))], (50671 ^ _775212) ^ [_1791538, _1791540] : [c_Wellfounded_Oacyclic(_1791538, hAPP(c_Set_OCollect(tc_prod(_1791538, _1791538)), hAPP(c_Product__Type_Oprod_Oprod__case(_1791538, _1791538, tc_HOL_Obool), _1791540))), -(c_Wellfounded_Oacyclic(_1791538, hAPP(c_Set_OCollect(tc_prod(_1791538, _1791538)), hAPP(c_Product__Type_Oprod_Oprod__case(_1791538, _1791538, tc_HOL_Obool), c_Predicate_Oconversep(_1791538, _1791538, _1791540)))))], (22176 ^ _775212) ^ [_1156290, _1156292] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1156290)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1156292)), hAPP(c_Int_Onat, _1156290)) = hAPP(c_Int_Onat, _1156292))], (41839 ^ _775212) ^ [_1582647, _1582649] : [-(c_Relation_Orefl__on(_1582647, c_Orderings_Otop__class_Otop(tc_fun(_1582647, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1582647, _1582649)))], (47581 ^ _775212) ^ [_1724485, _1724487, _1724489] : [class_Orderings_Olinorder(_1724485), -(hBOOL(hAPP(hAPP(c_member(_1724485), _1724487), hAPP(c_List_Oset(_1724485), _1724489)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1724485, _1724485, c_COMBI(_1724485), _1724487, _1724489) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1724485, _1724485, c_COMBI(_1724485)), _1724487), _1724489))], (30755 ^ _775212) ^ [_1330283, _1330285, _1330287, _1330289] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1330283, tc_fun(_1330285, tc_HOL_Obool))), _1330287), _1330289))], (4016 ^ _775212) ^ [_836148, _836150, _836152, _836154, _836156, _836158, _836160, _836162] : [-(c_Enum_Oproduct(_836162, _836158, _836154, _836150) = c_Enum_Oproduct(_836160, _836156, _836152, _836148)), _836162 = _836160, _836158 = _836156, _836154 = _836152, _836150 = _836148], (44503 ^ _775212) ^ [_1652314, _1652316, _1652318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1652314, _1652314), tc_HOL_Obool)), _1652316), hAPP(hAPP(c_Product__Type_OSigma(_1652314, _1652314), _1652318), hAPP(c_COMBK(tc_fun(_1652314, tc_HOL_Obool), _1652314), _1652318)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1652314), tc_List_Olist(_1652314)), tc_HOL_Obool)), c_List_Olistrel(_1652314, _1652316)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1652314), tc_List_Olist(_1652314)), c_List_Olists(_1652314, _1652318)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1652314), tc_HOL_Obool), tc_List_Olist(_1652314)), c_List_Olists(_1652314, _1652318))))))], (19631 ^ _775212) ^ [_1109470, _1109472, _1109474, _1109476] : [class_Fields_Ofield(_1109470), -(_1109472 = c_Groups_Ozero__class_Ozero(_1109470)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1109470), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109470), _1109474), _1109472)), _1109476) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109470), hAPP(hAPP(c_Power_Opower__class_Opower(_1109470), _1109474), _1109476)), hAPP(hAPP(c_Power_Opower__class_Opower(_1109470), _1109472), _1109476)))], (44445 ^ _775212) ^ [_1650577, _1650579, _1650581, _1650583] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650577), tc_List_Olist(_1650577))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650577), tc_List_Olist(_1650577)), _1650581), _1650583)), c_List_Olistrel(_1650577, _1650579))), -(c_List_Olistrelp(_1650577, hAPP(hAPP(c_COMBC(_1650577, tc_fun(tc_prod(_1650577, _1650577), tc_HOL_Obool), tc_fun(_1650577, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650577, tc_fun(tc_fun(tc_prod(_1650577, _1650577), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1650577, _1650577), tc_HOL_Obool), tc_fun(_1650577, tc_HOL_Obool)), _1650577), c_COMBC(_1650577, tc_fun(tc_prod(_1650577, _1650577), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650577, tc_prod(_1650577, _1650577)), tc_fun(_1650577, tc_fun(tc_fun(tc_prod(_1650577, _1650577), tc_HOL_Obool), tc_HOL_Obool)), _1650577), hAPP(c_COMBB(tc_prod(_1650577, _1650577), tc_fun(tc_fun(tc_prod(_1650577, _1650577), tc_HOL_Obool), tc_HOL_Obool), _1650577), c_member(tc_prod(_1650577, _1650577)))), c_Product__Type_OPair(_1650577, _1650577)))), _1650579), _1650581, _1650583))], (8910 ^ _775212) ^ [_919686, _919688, _919690, _919692] : [class_Orderings_Opreorder(_919686), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919686), _919688), _919690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919686), _919690), _919692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919686), _919688), _919692)))], (32469 ^ _775212) ^ [_1363442, _1363444, _1363446] : [class_Orderings_Olinorder(_1363442), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363442), _1363444)), -(_1363444 = c_Orderings_Obot__class_Obot(tc_fun(_1363442, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363442), _1363446)), -(_1363446 = c_Orderings_Obot__class_Obot(tc_fun(_1363442, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1363442, c_Orderings_Oord__class_Omax(_1363442), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363442, tc_HOL_Obool)), _1363444), _1363446)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363442), c_Big__Operators_Olattice_OSup__fin(_1363442, c_Orderings_Oord__class_Omax(_1363442), _1363444)), c_Big__Operators_Olattice_OSup__fin(_1363442, c_Orderings_Oord__class_Omax(_1363442), _1363446)))], (17867 ^ _775212) ^ [_1078572] : [class_Int_Onumber__ring(_1078572), -(hAPP(c_Int_Onumber__class_Onumber__of(_1078572), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1078572))], (28241 ^ _775212) ^ [_1275981, _1275983, _1275985, _1275987] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1275981), _1275983)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1275985), hAPP(c_Set_Oimage(_1275981, _1275985, _1275987), _1275983))))], (29377 ^ _775212) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (46462 ^ _775212) ^ [_1700987, _1700989, _1700991] : [-(hAPP(c_List_Otl(_1700987), hAPP(hAPP(c_List_Odrop(_1700987), _1700989), _1700991)) = hAPP(hAPP(c_List_Odrop(_1700987), _1700989), hAPP(c_List_Otl(_1700987), _1700991)))], (47350 ^ _775212) ^ [_1719139, _1719141, _1719143, _1719145] : [-(c_List_Opartition(_1719139, _1719141, hAPP(hAPP(c_List_Olist_OCons(_1719139), _1719143), _1719145)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1719139), tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1719139), tc_fun(tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139))), tc_fun(tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1719139), tc_fun(tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)))), tc_fun(tc_fun(tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139))), tc_fun(tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)))), tc_List_Olist(_1719139)), c_COMBS(tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139))), tc_fun(tc_List_Olist(_1719139), tc_fun(tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)))), tc_List_Olist(_1719139)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)), tc_fun(tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139))), tc_List_Olist(_1719139)), hAPP(c_If(tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139))), hAPP(_1719141, _1719143)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1719139), tc_fun(tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139))), tc_List_Olist(_1719139)), c_Product__Type_OPair(tc_List_Olist(_1719139), tc_List_Olist(_1719139))), hAPP(c_List_Olist_OCons(_1719139), _1719143))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719139), tc_fun(tc_List_Olist(_1719139), tc_List_Olist(_1719139)), tc_fun(tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139))), tc_fun(tc_fun(tc_List_Olist(_1719139), tc_List_Olist(_1719139)), tc_fun(tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)))), tc_List_Olist(_1719139)), c_COMBB(tc_List_Olist(_1719139), tc_prod(tc_List_Olist(_1719139), tc_List_Olist(_1719139)), tc_List_Olist(_1719139))), c_Product__Type_OPair(tc_List_Olist(_1719139), tc_List_Olist(_1719139)))), hAPP(c_List_Olist_OCons(_1719139), _1719143)))), c_List_Opartition(_1719139, _1719141, _1719145)))], (16983 ^ _775212) ^ [_1064454] : [class_Int_Onumber__ring(_1064454), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1064454), c_Groups_Oone__class_Oone(_1064454)) = hAPP(c_Int_Onumber__class_Onumber__of(_1064454), c_Int_OMin))], (27688 ^ _775212) ^ [_1263970, _1263972, _1263974, _1263976, _1263978] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1263970, tc_fun(_1263972, tc_HOL_Obool)), _1263974), hAPP(hAPP(c_COMBC(_1263970, tc_fun(_1263972, tc_HOL_Obool), tc_fun(_1263972, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1263972, tc_HOL_Obool), tc_fun(tc_fun(_1263972, tc_HOL_Obool), tc_fun(_1263972, tc_HOL_Obool)), _1263970), c_Groups_Ominus__class_Ominus(tc_fun(_1263972, tc_HOL_Obool))), _1263976)), _1263978)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1263972, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1263970, tc_fun(_1263972, tc_HOL_Obool)), _1263974), _1263976)), _1263978))], (40490 ^ _775212) ^ [_1553181, _1553183, _1553185, _1553187, _1553189, _1553191] : [-(hAPP(c_Set_Ovimage(_1553181, _1553183, hAPP(c_Fun_Ocomp(_1553185, _1553183, _1553181, _1553187), _1553189)), _1553191) = hAPP(c_Set_Ovimage(_1553181, _1553185, _1553189), hAPP(c_Set_Ovimage(_1553185, _1553183, _1553187), _1553191)))], (38838 ^ _775212) ^ [_1505183, _1505185, _1505187, _1505189, _1505191, _1505193, _1505195, _1505197] : [c_Finite__Set_Ofolding__image__simple(_1505183, _1505185, _1505187, _1505189, _1505191, _1505193), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505185), _1505195)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505185), _1505197)), 38852 ^ _775212 : [(38855 ^ _775212) ^ [] : [hAPP(_1505191, 38851 ^ [_1505183, _1505185, _1505187, _1505189, _1505191, _1505193, _1505195, _1505197]) = _1505189], (38853 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1505185), 38851 ^ [_1505183, _1505185, _1505187, _1505189, _1505191, _1505193, _1505195, _1505197]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1505185, tc_HOL_Obool)), _1505195), _1505197))))]], -(hAPP(_1505193, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1505185, tc_HOL_Obool)), _1505195), _1505197)) = hAPP(hAPP(_1505187, hAPP(_1505193, _1505195)), hAPP(_1505193, _1505197)))], (48037 ^ _775212) ^ [_1734444, _1734446] : [class_Orderings_Olinorder(_1734444), -(c_List_Olinorder__class_Osorted__list__of__set(_1734444, hAPP(c_List_Oset(_1734444), _1734446)) = c_List_Olinorder__class_Osort__key(_1734444, _1734444, c_COMBI(_1734444), c_List_Oremdups(_1734444, _1734446)))], (50703 ^ _775212) ^ [_1792059, _1792061, _1792063] : [_1792061 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1792059, _1792061, _1792063) = c_List_Olist_ONil(_1792059))], (9625 ^ _775212) ^ [_930621, _930623, _930625, _930627] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_930621), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930621), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930621), _930623), _930625)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930621), _930623), _930627))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930621), _930625), _930627)))], (1154 ^ _775212) ^ [_792493, _792495] : [-(class_Rings_Olinordered__semiring__1(_792493)), _792495 = _792493, class_Rings_Olinordered__semiring__1(_792495)], (48436 ^ _775212) ^ [_1745064, _1745066, _1745068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1745064), _1745066)), -(c_List_Oupt(_1745064, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1745066), _1745068)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1745064, _1745066)), c_List_Oupt(_1745066, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1745066), _1745068))))], (14411 ^ _775212) ^ [_1015750, _1015752, _1015754] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015750), _1015752)), _1015754) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015750), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015752), _1015754)))], (17469 ^ _775212) ^ [_1071885] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1071885), c_Int_OMin) = c_Int_Osucc(_1071885))], (5965 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45672 ^ _775212) ^ [_1682266, _1682268, _1682270] : [class_Groups_Omonoid__add(_1682266), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1682266), hAPP(hAPP(c_List_Oappend(_1682266), _1682268), _1682270)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1682266), hAPP(c_List_Omonoid__add__class_Olistsum(_1682266), _1682268)), hAPP(c_List_Omonoid__add__class_Olistsum(_1682266), _1682270)))], (45274 ^ _775212) ^ [_1672451, _1672453, _1672455] : [-(_1672451 = _1672453), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672455)), _1672451) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672455)), _1672453), 45280 ^ _775212 : [(45283 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1672455, _1672455, tc_HOL_Obool), c_fequal), 45279 ^ [_1672451, _1672453, _1672455]))], (45281 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1672455, _1672455)), 45279 ^ [_1672451, _1672453, _1672455]), hAPP(c_List_Oset(tc_prod(_1672455, _1672455)), hAPP(hAPP(c_List_Ozip(_1672455, _1672455), _1672451), _1672453)))))]]], (5408 ^ _775212) ^ [_857738, _857740] : [_857740 = _857738, -(c_Orderings_Otop__class_Otop(_857740) = c_Orderings_Otop__class_Otop(_857738))], (42513 ^ _775212) ^ [_1600301, _1600303, _1600305, _1600307] : [_1600301 = c_Orderings_Obot__class_Obot(tc_fun(_1600303, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600303, tc_fun(_1600305, tc_HOL_Obool)), _1600301), hAPP(c_COMBK(tc_fun(_1600305, tc_HOL_Obool), _1600303), _1600307)) = c_Orderings_Otop__class_Otop(tc_fun(_1600305, tc_HOL_Obool)))], (20055 ^ _775212) ^ [_1117360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117360)), -(c_Nat__Transfer_Ois__nat(_1117360))], (34097 ^ _775212) ^ [_1399037] : [-(_1399037 = 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), 34094 ^ [_1399037]), 34095 ^ [_1399037])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (12135 ^ _775212) ^ [] : [-(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)))], (45317 ^ _775212) ^ [_1673582, _1673584, _1673586, _1673588, _1673590, _1673592] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1673582, _1673584)), hAPP(hAPP(c_Product__Type_OPair(_1673582, _1673584), _1673586), _1673588)), hAPP(c_List_Oset(tc_prod(_1673582, _1673584)), hAPP(hAPP(c_List_Ozip(_1673582, _1673584), _1673590), _1673592)))), 45320 ^ _775212 : [(45323 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1673584), _1673588), hAPP(c_List_Oset(_1673584), _1673592))))], (45321 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1673582), _1673586), hAPP(c_List_Oset(_1673582), _1673590))))]]], (50786 ^ _775212) ^ [_1793584, _1793586, _1793588, _1793590] : [50794 ^ _775212 : [(50797 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1793590, 50793 ^ [_1793584, _1793586, _1793588, _1793590])))], (50795 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1793584), 50793 ^ [_1793584, _1793586, _1793588, _1793590]), hAPP(c_List_Oset(_1793584), c_List_Oreplicate(_1793584, _1793586, _1793588)))))]], hBOOL(hAPP(_1793590, _1793588)), -(_1793586 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31087 ^ _775212) ^ [_1336970, _1336972, _1336974, _1336976, _1336978, _1336980, _1336982, _1336984] : [c_Finite__Set_Ofolding__image__simple(_1336970, _1336972, _1336974, _1336976, _1336978, _1336980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336972), _1336982)), hBOOL(hAPP(hAPP(c_member(_1336972), _1336984), _1336982)), -(hAPP(_1336980, _1336982) = hAPP(hAPP(_1336974, hAPP(_1336978, _1336984)), hAPP(_1336980, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336972, tc_HOL_Obool)), _1336982), hAPP(hAPP(c_Set_Oinsert(_1336972), _1336984), c_Orderings_Obot__class_Obot(tc_fun(_1336972, tc_HOL_Obool)))))))], (27117 ^ _775212) ^ [_1252913, _1252915, _1252917, _1252919] : [hBOOL(hAPP(_1252913, _1252915)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252917, tc_HOL_Obool)), _1252913), _1252919), _1252915)))], (37268 ^ _775212) ^ [_1468852, _1468854, _1468856, _1468858, _1468860, _1468862, _1468864] : [c_Typedef_Otype__definition(_1468852, _1468854, _1468856, _1468858, _1468860), 37271 ^ _775212 : [(37278 ^ _775212) ^ [] : [_1468862 = _1468864, -(hAPP(_1468856, _1468862) = hAPP(_1468856, _1468864))], (37272 ^ _775212) ^ [] : [hAPP(_1468856, _1468862) = hAPP(_1468856, _1468864), -(_1468862 = _1468864)]]], (37786 ^ _775212) ^ [_1480822, _1480824, _1480826] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1480822, _1480824, c_Orderings_Obot__class_Obot(tc_fun(_1480822, tc_HOL_Obool))), _1480826))], (29102 ^ _775212) ^ [_1292262, _1292264] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292262), _1292264))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292262, _1292264))], (46053 ^ _775212) ^ [_1690836, _1690838, _1690840, _1690842] : [-(c_List_Osublist(_1690836, hAPP(hAPP(c_List_Oappend(_1690836), _1690838), _1690840), _1690842) = hAPP(hAPP(c_List_Oappend(_1690836), c_List_Osublist(_1690836, _1690838, _1690842)), c_List_Osublist(_1690836, _1690840, 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(_1690836)), _1690838)))), _1690842)))))], (41937 ^ _775212) ^ [_1585043, _1585045, _1585047, _1585049] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585043, _1585043)), hAPP(hAPP(c_Product__Type_OPair(_1585043, _1585043), _1585045), _1585047)), c_Transitive__Closure_Ortrancl(_1585043, _1585049)))), 41938 ^ _775212 : [(41941 ^ _775212) ^ [] : [-(_1585045 = _1585047), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585043, _1585043)), hAPP(hAPP(c_Product__Type_OPair(_1585043, _1585043), _1585045), _1585047)), c_Transitive__Closure_Otrancl(_1585043, _1585049)))], (41939 ^ _775212) ^ [] : [_1585045 = _1585047]]], (49740 ^ _775212) ^ [_1771163, _1771165] : [-(c_List_OremoveAll(_1771163, _1771165) = c_List_Ofilter(_1771163, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1771163), c_fNot), hAPP(c_fequal, _1771165))))], (47392 ^ _775212) ^ [_1720461, _1720463, _1720465, _1720467] : [class_Orderings_Olinorder(_1720461), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1720463, _1720461, _1720465), _1720467), c_List_Olist_ONil(_1720463)) = hAPP(hAPP(c_List_Olist_OCons(_1720463), _1720467), c_List_Olist_ONil(_1720463)))], (19301 ^ _775212) ^ [_1104101, _1104103, _1104105] : [class_Fields_Olinordered__field(_1104101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104101), c_Groups_Ozero__class_Ozero(_1104101)), _1104103)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104101), c_Groups_Ozero__class_Ozero(_1104101)), _1104105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104101), c_Groups_Ozero__class_Ozero(_1104101)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104101), _1104103), _1104105))))], (5440 ^ _775212) ^ [_858214, _858216, _858218, _858220, _858222, _858224, _858226, _858228] : [-(c_Hilbert__Choice_Oinv__into(_858228, _858224, _858220, _858216) = c_Hilbert__Choice_Oinv__into(_858226, _858222, _858218, _858214)), _858228 = _858226, _858224 = _858222, _858220 = _858218, _858216 = _858214], (49145 ^ _775212) ^ [_1758411, _1758413, _1758415] : [hAPP(hAPP(c_List_Olist_OCons(_1758411), _1758413), c_List_Olist_ONil(_1758411)) = hAPP(c_List_Orev(_1758411), _1758415), -(_1758415 = hAPP(hAPP(c_List_Olist_OCons(_1758411), _1758413), c_List_Olist_ONil(_1758411)))], (14407 ^ _775212) ^ [_1015648, _1015650, _1015652] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015648), _1015650)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015652), _1015650)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015648), _1015652))], (22580 ^ _775212) ^ [_1164972, _1164974, _1164976] : [class_Orderings_Olinorder(_1164972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164972), _1164974), _1164976)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1164972), _1164976), _1164974) = _1164974)], (26939 ^ _775212) ^ [_1249067, _1249069, _1249071, _1249073] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249067, tc_HOL_Obool)), _1249069), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249067, tc_HOL_Obool)), _1249071), _1249073)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249067, tc_HOL_Obool)), _1249071), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249067, tc_HOL_Obool)), _1249069), _1249073)))], (42721 ^ _775212) ^ [_1605949, _1605951, _1605953, _1605955, _1605957] : [class_Complete__Lattice_Ocomplete__lattice(_1605949), hBOOL(hAPP(c_Finite__Set_Ofinite(_1605951), _1605953)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1605949), _1605955), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605951, _1605949), _1605953), _1605957)) = hAPP(hAPP(c_Finite__Set_Ofold(_1605951, _1605949, hAPP(hAPP(c_COMBB(_1605949, tc_fun(_1605949, _1605949), _1605951), c_Lattices_Osemilattice__inf__class_Oinf(_1605949)), _1605957)), _1605955), _1605953))], (22076 ^ _775212) ^ [_1154143, _1154145, _1154147, _1154149, _1154151] : [hAPP(c_Product__Type_Ofst(_1154143, _1154145), hAPP(hAPP(c_Product__Type_OPair(_1154143, _1154145), _1154147), _1154149)) = _1154151, -(_1154147 = _1154151)], (52607 ^ _775212) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (11843 ^ _775212) ^ [_969534, _969536] : [11844 ^ _775212 : [(11845 ^ _775212) ^ [_969584] : [_969536 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969534), _969584)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969534), _969536)))], (39053 ^ _775212) ^ [_1510188, _1510190] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1510188, tc_HOL_Obool)), _1510190) = hAPP(c_Set_OCollect(_1510188), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1510188), c_fNot), hAPP(hAPP(c_COMBC(_1510188, tc_fun(_1510188, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510188)), _1510190))))], (47144 ^ _775212) ^ [_1715053, _1715055, _1715057] : [_1715053 = c_List_Olist_ONil(_1715055), -(c_List_Obutlast(_1715055, hAPP(hAPP(c_List_Oappend(_1715055), _1715057), _1715053)) = c_List_Obutlast(_1715055, _1715057))], (11832 ^ _775212) ^ [_969340, _969342] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969340), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969342), _969340))))], (17285 ^ _775212) ^ [] : [c_Int_OPls = c_Int_OMin], (16911 ^ _775212) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (42976 ^ _775212) ^ [_1612702, _1612704, _1612706] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612702, _1612702)), _1612704), c_Transitive__Closure_Ortrancl(_1612702, _1612706))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612702, _1612702)), _1612704), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1612702, _1612702), 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(_1612702, _1612702), tc_HOL_Obool), tc_fun(tc_prod(_1612702, _1612702), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1612702, _1612702), tc_HOL_Obool)), _1612706)))))], (34285 ^ _775212) ^ [_1403423, _1403425, _1403427, _1403429, _1403431] : [c_Equiv__Relations_Oequiv(_1403423, _1403425, _1403427), hBOOL(hAPP(hAPP(c_member(_1403423), _1403429), _1403425)), hBOOL(hAPP(hAPP(c_member(_1403423), _1403431), _1403425)), 34296 ^ _775212 : [(34303 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1403423, _1403423)), hAPP(hAPP(c_Product__Type_OPair(_1403423, _1403423), _1403429), _1403431)), _1403427)), -(hAPP(c_Relation_OImage(_1403423, _1403423, _1403427), hAPP(hAPP(c_Set_Oinsert(_1403423), _1403429), c_Orderings_Obot__class_Obot(tc_fun(_1403423, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1403423, _1403423, _1403427), hAPP(hAPP(c_Set_Oinsert(_1403423), _1403431), c_Orderings_Obot__class_Obot(tc_fun(_1403423, tc_HOL_Obool)))))], (34297 ^ _775212) ^ [] : [hAPP(c_Relation_OImage(_1403423, _1403423, _1403427), hAPP(hAPP(c_Set_Oinsert(_1403423), _1403429), c_Orderings_Obot__class_Obot(tc_fun(_1403423, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1403423, _1403423, _1403427), hAPP(hAPP(c_Set_Oinsert(_1403423), _1403431), c_Orderings_Obot__class_Obot(tc_fun(_1403423, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1403423, _1403423)), hAPP(hAPP(c_Product__Type_OPair(_1403423, _1403423), _1403429), _1403431)), _1403427)))]]], (45062 ^ _775212) ^ [_1667337, _1667339, _1667341] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667337), tc_List_Olist(_1667337))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667337), tc_List_Olist(_1667337)), _1667339), c_List_Olist_ONil(_1667337))), c_List_Olistrel(_1667337, _1667341))), -(_1667339 = c_List_Olist_ONil(_1667337))], (44150 ^ _775212) ^ [_1641311, _1641313, _1641315] : [_1641311 = hAPP(hAPP(c_List_Olist_OCons(_1641313), _1641315), _1641311)], (15567 ^ _775212) ^ [_1038425, _1038427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038425), _1038427)), -(c_Nat__Transfer_Otsub(_1038427, _1038425) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1038427), _1038425))], (17267 ^ _775212) ^ [_1068889] : [-(c_Int_Osucc(c_Int_Opred(_1068889)) = _1068889)], (31443 ^ _775212) ^ [_1344178, _1344180] : [31444 ^ _775212 : [(31447 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344180), _1344178))], (31445 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344178), _1344180)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1344178, _1344180))], (10695 ^ _775212) ^ [_949941, _949943] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949941), hAPP(c_Nat_OSuc, _949943)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _949941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949941), _949943)))], (46206 ^ _775212) ^ [_1695277, _1695279] : [hAPP(c_List_Orotate1(_1695277), _1695279) = c_List_Olist_ONil(_1695277), -(_1695279 = c_List_Olist_ONil(_1695277))], (29624 ^ _775212) ^ [_1302819, _1302821, _1302823, _1302825] : [hBOOL(hAPP(hAPP(c_member(_1302819), _1302821), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1302819, tc_HOL_Obool)), _1302823), _1302825))), -(hBOOL(hAPP(hAPP(c_member(_1302819), _1302821), _1302823)))], (51300 ^ _775212) ^ [_1805338, _1805340] : [c_Relation_Otrans(_1805338, _1805340), -(c_Relation_Otrans(_1805338, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1805338, _1805338), tc_HOL_Obool)), _1805340), c_Relation_OId(_1805338))))], (16065 ^ _775212) ^ [_1047406, _1047408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047406), _1047408)), -(c_Divides_Odivmod__nat(_1047406, _1047408) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1047406))], (17557 ^ _775212) ^ [_1073251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1073251)), -(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), _1073251))))], (48502 ^ _775212) ^ [_1746177, _1746179] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1746177, _1746179))))], (7338 ^ _775212) ^ [_891737, _891739] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _891737) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _891739), -(_891737 = _891739)], (14971 ^ _775212) ^ [_1026096, _1026098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026096), _1026098)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1026098)), _1026096) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026098), _1026096)))], (46298 ^ _775212) ^ [_1697377, _1697379, _1697381, _1697383, _1697385] : [hAPP(hAPP(c_List_Oappend(_1697377), _1697379), _1697381) = hAPP(hAPP(c_List_Oappend(_1697377), _1697383), _1697385), 46301 ^ _775212 : [(46310 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697377)), _1697379)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697377)), _1697383)))), 46313 ^ _775212 : [(46316 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1697377), hAPP(hAPP(c_List_Odrop(_1697377), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697377)), _1697383)), _1697379)), _1697381) = _1697385)], (46314 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1697377), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697377)), _1697383)), _1697379) = _1697383)]]], (46302 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697377)), _1697379)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697377)), _1697383))), 46305 ^ _775212 : [(46308 ^ _775212) ^ [] : [-(_1697381 = hAPP(hAPP(c_List_Oappend(_1697377), hAPP(hAPP(c_List_Odrop(_1697377), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697377)), _1697379)), _1697383)), _1697385))], (46306 ^ _775212) ^ [] : [-(_1697379 = hAPP(hAPP(c_List_Otake(_1697377), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697377)), _1697379)), _1697383))]]]]], (45258 ^ _775212) ^ [_1671989, _1671991, _1671993] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671989), tc_List_Olist(_1671989))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671989), tc_List_Olist(_1671989)), _1671991), c_List_Olist_ONil(_1671989))), c_List_Olex(_1671989, _1671993)))], (42477 ^ _775212) ^ [_1599584, _1599586, _1599588, _1599590, _1599592] : [_1599584 = c_Orderings_Obot__class_Obot(tc_fun(_1599586, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599588, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599586, tc_fun(_1599588, tc_HOL_Obool)), _1599584), _1599590)), _1599592) = _1599592)], (8800 ^ _775212) ^ [_917930, _917932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _917930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _917932)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _917930)), hAPP(c_Int_Onat, _917932)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _917930), _917932)))], (52103 ^ _775212) ^ [_1822217, _1822219] : [class_Lattices_Obounded__lattice(_1822217), -(class_Lattices_Obounded__lattice(tc_fun(_1822219, _1822217)))], (51480 ^ _775212) ^ [_1810628, _1810630, _1810632, _1810634] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1810628), _1810630)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1810628), _1810632)), -(_1810632 = c_Orderings_Obot__class_Obot(tc_fun(_1810628, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1810628, _1810634, _1810630, _1810632)), 51494 ^ _775212 : [(51497 ^ _775212) ^ [_1810973] : [hBOOL(hAPP(hAPP(c_member(_1810628), _1810973), _1810632)), hBOOL(hAPP(hAPP(_1810634, 51493 ^ [_1810628, _1810630, _1810632, _1810634]), _1810973))], (51495 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1810628), 51493 ^ [_1810628, _1810630, _1810632, _1810634]), _1810630)))]]], (8067 ^ _775212) ^ [_904926, _904928, _904930, _904932] : [class_Rings_Ocomm__semiring__1(_904926), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904926), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904926), _904928), _904930)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904926), _904932), _904930)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904926), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904926), _904928), _904932)), _904930))], (44118 ^ _775212) ^ [_1639875, _1639877, _1639879] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639875)), _1639877) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639875)), _1639879)), _1639877 = _1639879], (27826 ^ _775212) ^ [_1267871, _1267873, _1267875, _1267877] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267871), _1267873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267871, tc_HOL_Obool)), _1267873), _1267875)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1267871, tc_Nat_Onat), _1267877), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1267871, tc_HOL_Obool)), _1267875), _1267873)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1267871, tc_Nat_Onat), _1267877), _1267875)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1267871, tc_Nat_Onat), _1267877), _1267873)))], (24902 ^ _775212) ^ [_1207852, _1207854, _1207856, _1207858, _1207860, _1207862] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1207852, _1207854, _1207856, _1207858), _1207860), _1207862) = hAPP(_1207858, hAPP(hAPP(c_Product__Type_OPair(_1207852, _1207854), _1207860), _1207862)))], (38781 ^ _775212) ^ [_1504250, _1504252] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1504250), c_Int_OInteg)), hBOOL(hAPP(_1504252, hAPP(c_Int_ORep__Integ, 38786 ^ [_1504250, _1504252]))), -(hBOOL(hAPP(_1504252, _1504250)))], (46790 ^ _775212) ^ [_1707927, _1707929] : [-(c_List_Orotate(_1707927, _1707929) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1707927), tc_List_Olist(_1707927)), _1707929), c_List_Orotate1(_1707927)))], (5010 ^ _775212) ^ [_851575, _851577] : [_851577 = _851575, -(c_Nat_Osize__class_Osize(_851577) = c_Nat_Osize__class_Osize(_851575))], (12422 ^ _775212) ^ [_979461, _979463] : [class_Divides_Osemiring__div(_979461), -(c_Divides_Odiv__class_Omod(_979461, _979463, c_Groups_Ozero__class_Ozero(_979461)) = _979463)], (51158 ^ _775212) ^ [_1802265, _1802267] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1802265)), _1802267)), 51162 ^ _775212 : [(51163 ^ _775212) ^ [_1802366] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1802265)), _1802366), _1802267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802265)), _1802366)), 51161 ^ [_1802265, _1802267])))]]], (49734 ^ _775212) ^ [_1771107, _1771109, _1771111] : [-(hBOOL(hAPP(hAPP(c_member(_1771107), _1771109), hAPP(c_List_Oset(_1771107), _1771111)))), -(hAPP(c_List_OremoveAll(_1771107, _1771109), _1771111) = _1771111)], (23002 ^ _775212) ^ [_1173388, _1173390, _1173392, _1173394] : [class_Orderings_Olinorder(_1173388), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173388), _1173390), _1173392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173388), _1173390), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173388), _1173394), _1173392))))], (7391 ^ _775212) ^ [_892697, _892699, _892701, _892703, _892705] : [c_Com_Ocom_OWhile(_892697, _892699) = c_Com_Ocom_OLocal(_892701, _892703, _892705)], (18181 ^ _775212) ^ [_1083895, _1083897] : [c_Int_OBit0(_1083895) = c_Int_OBit1(_1083897)], (39694 ^ _775212) ^ [_1534723, _1534725, _1534727] : [-(hAPP(c_Relation_ODomain(_1534723, _1534725), hAPP(c_Set_OCollect(tc_prod(_1534723, _1534725)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534723, _1534725, tc_HOL_Obool), _1534727))) = hAPP(c_Set_OCollect(_1534723), hAPP(hAPP(c_COMBB(tc_fun(_1534725, tc_HOL_Obool), tc_HOL_Obool, _1534723), c_HOL_OEx(_1534725)), _1534727)))], (29488 ^ _775212) ^ [_1300204, _1300206, _1300208, _1300210, _1300212, _1300214] : [_1300204 = hAPP(_1300206, _1300208), hBOOL(hAPP(hAPP(c_member(_1300210), _1300208), _1300212)), -(hBOOL(hAPP(hAPP(c_member(_1300214), _1300204), hAPP(c_Set_Oimage(_1300210, _1300214, _1300206), _1300212))))], (23536 ^ _775212) ^ [_1183799, _1183801] : [_1183799 = _1183801, -(c_Random_Oinc__shift(_1183799, _1183801) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (25641 ^ _775212) ^ [_1222904, _1222906, _1222908] : [class_Orderings_Olinorder(_1222904), 25644 ^ _775212 : [(25651 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222904), _1222906), _1222908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1222904, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1222904), _1222906)), hAPP(c_SetInterval_Oord__class_OlessThan(_1222904), _1222908))))], (25645 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1222904, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1222904), _1222906)), hAPP(c_SetInterval_Oord__class_OlessThan(_1222904), _1222908))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222904), _1222906), _1222908)))]]], (42555 ^ _775212) ^ [_1601559, _1601561, _1601563] : [-(hAPP(c_Relation_ORange(_1601559, _1601561), _1601563) = hAPP(c_Relation_ODomain(_1601561, _1601559), hAPP(c_Relation_Oconverse(_1601559, _1601561), _1601563)))], (38792 ^ _775212) ^ [_1504432] : [-(c_Finite__Set_Ofun__left__comm__idem(_1504432, tc_fun(_1504432, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1504432, tc_HOL_Obool), tc_fun(tc_fun(_1504432, tc_HOL_Obool), tc_fun(_1504432, tc_HOL_Obool)), _1504432), hAPP(c_COMBC(tc_fun(_1504432, tc_HOL_Obool), tc_fun(_1504432, tc_HOL_Obool), tc_fun(_1504432, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1504432, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1504432, tc_fun(_1504432, tc_HOL_Obool), tc_fun(_1504432, tc_HOL_Obool)), c_Set_Oinsert(_1504432)), c_Orderings_Obot__class_Obot(tc_fun(_1504432, tc_HOL_Obool))))))], (16413 ^ _775212) ^ [_1054124, _1054126] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1054124), _1054126)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1054124) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22992 ^ _775212) ^ [_1173227, _1173229, _1173231] : [class_Orderings_Olinorder(_1173227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173227), _1173229), _1173231)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173227), _1173229), _1173231) = _1173231)], (35315 ^ _775212) ^ [_1426243, _1426245, _1426247, _1426249, _1426251, _1426253, _1426255, _1426257] : [c_Finite__Set_Ofolding__image__simple(_1426243, _1426245, _1426247, _1426249, _1426251, _1426253), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426245), _1426255)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426245), _1426257)), -(hAPP(hAPP(_1426247, hAPP(_1426253, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426245, tc_HOL_Obool)), _1426255), _1426257))), hAPP(_1426253, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426245, tc_HOL_Obool)), _1426255), _1426257))) = hAPP(hAPP(_1426247, hAPP(_1426253, _1426255)), hAPP(_1426253, _1426257)))], (39434 ^ _775212) ^ [_1525905, _1525907, _1525909, _1525911] : [-(c_Product__Type_Oapsnd(_1525905, _1525907, _1525909, _1525911) = c_Product__Type_Omap__pair(_1525909, _1525909, _1525905, _1525907, c_Fun_Oid(_1525909), _1525911))], (35039 ^ _775212) ^ [_1419846, _1419848, _1419850, _1419852] : [hBOOL(hAPP(hAPP(c_member(_1419846), _1419848), _1419850)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419846, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1419846), _1419848), _1419852)), _1419850) = hAPP(hAPP(c_Set_Oinsert(_1419846), _1419848), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419846, tc_HOL_Obool)), _1419852), _1419850)))], (45502 ^ _775212) ^ [_1678568, _1678570, _1678572, _1678574] : [-(hAPP(c_List_Olist_Olist__case(_1678568, _1678570, _1678572, _1678574), c_List_Olist_ONil(_1678570)) = _1678572)], (26732 ^ _775212) ^ [_1244948] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1244948) = 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)), _1244948)))], (23060 ^ _775212) ^ [_1174382, _1174384, _1174386] : [class_Orderings_Olinorder(_1174382), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174382), _1174384), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174382), _1174386), _1174384))))], (48599 ^ _775212) ^ [_1748336, _1748338, _1748340, _1748342, _1748344] : [class_Orderings_Olinorder(_1748336), hBOOL(hAPP(hAPP(c_member(_1748338), _1748340), hAPP(c_List_Oset(_1748338), _1748342))), c_List_Olinorder__class_Osorted(_1748336, hAPP(hAPP(c_List_Omap(_1748338, _1748336), _1748344), _1748342)), hAPP(c_List_Ohd(_1748338), hAPP(c_List_Ofilter(_1748338, hAPP(hAPP(c_COMBB(_1748336, tc_HOL_Obool, _1748338), hAPP(c_fequal, hAPP(_1748344, _1748340))), _1748344)), _1748342)) = _1748340, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1748338, _1748336, _1748344), _1748340), c_List_Oremove1(_1748338, _1748340, _1748342)) = _1748342)], (38093 ^ _775212) ^ [_1489765, _1489767, _1489769, _1489771, _1489773, _1489775] : [class_Groups_Ocomm__monoid__mult(_1489765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1489767), _1489769)), 38103 ^ _775212 : [(38106 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1489771), hAPP(_1489773, 38102 ^ [_1489765, _1489767, _1489769, _1489771, _1489773, _1489775])))], (38104 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1489767), 38102 ^ [_1489765, _1489767, _1489769, _1489771, _1489773, _1489775]), _1489769)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1489765, _1489767, c_Groups_Otimes__class_Otimes(_1489765)), hAPP(hAPP(c_COMBS(_1489767, tc_fun(_1489771, tc_HOL_Obool), _1489765), hAPP(hAPP(c_COMBC(_1489767, _1489765, tc_fun(tc_fun(_1489771, tc_HOL_Obool), _1489765)), hAPP(hAPP(c_COMBB(tc_fun(_1489771, _1489765), tc_fun(_1489765, tc_fun(tc_fun(_1489771, tc_HOL_Obool), _1489765)), _1489767), c_Finite__Set_Ofold__image(_1489765, _1489771, c_Groups_Otimes__class_Otimes(_1489765))), _1489775)), c_Groups_Oone__class_Oone(_1489765))), _1489773)), c_Groups_Oone__class_Oone(_1489765)), _1489769) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1489765, tc_prod(_1489767, _1489771), c_Groups_Otimes__class_Otimes(_1489765)), hAPP(c_Product__Type_Oprod_Oprod__case(_1489767, _1489771, _1489765), _1489775)), c_Groups_Oone__class_Oone(_1489765)), hAPP(hAPP(c_Product__Type_OSigma(_1489767, _1489771), _1489769), _1489773)))], (250 ^ _775212) ^ [_778875, _778877, _778879, _778881, _778883, _778885, _778887, _778889, _778891, _778893, _778895, _778897] : [-(c_Equiv__Relations_Ocongruent2(_778895, _778891, _778887, _778883, _778879, _778875)), c_Equiv__Relations_Ocongruent2(_778897, _778893, _778889, _778885, _778881, _778877), _778897 = _778895, _778893 = _778891, _778889 = _778887, _778885 = _778883, _778881 = _778879, _778877 = _778875], (23558 ^ _775212) ^ [_1184085, _1184087, _1184089, _1184091, _1184093, _1184095] : [-(c_Nitpick_Opair__box_Opair__box__size(_1184085, _1184087, _1184089, _1184091, c_Nitpick_Opair__box_OPairBox(_1184085, _1184087, _1184093, _1184095)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1184089, _1184093)), hAPP(_1184091, _1184095))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28870 ^ _775212) ^ [_1288249, _1288251, _1288253] : [class_Orderings_Oorder(_1288249), 28873 ^ _775212 : [(28880 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288249), _1288251), _1288253))), -(c_Orderings_Obot__class_Obot(tc_fun(_1288249, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1288249, _1288251, _1288253))], (28874 ^ _775212) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1288249, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1288249, _1288251, _1288253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288249), _1288251), _1288253))]]], (18451 ^ _775212) ^ [_1088660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1088660))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1088660)))], (8505 ^ _775212) ^ [_912980, _912982, _912984, _912986] : [class_Rings_Olinordered__ring__strict(_912980), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912980), _912982), _912984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912980), _912986), c_Groups_Ozero__class_Ozero(_912980))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912980), _912986), _912984)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912980), _912986), _912982))))], (47246 ^ _775212) ^ [_1717068, _1717070] : [-(c_List_Oremove1(_1717068, _1717070, c_List_Olist_ONil(_1717068)) = c_List_Olist_ONil(_1717068))], (23950 ^ _775212) ^ [_1191445, _1191447, _1191449, _1191451] : [class_Rings_Ocomm__ring__1(_1191445), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1191445), _1191447), _1191449)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1191445), _1191447), _1191451)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1191445), _1191447), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1191445), _1191449), _1191451))))], (45325 ^ _775212) ^ [_1673817, _1673819, _1673821, _1673823, _1673825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673817), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673819)), _1673821))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673817), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673823)), _1673825))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1673819, _1673823)), hAPP(hAPP(c_List_Ozip(_1673819, _1673823), _1673821), _1673825)), _1673817) = hAPP(hAPP(c_Product__Type_OPair(_1673819, _1673823), hAPP(hAPP(c_List_Onth(_1673819), _1673821), _1673817)), hAPP(hAPP(c_List_Onth(_1673823), _1673825), _1673817)))], (44517 ^ _775212) ^ [_1652732, _1652734, _1652736] : [c_Equiv__Relations_Oequiv(_1652732, _1652734, _1652736), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1652732), c_List_Olists(_1652732, _1652734), c_List_Olistrel(_1652732, _1652736)))], (37628 ^ _775212) ^ [_1477322, _1477324, _1477326, _1477328, _1477330] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1477322, _1477324, _1477326, _1477328, c_Orderings_Obot__class_Obot(tc_fun(_1477322, tc_HOL_Obool))), _1477330)), -(_1477330 = _1477328)], (31783 ^ _775212) ^ [_1350176, _1350178, _1350180] : [class_Orderings_Olinorder(_1350176), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350176), _1350178)), hBOOL(hAPP(hAPP(c_member(_1350176), _1350180), _1350178)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350176), _1350180), c_Big__Operators_Olinorder__class_OMax(_1350176, _1350178)) = c_Big__Operators_Olinorder__class_OMax(_1350176, _1350178))], (5945 ^ _775212) ^ [_869437, _869439, _869441, _869443, _869445, _869447] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_869437, _869439, _869441), _869443, _869445, _869447)), 5946 ^ _775212 : [(5953 ^ _775212) ^ [] : [-(hBOOL(hAPP(_869437, _869443))), c_Natural_Oevaln(_869441, _869443, _869445, _869447)], (5947 ^ _775212) ^ [] : [hBOOL(hAPP(_869437, _869443)), c_Natural_Oevaln(_869439, _869443, _869445, _869447)]]], (5414 ^ _775212) ^ [_857823, _857825] : [_857825 = _857823, -(c_Fun_Oid(_857825) = c_Fun_Oid(_857823))], (14549 ^ _775212) ^ [_1018385, _1018387] : [-(_1018385 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1018387), _1018385) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1018387), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1018387), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1018385), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (32119 ^ _775212) ^ [_1355784, _1355786, _1355788] : [class_Orderings_Olinorder(_1355784), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355784), _1355786)), 32126 ^ _775212 : [(32133 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355784, tc_HOL_Obool)), _1355786), hAPP(hAPP(c_Set_Oinsert(_1355784), _1355788), c_Orderings_Obot__class_Obot(tc_fun(_1355784, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1355784, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1355784, hAPP(hAPP(c_Set_Oinsert(_1355784), _1355788), _1355786)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355784), _1355788), c_Big__Operators_Olinorder__class_OMax(_1355784, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355784, tc_HOL_Obool)), _1355786), hAPP(hAPP(c_Set_Oinsert(_1355784), _1355788), c_Orderings_Obot__class_Obot(tc_fun(_1355784, tc_HOL_Obool)))))))], (32127 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355784, tc_HOL_Obool)), _1355786), hAPP(hAPP(c_Set_Oinsert(_1355784), _1355788), c_Orderings_Obot__class_Obot(tc_fun(_1355784, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1355784, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1355784, hAPP(hAPP(c_Set_Oinsert(_1355784), _1355788), _1355786)) = _1355788)]]], (25617 ^ _775212) ^ [_1222198, _1222200, _1222202, _1222204, _1222206] : [class_Groups_Oab__group__add(_1222198), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222200, _1222198), hAPP(hAPP(c_COMBS(_1222200, _1222198, _1222198), hAPP(hAPP(c_COMBB(_1222198, tc_fun(_1222198, _1222198), _1222200), c_Groups_Ominus__class_Ominus(_1222198)), _1222202)), _1222204)), _1222206) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1222198), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222200, _1222198), _1222202), _1222206)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222200, _1222198), _1222204), _1222206)))], (25512 ^ _775212) ^ [_1219365, _1219367, _1219369] : [-(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), _1219365)), 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))), _1219367))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1219369))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1219369)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1219365), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1219365), 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), _1219369), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1219367)))))], (17189 ^ _775212) ^ [_1067696] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1067696)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067696)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1067696)))], (28073 ^ _775212) ^ [_1272410, _1272412, _1272414, _1272416, _1272418] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272410, tc_fun(_1272412, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1272410), _1272414), _1272416)), _1272418) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272412, tc_HOL_Obool)), hAPP(_1272418, _1272414)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272410, tc_fun(_1272412, tc_HOL_Obool)), _1272416), _1272418)))], (48228 ^ _775212) ^ [_1739415, _1739417, _1739419] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739415)), hAPP(c_List_Ofilter(_1739415, _1739417), _1739419))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739415)), _1739419))))], (18041 ^ _775212) ^ [_1081334, _1081336] : [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), _1081334))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1081336)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1081334))) = 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), _1081336), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081334)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23170 ^ _775212) ^ [_1176350] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1176350), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1176350)], (33376 ^ _775212) ^ [_1381542] : [-(_1381542 = 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)), _1381542), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (45082 ^ _775212) ^ [_1667778, _1667780] : [_1667780 = c_List_Olist_ONil(_1667778), -(c_Orderings_Obot__class_Obot(tc_fun(_1667778, tc_HOL_Obool)) = hAPP(c_List_Oset(_1667778), _1667780))], (36002 ^ _775212) ^ [_1442647, _1442649, _1442651, _1442653, _1442655, _1442657] : [hBOOL(hAPP(hAPP(_1442647, _1442649), _1442651)), hBOOL(hAPP(hAPP(_1442653, _1442649), _1442651)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442655, tc_fun(_1442657, tc_HOL_Obool))), _1442647), _1442653), _1442649), _1442651)))], (42379 ^ _775212) ^ [_1596363, _1596365, _1596367, _1596369, _1596371] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596363, _1596365)), hAPP(hAPP(c_Product__Type_OPair(_1596363, _1596365), _1596367), _1596369)), hAPP(c_Relation_Oconverse(_1596365, _1596363), _1596371))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596365, _1596363)), hAPP(hAPP(c_Product__Type_OPair(_1596365, _1596363), _1596369), _1596367)), _1596371)))], (47372 ^ _775212) ^ [_1720074, _1720076] : [-(hBOOL(hAPP(c_List_Olistsp(_1720074, _1720076), c_List_Olist_ONil(_1720074))))], (14757 ^ _775212) ^ [_1022280, _1022282] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1022280), c_Groups_Ozero__class_Ozero(_1022280)), hAPP(c_Nat_OSuc, _1022282)) = c_Groups_Ozero__class_Ozero(_1022280)), class_Power_Opower(_1022280), class_Rings_Osemiring__0(_1022280)], (34883 ^ _775212) ^ [_1415870, _1415872, _1415874, _1415876] : [class_Lattices_Osemilattice__inf(_1415870), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415870), _1415872), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415870), _1415874), _1415876)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415870), _1415874), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415870), _1415872), _1415876)))], (26734 ^ _775212) ^ [_1244980, _1244982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1244980), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244982), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244982), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1244980))))), -(_1244980 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244982), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244982), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1244980))))], (52145 ^ _775212) ^ [_1822770, _1822772] : [class_Lattices_Oboolean__algebra(_1822770), -(class_Lattices_Oboolean__algebra(tc_fun(_1822772, _1822770)))], (46976 ^ _775212) ^ [_1711981, _1711983, _1711985] : [_1711981 = c_List_Olist_ONil(_1711983), -(c_List_Olast(_1711983, hAPP(hAPP(c_List_Olist_OCons(_1711983), _1711985), _1711981)) = _1711985)], (6603 ^ _775212) ^ [_879920, _879922, _879924, _879926, _879928] : [class_Groups_Oordered__cancel__ab__semigroup__add(_879920), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879920), _879922), _879924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879920), _879926), _879928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879920), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879920), _879922), _879926)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879920), _879924), _879928))))], (15377 ^ _775212) ^ [_1034393, _1034395, _1034397] : [hBOOL(hAPP(_1034393, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034395), _1034397))), 15380 ^ _775212 : [(15387 ^ _775212) ^ [_1034584] : [_1034395 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034397), _1034584), -(hBOOL(hAPP(_1034393, _1034584)))], (15381 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034395), _1034397)), -(hBOOL(hAPP(_1034393, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (24534 ^ _775212) ^ [_1201160, _1201162, _1201164, _1201166] : [class_Rings_Ocomm__semiring__1(_1201160), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1201160), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201160), _1201162), _1201164)), _1201166)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1201160), _1201162), _1201166)))], (16921 ^ _775212) ^ [_1063585] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1063585) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1063585))], (42705 ^ _775212) ^ [] : [-(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)))], (17997 ^ _775212) ^ [_1080499, _1080501] : [class_Int_Onumber__ring(_1080499), class_Rings_Olinordered__idom(_1080499), 18004 ^ _775212 : [(18011 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1080501), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080499), hAPP(c_Int_Onumber__class_Onumber__of(_1080499), _1080501)), c_Groups_Oone__class_Oone(_1080499))))], (18005 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080499), hAPP(c_Int_Onumber__class_Onumber__of(_1080499), _1080501)), c_Groups_Oone__class_Oone(_1080499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1080501), c_Int_OBit1(c_Int_OPls))))]]], (18845 ^ _775212) ^ [_1095749] : [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, _1095749, 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, _1095749, 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))], (46652 ^ _775212) ^ [_1704991, _1704993, _1704995] : [-(hBOOL(hAPP(c_List_Odistinct(_1704991), hAPP(hAPP(c_List_Oappend(_1704991), _1704993), _1704995)))), hBOOL(hAPP(c_List_Odistinct(_1704991), _1704993)), hBOOL(hAPP(c_List_Odistinct(_1704991), _1704995)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1704991, tc_HOL_Obool)), hAPP(c_List_Oset(_1704991), _1704993)), hAPP(c_List_Oset(_1704991), _1704995)) = c_Orderings_Obot__class_Obot(tc_fun(_1704991, tc_HOL_Obool))], (12570 ^ _775212) ^ [_982527, _982529] : [class_Rings_Olinordered__idom(_982527), 12573 ^ _775212 : [(12580 ^ _775212) ^ [] : [_982529 = c_Groups_Ozero__class_Ozero(_982527), -(c_Groups_Osgn__class_Osgn(_982527, _982529) = c_Groups_Ozero__class_Ozero(_982527))], (12574 ^ _775212) ^ [] : [c_Groups_Osgn__class_Osgn(_982527, _982529) = c_Groups_Ozero__class_Ozero(_982527), -(_982529 = c_Groups_Ozero__class_Ozero(_982527))]]], (49295 ^ _775212) ^ [_1761778, _1761780, _1761782, _1761784] : [class_Orderings_Olinorder(_1761778), c_List_Olinorder__class_Osorted(_1761778, hAPP(c_List_Orev(_1761778), _1761780)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1761782), _1761784)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761784), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761778)), _1761780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1761778), hAPP(hAPP(c_List_Onth(_1761778), _1761780), _1761784)), hAPP(hAPP(c_List_Onth(_1761778), _1761780), _1761782))))], (4060 ^ _775212) ^ [_836832, _836834, _836836, _836838] : [-(c_Enum_Osublists(_836838, _836834) = c_Enum_Osublists(_836836, _836832)), _836838 = _836836, _836834 = _836832], (32759 ^ _775212) ^ [_1369123, _1369125, _1369127, _1369129, _1369131, _1369133] : [-(hBOOL(hAPP(hAPP(c_member(_1369123), _1369125), _1369127))), -(hAPP(c_Set_Oimage(_1369123, _1369129, c_Fun_Ofun__upd(_1369123, _1369129, _1369131, _1369125, _1369133)), _1369127) = hAPP(c_Set_Oimage(_1369123, _1369129, _1369131), _1369127))], (4192 ^ _775212) ^ [_838868, _838870, _838872, _838874] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_838874, _838870) = c_SetInterval_Oord__class_OatLeastLessThan(_838872, _838868)), _838874 = _838872, _838870 = _838868], (26661 ^ _775212) ^ [_1243699, _1243701] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1243699), _1243701)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243701), _1243699))], (43818 ^ _775212) ^ [_1633023, _1633025, _1633027, _1633029] : [class_Orderings_Olinorder(_1633023), hBOOL(hAPP(c_Finite__Set_Ofinite(_1633023), _1633025)), 43828 ^ _775212 : [(43831 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1633023), _1633027), 43827 ^ [_1633023, _1633025, _1633027, _1633029]))], (43829 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633023), 43827 ^ [_1633023, _1633025, _1633027, _1633029]), _1633025)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1633023), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1633023), _1633027), _1633029)), hAPP(hAPP(c_Finite__Set_Ofold(_1633023, _1633023, c_Orderings_Oord__class_Omin(_1633023)), _1633029), _1633025))))], (9024 ^ _775212) ^ [_921493, _921495, _921497] : [class_Orderings_Opreorder(_921493), _921495 = _921497, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921493), _921495), _921497)))], (27327 ^ _775212) ^ [_1256704, _1256706, _1256708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256704, tc_HOL_Obool)), _1256706), _1256708)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256704, tc_HOL_Obool)), _1256708), _1256706) = _1256708)], (46075 ^ _775212) ^ [_1691543, _1691545, _1691547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691543), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691545)), _1691547))), -(hAPP(hAPP(c_List_Otake(_1691545), hAPP(c_Nat_OSuc, _1691543)), _1691547) = hAPP(hAPP(c_List_Oappend(_1691545), hAPP(hAPP(c_List_Otake(_1691545), _1691543), _1691547)), hAPP(hAPP(c_List_Olist_OCons(_1691545), hAPP(hAPP(c_List_Onth(_1691545), _1691547), _1691543)), c_List_Olist_ONil(_1691545))))], (16537 ^ _775212) ^ [_1056585, _1056587] : [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), _1056585)), _1056587))), _1056585 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1056587 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38496 ^ _775212) ^ [_1498800, _1498802, _1498804] : [class_Orderings_Olinorder(_1498800), hBOOL(hAPP(c_Finite__Set_Ofinite(_1498800), _1498802)), -(_1498802 = c_Orderings_Obot__class_Obot(tc_fun(_1498800, tc_HOL_Obool))), 38507 ^ _775212 : [(38508 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498800), _1498804), hAPP(c_Finite__Set_Ofold1(_1498800, c_Orderings_Oord__class_Omin(_1498800)), _1498802))), 38511 ^ _775212 : [(38512 ^ _775212) ^ [_1499093] : [hBOOL(hAPP(hAPP(c_member(_1498800), _1499093), _1498802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498800), _1498804), _1499093)))]]], (38518 ^ _775212) ^ [] : [38520 ^ _775212 : [(38523 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498800), _1498804), 38519 ^ [_1498800, _1498802, _1498804]))], (38521 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1498800), 38519 ^ [_1498800, _1498802, _1498804]), _1498802)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498800), _1498804), hAPP(c_Finite__Set_Ofold1(_1498800, c_Orderings_Oord__class_Omin(_1498800)), _1498802))))]]], (7815 ^ _775212) ^ [_900752] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _900752))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52231 ^ _775212) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (14533 ^ _775212) ^ [_1018108, _1018110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018108)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018108), _1018110)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018110), _1018108)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1018110)), hAPP(c_Int_Onat, _1018108)))], (21665 ^ _775212) ^ [_1146370, _1146372] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146370, tc_HOL_Obool)), _1146372), _1146372)))], (35291 ^ _775212) ^ [_1425735, _1425737, _1425739, _1425741] : [class_Orderings_Oorder(_1425735), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425735, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1425735, _1425737, _1425739)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1425735, _1425739, _1425741)) = c_Orderings_Obot__class_Obot(tc_fun(_1425735, tc_HOL_Obool)))], (38688 ^ _775212) ^ [_1502225, _1502227, _1502229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1502225, _1502225), tc_HOL_Obool)), _1502227), hAPP(hAPP(c_Product__Type_OSigma(_1502225, _1502225), _1502229), hAPP(c_COMBK(tc_fun(_1502225, tc_HOL_Obool), _1502225), _1502229)))), 38694 ^ _775212 : [(38697 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1502225, _1502225)), hAPP(hAPP(c_Product__Type_OPair(_1502225, _1502225), 38693 ^ [_1502225, _1502227, _1502229]), 38693 ^ [_1502225, _1502227, _1502229])), _1502227))], (38695 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502225), 38693 ^ [_1502225, _1502227, _1502229]), _1502229)))]], -(c_Relation_Orefl__on(_1502225, _1502229, _1502227))], (52301 ^ _775212) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (26927 ^ _775212) ^ [_1248785, _1248787, _1248789, _1248791, _1248793] : [class_Lattices_Olattice(_1248785), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248787, _1248785)), _1248789), _1248791), _1248793) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1248785), hAPP(_1248789, _1248793)), hAPP(_1248791, _1248793)))], (52353 ^ _775212) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (45844 ^ _775212) ^ [_1685761, _1685763] : [-(hAPP(hAPP(c_List_Oappend(_1685761), c_List_Olist_ONil(_1685761)), _1685763) = _1685763)], (42313 ^ _775212) ^ [_1594436, _1594438, _1594440, _1594442] : [-(hAPP(c_Set_OPow(_1594436), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594438, tc_fun(_1594436, tc_HOL_Obool)), _1594440), _1594442)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1594438, tc_fun(tc_fun(_1594436, tc_HOL_Obool), tc_HOL_Obool)), _1594440), hAPP(hAPP(c_COMBB(tc_fun(_1594436, tc_HOL_Obool), tc_fun(tc_fun(_1594436, tc_HOL_Obool), tc_HOL_Obool), _1594438), c_Set_OPow(_1594436)), _1594442)))], (50415 ^ _775212) ^ [_1785994, _1785996, _1785998] : [-(hBOOL(hAPP(hAPP(c_member(_1785994), _1785996), hAPP(c_List_Oset(_1785994), _1785998)))), 50416 ^ _775212 : [(50417 ^ _775212) ^ [_1786083] : [50418 ^ _775212 : [(50419 ^ _775212) ^ [_1786156] : [_1785998 = hAPP(hAPP(c_List_Oappend(_1785994), _1786083), hAPP(hAPP(c_List_Olist_OCons(_1785994), _1785996), _1786156))]], -(hBOOL(hAPP(hAPP(c_member(_1785994), _1785996), hAPP(c_List_Oset(_1785994), _1786083))))]]], (29788 ^ _775212) ^ [_1305992, _1305994] : [_1305992 = _1305994, -(hAPP(c_Int_ORep__Integ, _1305992) = hAPP(c_Int_ORep__Integ, _1305994))], (12663 ^ _775212) ^ [_984094, _984096] : [12664 ^ _775212 : [(12665 ^ _775212) ^ [_984143] : [_984094 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _984096), _984143)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _984094, _984096) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29406 ^ _775212) ^ [_1298543, _1298545, _1298547] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1298543), _1298545)), hBOOL(hAPP(hAPP(c_member(_1298543), _1298547), _1298545)), -(hAPP(c_Finite__Set_Ocard(_1298543), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1298543, tc_HOL_Obool)), _1298545), hAPP(hAPP(c_Set_Oinsert(_1298543), _1298547), c_Orderings_Obot__class_Obot(tc_fun(_1298543, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1298543), _1298545)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (52493 ^ _775212) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (37144 ^ _775212) ^ [_1466341, _1466343, _1466345, _1466347] : [class_Groups_Ocomm__monoid__add(_1466341), 37147 ^ _775212 : [(37154 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1466343), _1466345))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466343, _1466341), _1466347), _1466345) = c_Groups_Ozero__class_Ozero(_1466341))], (37148 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466343), _1466345)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466343, _1466341), _1466347), _1466345) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1466341, _1466343, c_Groups_Oplus__class_Oplus(_1466341)), _1466347), c_Groups_Ozero__class_Ozero(_1466341)), _1466345))]]], (12476 ^ _775212) ^ [_980536, _980538, _980540, _980542, _980544, _980546] : [class_Divides_Osemiring__div(_980536), c_Divides_Odiv__class_Omod(_980536, _980538, _980540) = c_Divides_Odiv__class_Omod(_980536, _980542, _980540), c_Divides_Odiv__class_Omod(_980536, _980544, _980540) = c_Divides_Odiv__class_Omod(_980536, _980546, _980540), -(c_Divides_Odiv__class_Omod(_980536, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980536), _980538), _980544), _980540) = c_Divides_Odiv__class_Omod(_980536, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980536), _980542), _980546), _980540))], (52631 ^ _775212) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (48460 ^ _775212) ^ [_1745490] : [-(c_List_Oupt(_1745490, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (34725 ^ _775212) ^ [_1412893, _1412895, _1412897] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412893, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412893, tc_HOL_Obool)), _1412895), _1412897)), _1412895)))], (37946 ^ _775212) ^ [_1485659, _1485661, _1485663, _1485665, _1485667] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1485659, _1485661), _1485663), hAPP(hAPP(c_COMBS(_1485659, tc_fun(_1485661, tc_HOL_Obool), tc_fun(_1485661, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485661, tc_HOL_Obool), tc_fun(tc_fun(_1485661, tc_HOL_Obool), tc_fun(_1485661, tc_HOL_Obool)), _1485659), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485661, tc_HOL_Obool))), _1485665)), _1485667)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1485659, _1485661), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1485659, _1485661), _1485663), _1485665)), hAPP(hAPP(c_Product__Type_OSigma(_1485659, _1485661), _1485663), _1485667)))], (34443 ^ _775212) ^ [_1407077, _1407079, _1407081] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407077, tc_HOL_Obool)), _1407079), _1407081) = c_Orderings_Obot__class_Obot(tc_fun(_1407077, tc_HOL_Obool)), 34446 ^ _775212 : [(34447 ^ _775212) ^ [_1407201] : [hBOOL(hAPP(hAPP(c_member(_1407077), _1407201), _1407079)), 34450 ^ _775212 : [(34451 ^ _775212) ^ [_1407291] : [hBOOL(hAPP(hAPP(c_member(_1407077), _1407291), _1407081)), _1407201 = _1407291]]]]], (4266 ^ _775212) ^ [_840015, _840017, _840019, _840021, _840023, _840025, _840027, _840029, _840031, _840033] : [-(c_List_Olinorder__class_Oinsort__insert__key(_840033, _840029, _840025, _840021, _840017) = c_List_Olinorder__class_Oinsort__insert__key(_840031, _840027, _840023, _840019, _840015)), _840033 = _840031, _840029 = _840027, _840025 = _840023, _840021 = _840019, _840017 = _840015], (47362 ^ _775212) ^ [_1719797, _1719799, _1719801, _1719803] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1719797)), _1719799), c_List_Olists(_1719797, _1719801))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1719797)), _1719799), c_List_Olists(_1719797, _1719803))), -(hBOOL(hAPP(c_List_Olistsp(_1719797, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1719797, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1719797, tc_fun(_1719797, tc_HOL_Obool), tc_HOL_Obool), c_member(_1719797)), _1719801)), hAPP(hAPP(c_COMBC(_1719797, tc_fun(_1719797, tc_HOL_Obool), tc_HOL_Obool), c_member(_1719797)), _1719803))), _1719799)))], (24566 ^ _775212) ^ [_1201749, _1201751, _1201753] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201749), _1201751)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201749), _1201753)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201749), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1201751), _1201753))))], (51717 ^ _775212) ^ [_1814964, _1814966] : [c_Relation_Oantisym(_1814964, _1814966), -(c_Relation_Oantisym(_1814964, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1814964, _1814964), tc_HOL_Obool)), _1814966), c_Relation_OId(_1814964))))], (32361 ^ _775212) ^ [_1361437, _1361439, _1361441, _1361443] : [c_Sum__Type_OPlus(_1361437, _1361439, _1361441, _1361443) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1361437, _1361439), tc_HOL_Obool)), 32364 ^ _775212 : [(32367 ^ _775212) ^ [] : [-(_1361443 = c_Orderings_Obot__class_Obot(tc_fun(_1361439, tc_HOL_Obool)))], (32365 ^ _775212) ^ [] : [-(_1361441 = c_Orderings_Obot__class_Obot(tc_fun(_1361437, tc_HOL_Obool)))]]], (15961 ^ _775212) ^ [_1045563, _1045565, _1045567] : [class_Groups_Oordered__ab__group__add__abs(_1045563), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045563), hAPP(c_Groups_Oabs__class_Oabs(_1045563), _1045565)), _1045567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045563), _1045565), _1045567)))], (24756 ^ _775212) ^ [_1205212, _1205214, _1205216, _1205218, _1205220] : [class_Rings_Ocomm__semiring__1(_1205212), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205212), _1205214), _1205216)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1205218), _1205220)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205212), hAPP(hAPP(c_Power_Opower__class_Opower(_1205212), _1205214), _1205218)), hAPP(hAPP(c_Power_Opower__class_Opower(_1205212), _1205216), _1205220))))], (38981 ^ _775212) ^ [_1508441, _1508443, _1508445] : [-(hAPP(hAPP(c_Set_Oinsert(_1508441), _1508443), _1508445) = hAPP(c_Set_OCollect(_1508441), hAPP(hAPP(c_COMBS(_1508441, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508441), c_fdisj), hAPP(hAPP(c_COMBC(_1508441, _1508441, tc_HOL_Obool), c_fequal), _1508443))), hAPP(hAPP(c_COMBC(_1508441, tc_fun(_1508441, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508441)), _1508445))))], (40674 ^ _775212) ^ [_1557319, _1557321, _1557323, _1557325, _1557327, _1557329, _1557331, _1557333, _1557335, _1557337, _1557339] : [c_Finite__Set_Ofolding(_1557319, _1557321, _1557323, _1557325), -(hAPP(c_Fun_Ocomp(_1557327, _1557329, _1557331, _1557333), hAPP(c_Fun_Ocomp(_1557335, _1557327, _1557331, _1557337), _1557339)) = hAPP(c_Fun_Ocomp(_1557335, _1557329, _1557331, hAPP(c_Fun_Ocomp(_1557327, _1557329, _1557335, _1557333), _1557337)), _1557339))], (7256 ^ _775212) ^ [_890523] : [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), _890523))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _890523)))], (43071 ^ _775212) ^ [_1615155, _1615157, _1615159] : [-(hAPP(hAPP(c_Nat_Ocompow(_1615155, _1615155), hAPP(c_Nat_OSuc, _1615157)), _1615159) = hAPP(c_Fun_Ocomp(_1615155, _1615155, _1615155, _1615159), hAPP(hAPP(c_Nat_Ocompow(_1615155, _1615155), _1615157), _1615159)))], (40508 ^ _775212) ^ [_1553781, _1553783, _1553785, _1553787, _1553789, _1553791] : [-(hAPP(c_Set_Oimage(_1553781, _1553783, hAPP(c_Fun_Ocomp(_1553785, _1553783, _1553781, _1553787), _1553789)), _1553791) = hAPP(c_Set_Oimage(_1553785, _1553783, _1553787), hAPP(c_Set_Oimage(_1553781, _1553785, _1553789), _1553791)))], (32281 ^ _775212) ^ [_1359682, _1359684, _1359686] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1359682, tc_HOL_Obool), tc_fun(_1359682, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1359682, tc_HOL_Obool), tc_fun(_1359682, tc_HOL_Obool)), _1359684), _1359686)), c_Wellfounded_Ofinite__psubset(_1359682))), 32284 ^ _775212 : [(32287 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1359682), _1359686)))], (32285 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1359682, tc_HOL_Obool)), _1359684), _1359686)))]]], (4242 ^ _775212) ^ [_839629, _839631] : [_839631 = _839629, -(c_SetInterval_Oord__class_OatMost(_839631) = c_SetInterval_Oord__class_OatMost(_839629))], (15451 ^ _775212) ^ [_1035796, _1035798, _1035800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035796), _1035798)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035798), _1035796))), _1035800) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1035798)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035796), _1035800)))], (22168 ^ _775212) ^ [_1156039, _1156041] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1156039), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1156041))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1156039), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156041))), 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))))], (8463 ^ _775212) ^ [_912173, _912175, _912177, _912179] : [class_Rings_Olinordered__semiring__strict(_912173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912173), _912175), _912177)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912173), c_Groups_Ozero__class_Ozero(_912173)), _912179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912173), _912179), _912175)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912173), _912179), _912177))))], (24478 ^ _775212) ^ [_1200152, _1200154, _1200156] : [class_Rings_Ocomm__semiring__1(_1200152), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1200152), _1200154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200152), _1200154), _1200156))))], (47286 ^ _775212) ^ [_1717788, _1717790, _1717792, _1717794] : [hBOOL(hAPP(hAPP(c_member(_1717788), _1717790), hAPP(c_List_Oset(_1717788), _1717792))), -(c_List_Oremove1(_1717788, _1717790, hAPP(hAPP(c_List_Oappend(_1717788), _1717792), _1717794)) = hAPP(hAPP(c_List_Oappend(_1717788), c_List_Oremove1(_1717788, _1717790, _1717792)), _1717794))], (10473 ^ _775212) ^ [_946048, _946050, _946052, _946054, _946056] : [class_Groups_Oordered__cancel__ab__semigroup__add(_946048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946048), _946050), _946052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946048), _946054), _946056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946048), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946048), _946050), _946054)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946048), _946052), _946056))))], (24770 ^ _775212) ^ [_1205479, _1205481, _1205483, _1205485, _1205487] : [class_Rings_Ocomm__semiring__1(_1205479), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205479), hAPP(hAPP(c_Power_Opower__class_Opower(_1205479), _1205481), _1205483)), _1205485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1205487), _1205483)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205479), hAPP(hAPP(c_Power_Opower__class_Opower(_1205479), _1205481), _1205487)), _1205485)))], (11628 ^ _775212) ^ [_966211] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _966211)))], (42435 ^ _775212) ^ [_1597937, _1597939, _1597941, _1597943, _1597945] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597937, tc_HOL_Obool)), _1597939), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597941, tc_fun(_1597937, tc_HOL_Obool)), _1597943), _1597945)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597941, tc_fun(_1597937, tc_HOL_Obool)), _1597943), hAPP(hAPP(c_COMBB(tc_fun(_1597937, tc_HOL_Obool), tc_fun(_1597937, tc_HOL_Obool), _1597941), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597937, tc_HOL_Obool)), _1597939)), _1597945)))], (23136 ^ _775212) ^ [_1175652, _1175654, _1175656, _1175658] : [class_Orderings_Olinorder(_1175652), 23139 ^ _775212 : [(23148 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175652), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1175652), _1175654), _1175656)), _1175658))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175652), _1175654), _1175658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175652), _1175656), _1175658))], (23140 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175652), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1175652), _1175654), _1175656)), _1175658)), 23143 ^ _775212 : [(23146 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175652), _1175656), _1175658)))], (23144 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175652), _1175654), _1175658)))]]]]], (25681 ^ _775212) ^ [_1223892, _1223894, _1223896, _1223898] : [class_Groups_Oab__group__add(_1223892), 25684 ^ _775212 : [(25691 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223894), _1223896))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223892), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1223892, _1223892), hAPP(hAPP(c_COMBB(_1223892, tc_fun(_1223892, _1223892), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1223892)), _1223898)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1223892, tc_Nat_Onat), _1223898), 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, _1223894, _1223896)) = c_Groups_Ozero__class_Ozero(_1223892))], (25685 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223894), _1223896)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223892), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1223892, _1223892), hAPP(hAPP(c_COMBB(_1223892, tc_fun(_1223892, _1223892), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1223892)), _1223898)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1223892, tc_Nat_Onat), _1223898), 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, _1223894, _1223896)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1223892), hAPP(_1223898, _1223894)), hAPP(_1223898, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1223896), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (27632 ^ _775212) ^ [_1262843, _1262845, _1262847] : [class_Orderings_Oorder(_1262843), 27635 ^ _775212 : [(27642 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262843), _1262847), _1262845)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1262843, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1262843), _1262845)), hAPP(c_SetInterval_Oord__class_OatLeast(_1262843), _1262847))))], (27636 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1262843, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1262843), _1262845)), hAPP(c_SetInterval_Oord__class_OatLeast(_1262843), _1262847))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262843), _1262847), _1262845)))]]], (21627 ^ _775212) ^ [_1145529] : [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), _1145529))), -(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), _1145529)) = 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), _1145529))))], (24904 ^ _775212) ^ [_1207908, _1207910, _1207912, _1207914] : [class_Rings_Ocomm__ring(_1207908), class_Rings_Odvd(_1207908), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207908), _1207910), _1207912)), 24915 ^ _775212 : [(24922 ^ _775212) ^ [_1208334, _1208336] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207908), _1207910), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207908), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1207908), _1208336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207908), _1208334), _1207912))), _1207914))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207908), _1207910), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207908), _1208336), _1207914))))], (24916 ^ _775212) ^ [_1208161, _1208163] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207908), _1207910), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207908), _1208163), _1207914))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207908), _1207910), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207908), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1207908), _1208163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207908), _1208161), _1207912))), _1207914))))]]], (23482 ^ _775212) ^ [_1182698, _1182700, _1182702, _1182704, _1182706, _1182708] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1182698, _1182700, _1182702), _1182704), hAPP(hAPP(c_Product__Type_OPair(_1182698, _1182700), _1182706), _1182708)) = hAPP(hAPP(_1182704, _1182706), _1182708))], (50677 ^ _775212) ^ [_1791681, _1791683, _1791685] : [-(_1791681 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1791683), c_List_Oreplicate(_1791683, _1791681, _1791685)) = c_List_Oreplicate(_1791683, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1791681), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1791685))], (22824 ^ _775212) ^ [_1169987, _1169989, _1169991, _1169993, _1169995, _1169997, _1169999] : [-(hAPP(c_Product__Type_Oapsnd(_1169987, _1169989, _1169991, _1169993), hAPP(c_Product__Type_Oapfst(_1169995, _1169991, _1169987, _1169997), _1169999)) = hAPP(hAPP(c_Product__Type_OPair(_1169991, _1169989), hAPP(_1169997, hAPP(c_Product__Type_Ofst(_1169995, _1169987), _1169999))), hAPP(_1169993, hAPP(c_Product__Type_Osnd(_1169995, _1169987), _1169999))))], (7471 ^ _775212) ^ [_894332, _894334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894332)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894334))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894332), _894334)))], (44509 ^ _775212) ^ [_1652559] : [-(c_List_Olists(_1652559, c_Orderings_Otop__class_Otop(tc_fun(_1652559, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1652559), tc_HOL_Obool)))], (40423 ^ _775212) ^ [_1551693, _1551695, _1551697] : [hBOOL(hAPP(_1551693, _1551695)), -(hBOOL(hAPP(_1551693, c_Hilbert__Choice_OEps(_1551697, _1551693))))], (1594 ^ _775212) ^ [_797993, _797995] : [-(class_Groups_Ocancel__semigroup__add(_797993)), _797995 = _797993, class_Groups_Ocancel__semigroup__add(_797995)], (17805 ^ _775212) ^ [_1077539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1077539), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1077539)), c_Int_OMin)))], (47928 ^ _775212) ^ [_1732279, _1732281, _1732283, _1732285] : [47930 ^ _775212 : [(47933 ^ _775212) ^ [] : [hBOOL(hAPP(_1732283, hAPP(hAPP(c_List_Onth(_1732279), _1732281), 47929 ^ [_1732279, _1732281, _1732283, _1732285])))], (47931 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47929 ^ [_1732279, _1732281, _1732283, _1732285]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732279)), _1732281))))]], hBOOL(hAPP(hAPP(c_member(_1732279), _1732285), hAPP(c_List_Oset(_1732279), _1732281))), -(hBOOL(hAPP(_1732283, _1732285)))], (15573 ^ _775212) ^ [_1038524, _1038526] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038524), _1038526))), -(c_Nat__Transfer_Otsub(_1038526, _1038524) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (1006 ^ _775212) ^ [_790493, _790495, _790497, _790499] : [-(c_Equiv__Relations_Oequivp(_790497, _790493)), c_Equiv__Relations_Oequivp(_790499, _790495), _790499 = _790497, _790495 = _790493], (42085 ^ _775212) ^ [_1588503, _1588505, _1588507, _1588509, _1588511] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588503, _1588503)), hAPP(hAPP(c_Product__Type_OPair(_1588503, _1588503), _1588505), _1588507)), c_Transitive__Closure_Ortrancl(_1588503, _1588509))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588503, _1588503), tc_HOL_Obool)), _1588509), hAPP(hAPP(c_Product__Type_OSigma(_1588503, _1588503), _1588511), hAPP(c_COMBK(tc_fun(_1588503, tc_HOL_Obool), _1588503), _1588511)))), -(_1588505 = _1588507), -(hBOOL(hAPP(hAPP(c_member(_1588503), _1588505), _1588511)))], (40468 ^ _775212) ^ [_1552597, _1552599, _1552601, _1552603, _1552605, _1552607] : [-(hAPP(hAPP(c_Fun_Ocomp(_1552597, _1552599, _1552601, _1552603), _1552605), _1552607) = hAPP(_1552603, hAPP(_1552605, _1552607)))], (44770 ^ _775212) ^ [_1659457, _1659459, _1659461, _1659463, _1659465] : [c_Fun_Oinj__on(_1659457, _1659459, _1659461, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659457, tc_HOL_Obool)), hAPP(c_List_Oset(_1659457), _1659463)), hAPP(c_List_Oset(_1659457), _1659465))), 44773 ^ _775212 : [(44780 ^ _775212) ^ [] : [_1659463 = _1659465, -(hAPP(hAPP(c_List_Omap(_1659457, _1659459), _1659461), _1659463) = hAPP(hAPP(c_List_Omap(_1659457, _1659459), _1659461), _1659465))], (44774 ^ _775212) ^ [] : [hAPP(hAPP(c_List_Omap(_1659457, _1659459), _1659461), _1659463) = hAPP(hAPP(c_List_Omap(_1659457, _1659459), _1659461), _1659465), -(_1659463 = _1659465)]]], (37196 ^ _775212) ^ [_1467275, _1467277, _1467279, _1467281, _1467283] : [class_Groups_Ocomm__monoid__mult(_1467275), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467277), _1467279)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467277), _1467281)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1467275), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1467275, _1467277, c_Groups_Otimes__class_Otimes(_1467275)), _1467283), c_Groups_Oone__class_Oone(_1467275)), _1467279)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1467275, _1467277, c_Groups_Otimes__class_Otimes(_1467275)), _1467283), c_Groups_Oone__class_Oone(_1467275)), _1467281)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1467275), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1467275, _1467277, c_Groups_Otimes__class_Otimes(_1467275)), _1467283), c_Groups_Oone__class_Oone(_1467275)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467277, tc_HOL_Obool)), _1467279), _1467281))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1467275, _1467277, c_Groups_Otimes__class_Otimes(_1467275)), _1467283), c_Groups_Oone__class_Oone(_1467275)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467277, tc_HOL_Obool)), _1467279), _1467281))))], (13987 ^ _775212) ^ [_1007872, _1007874] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007872))), -(c_SMT_Oz3div(_1007874, _1007872) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1007874), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1007872))))], (44288 ^ _775212) ^ [_1645486, _1645488] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1645486), tc_List_Olist(_1645486)), tc_HOL_Obool)), c_List_Olistrel1(_1645486, c_Transitive__Closure_Ortrancl(_1645486, _1645488))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1645486), c_List_Olistrel1(_1645486, _1645488)))))], (42539 ^ _775212) ^ [_1601159, _1601161, _1601163, _1601165, _1601167] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1601159, tc_fun(_1601161, tc_HOL_Obool)), _1601163), hAPP(hAPP(c_COMBB(tc_fun(_1601161, tc_HOL_Obool), tc_fun(_1601161, tc_HOL_Obool), _1601159), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1601161, tc_HOL_Obool)), _1601165)), _1601167)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1601161, tc_HOL_Obool)), _1601165), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601159, tc_fun(_1601161, tc_HOL_Obool)), _1601163), _1601167)))], (31993 ^ _775212) ^ [_1353598, _1353600, _1353602] : [class_Orderings_Olinorder(_1353598), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353598), _1353600)), -(_1353600 = c_Orderings_Obot__class_Obot(tc_fun(_1353598, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353598), _1353602)), -(_1353602 = c_Orderings_Obot__class_Obot(tc_fun(_1353598, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1353598, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353598, tc_HOL_Obool)), _1353600), _1353602)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353598), c_Big__Operators_Olinorder__class_OMax(_1353598, _1353600)), c_Big__Operators_Olinorder__class_OMax(_1353598, _1353602)))], (30182 ^ _775212) ^ [_1316116, _1316118, _1316120] : [class_Orderings_Oord(_1316116), 30185 ^ _775212 : [(30192 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316116), _1316120), _1316118)), -(hBOOL(hAPP(hAPP(c_member(_1316116), _1316118), hAPP(c_SetInterval_Oord__class_OatLeast(_1316116), _1316120))))], (30186 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1316116), _1316118), hAPP(c_SetInterval_Oord__class_OatLeast(_1316116), _1316120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316116), _1316120), _1316118)))]]], (46855 ^ _775212) ^ [_1709188, _1709190] : [class_Complete__Lattice_Ocomplete__lattice(_1709188), -(c_Complete__Lattice_OInf__class_OInf(_1709188, hAPP(c_List_Oset(_1709188), _1709190)) = hAPP(c_List_Ofoldl(_1709188, _1709188, c_Lattices_Osemilattice__inf__class_Oinf(_1709188), c_Orderings_Otop__class_Otop(_1709188)), _1709190))], (42501 ^ _775212) ^ [_1600103, _1600105, _1600107, _1600109] : [class_Complete__Lattice_Ocomplete__lattice(_1600103), -(_1600105 = c_Orderings_Obot__class_Obot(tc_fun(_1600107, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600107, _1600103), _1600105), hAPP(c_COMBK(_1600103, _1600107), _1600109)) = _1600109)], (47250 ^ _775212) ^ [_1717146, _1717148, _1717150] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1717146, tc_HOL_Obool)), hAPP(c_List_Oset(_1717146), c_List_Oremove1(_1717146, _1717148, _1717150))), hAPP(c_List_Oset(_1717146), _1717150))))], (35411 ^ _775212) ^ [_1428603, _1428605, _1428607, _1428609, _1428611] : [class_Groups_Ocomm__monoid__add(_1428603), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428605), _1428607)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428605, _1428603), _1428609), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428605, tc_HOL_Obool)), _1428607), _1428611)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428605, _1428603), hAPP(hAPP(c_COMBC(_1428605, _1428603, _1428603), hAPP(hAPP(c_COMBS(_1428605, _1428603, tc_fun(_1428603, _1428603)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1428603, tc_fun(_1428603, _1428603)), _1428605), c_If(_1428603)), hAPP(hAPP(c_COMBC(_1428605, tc_fun(_1428605, tc_HOL_Obool), tc_HOL_Obool), c_member(_1428605)), _1428611))), _1428609)), c_Groups_Ozero__class_Ozero(_1428603))), _1428607))], (33203 ^ _775212) ^ [_1377978, _1377980, _1377982, _1377984, _1377986] : [class_Groups_Ocomm__monoid__mult(_1377978), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377980), _1377982)), hBOOL(hAPP(hAPP(c_member(_1377980), _1377984), _1377982)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377980, _1377978), _1377986), _1377982) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377978), hAPP(_1377986, _1377984)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377980, _1377978), _1377986), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377980, tc_HOL_Obool)), _1377982), hAPP(hAPP(c_Set_Oinsert(_1377980), _1377984), c_Orderings_Obot__class_Obot(tc_fun(_1377980, tc_HOL_Obool)))))))], (44718 ^ _775212) ^ [_1658029, _1658031, _1658033] : [-(c_List_Osublist(_1658029, _1658031, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1658033)) = hAPP(hAPP(c_List_Otake(_1658029), _1658033), _1658031))], (13081 ^ _775212) ^ [_991616, _991618, _991620] : [hBOOL(hAPP(_991616, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _991618), _991620))), 13084 ^ _775212 : [(13109 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _991620), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13112 ^ _775212 : [(13113 ^ _775212) ^ [_992280] : [-(hBOOL(hAPP(_991616, _992280))), 13114 ^ _775212 : [(13115 ^ _775212) ^ [_992354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _991620), _992354)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _992354), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _991618 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _991620), _992280)), _992354)]]]]], (13091 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991620)), 13094 ^ _775212 : [(13095 ^ _775212) ^ [_991950] : [-(hBOOL(hAPP(_991616, _991950))), 13096 ^ _775212 : [(13097 ^ _775212) ^ [_992021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _992021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992021), _991620)), _991618 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _991620), _991950)), _992021)]]]]], (13085 ^ _775212) ^ [] : [_991620 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_991616, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (12987 ^ _775212) ^ [_989798, _989800] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989798))), -(c_SMT_Oz3mod(_989800, _989798) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _989800, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _989798)))], (39410 ^ _775212) ^ [_1525490, _1525492] : [-(hAPP(c_Fun_Oid(_1525490), _1525492) = _1525492)], (4034 ^ _775212) ^ [_836449, _836451, _836453, _836455] : [-(c_Product__Type_OSigma(_836455, _836451) = c_Product__Type_OSigma(_836453, _836449)), _836455 = _836453, _836451 = _836449], (23480 ^ _775212) ^ [] : [-(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)))], (5522 ^ _775212) ^ [_859451, _859453, _859455, _859457] : [-(c_COMBK(_859457, _859453) = c_COMBK(_859455, _859451)), _859457 = _859455, _859453 = _859451], (17143 ^ _775212) ^ [_1067032] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1067032))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067032)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44511 ^ _775212) ^ [_1652597, _1652599, _1652601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1652597, tc_HOL_Obool)), _1652599), _1652601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1652597), tc_HOL_Obool)), c_List_Olists(_1652597, _1652599)), c_List_Olists(_1652597, _1652601))))], (11506 ^ _775212) ^ [_964000, _964002, _964004, _964006, _964008] : [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), _964000), _964002)), _964004)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _964000), _964006)), _964008))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _964008), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _964000), _964008)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _964000), _964004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _964006), _964002)))], (10637 ^ _775212) ^ [_948829, _948831, _948833] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948829), _948831)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948833), _948831)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _948831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948829), _948833))], (1364 ^ _775212) ^ [_795118, _795120] : [-(class_Lattices_Obounded__lattice__top(_795118)), _795120 = _795118, class_Lattices_Obounded__lattice__top(_795120)], (45134 ^ _775212) ^ [_1668825, _1668827, _1668829, _1668831, _1668833] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668825)), _1668827) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668829)), _1668831), 45137 ^ _775212 : [(45146 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1668825, _1668829), _1668827), _1668831) = _1668833), hAPP(hAPP(c_List_Omap(tc_prod(_1668825, _1668829), _1668825), c_Product__Type_Ofst(_1668825, _1668829)), _1668833) = _1668827, hAPP(hAPP(c_List_Omap(tc_prod(_1668825, _1668829), _1668829), c_Product__Type_Osnd(_1668825, _1668829)), _1668833) = _1668831], (45138 ^ _775212) ^ [] : [hAPP(hAPP(c_List_Ozip(_1668825, _1668829), _1668827), _1668831) = _1668833, 45141 ^ _775212 : [(45144 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1668825, _1668829), _1668829), c_Product__Type_Osnd(_1668825, _1668829)), _1668833) = _1668831)], (45142 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1668825, _1668829), _1668825), c_Product__Type_Ofst(_1668825, _1668829)), _1668833) = _1668827)]]]]], (40256 ^ _775212) ^ [_1547918, _1547920, _1547922, _1547924] : [c_Equiv__Relations_Ocongruent(_1547918, _1547920, _1547922, _1547924), 40259 ^ _775212 : [(40260 ^ _775212) ^ [_1548063] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547918, _1547918)), _1548063), _1547922)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1547918, _1547918, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1547918, tc_fun(_1547918, _1547920), tc_fun(_1547918, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547920, tc_HOL_Obool), tc_fun(tc_fun(_1547918, _1547920), tc_fun(_1547918, tc_HOL_Obool)), _1547918), c_COMBB(_1547920, tc_HOL_Obool, _1547918)), hAPP(hAPP(c_COMBB(_1547920, tc_fun(_1547920, tc_HOL_Obool), _1547918), c_fequal), _1547924))), _1547924)), _1548063)))]]], (23412 ^ _775212) ^ [_1181213, _1181215, _1181217] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1181213), _1181215), _1181217) = c_Nitpick_OAbs__Frac(_1181213, c_Nitpick_Onorm__frac(_1181215, _1181217)))], (51022 ^ _775212) ^ [_1798958, _1798960, _1798962, _1798964] : [51023 ^ _775212 : [(51026 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1798958), _1798962), _1798964))], (51024 ^ _775212) ^ [] : [_1798960 = _1798964]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1798958), hAPP(hAPP(c_List_Olist_OCons(_1798958), _1798960), _1798962)), _1798964)))], (42135 ^ _775212) ^ [_1589576, _1589578, _1589580, _1589582, _1589584, _1589586] : [hBOOL(hAPP(hAPP(c_member(_1589576), _1589578), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589580, tc_fun(_1589576, tc_HOL_Obool)), _1589582), _1589584))), hBOOL(hAPP(hAPP(c_member(_1589580), _1589586), _1589582)), -(hBOOL(hAPP(hAPP(c_member(_1589576), _1589578), hAPP(_1589584, _1589586))))], (6461 ^ _775212) ^ [_877449, _877451, _877453, _877455] : [class_Groups_Ocancel__semigroup__add(_877449), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877449), _877451), _877453) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877449), _877451), _877455), -(_877453 = _877455)], (30931 ^ _775212) ^ [_1333797, _1333799, _1333801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333797)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1333799), _1333801)), 30938 ^ _775212 : [(30939 ^ _775212) ^ [_1333993] : [30941 ^ _775212 : [(30947 ^ _775212) ^ [] : [-(_1333993 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30943 ^ [_1333797, _1333799, _1333801, _1333993]), 30940 ^ [_1333797, _1333799, _1333801, _1333993]))], (30945 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30943 ^ [_1333797, _1333799, _1333801, _1333993]), _1333801)))], (30942 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30940 ^ [_1333797, _1333799, _1333801, _1333993]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1333797))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1333993), _1333799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1333993), _1333797)), _1333799)))]]], (49762 ^ _775212) ^ [_1771498, _1771500, _1771502] : [hBOOL(hAPP(c_List_Odistinct(_1771498), _1771500)), -(hBOOL(hAPP(c_List_Odistinct(_1771498), hAPP(c_List_OremoveAll(_1771498, _1771502), _1771500))))], (10333 ^ _775212) ^ [_943372, _943374, _943376, _943378] : [class_Rings_Oordered__comm__semiring(_943372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943372), _943374), _943376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943372), c_Groups_Ozero__class_Ozero(_943372)), _943378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943372), _943378), _943374)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943372), _943378), _943376))))], (50943 ^ _775212) ^ [_1797168, _1797170, _1797172] : [-(_1797168 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1797170), c_List_Oreplicate(_1797170, _1797168, _1797172)) = hAPP(hAPP(c_Set_Oinsert(_1797170), _1797172), c_Orderings_Obot__class_Obot(tc_fun(_1797170, tc_HOL_Obool))))], (13613 ^ _775212) ^ [_1000946, _1000948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000946)), 13616 ^ _775212 : [(13623 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1000946), _1000948)), -(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), _1000948), _1000946))))], (13617 ^ _775212) ^ [] : [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), _1000948), _1000946))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1000946), _1000948)))]]], (37948 ^ _775212) ^ [_1485774, _1485776] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1485774, _1485774), tc_HOL_Obool)), c_Relation_OId__on(_1485774, _1485776)), hAPP(hAPP(c_Product__Type_OSigma(_1485774, _1485774), _1485776), hAPP(c_COMBK(tc_fun(_1485774, tc_HOL_Obool), _1485774), _1485776)))))], (38182 ^ _775212) ^ [_1492202, _1492204, _1492206, _1492208, _1492210, _1492212] : [hAPP(c_Set_Oimage(_1492202, _1492204, _1492206), c_Orderings_Otop__class_Otop(tc_fun(_1492202, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1492204, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492208, _1492210, _1492212), c_Orderings_Otop__class_Otop(tc_fun(_1492208, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1492210, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1492202, _1492208), tc_prod(_1492204, _1492210), c_Product__Type_Omap__pair(_1492202, _1492204, _1492208, _1492210, _1492206, _1492212)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1492202, _1492208), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1492204, _1492210), tc_HOL_Obool)))], (45060 ^ _775212) ^ [_1667298, _1667300] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1667298)), c_List_Olist_ONil(_1667298)), c_List_Olists(_1667298, _1667300))))], (33193 ^ _775212) ^ [_1377709, _1377711, _1377713, _1377715, _1377717] : [class_Groups_Ocomm__monoid__mult(_1377709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377711), _1377713)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377711, _1377709), _1377715), hAPP(hAPP(c_Set_Oinsert(_1377711), _1377717), _1377713)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377709), hAPP(_1377715, _1377717)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377711, _1377709), _1377715), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377711, tc_HOL_Obool)), _1377713), hAPP(hAPP(c_Set_Oinsert(_1377711), _1377717), c_Orderings_Obot__class_Obot(tc_fun(_1377711, tc_HOL_Obool)))))))], (39624 ^ _775212) ^ [_1532232, _1532234, _1532236, _1532238, _1532240, _1532242, _1532244] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1532232, _1532234, _1532236, hAPP(hAPP(c_COMBC(_1532232, tc_fun(tc_prod(_1532232, _1532234), tc_HOL_Obool), tc_fun(_1532234, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532234, tc_fun(tc_fun(tc_prod(_1532232, _1532234), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1532232, _1532234), tc_HOL_Obool), tc_fun(_1532234, tc_HOL_Obool)), _1532232), c_COMBC(_1532234, tc_fun(tc_prod(_1532232, _1532234), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532234, tc_prod(_1532232, _1532234)), tc_fun(_1532234, tc_fun(tc_fun(tc_prod(_1532232, _1532234), tc_HOL_Obool), tc_HOL_Obool)), _1532232), hAPP(c_COMBB(tc_prod(_1532232, _1532234), tc_fun(tc_fun(tc_prod(_1532232, _1532234), tc_HOL_Obool), tc_HOL_Obool), _1532234), c_member(tc_prod(_1532232, _1532234)))), c_Product__Type_OPair(_1532232, _1532234)))), _1532238), hAPP(hAPP(c_COMBC(_1532234, tc_fun(tc_prod(_1532234, _1532236), tc_HOL_Obool), tc_fun(_1532236, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532236, tc_fun(tc_fun(tc_prod(_1532234, _1532236), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1532234, _1532236), tc_HOL_Obool), tc_fun(_1532236, tc_HOL_Obool)), _1532234), c_COMBC(_1532236, tc_fun(tc_prod(_1532234, _1532236), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532236, tc_prod(_1532234, _1532236)), tc_fun(_1532236, tc_fun(tc_fun(tc_prod(_1532234, _1532236), tc_HOL_Obool), tc_HOL_Obool)), _1532234), hAPP(c_COMBB(tc_prod(_1532234, _1532236), tc_fun(tc_fun(tc_prod(_1532234, _1532236), tc_HOL_Obool), tc_HOL_Obool), _1532236), c_member(tc_prod(_1532234, _1532236)))), c_Product__Type_OPair(_1532234, _1532236)))), _1532240)), _1532242), _1532244)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532232, _1532236)), hAPP(hAPP(c_Product__Type_OPair(_1532232, _1532236), _1532242), _1532244)), hAPP(hAPP(c_Relation_Orel__comp(_1532232, _1532234, _1532236), _1532238), _1532240))))], (46081 ^ _775212) ^ [_1691763, _1691765, _1691767, _1691769, _1691771, _1691773] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691763), tc_List_Olist(_1691763))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691763), tc_List_Olist(_1691763)), hAPP(hAPP(c_List_Oappend(_1691763), _1691765), hAPP(hAPP(c_List_Olist_OCons(_1691763), _1691767), c_List_Olist_ONil(_1691763)))), hAPP(hAPP(c_List_Oappend(_1691763), _1691769), hAPP(hAPP(c_List_Olist_OCons(_1691763), _1691771), c_List_Olist_ONil(_1691763))))), c_List_Olistrel1(_1691763, _1691773))), 46086 ^ _775212 : [(46089 ^ _775212) ^ [] : [-(_1691767 = _1691771)], (46087 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691763), tc_List_Olist(_1691763))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691763), tc_List_Olist(_1691763)), _1691765), _1691769)), c_List_Olistrel1(_1691763, _1691773))))]], 46090 ^ _775212 : [(46093 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1691763, _1691763)), hAPP(hAPP(c_Product__Type_OPair(_1691763, _1691763), _1691767), _1691771)), _1691773)))], (46091 ^ _775212) ^ [] : [-(_1691765 = _1691769)]]], (52707 ^ _775212) ^ [_1828669] : [-(hBOOL(_1828669)), -(hBOOL(hAPP(c_fNot, _1828669)))], (49367 ^ _775212) ^ [_1763259, _1763261, _1763263] : [class_Orderings_Olinorder(_1763259), c_List_Olinorder__class_Osorted(_1763259, _1763261), -(c_List_Olinorder__class_Osorted(_1763259, c_List_OtakeWhile(_1763259, _1763263, _1763261)))], (26696 ^ _775212) ^ [_1244312, _1244314, _1244316] : [class_Orderings_Oorder(_1244312), 26699 ^ _775212 : [(26706 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244312), _1244314), _1244316)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1244312, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1244312), _1244314)), hAPP(c_SetInterval_Oord__class_OatMost(_1244312), _1244316))))], (26700 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1244312, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1244312), _1244314)), hAPP(c_SetInterval_Oord__class_OatMost(_1244312), _1244316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244312), _1244314), _1244316)))]]], (45957 ^ _775212) ^ [_1688480, _1688482, _1688484, _1688486] : [-(hAPP(hAPP(c_List_Onth(_1688480), hAPP(hAPP(c_List_Oappend(_1688480), _1688482), _1688484)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688480)), _1688482)), _1688486)) = hAPP(hAPP(c_List_Onth(_1688480), _1688484), _1688486))], (39921 ^ _775212) ^ [_1539439, _1539441] : [39923 ^ _775212 : [(39924 ^ _775212) ^ [_1539464] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539439, _1539439)), hAPP(hAPP(c_Product__Type_OPair(_1539439, _1539439), hAPP(39922 ^ [_1539439, _1539441], hAPP(c_Nat_OSuc, _1539464))), hAPP(39922 ^ [_1539439, _1539441], _1539464))), _1539441)))]], -(c_Wellfounded_Owf(_1539439, _1539441))], (17155 ^ _775212) ^ [_1067173, _1067175] : [class_Int_Onumber__ring(_1067173), 17158 ^ _775212 : [(17165 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1067175)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1067173), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067175)) = hAPP(c_Int_Onumber__class_Onumber__of(_1067173), _1067175))], (17159 ^ _775212) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1067175))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1067173), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067175)) = c_Groups_Ozero__class_Ozero(_1067173))]]], (34901 ^ _775212) ^ [_1416299, _1416301, _1416303, _1416305] : [class_Lattices_Osemilattice__inf(_1416299), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416299), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416299), _1416301), _1416303)), _1416305) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416299), _1416301), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416299), _1416303), _1416305)))], (7306 ^ _775212) ^ [_891276, _891278] : [class_Rings_Ocomm__semiring__1(_891276), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_891276), c_Groups_Ozero__class_Ozero(_891276)), _891278) = _891278)], (3730 ^ _775212) ^ [_831695, _831697, _831699, _831701, _831703, _831705, _831707, _831709, _831711, _831713] : [-(c_Fun_Ofun__upd(_831713, _831709, _831705, _831701, _831697) = c_Fun_Ofun__upd(_831711, _831707, _831703, _831699, _831695)), _831713 = _831711, _831709 = _831707, _831705 = _831703, _831701 = _831699, _831697 = _831695], (33988 ^ _775212) ^ [_1395935, _1395937, _1395939, _1395941, _1395943] : [-(hAPP(c_Relation_OImage(_1395935, _1395937, _1395939), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395935, tc_HOL_Obool)), _1395941), _1395943)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395937, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1395935, _1395937, _1395939), _1395941)), hAPP(c_Relation_OImage(_1395935, _1395937, _1395939), _1395943)))], (34965 ^ _775212) ^ [_1417620, _1417622, _1417624, _1417626] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417620, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417620, tc_HOL_Obool)), _1417622), _1417624)), _1417626) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417620, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417620, tc_HOL_Obool)), _1417622), _1417626)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417620, tc_HOL_Obool)), _1417624), _1417626)))], (38832 ^ _775212) ^ [_1505104] : [class_Orderings_Olinorder(_1505104), -(c_Finite__Set_Ofun__left__comm__idem(_1505104, _1505104, c_Orderings_Oord__class_Omax(_1505104)))], (25322 ^ _775212) ^ [_1215877, _1215879] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1215877)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1215879))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1215879), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1215877)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47816 ^ _775212) ^ [_1729626, _1729628, _1729630, _1729632, _1729634] : [-(c_List_Olist__all2(_1729626, _1729628, _1729630, _1729632, _1729634)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729626)), _1729632) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729628)), _1729634), 47822 ^ _775212 : [(47825 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1729630, hAPP(hAPP(c_List_Onth(_1729626), _1729632), 47821 ^ [_1729626, _1729628, _1729630, _1729632, _1729634])), hAPP(hAPP(c_List_Onth(_1729628), _1729634), 47821 ^ [_1729626, _1729628, _1729630, _1729632, _1729634])))], (47823 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47821 ^ [_1729626, _1729628, _1729630, _1729632, _1729634]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729626)), _1729632))))]]], (34439 ^ _775212) ^ [_1406967, _1406969] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406967, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1406967, tc_HOL_Obool))), _1406969) = c_Orderings_Obot__class_Obot(tc_fun(_1406967, tc_HOL_Obool)))], (34118 ^ _775212) ^ [_1399649, _1399651, _1399653] : [_1399651 = c_Orderings_Obot__class_Obot(tc_fun(_1399649, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399649, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399649), _1399651), _1399653))], (27743 ^ _775212) ^ [_1265810, _1265812, _1265814, _1265816, _1265818] : [class_Complete__Lattice_Ocomplete__lattice(_1265810), 27746 ^ _775212 : [(27747 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265810), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265812, _1265810), _1265814), _1265816)), _1265818)), 27750 ^ _775212 : [(27751 ^ _775212) ^ [_1265991] : [hBOOL(hAPP(hAPP(c_member(_1265812), _1265991), _1265814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265810), hAPP(_1265816, _1265991)), _1265818)))]]], (27757 ^ _775212) ^ [] : [27759 ^ _775212 : [(27762 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265810), hAPP(_1265816, 27758 ^ [_1265810, _1265812, _1265814, _1265816, _1265818])), _1265818))], (27760 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1265812), 27758 ^ [_1265810, _1265812, _1265814, _1265816, _1265818]), _1265814)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265810), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265812, _1265810), _1265814), _1265816)), _1265818)))]]], (26208 ^ _775212) ^ [_1234648, _1234650, _1234652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234648)), 26211 ^ _775212 : [(26212 ^ _775212) ^ [_1234782] : [26214 ^ _775212 : [(26220 ^ _775212) ^ [] : [-(_1234782 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26216 ^ [_1234648, _1234650, _1234652, _1234782]), 26213 ^ [_1234648, _1234650, _1234652, _1234782]))], (26218 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26216 ^ [_1234648, _1234650, _1234652, _1234782]), _1234650)))], (26215 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26213 ^ [_1234648, _1234650, _1234652, _1234782]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1234648))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234652), _1234782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234652), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1234782), _1234648))))]]], (40174 ^ _775212) ^ [_1545744, _1545746, _1545748] : [c_Relation_Orefl__on(_1545744, _1545746, _1545748), 40177 ^ _775212 : [(40184 ^ _775212) ^ [_1546228] : [hBOOL(hAPP(hAPP(c_member(_1545744), _1546228), _1545746)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545744, _1545744)), hAPP(hAPP(c_Product__Type_OPair(_1545744, _1545744), _1546228), _1546228)), _1545748)))], (40178 ^ _775212) ^ [_1545955] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545744, _1545744)), _1545955), _1545748)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1545744, _1545744, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1545744, tc_fun(_1545744, tc_HOL_Obool), tc_fun(_1545744, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1545744, tc_HOL_Obool), tc_fun(_1545744, tc_HOL_Obool)), _1545744), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1545744)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545744), c_fconj), hAPP(hAPP(c_COMBC(_1545744, tc_fun(_1545744, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545744)), _1545746)))), hAPP(hAPP(c_COMBC(_1545744, tc_fun(_1545744, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545744)), _1545746))), _1545955)))]]], (37471 ^ _775212) ^ [_1473264, _1473266, _1473268, _1473270, _1473272] : [-(hAPP(c_Set_Ovimage(_1473264, _1473266, _1473268), hAPP(hAPP(c_Set_Oinsert(_1473266), _1473270), _1473272)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473264, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1473264, _1473266, _1473268), hAPP(hAPP(c_Set_Oinsert(_1473266), _1473270), c_Orderings_Obot__class_Obot(tc_fun(_1473266, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1473264, _1473266, _1473268), _1473272)))], (27906 ^ _775212) ^ [_1269538, _1269540, _1269542, _1269544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269538, tc_HOL_Obool)), _1269540), _1269542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269538, tc_HOL_Obool)), _1269540), hAPP(hAPP(c_Set_Oinsert(_1269538), _1269544), _1269542))))], (11384 ^ _775212) ^ [_961998] : [-(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), _961998))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12560 ^ _775212) ^ [_982298, _982300, _982302] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _982298), _982300), _982302) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _982298), c_Divides_Odiv__class_Omod(tc_Int_Oint, _982300, _982302)), _982302))], (26937 ^ _775212) ^ [_1249007, _1249009, _1249011] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249007, tc_HOL_Obool)), _1249009), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249007, tc_HOL_Obool)), _1249009), _1249011)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249007, tc_HOL_Obool)), _1249009), _1249011))], (12281 ^ _775212) ^ [_977223, _977225] : [-(hBOOL(hAPP(_977223, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_977223, _977225)), 12289 ^ _775212 : [(12292 ^ _775212) ^ [_977461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977461), 12288 ^ [_977223, _977225])), hBOOL(hAPP(_977223, _977461))], (12298 ^ _775212) ^ [] : [-(hBOOL(hAPP(_977223, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 12288 ^ [_977223, _977225]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (12290 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 12288 ^ [_977223, _977225]), _977225)))]]], (17935 ^ _775212) ^ [] : [-(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)))))], (44643 ^ _775212) ^ [_1655996, _1655998, _1656000, _1656002] : [-(_1655996 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1655998), hAPP(hAPP(c_List_Olist_OCons(_1655998), _1656000), _1656002)), _1655996) = hAPP(hAPP(c_List_Onth(_1655998), _1656002), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655996), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (21195 ^ _775212) ^ [_1138228, _1138230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1138228)), 21198 ^ _775212 : [(21205 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138230), _1138228))), -(c_Divides_OposDivAlg(_1138230, _1138228) = hAPP(c_Divides_Oadjust(_1138228), c_Divides_OposDivAlg(_1138230, 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)))), _1138228))))], (21199 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138230), _1138228)), -(c_Divides_OposDivAlg(_1138230, _1138228) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1138230))]]], (27878 ^ _775212) ^ [_1268940, _1268942, _1268944, _1268946] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1268940, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1268940), _1268942), _1268944)), _1268946) = hAPP(hAPP(c_Set_Oinsert(_1268940), _1268942), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1268940, tc_HOL_Obool)), _1268944), _1268946)))], (5510 ^ _775212) ^ [_859281, _859283] : [_859283 = _859281, -(tc_Lazy__Sequence_Olazy__sequence(_859283) = tc_Lazy__Sequence_Olazy__sequence(_859281))], (6835 ^ _775212) ^ [_884205, _884207] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884205), _884207) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6840 ^ _775212 : [(6843 ^ _775212) ^ [] : [-(_884207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6841 ^ _775212) ^ [] : [-(_884205 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6844 ^ _775212 : [(6847 ^ _775212) ^ [] : [-(_884207 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6845 ^ _775212) ^ [] : [-(_884205 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (36811 ^ _775212) ^ [_1458890, _1458892, _1458894, _1458896, _1458898] : [c_Fun_Oinj__on(_1458890, _1458892, _1458894, c_Orderings_Otop__class_Otop(tc_fun(_1458890, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1458890, _1458892, _1458894), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458890, tc_HOL_Obool)), _1458896), _1458898)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458892, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1458890, _1458892, _1458894), _1458896)), hAPP(c_Set_Oimage(_1458890, _1458892, _1458894), _1458898)))], (27481 ^ _775212) ^ [_1259904, _1259906, _1259908] : [class_Orderings_Olinorder(_1259904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259904), _1259906), _1259908)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259904, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1259904, _1259906, _1259908)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1259904), _1259908)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1259904), _1259906))], (49642 ^ _775212) ^ [_1769100, _1769102, _1769104] : [49644 ^ _775212 : [(49647 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1769102, 49643 ^ [_1769100, _1769102, _1769104])))], (49645 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769100), 49643 ^ [_1769100, _1769102, _1769104]), hAPP(c_List_Oset(_1769100), c_List_OdropWhile(_1769100, _1769102, _1769104)))))]], -(c_List_OtakeWhile(_1769100, _1769102, _1769104) = hAPP(c_List_Ofilter(_1769100, _1769102), _1769104))], (21685 ^ _775212) ^ [_1146739, _1146741, _1146743] : [_1146739 = _1146741, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146743, tc_HOL_Obool)), _1146739), _1146741)))], (43332 ^ _775212) ^ [_1621186, _1621188, _1621190] : [class_Complete__Lattice_Ocomplete__lattice(_1621186), -(c_Complete__Lattice_OInf__class_OInf(_1621186, hAPP(hAPP(c_Set_Oinsert(_1621186), _1621188), hAPP(hAPP(c_Set_Oinsert(_1621186), _1621190), c_Orderings_Obot__class_Obot(tc_fun(_1621186, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1621186), _1621188), _1621190))], (48797 ^ _775212) ^ [_1751420, _1751422, _1751424, _1751426] : [class_Orderings_Olinorder(_1751420), -(c_List_Olinorder__class_Osorted(_1751420, hAPP(hAPP(c_List_Omap(_1751422, _1751420), _1751424), c_List_Olinorder__class_Osort__key(_1751422, _1751420, _1751424, _1751426))))], (35249 ^ _775212) ^ [_1424778, _1424780, _1424782, _1424784] : [class_Orderings_Olinorder(_1424778), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424778, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1424778), _1424780)), c_SetInterval_Oord__class_OatLeastAtMost(_1424778, _1424782, _1424784)) = c_SetInterval_Oord__class_OatLeastAtMost(_1424778, _1424782, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424778), _1424780), _1424784)))], (18497 ^ _775212) ^ [_1089500] : [class_Int_Onumber__ring(_1089500), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089500), c_Groups_Oone__class_Oone(_1089500)), c_Groups_Oone__class_Oone(_1089500)) = hAPP(c_Int_Onumber__class_Onumber__of(_1089500), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (24928 ^ _775212) ^ [_1208521, _1208523, _1208525, _1208527] : [class_Rings_Ocomm__ring(_1208521), class_Rings_Odvd(_1208521), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208521), _1208523), _1208525)), 24939 ^ _775212 : [(24946 ^ _775212) ^ [_1208947, _1208949] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208521), _1208523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208521), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1208521), _1208949), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208521), _1208947), _1208525))), _1208527))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208521), _1208523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208521), _1208949), _1208527))))], (24940 ^ _775212) ^ [_1208774, _1208776] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208521), _1208523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208521), _1208776), _1208527))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208521), _1208523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208521), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1208521), _1208776), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208521), _1208774), _1208525))), _1208527))))]]], (9747 ^ _775212) ^ [_932847, _932849] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932847), _932849) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_932847 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_932849 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23328 ^ _775212) ^ [_1179787, _1179789] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1179787), _1179789) = 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), _1179787)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1179789)))))], (5823 ^ _775212) ^ [_867250, _867252, _867254] : [c_Com_Ocom_OCond(_867250, _867252, _867254) = c_Com_Ocom_OSKIP], (11921 ^ _775212) ^ [_971041, _971043, _971045, _971047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971041), _971043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971045), _971047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971041), _971045)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971043), _971047))))], (44276 ^ _775212) ^ [_1645185, _1645187, _1645189, _1645191] : [-(c_List_Olist_Olist__size(_1645185, _1645187, hAPP(hAPP(c_List_Olist_OCons(_1645185), _1645189), _1645191)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1645187, _1645189)), c_List_Olist_Olist__size(_1645185, _1645187, _1645191))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27587 ^ _775212) ^ [_1261993, _1261995] : [class_Groups_Oordered__ab__group__add(_1261993), -(hAPP(c_Set_Oimage(_1261993, _1261993, c_Groups_Ouminus__class_Ouminus(_1261993)), hAPP(c_SetInterval_Oord__class_OatMost(_1261993), _1261995)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1261993), hAPP(c_Groups_Ouminus__class_Ouminus(_1261993), _1261995)))], (32219 ^ _775212) ^ [_1358090, _1358092, _1358094, _1358096, _1358098, _1358100, _1358102] : [-(c_Nitpick_Ofold__graph_H(_1358090, _1358092, _1358094, _1358096, _1358098, hAPP(hAPP(_1358094, _1358100), _1358102))), 32220 ^ _775212 : [(32227 ^ _775212) ^ [_1358319, _1358321] : [hAPP(hAPP(_1358094, _1358100), _1358102) = hAPP(hAPP(_1358094, _1358321), _1358319), hBOOL(hAPP(hAPP(c_member(_1358090), _1358321), _1358098)), c_Nitpick_Ofold__graph_H(_1358090, _1358092, _1358094, _1358096, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1358090, tc_HOL_Obool)), _1358098), hAPP(hAPP(c_Set_Oinsert(_1358090), _1358321), c_Orderings_Obot__class_Obot(tc_fun(_1358090, tc_HOL_Obool)))), _1358319)], (32221 ^ _775212) ^ [] : [_1358098 = c_Orderings_Obot__class_Obot(tc_fun(_1358090, tc_HOL_Obool)), hAPP(hAPP(_1358094, _1358100), _1358102) = _1358096]]], (16861 ^ _775212) ^ [_1062684, _1062686] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062684)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062684)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062686)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062684)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062686))))], (39593 ^ _775212) ^ [_1530566, _1530568, _1530570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530566, _1530566), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530566, _1530566, _1530566), _1530568), _1530570)), _1530568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1530566, tc_HOL_Obool), tc_fun(_1530566, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1530566, tc_HOL_Obool), tc_fun(_1530566, tc_HOL_Obool), tc_fun(_1530566, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1530566, _1530568)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1530566, tc_HOL_Obool), tc_fun(_1530566, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1530566, _1530570)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1530566, tc_HOL_Obool), tc_fun(_1530566, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1530566, tc_HOL_Obool), tc_fun(_1530566, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1530566, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1530566, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1530566, tc_HOL_Obool), tc_fun(_1530566, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1530566, _1530568))))], (11650 ^ _775212) ^ [_966548, _966550] : [_966548 = _966550, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966548), _966550)))], (43756 ^ _775212) ^ [_1631207, _1631209, _1631211, _1631213, _1631215] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631207, _1631207)), hAPP(hAPP(c_Product__Type_OPair(_1631207, _1631207), _1631209), _1631211)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631207, _1631207), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1631213)), _1631215))), 43760 ^ _775212 : [(43763 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631207, _1631207)), hAPP(hAPP(c_Product__Type_OPair(_1631207, _1631207), 43759 ^ [_1631207, _1631209, _1631211, _1631213, _1631215]), _1631211)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631207, _1631207), tc_HOL_Obool), _1631213), _1631215))))], (43761 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631207, _1631207)), hAPP(hAPP(c_Product__Type_OPair(_1631207, _1631207), _1631209), 43759 ^ [_1631207, _1631209, _1631211, _1631213, _1631215])), _1631215)))]]], (17897 ^ _775212) ^ [_1079037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1079037), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1079037)), c_Int_OPls)))], (4664 ^ _775212) ^ [_846294, _846296, _846298, _846300] : [-(c_Wellfounded_Oaccp(_846300, _846296) = c_Wellfounded_Oaccp(_846298, _846294)), _846300 = _846298, _846296 = _846294], (25629 ^ _775212) ^ [_1222548, _1222550, _1222552, _1222554, _1222556] : [class_Fields_Ofield(_1222548), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222548), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222550, _1222548), _1222552), _1222554)), _1222556) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222550, _1222548), hAPP(hAPP(c_COMBC(_1222550, _1222548, _1222548), hAPP(hAPP(c_COMBB(_1222548, tc_fun(_1222548, _1222548), _1222550), c_Rings_Oinverse__class_Odivide(_1222548)), _1222552)), _1222556)), _1222554))], (22698 ^ _775212) ^ [_1167033, _1167035, _1167037, _1167039] : [class_Orderings_Olinorder(_1167033), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167033), _1167035), _1167037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167033), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1167033), _1167039), _1167035)), _1167037)))], (9871 ^ _775212) ^ [_934978] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _934978), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _934978)], (28379 ^ _775212) ^ [_1278479, _1278481, _1278483] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278479), _1278481)), 28382 ^ _775212 : [(28389 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278479), _1278483)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1278479), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278479, tc_HOL_Obool)), _1278483), _1278481))))], (28383 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278479), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278479, tc_HOL_Obool)), _1278483), _1278481))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1278479), _1278483)))]]], (22252 ^ _775212) ^ [_1157938, _1157940] : [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(_1157940))), 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), _1157938)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1157938)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157940))))], (48091 ^ _775212) ^ [_1735557, _1735559, _1735561, _1735563] : [-(hAPP(hAPP(c_List_Omap(_1735557, _1735559), _1735561), c_List_Oconcat(_1735557, _1735563)) = c_List_Oconcat(_1735559, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1735557), tc_List_Olist(_1735559)), hAPP(c_List_Omap(_1735557, _1735559), _1735561)), _1735563)))], (28714 ^ _775212) ^ [_1285317, _1285319, _1285321, _1285323] : [hAPP(c_Set_Oimage(_1285317, _1285319, _1285321), _1285323) = c_Orderings_Obot__class_Obot(tc_fun(_1285319, tc_HOL_Obool)), -(_1285323 = c_Orderings_Obot__class_Obot(tc_fun(_1285317, tc_HOL_Obool)))], (39432 ^ _775212) ^ [_1525863] : [-(hAPP(c_Set_Oimage(_1525863, _1525863, c_Fun_Oid(_1525863)), c_Orderings_Otop__class_Otop(tc_fun(_1525863, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1525863, tc_HOL_Obool)))], (19651 ^ _775212) ^ [_1109806, _1109808, _1109810] : [class_Fields_Ofield__inverse__zero(_1109806), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109806), c_Groups_Oone__class_Oone(_1109806)), hAPP(hAPP(c_Power_Opower__class_Opower(_1109806), _1109808), _1109810)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1109806), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109806), c_Groups_Oone__class_Oone(_1109806)), _1109808)), _1109810))], (40814 ^ _775212) ^ [_1560504, _1560506, _1560508, _1560510, _1560512, _1560514, _1560516, _1560518] : [c_Finite__Set_Ofolding__image(_1560504, _1560506, _1560508, _1560510, _1560512), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560506), _1560514)), c_Fun_Oinj__on(_1560506, _1560506, _1560516, _1560514), -(hAPP(hAPP(_1560512, _1560518), hAPP(c_Set_Oimage(_1560506, _1560506, _1560516), _1560514)) = hAPP(hAPP(_1560512, hAPP(c_Fun_Ocomp(_1560506, _1560504, _1560506, _1560518), _1560516)), _1560514))], (50064 ^ _775212) ^ [_1778512, _1778514, _1778516] : [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), _1778512), _1778514))), -(hBOOL(hAPP(hAPP(_1778516, _1778512), _1778514))), 50071 ^ _775212 : [(50074 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 50069 ^ [_1778512, _1778514, _1778516]), 50070 ^ [_1778512, _1778514, _1778516]))), -(hBOOL(hAPP(hAPP(_1778516, 50069 ^ [_1778512, _1778514, _1778516]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 50070 ^ [_1778512, _1778514, _1778516]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50080 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1778516, 50069 ^ [_1778512, _1778514, _1778516]), 50070 ^ [_1778512, _1778514, _1778516]))], (50072 ^ _775212) ^ [] : [-(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), 50069 ^ [_1778512, _1778514, _1778516]), 50070 ^ [_1778512, _1778514, _1778516]))))]]], (47871 ^ _775212) ^ [_1730890, _1730892] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1730890))), c_Enum_Osublists(_1730890, _1730892)) = 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(_1730890)), _1730892)))], (25306 ^ _775212) ^ [_1215580, _1215582] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1215580), _1215582)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215582), _1215580)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1215582)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1215580)))], (792 ^ _775212) ^ [_787368, _787370, _787372, _787374] : [-(c_List_Olinorder__class_Osorted(_787372, _787368)), c_List_Olinorder__class_Osorted(_787374, _787370), _787374 = _787372, _787370 = _787368], (35113 ^ _775212) ^ [_1421704, _1421706] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421704, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1421704, tc_HOL_Obool)), _1421706)), _1421706) = c_Orderings_Obot__class_Obot(tc_fun(_1421704, tc_HOL_Obool)))], (18111 ^ _775212) ^ [_1082712, _1082714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1082712), _1082714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1082712)), c_Int_OBit0(_1082714))))], (13441 ^ _775212) ^ [_998135] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _998135, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _998135)], (52381 ^ _775212) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (36843 ^ _775212) ^ [_1459540, _1459542, _1459544, _1459546, _1459548, _1459550] : [c_Fun_Oinj__on(_1459540, _1459542, _1459544, _1459546), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459540, tc_HOL_Obool)), _1459548), _1459546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459540, tc_HOL_Obool)), _1459550), _1459546)), -(hAPP(c_Set_Oimage(_1459540, _1459542, _1459544), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1459540, tc_HOL_Obool)), _1459548), _1459550)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1459542, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1459540, _1459542, _1459544), _1459548)), hAPP(c_Set_Oimage(_1459540, _1459542, _1459544), _1459550)))], (27129 ^ _775212) ^ [_1253135, _1253137, _1253139, _1253141] : [class_Lattices_Osemilattice__sup(_1253135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253135), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1253135), _1253137), _1253139)), _1253141)), 27136 ^ _775212 : [(27139 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253135), _1253139), _1253141)))], (27137 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253135), _1253137), _1253141)))]]], (29738 ^ _775212) ^ [_1305014, _1305016, _1305018, _1305020] : [hBOOL(hAPP(hAPP(c_member(_1305014), _1305016), _1305018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1305014, tc_HOL_Obool)), _1305018), _1305020)), -(hBOOL(hAPP(hAPP(c_member(_1305014), _1305016), _1305020)))], (39711 ^ _775212) ^ [_1535273] : [-(c_Wellfounded_Owf(_1535273, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1535273, _1535273), tc_HOL_Obool))))], (7477 ^ _775212) ^ [_894437, _894439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894437), _894439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894437)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894439))))], (48258 ^ _775212) ^ [_1740018] : [-(c_List_Otranspose(_1740018, c_List_Olist_ONil(tc_List_Olist(_1740018))) = c_List_Olist_ONil(tc_List_Olist(_1740018)))], (11452 ^ _775212) ^ [_963037, _963039, _963041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _963037)), _963037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _963039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _963037), _963041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _963039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _963041), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (40391 ^ _775212) ^ [_1551097, _1551099, _1551101] : [-(hAPP(c_Fun_Ocomp(_1551097, _1551097, _1551099, c_Fun_Oid(_1551097)), _1551101) = _1551101)], (44926 ^ _775212) ^ [_1662994, _1662996, _1662998] : [44928 ^ _775212 : [(44931 ^ _775212) ^ [] : [hBOOL(hAPP(_1662998, hAPP(hAPP(c_List_Onth(_1662994), _1662996), 44927 ^ [_1662994, _1662996, _1662998])))], (44929 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44927 ^ [_1662994, _1662996, _1662998]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662994)), _1662996))))]], 44932 ^ _775212 : [(44933 ^ _775212) ^ [_1663196] : [hBOOL(hAPP(hAPP(c_member(_1662994), _1663196), hAPP(c_List_Oset(_1662994), _1662996))), -(hBOOL(hAPP(_1662998, _1663196)))]]], (15691 ^ _775212) ^ [_1040635, _1040637, _1040639, _1040641] : [class_Rings_Olinordered__semidom(_1040635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040635), c_Groups_Oone__class_Oone(_1040635)), _1040637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040635), hAPP(hAPP(c_Power_Opower__class_Opower(_1040635), _1040637), _1040639)), hAPP(hAPP(c_Power_Opower__class_Opower(_1040635), _1040637), _1040641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040639), _1040641)))], (3506 ^ _775212) ^ [_828209, _828211, _828213, _828215] : [-(c_New__DSequence_Oneg__single(_828215, _828211) = c_New__DSequence_Oneg__single(_828213, _828209)), _828215 = _828213, _828211 = _828209], (42585 ^ _775212) ^ [_1602381, _1602383, _1602385, _1602387, _1602389] : [_1602381 = c_Orderings_Obot__class_Obot(tc_fun(_1602383, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602383, tc_fun(_1602385, tc_HOL_Obool)), _1602381), hAPP(hAPP(c_COMBC(_1602383, tc_fun(_1602385, tc_HOL_Obool), tc_fun(_1602385, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602385, tc_HOL_Obool), tc_fun(tc_fun(_1602385, tc_HOL_Obool), tc_fun(_1602385, tc_HOL_Obool)), _1602383), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602385, tc_HOL_Obool))), _1602387)), _1602389)) = c_Orderings_Otop__class_Otop(tc_fun(_1602385, tc_HOL_Obool)))], (32239 ^ _775212) ^ [_1358644, _1358646, _1358648, _1358650, _1358652, _1358654, _1358656, _1358658] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1358644, _1358646), tc_prod(_1358644, _1358646))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1358644, _1358646), tc_prod(_1358644, _1358646)), hAPP(hAPP(c_Product__Type_OPair(_1358644, _1358646), _1358648), _1358650)), hAPP(hAPP(c_Product__Type_OPair(_1358644, _1358646), _1358652), _1358654))), c_Wellfounded_Olex__prod(_1358644, _1358646, _1358656, _1358658))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1358644, _1358644)), hAPP(hAPP(c_Product__Type_OPair(_1358644, _1358644), _1358648), _1358652)), _1358656))), 32246 ^ _775212 : [(32249 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1358646, _1358646)), hAPP(hAPP(c_Product__Type_OPair(_1358646, _1358646), _1358650), _1358654)), _1358658)))], (32247 ^ _775212) ^ [] : [-(_1358648 = _1358652)]]], (7731 ^ _775212) ^ [_899368] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _899368) = _899368)], (22330 ^ _775212) ^ [_1159930, _1159932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159930), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159932)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159930)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159932))], (27854 ^ _775212) ^ [_1268506, _1268508] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1268506, _1268508))))], (17001 ^ _775212) ^ [_1064723, _1064725] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1064723), _1064725) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1064723 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1064723 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (13685 ^ _775212) ^ [_1002083, _1002085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002083), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13688 ^ _775212 : [(13695 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002085), 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), _1002085), _1002083))))], (13689 ^ _775212) ^ [] : [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), _1002085), _1002083))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002085), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (45500 ^ _775212) ^ [_1678513, _1678515, _1678517, _1678519, _1678521, _1678523] : [-(hAPP(c_List_Olist_Olist__case(_1678513, _1678515, _1678517, _1678519), hAPP(hAPP(c_List_Olist_OCons(_1678515), _1678521), _1678523)) = hAPP(hAPP(_1678519, _1678521), _1678523))], (37888 ^ _775212) ^ [_1483848, _1483850, _1483852] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1483848, _1483850), _1483852), hAPP(c_COMBK(tc_fun(_1483850, tc_HOL_Obool), _1483848), c_Orderings_Obot__class_Obot(tc_fun(_1483850, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1483848, _1483850), tc_HOL_Obool)))], (14417 ^ _775212) ^ [_1015875, _1015877, _1015879] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1015875), _1015877)), _1015879) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1015875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015877), _1015879)))], (37336 ^ _775212) ^ [_1469960, _1469962, _1469964, _1469966, _1469968] : [class_Groups_Ocomm__monoid__mult(_1469960), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469962), _1469964)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469962), _1469966)), 37350 ^ _775212 : [(37353 ^ _775212) ^ [] : [hAPP(_1469968, 37349 ^ [_1469960, _1469962, _1469964, _1469966, _1469968]) = c_Groups_Oone__class_Oone(_1469960)], (37351 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1469962), 37349 ^ [_1469960, _1469962, _1469964, _1469966, _1469968]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1469962, tc_HOL_Obool)), _1469964), _1469966))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1469960, _1469962, c_Groups_Otimes__class_Otimes(_1469960)), _1469968), c_Groups_Oone__class_Oone(_1469960)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1469962, tc_HOL_Obool)), _1469964), _1469966)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1469960), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1469960, _1469962, c_Groups_Otimes__class_Otimes(_1469960)), _1469968), c_Groups_Oone__class_Oone(_1469960)), _1469964)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1469960, _1469962, c_Groups_Otimes__class_Otimes(_1469960)), _1469968), c_Groups_Oone__class_Oone(_1469960)), _1469966)))], (50747 ^ _775212) ^ [_1792769, _1792771, _1792773, _1792775, _1792777, _1792779] : [-(hAPP(hAPP(c_List_Ozip(_1792769, _1792771), c_List_Oreplicate(_1792769, _1792773, _1792775)), c_List_Oreplicate(_1792771, _1792777, _1792779)) = c_List_Oreplicate(tc_prod(_1792769, _1792771), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1792773), _1792777), hAPP(hAPP(c_Product__Type_OPair(_1792769, _1792771), _1792775), _1792779)))], (5426 ^ _775212) ^ [_857993, _857995, _857997, _857999, _858001, _858003] : [-(c_Set_Oimage(_858003, _857999, _857995) = c_Set_Oimage(_858001, _857997, _857993)), _858003 = _858001, _857999 = _857997, _857995 = _857993], (6281 ^ _775212) ^ [_874377] : [6282 ^ _775212 : [(6283 ^ _775212) ^ [_874419] : [_874377 = hAPP(c_Nat_OSuc, _874419)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _874377)))], (6471 ^ _775212) ^ [_877616, _877618, _877620, _877622] : [class_Groups_Ocancel__ab__semigroup__add(_877616), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877616), _877618), _877620) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877616), _877618), _877622), -(_877620 = _877622)], (12458 ^ _775212) ^ [_980123, _980125, _980127, _980129] : [class_Divides_Osemiring__div(_980123), -(c_Divides_Odiv__class_Omod(_980123, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980123), _980125), _980127), _980129) = c_Divides_Odiv__class_Omod(_980123, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980123), c_Divides_Odiv__class_Omod(_980123, _980125, _980129)), c_Divides_Odiv__class_Omod(_980123, _980127, _980129)), _980129))], (47523 ^ _775212) ^ [_1723233, _1723235, _1723237] : [class_Orderings_Olinorder(_1723233), -(c_List_Oremove1(_1723233, _1723235, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1723233, _1723233, c_COMBI(_1723233)), _1723235), _1723237)) = _1723237)], (45367 ^ _775212) ^ [_1674607, _1674609] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1674607), tc_List_Olist(_1674607), c_List_Olistrel(_1674607, _1674609)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1674607)), c_List_Olist_ONil(_1674607)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1674607), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1674607)), c_List_Olist_ONil(_1674607)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1674607), tc_HOL_Obool))))], (16977 ^ _775212) ^ [_1064357] : [class_Int_Onumber__ring(_1064357), -(hAPP(c_Int_Onumber__class_Onumber__of(_1064357), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1064357), c_Groups_Oone__class_Oone(_1064357)))], (20049 ^ _775212) ^ [_1117287] : [c_Nat__Transfer_Ois__nat(_1117287), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117287)))], (22246 ^ _775212) ^ [_1157793, _1157795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1157793)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157795))), -(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(_1157795))), 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), _1157793)), c_Int_Onat))))))], (46873 ^ _775212) ^ [_1709561, _1709563, _1709565] : [class_Orderings_Olinorder(_1709561), -(c_Big__Operators_Olinorder__class_OMin(_1709561, hAPP(c_List_Oset(_1709561), hAPP(hAPP(c_List_Olist_OCons(_1709561), _1709563), _1709565))) = hAPP(c_List_Ofoldl(_1709561, _1709561, c_Orderings_Oord__class_Omin(_1709561), _1709563), _1709565))], (42982 ^ _775212) ^ [_1612913, _1612915, _1612917] : [c_Relation_Osingle__valued(_1612913, _1612913, _1612915), -(c_Relation_Osingle__valued(_1612913, _1612913, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1612913, _1612913), tc_HOL_Obool), _1612917), _1612915)))], (26764 ^ _775212) ^ [_1245579, _1245581, _1245583, _1245585, _1245587] : [class_Groups_Ocomm__monoid__add(_1245579), class_Groups_Ocomm__monoid__mult(_1245579), _1245581 = _1245583, c_Nat__Transfer_Onat__set(_1245583), 26782 ^ _775212 : [(26785 ^ _775212) ^ [] : [hAPP(_1245585, 26781 ^ [_1245579, _1245581, _1245583, _1245585, _1245587]) = hAPP(_1245587, 26781 ^ [_1245579, _1245581, _1245583, _1245585, _1245587])], (26783 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26781 ^ [_1245579, _1245581, _1245583, _1245585, _1245587])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1245579), _1245585), _1245581) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1245579), _1245587), _1245583))], (46374 ^ _775212) ^ [_1699297, _1699299, _1699301, _1699303, _1699305] : [-(hAPP(hAPP(c_List_Ozip(_1699297, _1699299), _1699301), hAPP(hAPP(c_List_Oappend(_1699299), _1699303), _1699305)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1699297, _1699299)), hAPP(hAPP(c_List_Ozip(_1699297, _1699299), hAPP(hAPP(c_List_Otake(_1699297), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699299)), _1699303)), _1699301)), _1699303)), hAPP(hAPP(c_List_Ozip(_1699297, _1699299), hAPP(hAPP(c_List_Odrop(_1699297), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699299)), _1699303)), _1699301)), _1699305)))], (23174 ^ _775212) ^ [_1176405, _1176407] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1176405)), hAPP(c_Nat_OSuc, _1176407)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1176405), _1176407)))], (33529 ^ _775212) ^ [_1385880, _1385882, _1385884] : [class_Orderings_Olinorder(_1385880), hAPP(_1385882, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1385880), 33534 ^ [_1385880, _1385882, _1385884]), 33535 ^ [_1385880, _1385882, _1385884])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1385880), hAPP(_1385882, 33534 ^ [_1385880, _1385882, _1385884])), hAPP(_1385882, 33535 ^ [_1385880, _1385882, _1385884])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385880), _1385884)), -(_1385884 = c_Orderings_Obot__class_Obot(tc_fun(_1385880, tc_HOL_Obool))), -(hAPP(_1385882, c_Big__Operators_Olinorder__class_OMin(_1385880, _1385884)) = c_Big__Operators_Olinorder__class_OMin(_1385880, hAPP(c_Set_Oimage(_1385880, _1385880, _1385882), _1385884)))], (11250 ^ _775212) ^ [_959952, _959954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _959952)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _959954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _959952), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _959954), _959952))))], (38218 ^ _775212) ^ [_1493288, _1493290, _1493292, _1493294, _1493296, _1493298, _1493300, _1493302, _1493304, _1493306] : [hAPP(c_Set_Oimage(_1493288, _1493290, _1493292), _1493294) = _1493296, hAPP(c_Set_Oimage(_1493298, _1493300, _1493302), _1493304) = _1493306, -(hAPP(c_Set_Oimage(tc_prod(_1493288, _1493298), tc_prod(_1493290, _1493300), c_Product__Type_Omap__pair(_1493288, _1493290, _1493298, _1493300, _1493292, _1493302)), hAPP(hAPP(c_Product__Type_OSigma(_1493288, _1493298), _1493294), hAPP(c_COMBK(tc_fun(_1493298, tc_HOL_Obool), _1493288), _1493304))) = hAPP(hAPP(c_Product__Type_OSigma(_1493290, _1493300), _1493296), hAPP(c_COMBK(tc_fun(_1493300, tc_HOL_Obool), _1493290), _1493306)))], (42453 ^ _775212) ^ [_1598770, _1598772, _1598774, _1598776] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598770, tc_fun(_1598772, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1598770, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1598772, tc_HOL_Obool), tc_fun(_1598772, tc_HOL_Obool), _1598770), hAPP(c_COMBC(_1598772, tc_fun(_1598772, tc_HOL_Obool), tc_HOL_Obool), c_member(_1598772))), _1598774)), _1598776)), -(hBOOL(hAPP(hAPP(c_member(_1598772), _1598776), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598770, tc_fun(_1598772, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1598770, tc_HOL_Obool))), _1598774))))], (16605 ^ _775212) ^ [_1057888, _1057890, _1057892, _1057894, _1057896] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1057888, _1057890), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1057892), _1057894))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1057890)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057896), _1057888), _1057890), 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), _1057896), _1057892)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057896), _1057894)), _1057890))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057896), _1057894), _1057890)))))], (46474 ^ _775212) ^ [_1701274, _1701276, _1701278, _1701280] : [hBOOL(hAPP(c_List_Odistinct(_1701274), _1701276)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1701278, _1701274)), hAPP(hAPP(c_List_Ozip(_1701278, _1701274), _1701280), _1701276))))], (13945 ^ _775212) ^ [_1007116, _1007118, _1007120, _1007122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1007116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1007118), _1007120)), -(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), _1007120), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1007122, _1007116))), _1007118)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1007120), _1007116))))], (17099 ^ _775212) ^ [_1066150, _1066152] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066150) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066152)), 17102 ^ _775212 : [(17105 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066152)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (17103 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066150))))]], 17106 ^ _775212 : [(17109 ^ _775212) ^ [] : [17110 ^ _775212 : [(17113 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066150) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (17111 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066152))))]], 17114 ^ _775212 : [(17117 ^ _775212) ^ [] : [_1066150 = _1066152], (17115 ^ _775212) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066152)))]]], (17107 ^ _775212) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066150)))]]], (6501 ^ _775212) ^ [_878173, _878175, _878177] : [class_Nat_Osemiring__char__0(_878173), 6504 ^ _775212 : [(6511 ^ _775212) ^ [] : [_878175 = _878177, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_878173), _878175) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_878173), _878177))], (6505 ^ _775212) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_878173), _878175) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_878173), _878177), -(_878175 = _878177)]]], (51008 ^ _775212) ^ [_1798742, _1798744] : [hBOOL(hAPP(hAPP(c_List_Omember(_1798742), c_List_Olist_ONil(_1798742)), _1798744))], (18135 ^ _775212) ^ [_1083158, _1083160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083158), _1083160)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1083158)), c_Int_OBit0(_1083160))))], (50774 ^ _775212) ^ [_1793342, _1793344, _1793346, _1793348] : [50781 ^ _775212 : [(50784 ^ _775212) ^ [] : [_1793344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50782 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1793348, _1793346)))]], 50775 ^ _775212 : [(50776 ^ _775212) ^ [_1793414] : [hBOOL(hAPP(hAPP(c_member(_1793342), _1793414), hAPP(c_List_Oset(_1793342), c_List_Oreplicate(_1793342, _1793344, _1793346)))), hBOOL(hAPP(_1793348, _1793414))]]], (18815 ^ _775212) ^ [_1095077, _1095079, _1095081] : [class_Groups_Omonoid__mult(_1095077), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1095077), _1095079), 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)))), _1095081))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095077), _1095079), hAPP(hAPP(c_Power_Opower__class_Opower(_1095077), hAPP(hAPP(c_Power_Opower__class_Opower(_1095077), _1095079), _1095081)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (45311 ^ _775212) ^ [_1673401, _1673403, _1673405, _1673407, _1673409, _1673411] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1673401, _1673403)), hAPP(hAPP(c_Product__Type_OPair(_1673401, _1673403), _1673405), _1673407)), hAPP(c_List_Oset(tc_prod(_1673401, _1673403)), hAPP(hAPP(c_List_Ozip(_1673401, _1673403), _1673409), _1673411)))), -(hBOOL(hAPP(hAPP(c_member(_1673403), _1673407), hAPP(c_List_Oset(_1673403), _1673411))))], (24484 ^ _775212) ^ [_1200259, _1200261, _1200263] : [class_Rings_Ocomm__semiring__1(_1200259), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1200259), _1200261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200259), _1200263), _1200261))))], (5666 ^ _775212) ^ [_864518, _864520] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _864518, _864520, _864518))], (14489 ^ _775212) ^ [_1017196, _1017198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1017196), _1017198)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1017198, _1017196) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1017198), _1017196), _1017196))], (47551 ^ _775212) ^ [_1723744, _1723746, _1723748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1723744, tc_HOL_Obool)), _1723746), _1723748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1723744), tc_HOL_Obool)), c_List_Olistsp(_1723744, _1723746)), c_List_Olistsp(_1723744, _1723748))))], (8175 ^ _775212) ^ [_907017, _907019] : [class_Rings_Olinordered__idom(_907017), 8178 ^ _775212 : [(8185 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907017), _907019), c_Groups_Ozero__class_Ozero(_907017))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907017), _907019), hAPP(c_Groups_Ouminus__class_Ouminus(_907017), _907019))))], (8179 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907017), _907019), hAPP(c_Groups_Ouminus__class_Ouminus(_907017), _907019))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907017), _907019), c_Groups_Ozero__class_Ozero(_907017))))]]], (11364 ^ _775212) ^ [_961662] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _961662)) = 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), _961662)))], (13284 ^ _775212) ^ [_995582, _995584, _995586] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995582), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _995584, _995586)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995582), _995584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995582), _995586)))], (11582 ^ _775212) ^ [_965442, _965444, _965446] : [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), _965442), _965444)), _965446))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _965446), _965442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _965442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _965444)))], (17339 ^ _775212) ^ [_1069865] : [class_Int_Onumber__ring(_1069865), -(c_Int_Oiszero(_1069865, hAPP(c_Int_Onumber__class_Onumber__of(_1069865), c_Int_OPls)))], (10894 ^ _775212) ^ [_953271] : [class_Rings_Olinordered__semidom(_953271), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953271), c_Groups_Ozero__class_Ozero(_953271)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953271), c_Groups_Oone__class_Oone(_953271)), c_Groups_Oone__class_Oone(_953271)))))], (31232 ^ _775212) ^ [_1340049, _1340051, _1340053, _1340055, _1340057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1340049, _1340051)), hAPP(_1340049, _1340053))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1340055, _1340055)), hAPP(hAPP(c_Product__Type_OPair(_1340055, _1340055), _1340051), _1340053)), c_Wellfounded_Omlex__prod(_1340055, _1340049, _1340057))))], (6519 ^ _775212) ^ [_878483, _878485, _878487] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878483), _878485) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878483), _878487), -(_878485 = _878487)], (47686 ^ _775212) ^ [_1726722, _1726724, _1726726, _1726728, _1726730, _1726732, _1726734] : [c_List_Olist__all2(_1726722, _1726724, _1726726, hAPP(hAPP(c_List_Olist_OCons(_1726722), _1726728), _1726730), hAPP(hAPP(c_List_Olist_OCons(_1726724), _1726732), _1726734)), 47689 ^ _775212 : [(47692 ^ _775212) ^ [] : [-(c_List_Olist__all2(_1726722, _1726724, _1726726, _1726730, _1726734))], (47690 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1726726, _1726728), _1726732)))]]], (52387 ^ _775212) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (12434 ^ _775212) ^ [_979635, _979637, _979639] : [class_Divides_Osemiring__div(_979635), -(c_Divides_Odiv__class_Omod(_979635, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979635), _979637), _979639), _979639) = c_Divides_Odiv__class_Omod(_979635, _979637, _979639))], (42311 ^ _775212) ^ [_1594377, _1594379, _1594381, _1594383] : [-(hAPP(c_Relation_Oconverse(_1594377, _1594377), hAPP(hAPP(c_Relation_Oinv__image(_1594379, _1594377), _1594381), _1594383)) = hAPP(hAPP(c_Relation_Oinv__image(_1594379, _1594377), hAPP(c_Relation_Oconverse(_1594379, _1594379), _1594381)), _1594383))], (25599 ^ _775212) ^ [_1221513, _1221515, _1221517, _1221519, _1221521] : [class_Rings_Osemiring__0(_1221513), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221513), _1221515), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221517, _1221513), _1221519), _1221521)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221517, _1221513), hAPP(hAPP(c_COMBB(_1221513, _1221513, _1221517), hAPP(c_Groups_Otimes__class_Otimes(_1221513), _1221515)), _1221519)), _1221521))], (52313 ^ _775212) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (8723 ^ _775212) ^ [_916733, _916735] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _916733) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _916735), -(_916733 = _916735)], (6158 ^ _775212) ^ [_872507, _872509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _872507)), hAPP(c_Nat_OSuc, _872509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872507), _872509)))], (23628 ^ _775212) ^ [_1185526, _1185528, _1185530] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1185526, _1185528, _1185530, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1185528)], (18355 ^ _775212) ^ [_1086954] : [-(c_Int_Opred(c_Int_OBit0(_1086954)) = c_Int_OBit1(c_Int_Opred(_1086954)))], (44811 ^ _775212) ^ [_1660413, _1660415, _1660417, _1660419, _1660421, _1660423] : [-(hAPP(hAPP(c_List_Omap(_1660413, _1660415), _1660417), hAPP(hAPP(c_List_Omap(_1660419, _1660413), _1660421), _1660423)) = hAPP(hAPP(c_List_Omap(_1660419, _1660415), hAPP(c_Fun_Ocomp(_1660413, _1660415, _1660419, _1660417), _1660421)), _1660423))], (7114 ^ _775212) ^ [_888508, _888510, _888512] : [class_Orderings_Opreorder(_888508), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888508), _888510), _888512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_888508), _888512), _888510))], (44809 ^ _775212) ^ [_1660378] : [-(hAPP(c_List_Omap(_1660378, _1660378), c_Fun_Oid(_1660378)) = c_Fun_Oid(tc_List_Olist(_1660378)))], (8756 ^ _775212) ^ [_917247, _917249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _917247)), 8759 ^ _775212 : [(8766 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _917247), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917249))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _917247)), _917249)))], (8760 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _917247)), _917249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _917247), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917249))))]]], (48089 ^ _775212) ^ [_1735525] : [-(c_List_Oconcat(_1735525, c_List_Olist_ONil(tc_List_Olist(_1735525))) = c_List_Olist_ONil(_1735525))], (15523 ^ _775212) ^ [_1037639, _1037641, _1037643, _1037645, _1037647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037639), _1037641)), 15526 ^ _775212 : [(15533 ^ _775212) ^ [] : [_1037645 = 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), _1037641), _1037639)), _1037643)), _1037647), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037639), _1037643)), _1037645) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037641), _1037643)), _1037647))], (15527 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037639), _1037643)), _1037645) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037641), _1037643)), _1037647), -(_1037645 = 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), _1037641), _1037639)), _1037643)), _1037647))]]], (10665 ^ _775212) ^ [_949377, _949379] : [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), _949377), _949379))), 10668 ^ _775212 : [(10671 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _949379)))], (10669 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _949377)))]]], (9807 ^ _775212) ^ [_933837, _933839, _933841] : [class_Groups_Oordered__ab__group__add(_933837), 9810 ^ _775212 : [(9817 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933837), hAPP(c_Groups_Ouminus__class_Ouminus(_933837), _933841)), _933839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933837), hAPP(c_Groups_Ouminus__class_Ouminus(_933837), _933839)), _933841)))], (9811 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933837), hAPP(c_Groups_Ouminus__class_Ouminus(_933837), _933839)), _933841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933837), hAPP(c_Groups_Ouminus__class_Ouminus(_933837), _933841)), _933839)))]]], (44740 ^ _775212) ^ [_1658712, _1658714, _1658716] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1658712, tc_HOL_Obool)), hAPP(c_List_Oset(_1658712), hAPP(hAPP(c_List_Otake(_1658712), _1658714), _1658716))), hAPP(c_List_Oset(_1658712), _1658716))))], (25122 ^ _775212) ^ [_1212310, _1212312] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1212310)), _1212312)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212310), _1212312)))], (38701 ^ _775212) ^ [_1502572, _1502574] : [class_Groups_Oab__semigroup__mult(_1502572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502572), _1502574)), -(_1502574 = c_Orderings_Obot__class_Obot(tc_fun(_1502572, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1502572), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1502572), 38714 ^ [_1502572, _1502574]), 38715 ^ [_1502572, _1502574])), hAPP(hAPP(c_Set_Oinsert(_1502572), 38714 ^ [_1502572, _1502574]), hAPP(hAPP(c_Set_Oinsert(_1502572), 38715 ^ [_1502572, _1502574]), c_Orderings_Obot__class_Obot(tc_fun(_1502572, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1502572), hAPP(c_Finite__Set_Ofold1(_1502572, c_Groups_Otimes__class_Otimes(_1502572)), _1502574)), _1502574)))], (27856 ^ _775212) ^ [_1268537, _1268539] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1268537, _1268539))))], (7469 ^ _775212) ^ [] : [-(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))], (48276 ^ _775212) ^ [_1740382, _1740384, _1740386] : [hAPP(c_List_Ofilter(_1740382, _1740384), _1740386) = c_List_Olist_ONil(_1740382), 48279 ^ _775212 : [(48280 ^ _775212) ^ [_1740479] : [hBOOL(hAPP(hAPP(c_member(_1740382), _1740479), hAPP(c_List_Oset(_1740382), _1740386))), hBOOL(hAPP(_1740384, _1740479))]]], (33799 ^ _775212) ^ [_1391851, _1391853, _1391855, _1391857] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1391851, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391853, tc_fun(tc_fun(_1391851, tc_HOL_Obool), tc_HOL_Obool)), _1391855), hAPP(hAPP(c_COMBB(tc_fun(_1391851, tc_HOL_Obool), tc_fun(tc_fun(_1391851, tc_HOL_Obool), tc_HOL_Obool), _1391853), c_Set_OPow(_1391851)), _1391857))), hAPP(c_Set_OPow(_1391851), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391853, tc_fun(_1391851, tc_HOL_Obool)), _1391855), _1391857)))))], (26373 ^ _775212) ^ [_1238373, _1238375] : [_1238373 = _1238375, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238373) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238375))], (51199 ^ _775212) ^ [_1803036, _1803038, _1803040] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1803036), _1803038, _1803040)), -(c_List_Olist__ex(tc_Int_Oint, _1803036, c_List_Oupto(_1803038, _1803040)))], (17929 ^ _775212) ^ [] : [-(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))))))], (18407 ^ _775212) ^ [_1087840, _1087842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087840), _1087842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1087840)), c_Int_OBit0(_1087842))))], (42964 ^ _775212) ^ [_1612474, _1612476, _1612478] : [c_Relation_Ototal__on(_1612474, _1612476, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1612474, _1612474), tc_HOL_Obool)), _1612478), c_Relation_OId(_1612474))), -(c_Relation_Ototal__on(_1612474, _1612476, _1612478))], (33517 ^ _775212) ^ [_1385500, _1385502, _1385504, _1385506, _1385508, _1385510] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1385500, _1385500)), hAPP(hAPP(c_Product__Type_OPair(_1385500, _1385500), _1385502), _1385504)), hAPP(hAPP(c_Relation_Oinv__image(_1385506, _1385500), _1385508), _1385510))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1385506, _1385506)), hAPP(hAPP(c_Product__Type_OPair(_1385506, _1385506), hAPP(_1385510, _1385502)), hAPP(_1385510, _1385504))), _1385508)))], (29076 ^ _775212) ^ [_1291720, _1291722, _1291724, _1291726, _1291728] : [-(_1291720 = c_Orderings_Obot__class_Obot(tc_fun(_1291722, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291722, tc_fun(_1291724, tc_HOL_Obool)), _1291720), hAPP(hAPP(c_COMBB(tc_fun(_1291724, tc_HOL_Obool), tc_fun(_1291724, tc_HOL_Obool), _1291722), hAPP(c_Set_Oinsert(_1291724), _1291726)), _1291728)) = hAPP(hAPP(c_Set_Oinsert(_1291724), _1291726), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291722, tc_fun(_1291724, tc_HOL_Obool)), _1291720), _1291728)))], (14357 ^ _775212) ^ [_1014766, _1014768, _1014770] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1014766)), _1014768)), hAPP(c_Nat_OSuc, _1014770)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014766), _1014768)), _1014770))], (6691 ^ _775212) ^ [_881519, _881521] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881519), _881521) = _881519, -(_881521 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36941 ^ _775212) ^ [_1461850, _1461852, _1461854, _1461856, _1461858] : [-(c_Fun_Oinj__on(_1461850, _1461852, _1461854, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461850, tc_HOL_Obool)), _1461856), _1461858))), c_Fun_Oinj__on(_1461850, _1461852, _1461854, _1461856), c_Fun_Oinj__on(_1461850, _1461852, _1461854, _1461858), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461852, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1461850, _1461852, _1461854), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1461850, tc_HOL_Obool)), _1461856), _1461858))), hAPP(c_Set_Oimage(_1461850, _1461852, _1461854), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1461850, tc_HOL_Obool)), _1461858), _1461856))) = c_Orderings_Obot__class_Obot(tc_fun(_1461852, tc_HOL_Obool))], (11947 ^ _775212) ^ [_971567, _971569] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971567), _971569) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 11950 ^ _775212 : [(11953 ^ _775212) ^ [] : [-(_971569 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11951 ^ _775212) ^ [] : [-(_971567 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (52409 ^ _775212) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (13817 ^ _775212) ^ [_1004482, _1004484, _1004486] : [class_Divides_Osemiring__div(_1004482), -(_1004484 = c_Groups_Ozero__class_Ozero(_1004482)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1004482), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004482), _1004486), _1004484)), _1004484) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004482), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1004482), _1004486), _1004484)), c_Groups_Oone__class_Oone(_1004482)))], (20095 ^ _775212) ^ [_1118042, _1118044, _1118046, _1118048] : [class_Fields_Ofield(_1118042), -(_1118044 = c_Groups_Ozero__class_Ozero(_1118042)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118042), _1118046), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118042), _1118048), _1118044)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118042), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118042), _1118044), _1118046)), _1118048)), _1118044))], (50955 ^ _775212) ^ [_1797370, _1797372, _1797374, _1797376] : [-(c_Lazy__Sequence_Oappend(_1797370, c_Lazy__Sequence_Olazy__sequence_OInsert(_1797370, _1797372, _1797374), _1797376) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1797370, _1797372, c_Lazy__Sequence_Oappend(_1797370, _1797374, _1797376)))], (44887 ^ _775212) ^ [_1662046, _1662048, _1662050, _1662052, _1662054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662046), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662048)), _1662050))), -(hAPP(hAPP(c_List_Onth(_1662052), hAPP(hAPP(c_List_Omap(_1662048, _1662052), _1662054), _1662050)), _1662046) = hAPP(_1662054, hAPP(hAPP(c_List_Onth(_1662048), _1662050), _1662046)))], (38967 ^ _775212) ^ [_1508142, _1508144, _1508146] : [hBOOL(hAPP(hAPP(c_member(_1508142), _1508144), hAPP(c_Set_OCollect(_1508142), _1508146))), -(hBOOL(hAPP(_1508146, _1508144)))], (34069 ^ _775212) ^ [_1398173] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1398173) = 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, _1398173)), 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))))))))], (27731 ^ _775212) ^ [_1265244, _1265246, _1265248, _1265250, _1265252, _1265254] : [class_Complete__Lattice_Ocomplete__lattice(_1265244), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265246, _1265244), _1265248), hAPP(hAPP(c_COMBB(tc_fun(_1265250, _1265244), _1265244, _1265246), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265250, _1265244), _1265252)), _1265254)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265250, _1265244), _1265252), hAPP(hAPP(c_COMBB(tc_fun(_1265246, _1265244), _1265244, _1265250), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1265246, _1265244), _1265248)), hAPP(c_COMBC(_1265246, _1265250, _1265244), _1265254))))], (38214 ^ _775212) ^ [_1493105, _1493107, _1493109, _1493111, _1493113, _1493115, _1493117] : [-(hAPP(c_Product__Type_Osnd(_1493105, _1493107), hAPP(c_Product__Type_Omap__pair(_1493109, _1493105, _1493111, _1493107, _1493113, _1493115), _1493117)) = hAPP(_1493115, hAPP(c_Product__Type_Osnd(_1493109, _1493111), _1493117)))], (12514 ^ _775212) ^ [_981375, _981377, _981379, _981381] : [class_Divides_Osemiring__div(_981375), -(c_Divides_Odiv__class_Omod(_981375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981375), _981377), _981379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981375), _981381), _981379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981375), c_Divides_Odiv__class_Omod(_981375, _981377, _981381)), _981379))], (22270 ^ _775212) ^ [_1158379, _1158381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158379)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158381))), -(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(_1158381))), 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), _1158379)), c_Int_Onat))))))], (51452 ^ _775212) ^ [_1808700] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1808700, tc_HOL_Obool) = c_Set_OBex(_1808700))], (51643 ^ _775212) ^ [_1813480, _1813482, _1813484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1813480, _1813480), tc_HOL_Obool)), _1813482), _1813484)), c_Relation_Oantisym(_1813480, _1813484), -(c_Relation_Oantisym(_1813480, _1813482))], (22418 ^ _775212) ^ [_1161998, _1162000] : [class_Orderings_Olinorder(_1161998), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1161998), _1162000), _1162000) = _1162000)], (25270 ^ _775212) ^ [_1214916, _1214918] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214916), _1214918)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1214916)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1214918))))], (6328 ^ _775212) ^ [_875169, _875171, _875173] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_875169, _875171, _875173)) = 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), _875171)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _875173))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36419 ^ _775212) ^ [_1451336, _1451338, _1451340, _1451342, _1451344] : [c_Fun_Oinj__on(_1451336, _1451338, _1451340, c_Orderings_Otop__class_Otop(tc_fun(_1451336, tc_HOL_Obool))), hAPP(_1451340, _1451342) = hAPP(_1451340, _1451344), -(_1451342 = _1451344)], (10515 ^ _775212) ^ [_946741, _946743] : [class_Groups_Olinordered__ab__group__add(_946741), 10518 ^ _775212 : [(10525 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946741), c_Groups_Ozero__class_Ozero(_946741)), _946743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946741), hAPP(c_Groups_Ouminus__class_Ouminus(_946741), _946743)), _946743)))], (10519 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946741), hAPP(c_Groups_Ouminus__class_Ouminus(_946741), _946743)), _946743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946741), c_Groups_Ozero__class_Ozero(_946741)), _946743)))]]], (35131 ^ _775212) ^ [_1422224, _1422226, _1422228] : [-(hAPP(c_Relation_OImage(_1422224, _1422224, c_Relation_OId__on(_1422224, _1422226)), _1422228) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422224, tc_HOL_Obool)), _1422226), _1422228))], (29678 ^ _775212) ^ [_1303815, _1303817, _1303819, _1303821] : [29679 ^ _775212 : [(29682 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1303815), _1303817), _1303821))], (29680 ^ _775212) ^ [] : [_1303817 = _1303819]], -(hBOOL(hAPP(hAPP(c_member(_1303815), _1303817), hAPP(hAPP(c_Set_Oinsert(_1303815), _1303819), _1303821))))], (26911 ^ _775212) ^ [_1248452, _1248454, _1248456] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248452, tc_HOL_Obool)), _1248454), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248452, tc_HOL_Obool)), _1248456), _1248454)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248452, tc_HOL_Obool)), _1248454), _1248456))], (14205 ^ _775212) ^ [_1011942, _1011944, _1011946] : [class_Groups_Oab__group__add(_1011942), 14208 ^ _775212 : [(14215 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1011942), _1011944), _1011946) = c_Groups_Ozero__class_Ozero(_1011942), -(_1011944 = _1011946)], (14209 ^ _775212) ^ [] : [_1011944 = _1011946, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1011942), _1011944), _1011946) = c_Groups_Ozero__class_Ozero(_1011942))]]], (30198 ^ _775212) ^ [_1316384, _1316386, _1316388] : [class_Orderings_Oord(_1316384), 30201 ^ _775212 : [(30208 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316384), _1316388), _1316386)), -(hBOOL(hAPP(hAPP(c_member(_1316384), _1316386), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1316384), _1316388))))], (30202 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1316384), _1316386), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1316384), _1316388))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316384), _1316388), _1316386)))]]], (52747 ^ _775212) ^ [_1829191, _1829193] : [hBOOL(hAPP(hAPP(c_fdisj, _1829191), _1829193)), -(hBOOL(_1829191)), -(hBOOL(_1829193))], (32880 ^ _775212) ^ [_1371421, _1371423, _1371425, _1371427, _1371429] : [class_Groups_Ocomm__monoid__mult(_1371421), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371423, _1371421), hAPP(hAPP(c_COMBS(_1371423, _1371421, _1371421), hAPP(hAPP(c_COMBB(_1371421, tc_fun(_1371421, _1371421), _1371423), c_Groups_Otimes__class_Otimes(_1371421)), _1371425)), _1371427)), _1371429) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1371421), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371423, _1371421), _1371425), _1371429)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371423, _1371421), _1371427), _1371429)))], (27998 ^ _775212) ^ [_1271242] : [c_Nat__Transfer_Onat__set(_1271242), 28001 ^ _775212 : [(28008 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1271242))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1271242)))], (28002 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1271242)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1271242))))]]], (52167 ^ _775212) ^ [_1823057, _1823059] : [class_Lattices_Olattice(_1823057), -(class_Lattices_Olattice(tc_fun(_1823059, _1823057)))], (17665 ^ _775212) ^ [_1075208, _1075210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1075208), _1075210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1075208)), c_Int_OBit1(_1075210))))], (46917 ^ _775212) ^ [_1710619, _1710621, _1710623, _1710625] : [46918 ^ _775212 : [(46919 ^ _775212) ^ [_1710716, _1710718] : [_1710619 = hAPP(hAPP(c_List_Olist_OCons(_1710621), _1710718), _1710716)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710621), tc_List_Olist(_1710621))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710621), tc_List_Olist(_1710621)), _1710623), hAPP(hAPP(c_List_Oappend(_1710621), _1710623), _1710619))), c_List_Olexord(_1710621, _1710625))))], (49947 ^ _775212) ^ [_1775764, _1775766] : [class_Enum_Oenum(_1775764), 49950 ^ _775212 : [(49957 ^ _775212) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1775764), _1775766)), -(hBOOL(hAPP(_1775766, 49960 ^ [_1775764, _1775766])))], (49951 ^ _775212) ^ [] : [49952 ^ _775212 : [(49953 ^ _775212) ^ [_1775866] : [hBOOL(hAPP(_1775766, _1775866))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1775764), _1775766)))]]], (22472 ^ _775212) ^ [_1163129, _1163131, _1163133, _1163135, _1163137, _1163139] : [_1163129 = _1163131, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1163133, _1163135, _1163137), _1163139), _1163129) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1163133, _1163135, _1163137), _1163139), _1163131))], (44714 ^ _775212) ^ [_1657906, _1657908, _1657910, _1657912] : [-(hAPP(hAPP(c_List_Otake(_1657906), hAPP(c_Nat_OSuc, _1657908)), hAPP(hAPP(c_List_Olist_OCons(_1657906), _1657910), _1657912)) = hAPP(hAPP(c_List_Olist_OCons(_1657906), _1657910), hAPP(hAPP(c_List_Otake(_1657906), _1657908), _1657912)))], (36261 ^ _775212) ^ [_1447799, _1447801, _1447803] : [class_Lattices_Olattice(_1447799), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447799), _1447801)), -(hBOOL(hAPP(hAPP(c_member(_1447799), _1447803), _1447801))), -(_1447801 = c_Orderings_Obot__class_Obot(tc_fun(_1447799, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1447799, hAPP(hAPP(c_Set_Oinsert(_1447799), _1447803), _1447801)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1447799), _1447803), c_Big__Operators_Olattice__class_OInf__fin(_1447799, _1447801)))], (26913 ^ _775212) ^ [_1248512, _1248514, _1248516] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248512, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248512, tc_HOL_Obool)), _1248514), _1248516)), _1248516) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248512, tc_HOL_Obool)), _1248514), _1248516))], (41738 ^ _775212) ^ [_1580389, _1580391, _1580393, _1580395, _1580397] : [c_Finite__Set_Ofun__left__comm(_1580389, _1580391, _1580393), -(c_Finite__Set_Ofun__left__comm(_1580395, _1580391, hAPP(hAPP(c_COMBB(_1580389, tc_fun(_1580391, _1580391), _1580395), _1580393), _1580397)))], (426 ^ _775212) ^ [_781795, _781797, _781799, _781801] : [-(c_Nitpick_Owf_H(_781799, _781795)), c_Nitpick_Owf_H(_781801, _781797), _781801 = _781799, _781797 = _781795], (16071 ^ _775212) ^ [_1047505, _1047507] : [class_Int_Onumber__ring(_1047505), class_Rings_Olinordered__idom(_1047505), 16078 ^ _775212 : [(16085 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047505), hAPP(c_Int_Onumber__class_Onumber__of(_1047505), _1047507)), c_Groups_Ozero__class_Ozero(_1047505)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1047505), hAPP(c_Int_Onumber__class_Onumber__of(_1047505), _1047507)) = hAPP(c_Int_Onumber__class_Onumber__of(_1047505), _1047507))], (16079 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047505), hAPP(c_Int_Onumber__class_Onumber__of(_1047505), _1047507)), c_Groups_Ozero__class_Ozero(_1047505))), -(hAPP(c_Groups_Oabs__class_Oabs(_1047505), hAPP(c_Int_Onumber__class_Onumber__of(_1047505), _1047507)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1047505), hAPP(c_Int_Onumber__class_Onumber__of(_1047505), _1047507)))]]], (14933 ^ _775212) ^ [_1025433, _1025435] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025433), _1025435) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025433), _1025435)))], (48033 ^ _775212) ^ [_1734333, _1734335] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734333)), c_List_Oremdups(_1734333, _1734335)) = hAPP(c_Finite__Set_Ocard(_1734333), hAPP(c_List_Oset(_1734333), _1734335)))], (48364 ^ _775212) ^ [_1743025, _1743027, _1743029, _1743031] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1743025, tc_Nat_Onat), _1743025), c_Product__Type_Ofst(_1743025, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1743025, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1743025, tc_Nat_Onat)), _1743027), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1743025, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1743025, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1743025, tc_Nat_Onat), _1743029), _1743031))) = hAPP(hAPP(c_List_Omap(tc_prod(_1743025, tc_Nat_Onat), _1743025), c_Product__Type_Ofst(_1743025, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1743025, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1743025, tc_Nat_Onat)), _1743027), c_Product__Type_Osnd(_1743025, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1743025, tc_Nat_Onat), _1743029), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1743031)))))], (12015 ^ _775212) ^ [_972605, _972607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _972605)), _972607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972605), _972607)))], (50576 ^ _775212) ^ [_1789435, _1789437, _1789439] : [50578 ^ _775212 : [(50581 ^ _775212) ^ [] : [hBOOL(hAPP(_1789437, 50577 ^ [_1789435, _1789437, _1789439]))], (50579 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1789435), 50577 ^ [_1789435, _1789437, _1789439]), hAPP(c_List_Oset(_1789435), _1789439))))]], -(c_List_Olist__all(_1789435, _1789437, _1789439))], (5743 ^ _775212) ^ [_865819, _865821, _865823, _865825, _865827, _865829] : [hBOOL(hAPP(_865819, _865821)), c_Natural_Oevaln(_865823, _865821, _865825, _865827), c_Natural_Oevaln(c_Com_Ocom_OWhile(_865819, _865823), _865827, _865825, _865829), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_865819, _865823), _865821, _865825, _865829))], (45560 ^ _775212) ^ [_1679871, _1679873] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1679871), _1679873))), -(c_List_Oupto(_1679871, _1679873) = c_List_Olist_ONil(tc_Int_Oint))], (51393 ^ _775212) ^ [_1807238, _1807240] : [c_Relation_Otrans(_1807238, _1807240), -(c_Transitive__Closure_Otrancl(_1807238, _1807240) = _1807240)], (7799 ^ _775212) ^ [_900490, _900492] : [class_Rings_Oring__1(_900490), 7802 ^ _775212 : [(7809 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _900492), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_900490), _900492) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_900490), hAPP(c_Int_Onat, _900492)))], (7803 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _900492), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_900490), _900492) = hAPP(c_Groups_Ouminus__class_Ouminus(_900490), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_900490), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _900492)))))]]], (50889 ^ _775212) ^ [_1795524, _1795526, _1795528, _1795530] : [-(hAPP(hAPP(c_List_Oappend(_1795524), c_List_Oreplicate(_1795524, _1795526, _1795528)), c_List_Oreplicate(_1795524, _1795530, _1795528)) = hAPP(hAPP(c_List_Oappend(_1795524), c_List_Oreplicate(_1795524, _1795530, _1795528)), c_List_Oreplicate(_1795524, _1795526, _1795528)))], (48562 ^ _775212) ^ [_1747293] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1747293) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1747293))))], (37108 ^ _775212) ^ [_1465453, _1465455, _1465457, _1465459, _1465461] : [class_Groups_Ocomm__monoid__mult(_1465453), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465455), _1465457)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1465453, _1465455, c_Groups_Otimes__class_Otimes(_1465453)), hAPP(hAPP(c_COMBS(_1465455, _1465453, _1465453), hAPP(hAPP(c_COMBB(_1465453, tc_fun(_1465453, _1465453), _1465455), c_Groups_Otimes__class_Otimes(_1465453)), _1465459)), _1465461)), c_Groups_Oone__class_Oone(_1465453)), _1465457) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1465453), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1465453, _1465455, c_Groups_Otimes__class_Otimes(_1465453)), _1465459), c_Groups_Oone__class_Oone(_1465453)), _1465457)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1465453, _1465455, c_Groups_Otimes__class_Otimes(_1465453)), _1465461), c_Groups_Oone__class_Oone(_1465453)), _1465457)))], (5500 ^ _775212) ^ [_859132, _859134, _859136, _859138] : [-(tc_prod(_859138, _859134) = tc_prod(_859136, _859132)), _859138 = _859136, _859134 = _859132], (31769 ^ _775212) ^ [_1349941, _1349943, _1349945] : [class_Orderings_Olinorder(_1349941), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349941), _1349943)), hBOOL(hAPP(hAPP(c_member(_1349941), _1349945), _1349943)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1349941), _1349945), c_Big__Operators_Olinorder__class_OMin(_1349941, _1349943)) = c_Big__Operators_Olinorder__class_OMin(_1349941, _1349943))], (23486 ^ _775212) ^ [_1182827, _1182829, _1182831] : [-(c_Nitpick_Oof__frac(_1182829, _1182827, _1182831) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182827), hAPP(c_Int_Oring__1__class_Oof__int(_1182827), hAPP(c_Nitpick_Onum(_1182829), _1182831))), hAPP(c_Int_Oring__1__class_Oof__int(_1182827), hAPP(c_Nitpick_Odenom(_1182829), _1182831)))), class_Rings_Oinverse(_1182827), class_Rings_Oring__1(_1182827)], (34633 ^ _775212) ^ [_1411310, _1411312, _1411314] : [class_Lattices_Osemilattice__inf(_1411310), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411310), _1411312), _1411314)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411310), _1411312), _1411314) = _1411312)], (36955 ^ _775212) ^ [_1462189, _1462191, _1462193, _1462195] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1462189), _1462191)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462193), _1462195)), 36962 ^ _775212 : [(36963 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1462189), _1462191)), hAPP(c_Finite__Set_Ocard(_1462193), _1462195)))), 36964 ^ _775212 : [(36965 ^ _775212) ^ [_1462400] : [c_Fun_Oinj__on(_1462189, _1462193, _1462400, _1462191), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462193, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1462189, _1462193, _1462400), _1462191)), _1462195))]]], (36973 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1462189), _1462191)), hAPP(c_Finite__Set_Ocard(_1462193), _1462195))), 36977 ^ _775212 : [(36980 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462193, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1462189, _1462193, 36976 ^ [_1462189, _1462191, _1462193, _1462195]), _1462191)), _1462195)))], (36978 ^ _775212) ^ [] : [-(c_Fun_Oinj__on(_1462189, _1462193, 36976 ^ [_1462189, _1462191, _1462193, _1462195], _1462191))]]]]], (14799 ^ _775212) ^ [_1023036, _1023038, _1023040] : [class_Rings_Ocomm__semiring__1(_1023036), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023036), hAPP(hAPP(c_Power_Opower__class_Opower(_1023036), _1023038), _1023040)), _1023038) = hAPP(hAPP(c_Power_Opower__class_Opower(_1023036), _1023038), hAPP(c_Nat_OSuc, _1023040)))], (33571 ^ _775212) ^ [_1386732, _1386734] : [c_Relation_Oirrefl(_1386732, _1386734), 33574 ^ _775212 : [(33575 ^ _775212) ^ [_1386814] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1386732, _1386732)), hAPP(hAPP(c_Product__Type_OPair(_1386732, _1386732), _1386814), _1386814)), _1386734))]]], (17417 ^ _775212) ^ [_1071009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071009), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071009) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23164 ^ _775212) ^ [_1176191, _1176193, _1176195, _1176197] : [class_Groups_Oordered__ab__group__add(_1176191), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1176191), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176191), _1176193), _1176195)), _1176197) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176191), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1176191), _1176193), _1176197)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1176191), _1176195), _1176197)))], (38899 ^ _775212) ^ [_1506799] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1506799, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1506799), hAPP(c_COMBK(tc_HOL_Obool, _1506799), c_fTrue)))], (35117 ^ _775212) ^ [_1421837, _1421839, _1421841] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1421837, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421837, tc_HOL_Obool)), _1421839), _1421841)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421837, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1421837, tc_HOL_Obool)), _1421839)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1421837, tc_HOL_Obool)), _1421841)))], (45128 ^ _775212) ^ [_1668668, _1668670, _1668672, _1668674] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668668)), _1668670) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668672)), _1668674), -(hAPP(hAPP(c_List_Omap(tc_prod(_1668668, _1668672), _1668672), c_Product__Type_Osnd(_1668668, _1668672)), hAPP(hAPP(c_List_Ozip(_1668668, _1668672), _1668670), _1668674)) = _1668674)], (45959 ^ _775212) ^ [_1688546, _1688548, _1688550, _1688552] : [-(hAPP(hAPP(c_List_Otake(_1688546), _1688548), hAPP(hAPP(c_List_Oappend(_1688546), _1688550), _1688552)) = hAPP(hAPP(c_List_Oappend(_1688546), hAPP(hAPP(c_List_Otake(_1688546), _1688548), _1688550)), hAPP(hAPP(c_List_Otake(_1688546), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1688548), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688546)), _1688550))), _1688552)))], (20391 ^ _775212) ^ [_1123037, _1123039, _1123041, _1123043] : [class_Fields_Olinordered__field(_1123037), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123037), _1123039), _1123041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123037), c_Groups_Ozero__class_Ozero(_1123037)), _1123043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123037), c_Groups_Ozero__class_Ozero(_1123037)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123037), _1123041), _1123039))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123037), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123037), _1123043), _1123041)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123037), _1123043), _1123039))))], (29228 ^ _775212) ^ [_1294763, _1294765, _1294767] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1294763, _1294765) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1294767), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 29231 ^ _775212 : [(29234 ^ _775212) ^ [] : [-(_1294765 = _1294767)], (29232 ^ _775212) ^ [] : [-(_1294763 = _1294765)]]], (42879 ^ _775212) ^ [_1610504, _1610506, _1610508, _1610510, _1610512] : [c_Relation_Osingle__valued(_1610504, _1610506, _1610508), c_Relation_Osingle__valued(_1610506, _1610510, _1610512), -(c_Relation_Osingle__valued(_1610504, _1610510, hAPP(hAPP(c_Relation_Orel__comp(_1610504, _1610506, _1610510), _1610508), _1610512)))], (23686 ^ _775212) ^ [_1186945, _1186947] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1186945), _1186947))), -(c_Quickcheck_Obeyond(_1186945, _1186947) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (48552 ^ _775212) ^ [_1747083, _1747085, _1747087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1747083), _1747085)), _1747087)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1747083, _1747087)), _1747085) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1747083), _1747085))], (51355 ^ _775212) ^ [_1806658, _1806660] : [c_Relation_Otrans(_1806658, _1806660), -(c_Relation_Otrans(tc_List_Olist(_1806658), c_List_Olistrel(_1806658, _1806660)))], (42559 ^ _775212) ^ [_1601649, _1601651, _1601653] : [-(hAPP(c_Relation_ORange(_1601649, _1601651), hAPP(c_Relation_Oconverse(_1601651, _1601649), _1601653)) = hAPP(c_Relation_ODomain(_1601651, _1601649), _1601653))], (47382 ^ _775212) ^ [_1720276, _1720278, _1720280, _1720282] : [-(hBOOL(hAPP(c_List_Olistsp(_1720276, _1720278), hAPP(hAPP(c_List_Oappend(_1720276), _1720280), _1720282)))), hBOOL(hAPP(c_List_Olistsp(_1720276, _1720278), _1720280)), hBOOL(hAPP(c_List_Olistsp(_1720276, _1720278), _1720282))], (47716 ^ _775212) ^ [_1727319, _1727321, _1727323, _1727325] : [_1727325 = c_List_Olist_ONil(_1727319), -(c_List_Olist__all2(_1727319, _1727321, _1727323, _1727325, c_List_Olist_ONil(_1727321)))], (30412 ^ _775212) ^ [_1322710, _1322712, _1322714, _1322716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322710, tc_HOL_Obool)), _1322712), hAPP(hAPP(c_Set_Oinsert(_1322710), _1322714), _1322716))), 30415 ^ _775212 : [(30422 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1322710), _1322714), _1322712))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322710, tc_HOL_Obool)), _1322712), _1322716)))], (30416 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1322710), _1322714), _1322712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322710, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322710, tc_HOL_Obool)), _1322712), hAPP(hAPP(c_Set_Oinsert(_1322710), _1322714), c_Orderings_Obot__class_Obot(tc_fun(_1322710, tc_HOL_Obool))))), _1322716)))]]], (48109 ^ _775212) ^ [_1735942, _1735944, _1735946, _1735948] : [class_Orderings_Olinorder(_1735942), 48112 ^ _775212 : [(48119 ^ _775212) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1735944), _1735948)), -(hBOOL(hAPP(c_List_Odistinct(_1735944), c_List_Olinorder__class_Osort__key(_1735944, _1735942, _1735946, _1735948))))], (48113 ^ _775212) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1735944), c_List_Olinorder__class_Osort__key(_1735944, _1735942, _1735946, _1735948))), -(hBOOL(hAPP(c_List_Odistinct(_1735944), _1735948)))]]], (10835 ^ _775212) ^ [_952218, _952220, _952222, _952224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _952218), _952220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _952222), _952224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _952218), _952222)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _952220), _952224))))], (12616 ^ _775212) ^ [_983304, _983306, _983308, _983310] : [class_Divides_Osemiring__div(_983304), -(c_Divides_Odiv__class_Omod(_983304, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983304), _983306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983304), _983308), _983310)), _983310) = c_Divides_Odiv__class_Omod(_983304, _983306, _983310))], (16737 ^ _775212) ^ [_1060691, _1060693] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060691)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060693)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1060691), _1060693)))], (8121 ^ _775212) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33445 ^ _775212) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (8037 ^ _775212) ^ [_904292] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _904292)) = _904292)], (32263 ^ _775212) ^ [_1359359, _1359361, _1359363, _1359365] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1359359, _1359363)), c_Sum__Type_OPlus(_1359359, _1359363, _1359361, _1359365)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1359359), _1359361)), hAPP(c_Finite__Set_Ocard(_1359363), _1359365))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359359), _1359361)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359363), _1359365))], (2904 ^ _775212) ^ [_818534, _818536, _818538, _818540, _818542, _818544, _818546, _818548] : [-(c_New__DSequence_Oneg__bind(_818548, _818544, _818540, _818536) = c_New__DSequence_Oneg__bind(_818546, _818542, _818538, _818534)), _818548 = _818546, _818544 = _818542, _818540 = _818538, _818536 = _818534], (48394 ^ _775212) ^ [_1744022, _1744024, _1744026] : [class_Groups_Omonoid__add(_1744022), -(hAPP(c_List_Ofoldl(_1744022, _1744022, c_Groups_Oplus__class_Oplus(_1744022), _1744024), _1744026) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1744022), _1744024), c_List_Ofoldr(_1744022, _1744022, c_Groups_Oplus__class_Oplus(_1744022), _1744026, c_Groups_Ozero__class_Ozero(_1744022))))], (34101 ^ _775212) ^ [_1399244, _1399246, _1399248, _1399250, _1399252] : [hBOOL(hAPP(hAPP(c_member(_1399244), _1399246), hAPP(c_Relation_OImage(_1399248, _1399244, _1399250), _1399252))), 34105 ^ _775212 : [(34108 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399248), 34104 ^ [_1399244, _1399246, _1399248, _1399250, _1399252]), _1399252)))], (34106 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1399248, _1399244)), hAPP(hAPP(c_Product__Type_OPair(_1399248, _1399244), 34104 ^ [_1399244, _1399246, _1399248, _1399250, _1399252]), _1399246)), _1399250)))]]], (7074 ^ _775212) ^ [_887896, _887898, _887900] : [class_Orderings_Oorder(_887896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887896), _887898), _887900)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_887896), _887900), _887898))], (42445 ^ _775212) ^ [_1598507, _1598509, _1598511, _1598513, _1598515] : [-(hAPP(c_Relation_Oconverse(_1598507, _1598509), hAPP(hAPP(c_Relation_Orel__comp(_1598507, _1598511, _1598509), _1598513), _1598515)) = hAPP(hAPP(c_Relation_Orel__comp(_1598509, _1598511, _1598507), hAPP(c_Relation_Oconverse(_1598511, _1598509), _1598515)), hAPP(c_Relation_Oconverse(_1598507, _1598511), _1598513)))], (28930 ^ _775212) ^ [_1289289, _1289291, _1289293] : [class_Orderings_Oorder(_1289289), 28933 ^ _775212 : [(28940 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289289), _1289291), _1289293))), -(c_Orderings_Obot__class_Obot(tc_fun(_1289289, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1289289, _1289291), _1289293))], (28934 ^ _775212) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1289289, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1289289, _1289291), _1289293), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289289), _1289291), _1289293))]]], (42838 ^ _775212) ^ [_1609459, _1609461, _1609463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1609459, _1609459), tc_HOL_Obool)), c_Relation_OId(_1609459)), _1609461)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1609459, _1609459), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1609459, _1609459, _1609459), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1609459, _1609459), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1609459, _1609463)), _1609461)), _1609463)), _1609461)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1609459, _1609459), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1609459, _1609463)), _1609461)))], (41819 ^ _775212) ^ [_1581979, _1581981, _1581983, _1581985] : [-(c_Transitive__Closure_Otrancl(_1581979, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1581979, _1581979)), hAPP(hAPP(c_Product__Type_OPair(_1581979, _1581979), _1581981), _1581983)), _1581985)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1581979, _1581979), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1581979, _1581985)), hAPP(c_Set_OCollect(tc_prod(_1581979, _1581979)), hAPP(c_Product__Type_Oprod_Oprod__case(_1581979, _1581979, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1581979, tc_fun(_1581979, tc_HOL_Obool), tc_fun(_1581979, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1581979, tc_HOL_Obool), tc_fun(_1581979, tc_HOL_Obool)), _1581979), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1581979)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1581979), c_fconj), hAPP(hAPP(c_COMBC(_1581979, tc_fun(tc_prod(_1581979, _1581979), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1581979, _1581979), tc_fun(tc_fun(tc_prod(_1581979, _1581979), tc_HOL_Obool), tc_HOL_Obool), _1581979), c_member(tc_prod(_1581979, _1581979))), hAPP(hAPP(c_COMBC(_1581979, _1581979, tc_prod(_1581979, _1581979)), c_Product__Type_OPair(_1581979, _1581979)), _1581981))), c_Transitive__Closure_Ortrancl(_1581979, _1581985))))), hAPP(hAPP(c_COMBC(_1581979, tc_fun(tc_prod(_1581979, _1581979), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1581979, _1581979), tc_fun(tc_fun(tc_prod(_1581979, _1581979), tc_HOL_Obool), tc_HOL_Obool), _1581979), c_member(tc_prod(_1581979, _1581979))), hAPP(c_Product__Type_OPair(_1581979, _1581979), _1581983))), c_Transitive__Closure_Ortrancl(_1581979, _1581985)))))))], (45295 ^ _775212) ^ [_1672985, _1672987, _1672989, _1672991] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1672985, _1672985)), hAPP(hAPP(c_Product__Type_OPair(_1672985, _1672985), _1672987), _1672989)), hAPP(c_List_Oset(tc_prod(_1672985, _1672985)), hAPP(hAPP(c_List_Ozip(_1672985, _1672985), _1672991), _1672991))))), hBOOL(hAPP(hAPP(c_member(_1672985), _1672987), hAPP(c_List_Oset(_1672985), _1672991))), _1672987 = _1672989], (52251 ^ _775212) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (25028 ^ _775212) ^ [_1210489, _1210491, _1210493, _1210495] : [-(c_Product__Type_Ocurry(_1210489, _1210491, _1210493, hAPP(c_Product__Type_Oprod_Oprod__case(_1210489, _1210491, _1210493), _1210495)) = _1210495)], (39938 ^ _775212) ^ [_1539717, _1539719, _1539721] : [c_Wellfounded_Owf(_1539717, _1539719), c_Wellfounded_Owf(_1539717, _1539721), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1539717, _1539717), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1539717, _1539717, _1539717), _1539719), _1539721)), _1539719)), -(c_Wellfounded_Owf(_1539717, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1539717, _1539717), tc_HOL_Obool)), _1539719), _1539721)))], (52247 ^ _775212) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (34763 ^ _775212) ^ [_1413736, _1413738] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413736, tc_HOL_Obool)), _1413738), c_Orderings_Otop__class_Otop(tc_fun(_1413736, tc_HOL_Obool))) = _1413738)], (1254 ^ _775212) ^ [_793743, _793745] : [-(class_Rings_Ocomm__ring(_793743)), _793745 = _793743, class_Rings_Ocomm__ring(_793745)], (12779 ^ _775212) ^ [_986021, _986023] : [class_Lattices_Oboolean__algebra(_986021), -(hAPP(c_Groups_Ouminus__class_Ouminus(_986021), hAPP(c_Groups_Ouminus__class_Ouminus(_986021), _986023)) = _986023)], (9227 ^ _775212) ^ [_924702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _924702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _924702)))], (24112 ^ _775212) ^ [_1194051, _1194053] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194051), _1194053)), -(_1194051 = _1194053), 24119 ^ _775212 : [(24122 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194053), _1194051))], (24120 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194051), _1194053)))]]], (11943 ^ _775212) ^ [_971478] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971478), _971478)))))], (4810 ^ _775212) ^ [_848467, _848469] : [_848469 = _848467, -(c_List_Oappend(_848469) = c_List_Oappend(_848467))], (25294 ^ _775212) ^ [_1215400] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1215400), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1215400) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (51030 ^ _775212) ^ [_1799141, _1799143, _1799145] : [hBOOL(hAPP(hAPP(c_List_Omember(_1799141), _1799143), _1799145)), -(hBOOL(hAPP(hAPP(c_member(_1799141), _1799145), hAPP(c_List_Oset(_1799141), _1799143))))], (14041 ^ _775212) ^ [_1008791, _1008793, _1008795, _1008797] : [class_Rings_Olinordered__semidom(_1008791), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008791), _1008793), _1008795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008791), c_Groups_Ozero__class_Ozero(_1008791)), _1008793)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1008797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008791), hAPP(hAPP(c_Power_Opower__class_Opower(_1008791), _1008793), _1008797)), hAPP(hAPP(c_Power_Opower__class_Opower(_1008791), _1008795), _1008797))))], (7399 ^ _775212) ^ [_892945, _892947, _892949, _892951, _892953] : [c_Com_Ocom_OSemi(_892945, _892947) = c_Com_Ocom_OLocal(_892949, _892951, _892953)], (49528 ^ _775212) ^ [_1766617, _1766619, _1766621] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766617)), c_List_OdropWhile(_1766617, _1766619, _1766621))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766617)), _1766621))))], (15319 ^ _775212) ^ [_1033267, _1033269, _1033271, _1033273] : [class_Rings_Olinordered__semidom(_1033267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033267), c_Groups_Oone__class_Oone(_1033267)), _1033269)), 15326 ^ _775212 : [(15333 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033271), _1033273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033267), hAPP(hAPP(c_Power_Opower__class_Opower(_1033267), _1033269), _1033271)), hAPP(hAPP(c_Power_Opower__class_Opower(_1033267), _1033269), _1033273))))], (15327 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033267), hAPP(hAPP(c_Power_Opower__class_Opower(_1033267), _1033269), _1033271)), hAPP(hAPP(c_Power_Opower__class_Opower(_1033267), _1033269), _1033273))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033271), _1033273)))]]], (17873 ^ _775212) ^ [_1078659] : [class_Int_Onumber__ring(_1078659), -(c_Groups_Oone__class_Oone(_1078659) = hAPP(c_Int_Onumber__class_Onumber__of(_1078659), c_Int_OBit1(c_Int_OPls)))], (16599 ^ _775212) ^ [_1057713, _1057715, _1057717, _1057719] : [class_Int_Onumber__ring(_1057713), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057713), hAPP(c_Int_Onumber__class_Onumber__of(_1057713), _1057715)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057713), _1057717), hAPP(c_Int_Onumber__class_Onumber__of(_1057713), _1057719))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057713), hAPP(c_Int_Onumber__class_Onumber__of(_1057713), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1057715), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1057719)))), _1057717))], (2670 ^ _775212) ^ [_814585, _814587, _814589, _814591, _814593, _814595] : [-(c_Random__Sequence_Oempty(_814595, _814591, _814587) = c_Random__Sequence_Oempty(_814593, _814589, _814585)), _814595 = _814593, _814591 = _814589, _814587 = _814585], (10563 ^ _775212) ^ [_947551, _947553] : [class_Groups_Oordered__ab__group__add(_947551), 10566 ^ _775212 : [(10573 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947551), _947553), c_Groups_Ozero__class_Ozero(_947551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947551), c_Groups_Ozero__class_Ozero(_947551)), hAPP(c_Groups_Ouminus__class_Ouminus(_947551), _947553))))], (10567 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947551), c_Groups_Ozero__class_Ozero(_947551)), hAPP(c_Groups_Ouminus__class_Ouminus(_947551), _947553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947551), _947553), c_Groups_Ozero__class_Ozero(_947551))))]]], (18071 ^ _775212) ^ [_1081978, _1081980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1081978)), -(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)))), _1081980)), 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)))), _1081978)) = 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, _1081980, _1081978))))], (24826 ^ _775212) ^ [_1206459, _1206461, _1206463] : [24827 ^ _775212 : [(24830 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206461), _1206463))], (24828 ^ _775212) ^ [] : [_1206459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206459), _1206461)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206459), _1206463))))], (9873 ^ _775212) ^ [_935007] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _935007) = _935007)], (48478 ^ _775212) ^ [_1745726, _1745728] : [48479 ^ _775212 : [(48482 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1745728), _1745726))], (48480 ^ _775212) ^ [] : [_1745728 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1745726, _1745728) = c_List_Olist_ONil(tc_Nat_Onat))], (15621 ^ _775212) ^ [_1039321, _1039323, _1039325] : [class_Rings_Olinordered__semidom(_1039321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039321), c_Groups_Ozero__class_Ozero(_1039321)), _1039323)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039321), _1039323), c_Groups_Oone__class_Oone(_1039321))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039321), hAPP(hAPP(c_Power_Opower__class_Opower(_1039321), _1039323), hAPP(c_Nat_OSuc, _1039325))), c_Groups_Oone__class_Oone(_1039321))))], (11784 ^ _775212) ^ [_968656, _968658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968656), _968658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968656), _968658))), -(_968656 = _968658)], (33135 ^ _775212) ^ [_1376472, _1376474, _1376476, _1376478, _1376480] : [class_Groups_Ocomm__monoid__mult(_1376472), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376474), _1376476)), 33142 ^ _775212 : [(33149 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1376474), _1376478), _1376476))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1376474, _1376472), hAPP(hAPP(c_COMBC(_1376474, _1376472, _1376472), hAPP(hAPP(c_COMBS(_1376474, _1376472, tc_fun(_1376472, _1376472)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1376472, tc_fun(_1376472, _1376472)), _1376474), c_If(_1376472)), hAPP(hAPP(c_COMBC(_1376474, _1376474, tc_HOL_Obool), c_fequal), _1376478))), _1376480)), c_Groups_Oone__class_Oone(_1376472))), _1376476) = c_Groups_Oone__class_Oone(_1376472))], (33143 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1376474), _1376478), _1376476)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1376474, _1376472), hAPP(hAPP(c_COMBC(_1376474, _1376472, _1376472), hAPP(hAPP(c_COMBS(_1376474, _1376472, tc_fun(_1376472, _1376472)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1376472, tc_fun(_1376472, _1376472)), _1376474), c_If(_1376472)), hAPP(hAPP(c_COMBC(_1376474, _1376474, tc_HOL_Obool), c_fequal), _1376478))), _1376480)), c_Groups_Oone__class_Oone(_1376472))), _1376476) = hAPP(_1376480, _1376478))]]], (28299 ^ _775212) ^ [_1276918, _1276920] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276918), c_Orderings_Otop__class_Otop(tc_fun(_1276918, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276920), c_Orderings_Otop__class_Otop(tc_fun(_1276920, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1276918, _1276920)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1276918, _1276920), tc_HOL_Obool)))))], (33793 ^ _775212) ^ [_1391667, _1391669] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1391667, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1391667, tc_HOL_Obool))), hAPP(c_Set_OPow(_1391667), _1391669))))], (45692 ^ _775212) ^ [_1682743, _1682745, _1682747, _1682749] : [-(hAPP(hAPP(c_List_Olist__update(_1682743, hAPP(hAPP(c_List_Olist_OCons(_1682743), _1682745), _1682747)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1682749) = hAPP(hAPP(c_List_Olist_OCons(_1682743), _1682749), _1682747))], (13551 ^ _775212) ^ [_1000005, _1000007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1000005)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1000007)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1000007), _1000005)), _1000007)))], (50246 ^ _775212) ^ [_1782886, _1782888] : [class_Enum_Oenum(_1782886), 50249 ^ _775212 : [(50256 ^ _775212) ^ [] : [hBOOL(hAPP(_1782888, 50257 ^ [_1782886, _1782888])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1782886), _1782888)))], (50250 ^ _775212) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1782886), _1782888)), 50253 ^ _775212 : [(50254 ^ _775212) ^ [_1783012] : [-(hBOOL(hAPP(_1782888, _1783012)))]]]]], (52443 ^ _775212) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (35085 ^ _775212) ^ [_1420870, _1420872, _1420874, _1420876] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420870, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420870, tc_HOL_Obool)), _1420872), _1420874)), _1420876) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420870, tc_HOL_Obool)), _1420872), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420870, tc_HOL_Obool)), _1420874), _1420876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1420870, tc_HOL_Obool)), _1420876), _1420872)))], (30086 ^ _775212) ^ [_1314333, _1314335, _1314337, _1314339] : [-(hBOOL(hAPP(hAPP(c_member(_1314333), hAPP(_1314335, _1314337)), hAPP(c_Set_Oimage(_1314339, _1314333, _1314335), c_Orderings_Otop__class_Otop(tc_fun(_1314339, tc_HOL_Obool))))))], (21953 ^ _775212) ^ [_1151875, _1151877] : [_1151875 = _1151877, -(c_Code__Numeral_OSuc__code__numeral(_1151875) = c_Code__Numeral_OSuc__code__numeral(_1151877))], (19131 ^ _775212) ^ [_1101118, _1101120] : [c_Nat__Transfer_Ois__nat(_1101118), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1101118), _1101120)))], (46252 ^ _775212) ^ [_1696270, _1696272, _1696274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696270)), _1696272)), _1696274)), -(hAPP(hAPP(c_List_Odrop(_1696270), _1696274), _1696272) = c_List_Olist_ONil(_1696270))], (29324 ^ _775212) ^ [_1296750, _1296752, _1296754] : [class_Orderings_Olinorder(_1296750), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296750), _1296752), _1296754)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296750, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1296750), _1296752), c_Orderings_Obot__class_Obot(tc_fun(_1296750, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1296750, _1296752, _1296754)) = c_SetInterval_Oord__class_OatLeastAtMost(_1296750, _1296752, _1296754))], (38373 ^ _775212) ^ [_1496571, _1496573] : [class_Orderings_Olinorder(_1496571), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496571), _1496573)), -(c_Big__Operators_Olattice_OInf__fin(_1496571, c_Orderings_Oord__class_Omin(_1496571), _1496573) = hAPP(c_Finite__Set_Ofold1(_1496571, c_Orderings_Oord__class_Omin(_1496571)), _1496573))], (10711 ^ _775212) ^ [_950204] : [-(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), _950204))))], (48350 ^ _775212) ^ [_1742181, _1742183] : [-(c_List_Oconcat(tc_List_Olist(_1742181), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1742181), tc_List_Olist(tc_List_Olist(_1742181))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1742181)), _1742181, c_List_Olist_ONil(tc_List_Olist(_1742181)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1742181), tc_List_Olist(tc_List_Olist(_1742181))), _1742181), hAPP(hAPP(c_COMBC(tc_List_Olist(_1742181), tc_List_Olist(tc_List_Olist(_1742181)), tc_List_Olist(tc_List_Olist(_1742181))), c_List_Olist_OCons(tc_List_Olist(_1742181))), c_List_Olist_ONil(tc_List_Olist(_1742181)))))), _1742183)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1742181), tc_List_Olist(_1742181)), c_List_Otl(_1742181)), hAPP(c_List_Ofilter(tc_List_Olist(_1742181), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1742181)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1742181), tc_List_Olist(_1742181), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1742181)))), _1742183)))], (39406 ^ _775212) ^ [_1525443, _1525445] : [-(c_Fun_Oinj__on(_1525443, _1525443, c_Fun_Oid(_1525443), _1525445))], (46246 ^ _775212) ^ [_1696145, _1696147, _1696149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696145)), _1696149)), _1696147)), -(hAPP(hAPP(c_List_Odrop(_1696145), _1696147), _1696149) = c_List_Olist_ONil(_1696145))], (37411 ^ _775212) ^ [_1471745, _1471747, _1471749, _1471751, _1471753] : [hBOOL(hAPP(hAPP(c_member(_1471749), hAPP(_1471751, _1471747)), _1471753)), -(hBOOL(hAPP(hAPP(c_member(_1471745), _1471747), hAPP(c_Set_Ovimage(_1471745, _1471749, _1471751), _1471753))))], (5763 ^ _775212) ^ [_866095, _866097, _866099] : [-(hAPP(c_Nat_Onat_Onat__rec(_866095, _866097, _866099), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _866097)], (12568 ^ _775212) ^ [_982484, _982486] : [-(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, _982484, _982486)), _982486) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _982484), _982486))], (11861 ^ _775212) ^ [_969910, _969912, _969914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969910), _969912)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969910), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969912), _969914))))], (39138 ^ _775212) ^ [_1513477, _1513479, _1513481] : [class_Orderings_Olinorder(_1513477), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513477), _1513479)), -(_1513479 = c_Orderings_Obot__class_Obot(tc_fun(_1513477, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1513477), _1513481), c_Big__Operators_Olattice_OInf__fin(_1513477, c_Orderings_Oord__class_Omin(_1513477), _1513479)) = c_Big__Operators_Olattice_OInf__fin(_1513477, c_Orderings_Oord__class_Omin(_1513477), hAPP(c_Set_OCollect(_1513477), hAPP(hAPP(c_COMBB(tc_fun(_1513477, tc_HOL_Obool), tc_HOL_Obool, _1513477), c_HOL_OEx(_1513477)), hAPP(hAPP(c_COMBC(_1513477, tc_fun(_1513477, tc_HOL_Obool), tc_fun(_1513477, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1513477, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1513477, tc_HOL_Obool), tc_fun(_1513477, tc_HOL_Obool)), _1513477), c_COMBS(_1513477, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1513477, tc_HOL_Obool), tc_fun(_1513477, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1513477), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513477), c_fconj)), hAPP(hAPP(c_COMBC(_1513477, tc_fun(_1513477, _1513477), tc_fun(_1513477, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1513477, tc_HOL_Obool), tc_fun(tc_fun(_1513477, _1513477), tc_fun(_1513477, tc_HOL_Obool)), _1513477), c_COMBB(_1513477, tc_HOL_Obool, _1513477)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1513477), _1513481))))), hAPP(hAPP(c_COMBC(_1513477, tc_fun(_1513477, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513477)), _1513479))))))], (15801 ^ _775212) ^ [_1042679, _1042681] : [_1042679 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042679), _1042681) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50987 ^ _775212) ^ [_1798212, _1798214, _1798216, _1798218, _1798220] : [50989 ^ _775212 : [(50992 ^ _775212) ^ [] : [c_Relation_Orefl__on(_1798216, hAPP(_1798218, 50988 ^ [_1798212, _1798214, _1798216, _1798218, _1798220]), hAPP(_1798220, 50988 ^ [_1798212, _1798214, _1798216, _1798218, _1798220]))], (50990 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798212), 50988 ^ [_1798212, _1798214, _1798216, _1798218, _1798220]), _1798214)))]], -(c_Relation_Orefl__on(_1798216, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1798212, tc_fun(_1798216, tc_HOL_Obool)), _1798214), _1798218), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1798212, tc_fun(tc_prod(_1798216, _1798216), tc_HOL_Obool)), _1798214), _1798220)))], (18895 ^ _775212) ^ [_1096768, _1096770] : [class_Int_Onumber__ring(_1096768), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096768), hAPP(c_Int_Onumber__class_Onumber__of(_1096768), 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)))), _1096770)) = c_Groups_Oone__class_Oone(_1096768))], (3552 ^ _775212) ^ [_828890, _828892] : [_828892 = _828890, -(c_Rings_Odvd__class_Odvd(_828892) = c_Rings_Odvd__class_Odvd(_828890))], (33479 ^ _775212) ^ [_1384205, _1384207, _1384209, _1384211] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1384205), _1384211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1384209), _1384207), -(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), _1384205), _1384207)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1384209), _1384211))), c_Int_Ointrel)))], (12141 ^ _775212) ^ [_974792, _974794] : [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), _974792), _974794))), 12144 ^ _775212 : [(12147 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _974794)))], (12145 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _974792)))]]], (30094 ^ _775212) ^ [_1314511, _1314513, _1314515, _1314517] : [hBOOL(hAPP(hAPP(c_member(_1314511), _1314513), _1314515)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314511, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1314511), _1314513), _1314517)), _1314515) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314511, tc_HOL_Obool)), _1314517), _1314515))], (52449 ^ _775212) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (28600 ^ _775212) ^ [_1283005] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283005), c_Orderings_Obot__class_Obot(tc_fun(_1283005, tc_HOL_Obool)))))], (9547 ^ _775212) ^ [_929352, _929354, _929356, _929358] : [class_Orderings_Oorder(_929352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929352), _929354), _929356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929352), _929358), _929354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929352), _929358), _929356)))], (32810 ^ _775212) ^ [_1370306, _1370308, _1370310, _1370312] : [-(c_Fun_Ofun__upd(_1370306, _1370308, _1370310, _1370312, hAPP(_1370310, _1370312)) = _1370310)], (34393 ^ _775212) ^ [_1406037, _1406039, _1406041, _1406043] : [hBOOL(hAPP(_1406037, _1406039)), hBOOL(hAPP(_1406041, _1406039)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406043, tc_HOL_Obool)), _1406037), _1406041), _1406039)))], (48053 ^ _775212) ^ [_1734776, _1734778] : [48055 ^ _775212 : [(48058 ^ _775212) ^ [] : [48054 ^ [_1734776, _1734778] = c_List_Olist_ONil(_1734776)], (48056 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1734776)), 48054 ^ [_1734776, _1734778]), hAPP(c_List_Oset(tc_List_Olist(_1734776)), _1734778))))]], -(c_List_Olist_ONil(_1734776) = c_List_Oconcat(_1734776, _1734778))], (20905 ^ _775212) ^ [_1132717, _1132719] : [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), _1132717))), 20908 ^ _775212 : [(20915 ^ _775212) ^ [] : [-(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), _1132719)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132717))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132719), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132717)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132717)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132719), 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), _1132717)))))], (20909 ^ _775212) ^ [] : [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), _1132719)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132717)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132719), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132717)) = 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), _1132719)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1132717))))]]], (14889 ^ _775212) ^ [_1024636, _1024638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024636)), -(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), _1024636), _1024638))))], (42187 ^ _775212) ^ [_1590735, _1590737] : [-(c_Transitive__Closure_Otrancl(_1590735, hAPP(c_Relation_Oconverse(_1590735, _1590735), _1590737)) = hAPP(c_Relation_Oconverse(_1590735, _1590735), c_Transitive__Closure_Otrancl(_1590735, _1590737)))], (41897 ^ _775212) ^ [_1584094, _1584096, _1584098] : [-(c_Transitive__Closure_Ortrancl(_1584094, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584094, _1584094), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1584094, _1584096)), c_Transitive__Closure_Ortrancl(_1584094, _1584098))) = c_Transitive__Closure_Ortrancl(_1584094, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584094, _1584094), tc_HOL_Obool)), _1584096), _1584098)))], (23786 ^ _775212) ^ [_1188590, _1188592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1188590), _1188592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1188590)), hAPP(c_Code__Numeral_Onat__of, _1188592))))], (7572 ^ _775212) ^ [_896070, _896072] : [-(hBOOL(hAPP(_896070, hAPP(c_Int_Onat, _896072)))), 7576 ^ _775212 : [(7579 ^ _775212) ^ [] : [hBOOL(hAPP(_896070, 7575 ^ [_896070, _896072]))], (7577 ^ _775212) ^ [] : [-(_896072 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 7575 ^ [_896070, _896072]))]], 7580 ^ _775212 : [(7583 ^ _775212) ^ [] : [hBOOL(hAPP(_896070, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7581 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _896072), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (50489 ^ _775212) ^ [_1787821, _1787823, _1787825] : [c_List_Olist__all(_1787821, _1787825, _1787823), 50492 ^ _775212 : [(50493 ^ _775212) ^ [_1787902] : [hBOOL(hAPP(hAPP(c_member(_1787821), _1787902), hAPP(c_List_Oset(_1787821), _1787823))), -(hBOOL(hAPP(_1787825, _1787902)))]]], (21653 ^ _775212) ^ [_1146066, _1146068, _1146070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146066, tc_HOL_Obool)), _1146070), _1146068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146066, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1146066, tc_HOL_Obool)), _1146068)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1146066, tc_HOL_Obool)), _1146070))))], (11774 ^ _775212) ^ [_968487, _968489] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968487), _968489))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968487), _968489)), -(_968487 = _968489)], (33577 ^ _775212) ^ [_1386854, _1386856] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1386854, _1386854)), hAPP(hAPP(c_Product__Type_OPair(_1386854, _1386854), 33578 ^ [_1386854, _1386856]), 33578 ^ [_1386854, _1386856])), _1386856))), -(c_Relation_Oirrefl(_1386854, _1386856))], (15393 ^ _775212) ^ [_1034685, _1034687, _1034689] : [-(hBOOL(hAPP(_1034685, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034687), _1034689)))), 15396 ^ _775212 : [(15399 ^ _775212) ^ [] : [hBOOL(hAPP(_1034685, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15397 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034687), _1034689)))]], 15401 ^ _775212 : [(15404 ^ _775212) ^ [] : [hBOOL(hAPP(_1034685, 15400 ^ [_1034685, _1034687, _1034689]))], (15402 ^ _775212) ^ [] : [-(_1034687 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034689), 15400 ^ [_1034685, _1034687, _1034689]))]]], (37056 ^ _775212) ^ [_1464467, _1464469, _1464471, _1464473, _1464475, _1464477, _1464479] : [c_Finite__Set_Ofolding__image__simple(_1464467, _1464469, _1464471, _1464473, _1464475, _1464477), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464469), _1464479)), -(hAPP(_1464477, _1464479) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1464467, _1464469, _1464471), _1464475), _1464473), _1464479))], (28315 ^ _775212) ^ [_1277253, _1277255] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1277253, _1277255)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1277253, _1277255), tc_HOL_Obool)))), 28318 ^ _775212 : [(28321 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1277255), c_Orderings_Otop__class_Otop(tc_fun(_1277255, tc_HOL_Obool)))))], (28319 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1277253), c_Orderings_Otop__class_Otop(tc_fun(_1277253, tc_HOL_Obool)))))]]], (29836 ^ _775212) ^ [_1306788, _1306790, _1306792] : [hBOOL(hAPP(hAPP(c_member(_1306788), _1306790), _1306792)), -(hBOOL(hAPP(_1306792, _1306790)))], (41921 ^ _775212) ^ [_1584696, _1584698] : [-(c_Transitive__Closure_Otrancl(_1584696, c_Transitive__Closure_Ortrancl(_1584696, _1584698)) = c_Transitive__Closure_Ortrancl(_1584696, _1584698))], (50621 ^ _775212) ^ [_1790394, _1790396] : [c_List_Olist__ex1(_1790394, _1790396, c_List_Olist_ONil(_1790394))], (25907 ^ _775212) ^ [_1228712, _1228714, _1228716] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1228712, tc_Nat_Onat), _1228714), _1228716) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1228712, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1228712), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1228714)), _1228716)))], (48384 ^ _775212) ^ [_1743783, _1743785, _1743787, _1743789, _1743791, _1743793] : [-(c_List_Ofoldr(_1743783, _1743785, _1743787, hAPP(hAPP(c_List_Oappend(_1743783), _1743789), _1743791), _1743793) = c_List_Ofoldr(_1743783, _1743785, _1743787, _1743789, c_List_Ofoldr(_1743783, _1743785, _1743787, _1743791, _1743793)))], (7709 ^ _775212) ^ [_899049, _899051, _899053] : [class_Rings_Oidom(_899049), 7712 ^ _775212 : [(7713 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899049), _899051), _899051) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899049), _899053), _899053), -(_899051 = _899053), -(_899051 = hAPP(c_Groups_Ouminus__class_Ouminus(_899049), _899053))], (7723 ^ _775212) ^ [] : [7724 ^ _775212 : [(7727 ^ _775212) ^ [] : [_899051 = hAPP(c_Groups_Ouminus__class_Ouminus(_899049), _899053)], (7725 ^ _775212) ^ [] : [_899051 = _899053]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899049), _899051), _899051) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899049), _899053), _899053))]]], (19707 ^ _775212) ^ [_1110810, _1110812, _1110814, _1110816, _1110818] : [class_Fields_Olinordered__field(_1110810), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110810), c_Groups_Ozero__class_Ozero(_1110810)), _1110812)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110810), _1110812), _1110814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110810), c_Groups_Ozero__class_Ozero(_1110810)), _1110816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110810), _1110816), _1110818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110810), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110810), _1110812), _1110818)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110810), _1110814), _1110816))))], (48370 ^ _775212) ^ [_1743294] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1743294)), c_List_Otranspose__rel(_1743294)), c_List_Olist_ONil(tc_List_Olist(_1743294)))), -(c_List_Otranspose(_1743294, c_List_Olist_ONil(tc_List_Olist(_1743294))) = c_List_Olist_ONil(tc_List_Olist(_1743294)))], (25528 ^ _775212) ^ [_1219805, _1219807, _1219809] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1219805, _1219807) = _1219809, -(_1219805 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1219809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), 25531 ^ [_1219805, _1219807, _1219809]), _1219807)))], (29686 ^ _775212) ^ [_1303980, _1303982, _1303984] : [-(hBOOL(hAPP(hAPP(c_member(_1303980), _1303982), hAPP(hAPP(c_Set_Oinsert(_1303980), _1303982), _1303984))))], (48358 ^ _775212) ^ [_1742866, _1742868] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1742866)), c_List_Otranspose__rel(_1742866)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1742866)), c_List_Olist_ONil(_1742866)), _1742868))), -(c_List_Otranspose(_1742866, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1742866)), c_List_Olist_ONil(_1742866)), _1742868)) = c_List_Otranspose(_1742866, _1742868))], (42713 ^ _775212) ^ [_1605665, _1605667, _1605669, _1605671, _1605673] : [-(_1605665 = c_Orderings_Obot__class_Obot(tc_fun(_1605667, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605667, tc_fun(_1605669, tc_HOL_Obool)), _1605665), hAPP(hAPP(c_COMBB(tc_fun(_1605669, tc_HOL_Obool), tc_fun(_1605669, tc_HOL_Obool), _1605667), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1605669, tc_HOL_Obool)), _1605671)), _1605673)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1605669, tc_HOL_Obool)), _1605671), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1605667, tc_fun(_1605669, tc_HOL_Obool)), _1605665), _1605673)))], (17855 ^ _775212) ^ [_1078370, _1078372] : [class_Int_Onumber__ring(_1078370), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078370), _1078372), hAPP(c_Int_Onumber__class_Onumber__of(_1078370), c_Int_OBit1(c_Int_OPls))) = _1078372)], (52469 ^ _775212) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (41634 ^ _775212) ^ [_1577911, _1577913, _1577915, _1577917, _1577919] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577911, _1577911)), hAPP(hAPP(c_Product__Type_OPair(_1577911, _1577911), _1577913), _1577915)), _1577917)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1577911, _1577911)), hAPP(hAPP(c_Product__Type_OPair(_1577911, _1577911), _1577915), _1577919)), c_Transitive__Closure_Otrancl(_1577911, _1577917))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577911, _1577911)), hAPP(hAPP(c_Product__Type_OPair(_1577911, _1577911), _1577913), _1577919)), c_Transitive__Closure_Otrancl(_1577911, _1577917))))], (3218 ^ _775212) ^ [_823571, _823573, _823575, _823577, _823579, _823581] : [-(c_Wellfounded_Omlex__prod(_823581, _823577, _823573) = c_Wellfounded_Omlex__prod(_823579, _823575, _823571)), _823581 = _823579, _823577 = _823575, _823573 = _823571], (43324 ^ _775212) ^ [_1620846, _1620848, _1620850, _1620852] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1620846, tc_fun(_1620848, tc_HOL_Obool)), _1620850), _1620852) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620848, tc_HOL_Obool), hAPP(c_Set_Oimage(_1620846, tc_fun(_1620848, tc_HOL_Obool), _1620852), _1620850)))], (18485 ^ _775212) ^ [_1089266, _1089268] : [class_Int_Onumber__ring(_1089266), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089266), _1089268), hAPP(c_Int_Onumber__class_Onumber__of(_1089266), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089266), _1089268), _1089268))], (30452 ^ _775212) ^ [_1323661, _1323663, _1323665] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1323661), _1323663)), -(hBOOL(hAPP(hAPP(c_member(_1323661), _1323665), _1323663))), -(hAPP(c_Finite__Set_Ocard(_1323661), hAPP(hAPP(c_Set_Oinsert(_1323661), _1323665), _1323663)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1323661), _1323663)))], (50895 ^ _775212) ^ [_1795709, _1795711, _1795713] : [-(c_List_Oreplicate(_1795709, hAPP(c_Nat_OSuc, _1795711), _1795713) = hAPP(hAPP(c_List_Olist_OCons(_1795709), _1795713), c_List_Oreplicate(_1795709, _1795711, _1795713)))], (52613 ^ _775212) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (26941 ^ _775212) ^ [_1249140, _1249142, _1249144, _1249146] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249140, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249140, tc_HOL_Obool)), _1249142), _1249144)), _1249146) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249140, tc_HOL_Obool)), _1249142), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249140, tc_HOL_Obool)), _1249144), _1249146)))], (3068 ^ _775212) ^ [_821162, _821164] : [_821164 = _821162, -(c_Nat_Osemiring__1__class_ONats(_821164) = c_Nat_Osemiring__1__class_ONats(_821162))], (34701 ^ _775212) ^ [_1412465, _1412467, _1412469] : [class_Lattices_Osemilattice__inf(_1412465), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412465), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1412465), _1412467), _1412469)), _1412469)))], (33455 ^ _775212) ^ [_1383415, _1383417, _1383419, _1383421] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1383415, tc_HOL_Obool), tc_fun(_1383415, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1383415, tc_HOL_Obool), tc_fun(_1383415, tc_HOL_Obool)), _1383419), _1383421)), c_Wellfounded_Omax__ext(_1383415, _1383417))), -(c_Wellfounded_Omax__extp(_1383415, hAPP(hAPP(c_COMBC(_1383415, tc_fun(tc_prod(_1383415, _1383415), tc_HOL_Obool), tc_fun(_1383415, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383415, tc_fun(tc_fun(tc_prod(_1383415, _1383415), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1383415, _1383415), tc_HOL_Obool), tc_fun(_1383415, tc_HOL_Obool)), _1383415), c_COMBC(_1383415, tc_fun(tc_prod(_1383415, _1383415), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383415, tc_prod(_1383415, _1383415)), tc_fun(_1383415, tc_fun(tc_fun(tc_prod(_1383415, _1383415), tc_HOL_Obool), tc_HOL_Obool)), _1383415), hAPP(c_COMBB(tc_prod(_1383415, _1383415), tc_fun(tc_fun(tc_prod(_1383415, _1383415), tc_HOL_Obool), tc_HOL_Obool), _1383415), c_member(tc_prod(_1383415, _1383415)))), c_Product__Type_OPair(_1383415, _1383415)))), _1383417), _1383419, _1383421))], (39440 ^ _775212) ^ [_1526034, _1526036, _1526038, _1526040] : [class_Groups_Ocomm__monoid__add(_1526034), c_Fun_Oinj__on(_1526036, _1526034, _1526038, _1526040), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526036, _1526034), _1526038), _1526040) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526034, _1526034), c_Fun_Oid(_1526034)), hAPP(c_Set_Oimage(_1526036, _1526034, _1526038), _1526040)))], (49430 ^ _775212) ^ [_1764494, _1764496] : [-(c_List_OtakeWhile(_1764494, _1764496, c_List_Olist_ONil(_1764494)) = c_List_Olist_ONil(_1764494))], (21145 ^ _775212) ^ [_1137431] : [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), _1137431))), 21148 ^ _775212 : [(21155 ^ _775212) ^ [] : [-(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), _1137431)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137431)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137431)), 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), _1137431)))))], (21149 ^ _775212) ^ [] : [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), _1137431))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137431)) = 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)))]]], (24416 ^ _775212) ^ [_1199102, _1199104, _1199106, _1199108] : [class_Divides_Osemiring__div(_1199102), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199102), _1199104), _1199106)), -(c_Divides_Odiv__class_Omod(_1199102, c_Divides_Odiv__class_Omod(_1199102, _1199108, _1199106), _1199104) = c_Divides_Odiv__class_Omod(_1199102, _1199108, _1199104))], (19693 ^ _775212) ^ [_1110555, _1110557, _1110559] : [class_Fields_Olinordered__field(_1110555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110555), c_Groups_Ozero__class_Ozero(_1110555)), _1110557)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110555), _1110559), c_Groups_Ozero__class_Ozero(_1110555))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110555), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110555), _1110557), _1110559)), c_Groups_Ozero__class_Ozero(_1110555))))], (8784 ^ _775212) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40215 ^ _775212) ^ [_1547173, _1547175, _1547177] : [hBOOL(hAPP(hAPP(c_member(_1547175), _1547173), c_Orderings_Obot__class_Obot(tc_fun(_1547175, tc_HOL_Obool)))), -(hBOOL(hAPP(_1547177, _1547173)))], (18477 ^ _775212) ^ [_1089127] : [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), _1089127))), 18480 ^ _775212 : [(18483 ^ _775212) ^ [] : [-(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(_1089127)))))], (18481 ^ _775212) ^ [] : [-(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(_1089127)))))]]], (32417 ^ _775212) ^ [_1362542, _1362544] : [class_Orderings_Olinorder(_1362542), -(c_Big__Operators_Olattice_OSup__fin(_1362542, c_Orderings_Oord__class_Omax(_1362542), hAPP(hAPP(c_Set_Oinsert(_1362542), _1362544), c_Orderings_Obot__class_Obot(tc_fun(_1362542, tc_HOL_Obool)))) = _1362544)], (280 ^ _775212) ^ [_779420, _779422] : [-(class_Fields_Ofield(_779420)), _779422 = _779420, class_Fields_Ofield(_779422)], (16579 ^ _775212) ^ [_1057328] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1057328), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1057328) = _1057328)], (21847 ^ _775212) ^ [_1149846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1149846)), 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), _1149846)) = 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), _1149846))))))], (48548 ^ _775212) ^ [_1747013, _1747015] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1747013, _1747015) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1747013, hAPP(c_Nat_OSuc, _1747015))))], (48462 ^ _775212) ^ [_1745516, _1745518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1745516), _1745518)), -(c_List_Oupt(_1745518, _1745516) = c_List_Olist_ONil(tc_Nat_Onat))], (37535 ^ _775212) ^ [_1474704, _1474706, _1474708, _1474710, _1474712, _1474714] : [hBOOL(hAPP(hAPP(c_member(_1474704), _1474706), _1474708)), 37538 ^ _775212 : [(37545 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1474704), _1474710), _1474708))), -(hAPP(c_Set_Ovimage(_1474712, _1474704, hAPP(hAPP(c_COMBC(_1474712, _1474704, _1474704), hAPP(hAPP(c_COMBC(_1474712, _1474704, tc_fun(_1474704, _1474704)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1474704, tc_fun(_1474704, _1474704)), _1474712), c_If(_1474704)), hAPP(hAPP(c_COMBC(_1474712, tc_fun(_1474712, tc_HOL_Obool), tc_HOL_Obool), c_member(_1474712)), _1474714))), _1474706)), _1474710)), _1474708) = _1474714)], (37539 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1474704), _1474710), _1474708)), -(hAPP(c_Set_Ovimage(_1474712, _1474704, hAPP(hAPP(c_COMBC(_1474712, _1474704, _1474704), hAPP(hAPP(c_COMBC(_1474712, _1474704, tc_fun(_1474704, _1474704)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1474704, tc_fun(_1474704, _1474704)), _1474712), c_If(_1474704)), hAPP(hAPP(c_COMBC(_1474712, tc_fun(_1474712, tc_HOL_Obool), tc_HOL_Obool), c_member(_1474712)), _1474714))), _1474706)), _1474710)), _1474708) = c_Orderings_Otop__class_Otop(tc_fun(_1474712, tc_HOL_Obool)))]]], (9875 ^ _775212) ^ [_935033, _935035, _935037, _935039, _935041, _935043] : [class_Rings_Olinordered__semiring__1(_935033), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935033), _935035), _935037)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935033), _935039), _935037)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935033), c_Groups_Ozero__class_Ozero(_935033)), _935041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935033), c_Groups_Ozero__class_Ozero(_935033)), _935043)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935033), _935041), _935043) = c_Groups_Oone__class_Oone(_935033), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935033), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935033), _935041), _935035)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935033), _935043), _935039))), _935037)))], (24816 ^ _775212) ^ [_1206327, _1206329, _1206331] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206327), _1206329)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206327), _1206331))), -(_1206327 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206329), _1206331)))], (25420 ^ _775212) ^ [_1217545, _1217547] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1217545)), _1217547))), 25423 ^ _775212 : [(25426 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217545), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217547)))], (25424 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217545)))]], 25427 ^ _775212 : [(25430 ^ _775212) ^ [] : [_1217547 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25428 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217545))]]], (5839 ^ _775212) ^ [_867558, _867560, _867562, _867564] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_867558, _867560), _867562, _867564, _867562), hBOOL(hAPP(_867558, _867562)), 5847 ^ _775212 : [(5850 ^ _775212) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_867558, _867560), 5846 ^ [_867558, _867560, _867562, _867564], _867564, _867562))], (5848 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_867560, _867562, _867564, 5846 ^ [_867558, _867560, _867562, _867564]))]]], (37465 ^ _775212) ^ [_1473119, _1473121, _1473123, _1473125, _1473127] : [hAPP(_1473125, _1473121) = _1473127, -(hBOOL(hAPP(hAPP(c_member(_1473119), _1473121), hAPP(c_Set_Ovimage(_1473119, _1473123, _1473125), hAPP(hAPP(c_Set_Oinsert(_1473123), _1473127), c_Orderings_Obot__class_Obot(tc_fun(_1473123, tc_HOL_Obool)))))))], (3350 ^ _775212) ^ [_825677, _825679, _825681, _825683, _825685, _825687, _825689, _825691] : [-(c_Fun_Othe__inv__into(_825691, _825687, _825683, _825679) = c_Fun_Othe__inv__into(_825689, _825685, _825681, _825677)), _825691 = _825689, _825687 = _825685, _825683 = _825681, _825679 = _825677], (44298 ^ _775212) ^ [_1645740, _1645742, _1645744, _1645746, _1645748] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645740), tc_List_Olist(_1645740))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645740), tc_List_Olist(_1645740)), _1645742), _1645744)), c_List_Olistrel1(_1645740, _1645746))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645740), tc_List_Olist(_1645740))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645740), tc_List_Olist(_1645740)), hAPP(hAPP(c_List_Olist_OCons(_1645740), _1645748), _1645742)), hAPP(hAPP(c_List_Olist_OCons(_1645740), _1645748), _1645744))), c_List_Olistrel1(_1645740, _1645746))))], (25849 ^ _775212) ^ [_1227264, _1227266, _1227268, _1227270, _1227272] : [class_Groups_Ocomm__monoid__add(_1227264), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227264), _1227266), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227268), _1227270)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227272), _1227270))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227264), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1227264, tc_Nat_Onat), _1227266), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1227270))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1227268), _1227272)))], (35237 ^ _775212) ^ [_1424488, _1424490, _1424492, _1424494] : [class_Orderings_Oorder(_1424488), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424488, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1424488, _1424490, _1424492)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1424488, _1424492), _1424494)) = c_Orderings_Obot__class_Obot(tc_fun(_1424488, tc_HOL_Obool)))], (17749 ^ _775212) ^ [_1076626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1076626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1076626)))], (14767 ^ _775212) ^ [_1022435, _1022437, _1022439, _1022441] : [class_Rings_Olinordered__semidom(_1022435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022435), c_Groups_Oone__class_Oone(_1022435)), _1022437)), 14774 ^ _775212 : [(14781 ^ _775212) ^ [] : [_1022439 = _1022441, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1022435), _1022437), _1022439) = hAPP(hAPP(c_Power_Opower__class_Opower(_1022435), _1022437), _1022441))], (14775 ^ _775212) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1022435), _1022437), _1022439) = hAPP(hAPP(c_Power_Opower__class_Opower(_1022435), _1022437), _1022441), -(_1022439 = _1022441)]]], (37357 ^ _775212) ^ [_1470503, _1470505, _1470507, _1470509] : [c_Fun_Oinj__on(_1470503, _1470505, _1470507, c_Orderings_Otop__class_Otop(tc_fun(_1470503, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470503, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1470503, _1470505, _1470507), hAPP(hAPP(c_Set_Oinsert(_1470505), _1470509), c_Orderings_Obot__class_Obot(tc_fun(_1470505, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1470503), c_HOL_OThe(_1470503, hAPP(hAPP(c_COMBC(_1470503, _1470505, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1470505, tc_fun(_1470505, tc_HOL_Obool), _1470503), c_fequal), _1470507)), _1470509))), c_Orderings_Obot__class_Obot(tc_fun(_1470503, tc_HOL_Obool))))))], (39581 ^ _775212) ^ [_1530171, _1530173, _1530175, _1530177] : [39582 ^ _775212 : [(39583 ^ _775212) ^ [_1530246] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530175, _1530171)), hAPP(hAPP(c_Product__Type_OPair(_1530175, _1530171), _1530246), _1530173)), _1530177))]], -(hBOOL(hAPP(hAPP(c_member(_1530171), _1530173), hAPP(c_Relation_ORange(_1530175, _1530171), _1530177))))], (24834 ^ _775212) ^ [_1206622, _1206624, _1206626] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206622), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206624), _1206626))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206622), _1206624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206626), _1206624)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206622), _1206626)))], (18851 ^ _775212) ^ [_1095840] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1095840, 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, _1095840, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (49806 ^ _775212) ^ [_1772258, _1772260, _1772262] : [hBOOL(hAPP(hAPP(c_member(_1772258), _1772260), hAPP(c_List_Oset(_1772258), _1772262))), -(c_List_Oinsert(_1772258, _1772260, _1772262) = _1772262)], (9109 ^ _775212) ^ [_922795, _922797, _922799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _922795), _922797)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _922797), _922799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _922795), _922799)))], (22904 ^ _775212) ^ [_1171636, _1171638, _1171640] : [class_Orderings_Olinorder(_1171636), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171636), _1171638), _1171640) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171636), _1171640), _1171638))], (32251 ^ _775212) ^ [_1358969, _1358971, _1358973, _1358975, _1358977, _1358979, _1358981, _1358983] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1358969, _1358971), tc_prod(_1358969, _1358971))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1358969, _1358971), tc_prod(_1358969, _1358971)), hAPP(hAPP(c_Product__Type_OPair(_1358969, _1358971), _1358973), _1358975)), hAPP(hAPP(c_Product__Type_OPair(_1358969, _1358971), _1358977), _1358979))), c_Wellfounded_Olex__prod(_1358969, _1358971, _1358981, _1358983)))), 32252 ^ _775212 : [(32255 ^ _775212) ^ [] : [_1358973 = _1358977, hBOOL(hAPP(hAPP(c_member(tc_prod(_1358971, _1358971)), hAPP(hAPP(c_Product__Type_OPair(_1358971, _1358971), _1358975), _1358979)), _1358983))], (32253 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1358969, _1358969)), hAPP(hAPP(c_Product__Type_OPair(_1358969, _1358969), _1358973), _1358977)), _1358981))]]], (22308 ^ _775212) ^ [_1159469, _1159471] : [-(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), _1159469)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1159471), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1159469))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (12255 ^ _775212) ^ [_976762, _976764, _976766] : [class_Lattices_Oboolean__algebra(_976762), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976762), _976764), _976766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976762), hAPP(c_Groups_Ouminus__class_Ouminus(_976762), _976766)), hAPP(c_Groups_Ouminus__class_Ouminus(_976762), _976764))))], (48137 ^ _775212) ^ [_1736498, _1736500] : [class_Orderings_Olinorder(_1736498), -(c_List_Olinorder__class_Osort__key(_1736498, _1736498, c_COMBI(_1736498), _1736500) = hAPP(c_List_Ofoldl(tc_List_Olist(_1736498), _1736498, hAPP(c_COMBC(_1736498, tc_List_Olist(_1736498), tc_List_Olist(_1736498)), c_List_Olinorder__class_Oinsort__key(_1736498, _1736498, c_COMBI(_1736498))), c_List_Olist_ONil(_1736498)), _1736500))], (16855 ^ _775212) ^ [_1062579, _1062581] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062579))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062579)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062581)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14111 ^ _775212) ^ [_1010189, _1010191, _1010193] : [class_Rings_Oring__1(_1010189), -(hAPP(c_Int_Oring__1__class_Oof__int(_1010189), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1010191), _1010193)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1010189), hAPP(c_Int_Oring__1__class_Oof__int(_1010189), _1010191)), _1010193))], (43490 ^ _775212) ^ [_1624916, _1624918, _1624920] : [43492 ^ _775212 : [(43495 ^ _775212) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624916, tc_HOL_Obool)), 43491 ^ [_1624916, _1624918, _1624920]), _1624920) = c_Orderings_Obot__class_Obot(tc_fun(_1624916, tc_HOL_Obool))], (43493 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1624916, tc_HOL_Obool)), 43491 ^ [_1624916, _1624918, _1624920]), _1624918)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624916, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1624916, tc_HOL_Obool), _1624918)), _1624920) = c_Orderings_Obot__class_Obot(tc_fun(_1624916, tc_HOL_Obool)))], (41488 ^ _775212) ^ [_1575142, _1575144, _1575146, _1575148] : [class_Complete__Lattice_Ocomplete__lattice(_1575142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575144), _1575146)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1575144, _1575142), _1575146), _1575148) = hAPP(hAPP(c_Finite__Set_Ofold(_1575144, _1575142, hAPP(hAPP(c_COMBB(_1575142, tc_fun(_1575142, _1575142), _1575144), c_Lattices_Osemilattice__sup__class_Osup(_1575142)), _1575148)), c_Orderings_Obot__class_Obot(_1575142)), _1575146))], (40476 ^ _775212) ^ [_1552810, _1552812, _1552814, _1552816, _1552818, _1552820, _1552822] : [-(hAPP(c_Product__Type_Oapfst(_1552810, _1552812, _1552814, _1552816), hAPP(c_Product__Type_Oapfst(_1552818, _1552810, _1552814, _1552820), _1552822)) = hAPP(c_Product__Type_Oapfst(_1552818, _1552812, _1552814, hAPP(c_Fun_Ocomp(_1552810, _1552812, _1552818, _1552816), _1552820)), _1552822))], (21757 ^ _775212) ^ [_1148052, _1148054, _1148056, _1148058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1148052, tc_HOL_Obool)), _1148054), _1148056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1148052, tc_HOL_Obool)), _1148056), _1148058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1148052, tc_HOL_Obool)), _1148054), _1148058)))], (2790 ^ _775212) ^ [_816571, _816573, _816575, _816577, _816579, _816581, _816583, _816585] : [-(c_New__DSequence_Opos__decr__bind(_816585, _816581, _816577, _816573) = c_New__DSequence_Opos__decr__bind(_816583, _816579, _816575, _816571)), _816585 = _816583, _816581 = _816579, _816577 = _816575, _816573 = _816571], (46756 ^ _775212) ^ [_1707198, _1707200, _1707202] : [class_Groups_Omonoid__add(_1707198), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1707198), _1707200), hAPP(c_List_Ofoldl(_1707198, _1707198, c_Groups_Oplus__class_Oplus(_1707198), c_Groups_Ozero__class_Ozero(_1707198)), _1707202)) = hAPP(c_List_Ofoldl(_1707198, _1707198, c_Groups_Oplus__class_Oplus(_1707198), _1707200), _1707202))], (46504 ^ _775212) ^ [_1701803, _1701805, _1701807] : [-(hAPP(c_List_Otl(_1701803), hAPP(hAPP(c_List_Olist_OCons(_1701803), _1701805), _1701807)) = _1701807)], (50845 ^ _775212) ^ [_1794768, _1794770, _1794772, _1794774, _1794776] : [hBOOL(hAPP(hAPP(_1794772, _1794776), _1794774)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1794768, _1794770, _1794772), _1794774), _1794776)))], (18401 ^ _775212) ^ [_1087739, _1087741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1087739)), c_Int_OBit0(_1087741))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087739), _1087741)))], (48400 ^ _775212) ^ [_1744155, _1744157] : [class_Groups_Omonoid__add(_1744155), -(hAPP(c_List_Ofoldl(_1744155, _1744155, c_Groups_Oplus__class_Oplus(_1744155), c_Groups_Ozero__class_Ozero(_1744155)), _1744157) = c_List_Ofoldr(_1744155, _1744155, c_Groups_Oplus__class_Oplus(_1744155), _1744157, c_Groups_Ozero__class_Ozero(_1744155)))], (34136 ^ _775212) ^ [_1400030, _1400032, _1400034, _1400036] : [hBOOL(hAPP(hAPP(c_member(_1400030), _1400032), _1400034)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1400030, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1400030, _1400030, _1400036), hAPP(hAPP(c_Set_Oinsert(_1400030), _1400032), c_Orderings_Obot__class_Obot(tc_fun(_1400030, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400030), _1400034), _1400036))))], (16489 ^ _775212) ^ [_1055766, _1055768] : [class_Groups_Oordered__ab__group__add__abs(_1055766), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055766), hAPP(c_Groups_Ouminus__class_Ouminus(_1055766), hAPP(c_Groups_Oabs__class_Oabs(_1055766), _1055768))), c_Groups_Ozero__class_Ozero(_1055766))))], (47156 ^ _775212) ^ [_1715222, _1715224, _1715226, _1715228] : [47157 ^ _775212 : [(47160 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1715222), _1715224), hAPP(c_List_Oset(_1715222), c_List_Obutlast(_1715222, _1715228))))], (47158 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1715222), _1715224), hAPP(c_List_Oset(_1715222), c_List_Obutlast(_1715222, _1715226))))]], -(hBOOL(hAPP(hAPP(c_member(_1715222), _1715224), hAPP(c_List_Oset(_1715222), c_List_Obutlast(_1715222, hAPP(hAPP(c_List_Oappend(_1715222), _1715226), _1715228))))))], (26473 ^ _775212) ^ [_1240422, _1240424] : [class_Groups_Oordered__ab__group__add(_1240422), -(hAPP(c_Set_Oimage(_1240422, _1240422, c_Groups_Ouminus__class_Ouminus(_1240422)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1240422), _1240424)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1240422), hAPP(c_Groups_Ouminus__class_Ouminus(_1240422), _1240424)))], (14409 ^ _775212) ^ [_1015699, _1015701, _1015703] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015699), _1015701)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015699), _1015703)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015701), _1015703))], (40025 ^ _775212) ^ [_1541949, _1541951, _1541953, _1541955] : [hBOOL(hAPP(c_Predicate_ODomainP(_1541949, _1541951, hAPP(hAPP(c_COMBC(_1541949, tc_fun(tc_prod(_1541949, _1541951), tc_HOL_Obool), tc_fun(_1541951, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541951, tc_fun(tc_fun(tc_prod(_1541949, _1541951), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1541949, _1541951), tc_HOL_Obool), tc_fun(_1541951, tc_HOL_Obool)), _1541949), c_COMBC(_1541951, tc_fun(tc_prod(_1541949, _1541951), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541951, tc_prod(_1541949, _1541951)), tc_fun(_1541951, tc_fun(tc_fun(tc_prod(_1541949, _1541951), tc_HOL_Obool), tc_HOL_Obool)), _1541949), hAPP(c_COMBB(tc_prod(_1541949, _1541951), tc_fun(tc_fun(tc_prod(_1541949, _1541951), tc_HOL_Obool), tc_HOL_Obool), _1541951), c_member(tc_prod(_1541949, _1541951)))), c_Product__Type_OPair(_1541949, _1541951)))), _1541953)), _1541955)), -(hBOOL(hAPP(hAPP(c_member(_1541949), _1541955), hAPP(c_Relation_ODomain(_1541949, _1541951), _1541953))))], (50585 ^ _775212) ^ [_1789638, _1789640, _1789642, _1789644] : [c_List_Olist__ex1(_1789638, _1789640, hAPP(hAPP(c_List_Olist_OCons(_1789638), _1789642), _1789644)), 50588 ^ _775212 : [(50595 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1789640, _1789642))), -(c_List_Olist__ex1(_1789638, _1789640, _1789644))], (50589 ^ _775212) ^ [] : [hBOOL(hAPP(_1789640, _1789642)), -(c_List_Olist__all(_1789638, hAPP(hAPP(c_COMBS(_1789638, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1789638), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1789638), c_fNot), _1789640))), hAPP(c_fequal, _1789642)), _1789644))]]], (13252 ^ _775212) ^ [_994863, _994865, _994867] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994863), _994865)), _994867) = 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), _994863), _994867)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _994865), _994867))), 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, _994863, _994867)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _994865, _994867))), _994867)))], (5723 ^ _775212) ^ [_865494, _865496, _865498, _865500, _865502, _865504] : [hBOOL(hAPP(_865494, _865496)), c_Natural_Oevaln(_865498, _865496, _865500, _865502), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_865494, _865498, _865504), _865496, _865500, _865502))], (21837 ^ _775212) ^ [_1149679, _1149681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1149679), 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)), _1149681)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1149679), _1149681) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1149679, _1149681)))], (28440 ^ _775212) ^ [_1279752, _1279754] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279752), _1279754))), -(hAPP(c_Finite__Set_Ocard(_1279752), _1279754) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27976 ^ _775212) ^ [_1270815, _1270817, _1270819, _1270821, _1270823] : [-(hAPP(c_Set_Oimage(_1270815, _1270817, _1270819), hAPP(hAPP(c_Set_Oinsert(_1270815), _1270821), _1270823)) = hAPP(hAPP(c_Set_Oinsert(_1270817), hAPP(_1270819, _1270821)), hAPP(c_Set_Oimage(_1270815, _1270817, _1270819), _1270823)))], (44316 ^ _775212) ^ [_1646399, _1646401, _1646403, _1646405] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646399), tc_List_Olist(_1646399))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646399), tc_List_Olist(_1646399)), _1646401), _1646403)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1646399), c_List_Olistrel1(_1646399, _1646405)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646399)), _1646401) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646399)), _1646403))], (7322 ^ _775212) ^ [_891546, _891548] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _891546), _891548))), -(_891546 = _891548), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _891548), _891546)))], (25344 ^ _775212) ^ [_1216271, _1216273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216271)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216273)), 25351 ^ _775212 : [(25358 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1216271), _1216273)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1216271)), hAPP(c_Int_Onat, _1216273))))], (25352 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1216271)), hAPP(c_Int_Onat, _1216273))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1216271), _1216273)))]]], (23714 ^ _775212) ^ [_1187323, _1187325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1187323)), hAPP(c_Code__Numeral_Oof__nat, _1187325))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1187323), _1187325)))], (23792 ^ _775212) ^ [_1188695, _1188697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1188695)), hAPP(c_Code__Numeral_Onat__of, _1188697))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1188695), _1188697)))], (50359 ^ _775212) ^ [_1784969, _1784971, _1784973] : [-(c_List_Olist__ex(_1784969, _1784971, _1784973)), 50360 ^ _775212 : [(50361 ^ _775212) ^ [_1785026] : [hBOOL(hAPP(hAPP(c_member(_1784969), _1785026), hAPP(c_List_Oset(_1784969), _1784973))), hBOOL(hAPP(_1784971, _1785026))]]], (43328 ^ _775212) ^ [_1620977, _1620979, _1620981, _1620983, _1620985] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1620977, tc_fun(_1620979, tc_HOL_Obool)), _1620981), hAPP(hAPP(c_COMBS(_1620977, tc_fun(_1620979, tc_HOL_Obool), tc_fun(_1620979, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1620979, tc_HOL_Obool), tc_fun(tc_fun(_1620979, tc_HOL_Obool), tc_fun(_1620979, tc_HOL_Obool)), _1620977), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620979, tc_HOL_Obool))), _1620983)), _1620985)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620979, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620979, tc_HOL_Obool), hAPP(c_Set_Oimage(_1620977, tc_fun(_1620979, tc_HOL_Obool), _1620983), _1620981))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620979, tc_HOL_Obool), hAPP(c_Set_Oimage(_1620977, tc_fun(_1620979, tc_HOL_Obool), _1620985), _1620981))))], (50425 ^ _775212) ^ [_1786295, _1786297, _1786299] : [hBOOL(hAPP(hAPP(c_member(_1786295), _1786297), hAPP(c_List_Oset(_1786295), _1786299))), 50430 ^ _775212 : [(50433 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1786295), _1786297), hAPP(c_List_Oset(_1786295), 50429 ^ [_1786295, _1786297, _1786299])))], (50431 ^ _775212) ^ [] : [-(_1786299 = hAPP(hAPP(c_List_Oappend(_1786295), 50428 ^ [_1786295, _1786297, _1786299]), hAPP(hAPP(c_List_Olist_OCons(_1786295), _1786297), 50429 ^ [_1786295, _1786297, _1786299])))]]], (45770 ^ _775212) ^ [_1684482, _1684484, _1684486] : [hAPP(hAPP(c_List_Oappend(_1684482), _1684484), _1684486) = _1684484, -(_1684486 = c_List_Olist_ONil(_1684482))], (42738 ^ _775212) ^ [_1606494, _1606496, _1606498, _1606500] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606494, tc_fun(_1606494, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1606494, tc_fun(tc_prod(_1606494, _1606494), tc_HOL_Obool), tc_fun(_1606494, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1606494, tc_fun(tc_fun(tc_prod(_1606494, _1606494), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1606494, _1606494), tc_HOL_Obool), tc_fun(_1606494, tc_HOL_Obool)), _1606494), c_COMBC(_1606494, tc_fun(tc_prod(_1606494, _1606494), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1606494, tc_prod(_1606494, _1606494)), tc_fun(_1606494, tc_fun(tc_fun(tc_prod(_1606494, _1606494), tc_HOL_Obool), tc_HOL_Obool)), _1606494), hAPP(c_COMBB(tc_prod(_1606494, _1606494), tc_fun(tc_fun(tc_prod(_1606494, _1606494), tc_HOL_Obool), tc_HOL_Obool), _1606494), c_member(tc_prod(_1606494, _1606494)))), c_Product__Type_OPair(_1606494, _1606494)))), _1606496)), c_fequal), _1606498), _1606500)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606494, _1606494)), hAPP(hAPP(c_Product__Type_OPair(_1606494, _1606494), _1606498), _1606500)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1606494, _1606494), tc_HOL_Obool)), _1606496), c_Relation_OId(_1606494)))))], (18193 ^ _775212) ^ [_1084124] : [c_Int_OBit0(_1084124) = c_Int_OMin], (21619 ^ _775212) ^ [_1145368] : [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), _1145368))), -(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), _1145368)) = 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), _1145368))))], (21935 ^ _775212) ^ [_1151522, _1151524, _1151526, _1151528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1151522, tc_HOL_Obool)), _1151524), _1151526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1151522, tc_HOL_Obool)), _1151526), _1151528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1151522, tc_HOL_Obool)), _1151524), _1151528)))], (31319 ^ _775212) ^ [_1342001, _1342003, _1342005, _1342007, _1342009, _1342011] : [-(hBOOL(hAPP(hAPP(c_member(_1342001), _1342003), c_SetInterval_Oord_OatLeastLessThan(_1342001, _1342005, _1342007, _1342009, _1342011)))), hBOOL(hAPP(hAPP(_1342005, _1342009), _1342003)), hBOOL(hAPP(hAPP(_1342007, _1342003), _1342011))], (47164 ^ _775212) ^ [_1715447, _1715449, _1715451] : [-(c_List_Obutlast(_1715447, hAPP(hAPP(c_List_Oappend(_1715447), _1715449), hAPP(hAPP(c_List_Olist_OCons(_1715447), _1715451), c_List_Olist_ONil(_1715447)))) = _1715449)], (390 ^ _775212) ^ [_781249, _781251, _781253, _781255] : [-(c_FunDef_Oreduction__pair(_781253, _781249)), c_FunDef_Oreduction__pair(_781255, _781251), _781255 = _781253, _781251 = _781249], (33382 ^ _775212) ^ [_1381587, _1381589, _1381591, _1381593] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1381587), _1381589)), 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)), _1381587), _1381591)), 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)), _1381589), _1381593)), 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)), _1381589), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1381591), _1381593))), c_FunDef_Omin__weak)))], (31797 ^ _775212) ^ [_1350411, _1350413] : [class_Int_Oring__char__0(_1350411), hBOOL(hAPP(hAPP(c_member(_1350411), _1350413), c_Int_Oring__1__class_OInts(_1350411))), 31804 ^ _775212 : [(31811 ^ _775212) ^ [] : [_1350413 = c_Groups_Ozero__class_Ozero(_1350411), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1350411), _1350413), _1350413) = c_Groups_Ozero__class_Ozero(_1350411))], (31805 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1350411), _1350413), _1350413) = c_Groups_Ozero__class_Ozero(_1350411), -(_1350413 = c_Groups_Ozero__class_Ozero(_1350411))]]], (39819 ^ _775212) ^ [_1537207, _1537209, _1537211] : [c_Wellfounded_Owf(_1537207, _1537209), -(c_Wellfounded_Owf(_1537207, c_Wellfounded_Omlex__prod(_1537207, _1537211, _1537209)))], (48215 ^ _775212) ^ [_1739094, _1739096, _1739098] : [48217 ^ _775212 : [(48220 ^ _775212) ^ [] : [hBOOL(hAPP(_1739096, 48216 ^ [_1739094, _1739096, _1739098]))], (48218 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739094), 48216 ^ [_1739094, _1739096, _1739098]), hAPP(c_List_Oset(_1739094), _1739098))))]], -(hAPP(c_List_Ofilter(_1739094, _1739096), _1739098) = _1739098)], (48244 ^ _775212) ^ [_1739754, _1739756, _1739758, _1739760] : [-(hAPP(c_List_Ofilter(_1739754, _1739756), c_List_Oremove1(_1739754, _1739758, _1739760)) = c_List_Oremove1(_1739754, _1739758, hAPP(c_List_Ofilter(_1739754, _1739756), _1739760)))], (29148 ^ _775212) ^ [_1293056, _1293058, _1293060, _1293062, _1293064] : [-(_1293056 = c_Orderings_Obot__class_Obot(tc_fun(_1293058, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293060, tc_HOL_Obool)), _1293062), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293058, tc_fun(_1293060, tc_HOL_Obool)), _1293056), _1293064)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293058, tc_fun(_1293060, tc_HOL_Obool)), _1293056), hAPP(hAPP(c_COMBB(tc_fun(_1293060, tc_HOL_Obool), tc_fun(_1293060, tc_HOL_Obool), _1293058), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293060, tc_HOL_Obool)), _1293062)), _1293064)))], (44967 ^ _775212) ^ [_1663948, _1663950, _1663952] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663948)), _1663950), c_List_Olists(_1663948, _1663952))), 44970 ^ _775212 : [(44971 ^ _775212) ^ [_1664056] : [hBOOL(hAPP(hAPP(c_member(_1663948), _1664056), hAPP(c_List_Oset(_1663948), _1663950))), -(hBOOL(hAPP(hAPP(c_member(_1663948), _1664056), _1663952)))]]], (34751 ^ _775212) ^ [_1413450, _1413452, _1413454, _1413456, _1413458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413450, tc_HOL_Obool)), _1413452), _1413454)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413450, tc_HOL_Obool)), _1413456), _1413458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413450, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413450, tc_HOL_Obool)), _1413452), _1413456)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413450, tc_HOL_Obool)), _1413454), _1413458))))], (31693 ^ _775212) ^ [_1348789, _1348791] : [class_Rings_Oring__1(_1348789), -(hBOOL(hAPP(hAPP(c_member(_1348789), hAPP(c_Int_Oring__1__class_Oof__int(_1348789), _1348791)), c_Int_Oring__1__class_OInts(_1348789))))], (27245 ^ _775212) ^ [_1255187, _1255189, _1255191] : [class_Lattices_Osemilattice__sup(_1255187), 27248 ^ _775212 : [(27255 ^ _775212) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255187), _1255189), _1255191) = _1255191, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255187), _1255189), _1255191)))], (27249 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255187), _1255189), _1255191)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255187), _1255189), _1255191) = _1255191)]]], (23818 ^ _775212) ^ [_1189169, _1189171] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1189169), _1189171) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1189169)), hAPP(c_Code__Numeral_Onat__of, _1189171))))], (3862 ^ _775212) ^ [_833825, _833827, _833829, _833831] : [-(c_Hilbert__Choice_OEps(_833831, _833827) = c_Hilbert__Choice_OEps(_833829, _833825)), _833831 = _833829, _833827 = _833825], (47899 ^ _775212) ^ [_1731659, _1731661] : [-(_1731659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1731661, _1731659, c_List_Olist_ONil(_1731661)) = c_List_Olist_ONil(tc_List_Olist(_1731661)))], (7554 ^ _775212) ^ [_895754] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _895754)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _895754)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19315 ^ _775212) ^ [_1104356, _1104358, _1104360] : [class_Fields_Olinordered__field(_1104356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104356), c_Groups_Ozero__class_Ozero(_1104356)), _1104358)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104356), _1104360), c_Groups_Ozero__class_Ozero(_1104356))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104356), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104356), _1104358), _1104360)), c_Groups_Ozero__class_Ozero(_1104356))))], (13761 ^ _775212) ^ [_1003377, _1003379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1003379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1003377), _1003379)), _1003377)))], (27852 ^ _775212) ^ [_1268473, _1268475] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1268473), _1268475))))], (43245 ^ _775212) ^ [_1619258, _1619260, _1619262] : [class_Complete__Lattice_Ocomplete__lattice(_1619258), class_Orderings_Olinorder(_1619258), 43252 ^ _775212 : [(43262 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1619258), c_Complete__Lattice_OInf__class_OInf(_1619258, _1619260)), _1619262))), 43263 ^ _775212 : [(43264 ^ _775212) ^ [_1619564] : [hBOOL(hAPP(hAPP(c_member(_1619258), _1619564), _1619260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1619258), _1619564), _1619262))]]], (43253 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1619258), c_Complete__Lattice_OInf__class_OInf(_1619258, _1619260)), _1619262)), 43257 ^ _775212 : [(43260 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1619258), 43256 ^ [_1619258, _1619260, _1619262]), _1619262)))], (43258 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1619258), 43256 ^ [_1619258, _1619260, _1619262]), _1619260)))]]]]], (34083 ^ _775212) ^ [_1398645, _1398647, _1398649, _1398651] : [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), _1398645), _1398647)), 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), _1398649), _1398651)), 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), _1398645), _1398651)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398649), _1398647))))], (43994 ^ _775212) ^ [_1636979, _1636981, _1636983, _1636985, _1636987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1636979, tc_HOL_Obool)), _1636981), _1636983)), 44000 ^ _775212 : [(44005 ^ _775212) ^ [] : [hBOOL(hAPP(_1636987, 43999 ^ [_1636979, _1636981, _1636983, _1636985, _1636987]))], (44003 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1636985, 43999 ^ [_1636979, _1636981, _1636983, _1636985, _1636987])))], (44001 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1636979), 43999 ^ [_1636979, _1636981, _1636983, _1636985, _1636987]), _1636981)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1636979, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1636979, tc_HOL_Obool)), _1636981), hAPP(c_Set_OCollect(_1636979), _1636985))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1636979, tc_HOL_Obool)), _1636983), hAPP(c_Set_OCollect(_1636979), _1636987)))))], (26328 ^ _775212) ^ [_1237336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237336)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237336) = 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, _1237336))))], (4134 ^ _775212) ^ [_837963, _837965, _837967, _837969, _837971, _837973, _837975, _837977] : [-(c_List_Olist_Olist__case(_837977, _837973, _837969, _837965) = c_List_Olist_Olist__case(_837975, _837971, _837967, _837963)), _837977 = _837975, _837973 = _837971, _837969 = _837967, _837965 = _837963], (490 ^ _775212) ^ [_782751, _782753, _782755, _782757, _782759, _782761, _782763, _782765] : [-(c_Finite__Set_Ofolding__idem(_782763, _782759, _782755, _782751)), c_Finite__Set_Ofolding__idem(_782765, _782761, _782757, _782753), _782765 = _782763, _782761 = _782759, _782757 = _782755, _782753 = _782751], (49611 ^ _775212) ^ [_1768338, _1768340, _1768342, _1768344, _1768346] : [class_Groups_Omonoid__add(_1768338), 49617 ^ _775212 : [(49622 ^ _775212) ^ [] : [hAPP(_1768346, 49616 ^ [_1768338, _1768340, _1768342, _1768344, _1768346]) = c_Groups_Ozero__class_Ozero(_1768338)], (49620 ^ _775212) ^ [] : [hBOOL(hAPP(_1768344, 49616 ^ [_1768338, _1768340, _1768342, _1768344, _1768346]))], (49618 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1768340), 49616 ^ [_1768338, _1768340, _1768342, _1768344, _1768346]), hAPP(c_List_Oset(_1768340), _1768342))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1768338), hAPP(hAPP(c_List_Omap(_1768340, _1768338), _1768346), hAPP(c_List_Ofilter(_1768340, _1768344), _1768342))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1768338), hAPP(hAPP(c_List_Omap(_1768340, _1768338), _1768346), _1768342)))], (29925 ^ _775212) ^ [_1308533, _1308535] : [hBOOL(hAPP(hAPP(c_member(_1308533), _1308535), c_Orderings_Obot__class_Obot(tc_fun(_1308533, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1308533, tc_HOL_Obool)), _1308535)))], (48311 ^ _775212) ^ [_1741265, _1741267, _1741269, _1741271] : [hBOOL(hAPP(hAPP(c_member(_1741265), _1741267), hAPP(c_List_Oset(_1741265), _1741269))), -(hBOOL(hAPP(_1741271, _1741267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741265)), hAPP(c_List_Ofilter(_1741265, _1741271), _1741269))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741265)), _1741269))))], (8345 ^ _775212) ^ [_909993, _909995, _909997] : [class_Rings_Olinordered__semiring__strict(_909993), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909993), c_Groups_Ozero__class_Ozero(_909993)), _909995)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909993), _909997), c_Groups_Ozero__class_Ozero(_909993))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909993), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909993), _909995), _909997)), c_Groups_Ozero__class_Ozero(_909993))))], (21251 ^ _775212) ^ [_1139193, _1139195, _1139197] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1139193, _1139195), _1139197)), 21254 ^ _775212 : [(21255 ^ _775212) ^ [_1139278] : [hBOOL(hAPP(hAPP(_1139195, _1139278), _1139197)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1139193, _1139195), _1139278)))]]], (1924 ^ _775212) ^ [_802118, _802120, _802122, _802124] : [-(v_fun1(_802122, _802118)), v_fun1(_802124, _802120), _802124 = _802122, _802120 = _802118], (10487 ^ _775212) ^ [_946319, _946321] : [class_Rings_Oring__1__no__zero__divisors(_946319), 10490 ^ _775212 : [(10491 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946319), _946321), _946321) = c_Groups_Oone__class_Oone(_946319), -(_946321 = c_Groups_Oone__class_Oone(_946319)), -(_946321 = hAPP(c_Groups_Ouminus__class_Ouminus(_946319), c_Groups_Oone__class_Oone(_946319)))], (10501 ^ _775212) ^ [] : [10502 ^ _775212 : [(10505 ^ _775212) ^ [] : [_946321 = hAPP(c_Groups_Ouminus__class_Ouminus(_946319), c_Groups_Oone__class_Oone(_946319))], (10503 ^ _775212) ^ [] : [_946321 = c_Groups_Oone__class_Oone(_946319)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946319), _946321), _946321) = c_Groups_Oone__class_Oone(_946319))]]], (22778 ^ _775212) ^ [_1168907, _1168909] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1168907)), _1168909) = 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), _1168907)), _1168909))], (22834 ^ _775212) ^ [_1170258, _1170260] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170258), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 22837 ^ _775212 : [(22846 ^ _775212) ^ [] : [-(c_Nitpick_Onorm__frac(_1170260, _1170258) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1170260), _1170258)), 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), _1170260))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1170258)))), -(_1170260 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1170258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22838 ^ _775212) ^ [] : [22839 ^ _775212 : [(22842 ^ _775212) ^ [] : [_1170258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (22840 ^ _775212) ^ [] : [_1170260 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1170260, _1170258) = 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)))]]], (17629 ^ _775212) ^ [_1074502, _1074504] : [class_Int_Onumber__ring(_1074502), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074502), hAPP(c_Int_Onumber__class_Onumber__of(_1074502), _1074504)), c_Groups_Oone__class_Oone(_1074502)) = hAPP(c_Int_Onumber__class_Onumber__of(_1074502), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1074504), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (49313 ^ _775212) ^ [_1762115, _1762117, _1762119] : [class_Orderings_Olinorder(_1762115), c_List_Olinorder__class_Osorted(_1762115, hAPP(c_List_Orev(_1762115), _1762117)), 49320 ^ _775212 : [(49327 ^ _775212) ^ [] : [-(_1762117 = c_List_Olist_ONil(_1762115)), -(c_List_Ofoldr(_1762115, _1762115, c_Orderings_Oord__class_Omax(_1762115), _1762117, _1762119) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1762115), hAPP(hAPP(c_List_Onth(_1762115), _1762117), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1762119))], (49321 ^ _775212) ^ [] : [_1762117 = c_List_Olist_ONil(_1762115), -(c_List_Ofoldr(_1762115, _1762115, c_Orderings_Oord__class_Omax(_1762115), _1762117, _1762119) = _1762119)]]], (49259 ^ _775212) ^ [_1760939, _1760941, _1760943] : [-(hAPP(c_List_Orev(_1760939), hAPP(hAPP(c_List_Olist_OCons(_1760939), _1760941), _1760943)) = hAPP(hAPP(c_List_Oappend(_1760939), hAPP(c_List_Orev(_1760939), _1760943)), hAPP(hAPP(c_List_Olist_OCons(_1760939), _1760941), c_List_Olist_ONil(_1760939))))], (48262 ^ _775212) ^ [_1740102, _1740104, _1740106, _1740108] : [hBOOL(hAPP(_1740102, _1740104)), -(hAPP(c_List_Ofilter(_1740106, _1740102), hAPP(hAPP(c_List_Olist_OCons(_1740106), _1740104), _1740108)) = hAPP(hAPP(c_List_Olist_OCons(_1740106), _1740104), hAPP(c_List_Ofilter(_1740106, _1740102), _1740108)))], (52323 ^ _775212) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (23104 ^ _775212) ^ [_1175124, _1175126, _1175128, _1175130] : [class_Orderings_Olinorder(_1175124), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175124), _1175126), _1175128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175124), _1175126), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1175124), _1175128), _1175130))))], (3924 ^ _775212) ^ [_834740, _834742, _834744, _834746] : [-(c_Big__Operators_Olattice__class_OInf__fin(_834746, _834742) = c_Big__Operators_Olattice__class_OInf__fin(_834744, _834740)), _834746 = _834744, _834742 = _834740], (39825 ^ _775212) ^ [_1537294] : [-(c_Wellfounded_Owf(tc_fun(_1537294, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1537294)))], (15099 ^ _775212) ^ [_1028599, _1028601] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1028599), _1028601) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1028599), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1028601)))], (46831 ^ _775212) ^ [_1708700, _1708702, _1708704] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1708700, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708702)), _1708704)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1708702, _1708700), _1708704) = _1708704)], (46318 ^ _775212) ^ [_1697890, _1697892, _1697894, _1697896, _1697898] : [-(hAPP(hAPP(c_List_Oappend(_1697890), _1697892), _1697894) = hAPP(hAPP(c_List_Oappend(_1697890), _1697896), _1697898)), 46321 ^ _775212 : [(46324 ^ _775212) ^ [] : [_1697892 = hAPP(hAPP(c_List_Otake(_1697890), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697890)), _1697892)), _1697896), _1697894 = hAPP(hAPP(c_List_Oappend(_1697890), hAPP(hAPP(c_List_Odrop(_1697890), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697890)), _1697892)), _1697896)), _1697898)], (46322 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697890)), _1697892)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697890)), _1697896))))]], 46329 ^ _775212 : [(46332 ^ _775212) ^ [] : [hAPP(hAPP(c_List_Otake(_1697890), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697890)), _1697896)), _1697892) = _1697896, hAPP(hAPP(c_List_Oappend(_1697890), hAPP(hAPP(c_List_Odrop(_1697890), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697890)), _1697896)), _1697892)), _1697894) = _1697898], (46330 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697890)), _1697892)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697890)), _1697896)))]]], (13629 ^ _775212) ^ [_1001196, _1001198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001196)), 13632 ^ _775212 : [(13641 ^ _775212) ^ [] : [-(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), _1001196), _1001198)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1001198), _1001196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001198))], (13633 ^ _775212) ^ [] : [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), _1001196), _1001198))), 13636 ^ _775212 : [(13639 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001198)))], (13637 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1001198), _1001196)))]]]]], (34144 ^ _775212) ^ [_1400288, _1400290, _1400292, _1400294, _1400296] : [c_Equiv__Relations_Oequiv(_1400288, _1400290, _1400292), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1400288, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1400288, _1400288, _1400292), hAPP(hAPP(c_Set_Oinsert(_1400288), _1400294), c_Orderings_Obot__class_Obot(tc_fun(_1400288, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1400288, _1400288, _1400292), hAPP(hAPP(c_Set_Oinsert(_1400288), _1400296), c_Orderings_Obot__class_Obot(tc_fun(_1400288, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1400288), _1400294), _1400290)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1400288, _1400288)), hAPP(hAPP(c_Product__Type_OPair(_1400288, _1400288), _1400296), _1400294)), _1400292)))], (27413 ^ _775212) ^ [_1258569, _1258571] : [c_Nat__Transfer_Onat__set(_1258569), c_Nat__Transfer_Onat__set(_1258571), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258569), _1258571) = 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), _1258569)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258571))))], (52273 ^ _775212) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (6497 ^ _775212) ^ [_878085, _878087] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878085), _878087) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878087), _878085))], (18035 ^ _775212) ^ [_1081184, _1081186] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1081184))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081186)) = 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)))), _1081184), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081186)))], (5597 ^ _775212) ^ [_863333] : [_863333 = hAPP(c_Nat_OSuc, _863333)], (34871 ^ _775212) ^ [_1415620, _1415622, _1415624] : [class_Lattices_Olattice(_1415620), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415620), _1415622), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415620), _1415622), _1415624)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415620), _1415622), _1415624))], (10956 ^ _775212) ^ [_954402, _954404, _954406] : [class_Groups_Oordered__comm__monoid__add(_954402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954402), c_Groups_Ozero__class_Ozero(_954402)), _954404)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954402), c_Groups_Ozero__class_Ozero(_954402)), _954406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954402), c_Groups_Ozero__class_Ozero(_954402)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954402), _954404), _954406))))], (8952 ^ _775212) ^ [_920351, _920353, _920355, _920357] : [class_Orderings_Oord(_920351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920351), _920353), _920355)), _920355 = _920357, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920351), _920353), _920357)))], (23592 ^ _775212) ^ [_1184811, _1184813, _1184815, _1184817, _1184819, _1184821] : [-(c_Nitpick_Opair__box_OPairBox(_1184811, _1184813, _1184815, _1184817) = c_Nitpick_Opair__box_OPairBox(_1184811, _1184813, _1184819, _1184821)), _1184815 = _1184819, _1184817 = _1184821], (39797 ^ _775212) ^ [_1536852, _1536854, _1536856] : [c_Wellfounded_Owf(_1536852, _1536854), -(c_Wellfounded_Owf(_1536852, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1536852, _1536852), tc_HOL_Obool)), _1536854), _1536856)))], (50855 ^ _775212) ^ [_1794967, _1794969, _1794971, _1794973, _1794975] : [c_List_Oreplicate(_1794967, _1794969, _1794971) = c_List_Oreplicate(_1794967, _1794973, _1794975), 50858 ^ _775212 : [(50861 ^ _775212) ^ [] : [-(_1794969 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1794971 = _1794975)], (50859 ^ _775212) ^ [] : [-(_1794969 = _1794973)]]], (52471 ^ _775212) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (24402 ^ _775212) ^ [_1198861, _1198863, _1198865, _1198867] : [class_Divides_Osemiring__div(_1198861), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1198861), _1198863), _1198865)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1198861), _1198863), _1198867)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1198861), _1198863), c_Divides_Odiv__class_Omod(_1198861, _1198865, _1198867))))], (39389 ^ _775212) ^ [_1524733, _1524735, _1524737, _1524739, _1524741, _1524743] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1524733), _1524735)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524737), _1524739)), 39399 ^ _775212 : [(39402 ^ _775212) ^ [] : [hAPP(c_Finite__Set_Ocard(_1524733), hAPP(c_Set_OCollect(_1524733), hAPP(hAPP(c_COMBS(_1524733, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524733), c_fconj), hAPP(hAPP(c_COMBC(_1524733, tc_fun(_1524733, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524733)), _1524735))), hAPP(hAPP(c_COMBC(_1524733, _1524737, tc_HOL_Obool), _1524741), 39398 ^ [_1524733, _1524735, _1524737, _1524739, _1524741, _1524743])))) = hAPP(_1524743, 39398 ^ [_1524733, _1524735, _1524737, _1524739, _1524741, _1524743])], (39400 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524737), 39398 ^ [_1524733, _1524735, _1524737, _1524739, _1524741, _1524743]), _1524739)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524733, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1524737, tc_HOL_Obool), tc_Nat_Onat, _1524733), c_Finite__Set_Ocard(_1524737)), hAPP(hAPP(c_COMBB(tc_fun(_1524737, tc_HOL_Obool), tc_fun(_1524737, tc_HOL_Obool), _1524733), c_Set_OCollect(_1524737)), hAPP(hAPP(c_COMBB(tc_fun(_1524737, tc_HOL_Obool), tc_fun(_1524737, tc_HOL_Obool), _1524733), hAPP(c_COMBS(_1524737, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524737), c_fconj), hAPP(hAPP(c_COMBC(_1524737, tc_fun(_1524737, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524737)), _1524739)))), _1524741)))), _1524735) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524737, tc_Nat_Onat), _1524743), _1524739))], (16843 ^ _775212) ^ [_1062383, _1062385] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062383))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062383)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062385)) = 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), _1062385)))], (7591 ^ _775212) ^ [_896432, _896434, _896436] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896432), _896434)), _896436) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896432), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _896434), _896436)))], (27033 ^ _775212) ^ [_1251125, _1251127, _1251129] : [class_Lattices_Osemilattice__sup(_1251125), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251125), _1251127), _1251129) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251125), _1251129), _1251127))], (15111 ^ _775212) ^ [_1028851, _1028853] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1028851), _1028853)), _1028853) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028851), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028851, _1028853)))], (10305 ^ _775212) ^ [_942834, _942836, _942838, _942840] : [class_Rings_Oordered__semiring(_942834), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942834), _942836), _942838)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942834), c_Groups_Ozero__class_Ozero(_942834)), _942840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942834), _942836), _942840)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942834), _942838), _942840))))], (18191 ^ _775212) ^ [_1084082] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1084082)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1084082)))], (23342 ^ _775212) ^ [_1180014, _1180016] : [class_Orderings_Olinorder(_1180014), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1180014), _1180016), _1180016) = _1180016)], (26128 ^ _775212) ^ [_1233097, _1233099] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1233097), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1233099), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1233097, _1233099))], (51531 ^ _775212) ^ [_1811610, _1811612] : [c_Equiv__Relations_Oequivp(_1811610, _1811612), 51534 ^ _775212 : [(51539 ^ _775212) ^ [] : [-(c_Predicate_Otransp(_1811610, _1811612))], (51537 ^ _775212) ^ [] : [-(c_Predicate_Osymp(_1811610, _1811612))], (51535 ^ _775212) ^ [] : [-(c_Predicate_Oreflp(_1811610, _1811612))]]], (3792 ^ _775212) ^ [_832688, _832690, _832692, _832694, _832696, _832698, _832700, _832702] : [-(c_Product__Type_Oscomp(_832702, _832698, _832694, _832690) = c_Product__Type_Oscomp(_832700, _832696, _832692, _832688)), _832702 = _832700, _832698 = _832696, _832694 = _832692, _832690 = _832688], (40658 ^ _775212) ^ [_1556971] : [-(c_Nitpick_Onum(_1556971) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1556971, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1556971)))], (51773 ^ _775212) ^ [_1816080, _1816082] : [hAPP(c_Relation_Oconverse(_1816080, _1816080), _1816082) = _1816082, -(c_Relation_Osym(_1816080, _1816082))], (9251 ^ _775212) ^ [_925138, _925140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _925138), _925140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _925138), c_Groups_Oone__class_Oone(tc_Int_Oint))), _925140)))], (24154 ^ _775212) ^ [_1194702, _1194704] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194702), _1194704)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194704), _1194702)), -(_1194702 = _1194704)], (29292 ^ _775212) ^ [_1295926, _1295928, _1295930, _1295932, _1295934] : [class_Groups_Ocomm__monoid__add(_1295926), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295928), _1295930)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1295928, _1295926), _1295932), hAPP(hAPP(c_Set_Oinsert(_1295928), _1295934), _1295930)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1295926), hAPP(_1295932, _1295934)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1295928, _1295926), _1295932), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1295928, tc_HOL_Obool)), _1295930), hAPP(hAPP(c_Set_Oinsert(_1295928), _1295934), c_Orderings_Obot__class_Obot(tc_fun(_1295928, tc_HOL_Obool)))))))], (40700 ^ _775212) ^ [_1558102, _1558104, _1558106, _1558108, _1558110, _1558112, _1558114, _1558116] : [c_Finite__Set_Ofolding(_1558102, _1558104, _1558106, _1558108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558102), _1558110)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558102), _1558112)), -(hAPP(c_Fun_Ocomp(_1558104, _1558104, _1558114, hAPP(_1558108, _1558112)), hAPP(c_Fun_Ocomp(_1558104, _1558104, _1558114, hAPP(_1558108, _1558110)), _1558116)) = hAPP(c_Fun_Ocomp(_1558104, _1558104, _1558114, hAPP(_1558108, _1558110)), hAPP(c_Fun_Ocomp(_1558104, _1558104, _1558114, hAPP(_1558108, _1558112)), _1558116)))], (25276 ^ _775212) ^ [_1215027, _1215029] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1215027), _1215029)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1215027), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215029), _1215027)) = _1215029)], (49504 ^ _775212) ^ [_1766073, _1766075, _1766077] : [hBOOL(hAPP(c_List_Odistinct(_1766073), _1766075)), hBOOL(hAPP(hAPP(c_member(_1766073), _1766077), hAPP(c_List_Oset(_1766073), _1766075))), -(c_List_OdropWhile(_1766073, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1766073), c_fNot), hAPP(hAPP(c_COMBC(_1766073, _1766073, tc_HOL_Obool), c_fequal), _1766077)), hAPP(c_List_Orev(_1766073), _1766075)) = hAPP(hAPP(c_List_Olist_OCons(_1766073), _1766077), hAPP(c_List_Orev(_1766073), c_List_OtakeWhile(_1766073, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1766073), c_fNot), hAPP(hAPP(c_COMBC(_1766073, _1766073, tc_HOL_Obool), c_fequal), _1766077)), _1766075))))], (37638 ^ _775212) ^ [_1477514, _1477516, _1477518, _1477520, _1477522, _1477524, _1477526] : [-(hBOOL(hAPP(hAPP(c_member(_1477514), _1477516), _1477518))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1477514, _1477520, _1477522, _1477524, _1477518), _1477526)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1477514, _1477520, _1477522, _1477524, hAPP(hAPP(c_Set_Oinsert(_1477514), _1477516), _1477518)), hAPP(hAPP(_1477522, _1477516), _1477526))))], (48669 ^ _775212) ^ [_1749463, _1749465, _1749467] : [class_Orderings_Olinorder(_1749463), c_List_Olinorder__class_Osorted(_1749463, _1749465), -(c_List_Olinorder__class_Osorted(_1749463, hAPP(hAPP(c_List_Odrop(_1749463), _1749467), _1749465)))], (22212 ^ _775212) ^ [_1156991, _1156993] : [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(_1156993))), 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)), _1156991))))), -(hAPP(c_Nat_OSuc, _1156991) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156993))], (20449 ^ _775212) ^ [_1124158, _1124160, _1124162, _1124164] : [class_Fields_Olinordered__field(_1124158), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124158), c_Groups_Ozero__class_Ozero(_1124158)), _1124160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124158), _1124162), _1124160)), _1124164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124158), _1124162), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124158), _1124164), _1124160))))], (39474 ^ _775212) ^ [_1526702, _1526704, _1526706, _1526708, _1526710] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1526702, _1526704, _1526706), _1526708), _1526710) = hAPP(c_Set_OCollect(tc_prod(_1526702, _1526706)), hAPP(c_Product__Type_Oprod_Oprod__case(_1526702, _1526706, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1526706, tc_fun(_1526704, tc_HOL_Obool)), tc_fun(_1526706, tc_HOL_Obool), _1526702), hAPP(c_COMBB(tc_fun(_1526704, tc_HOL_Obool), tc_HOL_Obool, _1526706), c_HOL_OEx(_1526704))), hAPP(hAPP(c_COMBC(_1526702, tc_fun(_1526706, tc_fun(_1526704, tc_HOL_Obool)), tc_fun(_1526706, tc_fun(_1526704, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1526704, tc_HOL_Obool), tc_fun(_1526704, tc_HOL_Obool)), tc_fun(tc_fun(_1526706, tc_fun(_1526704, tc_HOL_Obool)), tc_fun(_1526706, tc_fun(_1526704, tc_HOL_Obool))), _1526702), c_COMBB(tc_fun(_1526704, tc_HOL_Obool), tc_fun(_1526704, tc_HOL_Obool), _1526706)), hAPP(hAPP(c_COMBB(tc_fun(_1526704, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1526704, tc_HOL_Obool), tc_fun(_1526704, tc_HOL_Obool)), _1526702), c_COMBS(_1526704, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526704, tc_HOL_Obool), tc_fun(_1526704, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1526702), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1526704), c_fconj)), hAPP(hAPP(c_COMBC(_1526702, tc_fun(tc_prod(_1526702, _1526704), tc_HOL_Obool), tc_fun(_1526704, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526704, tc_fun(tc_fun(tc_prod(_1526702, _1526704), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526702, _1526704), tc_HOL_Obool), tc_fun(_1526704, tc_HOL_Obool)), _1526702), c_COMBC(_1526704, tc_fun(tc_prod(_1526702, _1526704), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526704, tc_prod(_1526702, _1526704)), tc_fun(_1526704, tc_fun(tc_fun(tc_prod(_1526702, _1526704), tc_HOL_Obool), tc_HOL_Obool)), _1526702), hAPP(c_COMBB(tc_prod(_1526702, _1526704), tc_fun(tc_fun(tc_prod(_1526702, _1526704), tc_HOL_Obool), tc_HOL_Obool), _1526704), c_member(tc_prod(_1526702, _1526704)))), c_Product__Type_OPair(_1526702, _1526704)))), _1526708))))), hAPP(hAPP(c_COMBC(_1526706, tc_fun(tc_prod(_1526704, _1526706), tc_HOL_Obool), tc_fun(_1526704, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526704, tc_fun(tc_fun(tc_prod(_1526704, _1526706), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526704, _1526706), tc_HOL_Obool), tc_fun(_1526704, tc_HOL_Obool)), _1526706), c_COMBC(_1526704, tc_fun(tc_prod(_1526704, _1526706), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526704, tc_prod(_1526704, _1526706)), tc_fun(_1526704, tc_fun(tc_fun(tc_prod(_1526704, _1526706), tc_HOL_Obool), tc_HOL_Obool)), _1526706), hAPP(c_COMBB(tc_prod(_1526704, _1526706), tc_fun(tc_fun(tc_prod(_1526704, _1526706), tc_HOL_Obool), tc_HOL_Obool), _1526704), c_member(tc_prod(_1526704, _1526706)))), hAPP(c_COMBC(_1526704, _1526706, tc_prod(_1526704, _1526706)), c_Product__Type_OPair(_1526704, _1526706))))), _1526710))))))], (40313 ^ _775212) ^ [_1549168, _1549170] : [-(c_Nitpick_Owf_H(_1549168, _1549170)), c_Wellfounded_Oacyclic(_1549168, _1549170), 40318 ^ _775212 : [(40321 ^ _775212) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (40319 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1549168, _1549168)), _1549170))]]], (46368 ^ _775212) ^ [_1699186, _1699188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699186)), _1699188)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1699186), _1699188) = _1699188)], (6180 ^ _775212) ^ [_872837, _872839, _872841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872837), _872839)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872839), _872841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _872837)), _872841)))], (52633 ^ _775212) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (45864 ^ _775212) ^ [_1686429, _1686431, _1686433, _1686435, _1686437] : [hAPP(hAPP(c_List_Oappend(_1686429), _1686431), _1686433) = hAPP(hAPP(c_List_Oappend(_1686429), _1686435), _1686437), 45870 ^ _775212 : [(45873 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1686429), 45867 ^ [_1686429, _1686431, _1686433, _1686435, _1686437]), _1686433) = _1686437)], (45871 ^ _775212) ^ [] : [-(_1686431 = hAPP(hAPP(c_List_Oappend(_1686429), _1686435), 45867 ^ [_1686429, _1686431, _1686433, _1686435, _1686437]))]], 45874 ^ _775212 : [(45877 ^ _775212) ^ [] : [-(_1686433 = hAPP(hAPP(c_List_Oappend(_1686429), 45867 ^ [_1686429, _1686431, _1686433, _1686435, _1686437]), _1686437))], (45875 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1686429), _1686431), 45867 ^ [_1686429, _1686431, _1686433, _1686435, _1686437]) = _1686435)]]], (43414 ^ _775212) ^ [_1623397, _1623399, _1623401] : [c_Equiv__Relations_Oequiv(_1623397, _1623399, _1623401), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623397, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1623397), _1623399), _1623401)) = _1623399)], (39005 ^ _775212) ^ [_1509115, _1509117, _1509119] : [hBOOL(hAPP(_1509115, _1509117)), -(hAPP(c_Set_OCollect(_1509119), hAPP(hAPP(c_COMBS(_1509119, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509119), c_fconj), hAPP(hAPP(c_COMBC(_1509119, _1509119, tc_HOL_Obool), c_fequal), _1509117))), _1509115)) = hAPP(hAPP(c_Set_Oinsert(_1509119), _1509117), c_Orderings_Obot__class_Obot(tc_fun(_1509119, tc_HOL_Obool))))], (47569 ^ _775212) ^ [_1724181, _1724183, _1724185] : [-(c_List_Olistsp(_1724181, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1724181, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1724181, tc_fun(_1724181, tc_HOL_Obool), tc_HOL_Obool), c_member(_1724181)), _1724183)), hAPP(hAPP(c_COMBC(_1724181, tc_fun(_1724181, tc_HOL_Obool), tc_HOL_Obool), c_member(_1724181)), _1724185))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1724181), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1724181), tc_fun(tc_List_Olist(_1724181), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1724181))), c_List_Olists(_1724181, _1724183))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1724181), tc_fun(tc_List_Olist(_1724181), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1724181))), c_List_Olists(_1724181, _1724185))))], (33040 ^ _775212) ^ [_1374402, _1374404, _1374406, _1374408, _1374410] : [class_Groups_Ocomm__monoid__mult(_1374402), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374404), _1374406)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1374404, _1374402), hAPP(hAPP(c_COMBS(_1374404, _1374402, _1374402), hAPP(hAPP(c_COMBB(_1374402, tc_fun(_1374402, _1374402), _1374404), c_Groups_Otimes__class_Otimes(_1374402)), _1374408)), _1374410)), _1374406) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374402), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1374404, _1374402), _1374408), _1374406)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1374404, _1374402), _1374410), _1374406)))], (6964 ^ _775212) ^ [_886220, _886222] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886220), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886220), _886222)))))], (15119 ^ _775212) ^ [_1029003, _1029005] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029003), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029005)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029003), _1029005)))], (52673 ^ _775212) ^ [_1828122] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1828122)))], (12925 ^ _775212) ^ [_988658, _988660, _988662, _988664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _988658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _988660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _988660), _988662)), -(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), _988662), c_Divides_Odiv__class_Omod(tc_Int_Oint, _988664, _988658))), _988660))))], (43559 ^ _775212) ^ [_1626530, _1626532, _1626534] : [class_Complete__Lattice_Ocomplete__lattice(_1626530), -(c_Complete__Lattice_OSup__class_OSup(_1626530, hAPP(hAPP(c_Set_Oinsert(_1626530), _1626532), hAPP(hAPP(c_Set_Oinsert(_1626530), _1626534), c_Orderings_Obot__class_Obot(tc_fun(_1626530, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1626530), _1626532), _1626534))], (14279 ^ _775212) ^ [_1013156, _1013158, _1013160] : [class_Groups_Oab__group__add(_1013156), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1013156), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1013156), _1013158), _1013160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1013156), _1013160), _1013158))], (33769 ^ _775212) ^ [_1391112, _1391114, _1391116] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1391112, tc_HOL_Obool)), _1391114), hAPP(c_Set_OPow(_1391112), _1391116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1391112, tc_HOL_Obool)), _1391114), _1391116)))], (45240 ^ _775212) ^ [_1671008, _1671010, _1671012, _1671014, _1671016, _1671018, _1671020, _1671022] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1671008, _1671010), _1671012), _1671014), hAPP(hAPP(c_List_Ozip(_1671008, _1671010), _1671016), hAPP(hAPP(c_List_Omap(_1671018, _1671010), _1671020), _1671022))) = hAPP(hAPP(c_List_Omap(tc_prod(_1671008, _1671018), _1671012), hAPP(c_Product__Type_Oprod_Oprod__case(_1671008, _1671018, _1671012), hAPP(hAPP(c_COMBB(tc_fun(_1671018, tc_prod(_1671008, _1671010)), tc_fun(_1671018, _1671012), _1671008), hAPP(c_COMBB(tc_prod(_1671008, _1671010), _1671012, _1671018), _1671014)), hAPP(hAPP(c_COMBC(_1671008, tc_fun(_1671018, _1671010), tc_fun(_1671018, tc_prod(_1671008, _1671010))), hAPP(hAPP(c_COMBB(tc_fun(_1671010, tc_prod(_1671008, _1671010)), tc_fun(tc_fun(_1671018, _1671010), tc_fun(_1671018, tc_prod(_1671008, _1671010))), _1671008), c_COMBB(_1671010, tc_prod(_1671008, _1671010), _1671018)), c_Product__Type_OPair(_1671008, _1671010))), _1671020)))), hAPP(hAPP(c_List_Ozip(_1671008, _1671018), _1671016), _1671022)))], (14257 ^ _775212) ^ [_1012779, _1012781, _1012783] : [class_Groups_Ogroup__add(_1012779), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1012779), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012779), _1012781), _1012783)), _1012783) = _1012781)], (7421 ^ _775212) ^ [_893269, _893271, _893273] : [class_Rings_Ocomm__semiring__1(_893269), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893269), _893271), _893273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893269), _893273), _893271))], (50923 ^ _775212) ^ [_1796561, _1796563, _1796565, _1796567, _1796569] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1796563, _1796561)), hAPP(hAPP(c_Product__Type_OPair(_1796563, _1796561), _1796567), _1796569)), hAPP(c_Relation_Oconverse(_1796561, _1796563), _1796565))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1796561, _1796563, hAPP(hAPP(c_COMBC(_1796561, tc_fun(tc_prod(_1796561, _1796563), tc_HOL_Obool), tc_fun(_1796563, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1796563, tc_fun(tc_fun(tc_prod(_1796561, _1796563), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1796561, _1796563), tc_HOL_Obool), tc_fun(_1796563, tc_HOL_Obool)), _1796561), c_COMBC(_1796563, tc_fun(tc_prod(_1796561, _1796563), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1796563, tc_prod(_1796561, _1796563)), tc_fun(_1796563, tc_fun(tc_fun(tc_prod(_1796561, _1796563), tc_HOL_Obool), tc_HOL_Obool)), _1796561), hAPP(c_COMBB(tc_prod(_1796561, _1796563), tc_fun(tc_fun(tc_prod(_1796561, _1796563), tc_HOL_Obool), tc_HOL_Obool), _1796563), c_member(tc_prod(_1796561, _1796563)))), c_Product__Type_OPair(_1796561, _1796563)))), _1796565)), _1796567), _1796569)))], (43740 ^ _775212) ^ [_1630648, _1630650, _1630652, _1630654, _1630656] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630648, _1630648)), hAPP(hAPP(c_Product__Type_OPair(_1630648, _1630648), _1630650), _1630652)), c_Transitive__Closure_Ortrancl(_1630648, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1630648, _1630648), tc_HOL_Obool)), _1630654), _1630656)))), 43746 ^ _775212 : [(43752 ^ _775212) ^ [] : [43745 ^ [_1630648, _1630650, _1630652, _1630654, _1630656] = 43748 ^ [_1630648, _1630650, _1630652, _1630654, _1630656]], (43750 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630648, _1630648)), hAPP(hAPP(c_Product__Type_OPair(_1630648, _1630648), 43745 ^ [_1630648, _1630650, _1630652, _1630654, _1630656]), 43748 ^ [_1630648, _1630650, _1630652, _1630654, _1630656])), _1630656)))], (43747 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630648, _1630648)), hAPP(hAPP(c_Product__Type_OPair(_1630648, _1630648), _1630650), 43745 ^ [_1630648, _1630650, _1630652, _1630654, _1630656])), c_Transitive__Closure_Ortrancl(_1630648, _1630654))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630648, _1630648)), hAPP(hAPP(c_Product__Type_OPair(_1630648, _1630648), _1630650), _1630652)), c_Transitive__Closure_Ortrancl(_1630648, _1630654))))], (46232 ^ _775212) ^ [_1695794, _1695796, _1695798] : [-(hAPP(hAPP(c_List_Oappend(_1695794), hAPP(hAPP(c_List_Otake(_1695794), _1695796), _1695798)), hAPP(hAPP(c_List_Odrop(_1695794), _1695796), _1695798)) = _1695798)], (15101 ^ _775212) ^ [_1028639, _1028641] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1028639), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1028641)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1028639), _1028641))], (50891 ^ _775212) ^ [_1795585, _1795587, _1795589, _1795591] : [-(c_List_Oreplicate(_1795585, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1795587), _1795589), _1795591) = hAPP(hAPP(c_List_Oappend(_1795585), c_List_Oreplicate(_1795585, _1795587, _1795591)), c_List_Oreplicate(_1795585, _1795589, _1795591)))], (29002 ^ _775212) ^ [_1290519] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1290519), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (11320 ^ _775212) ^ [_961079, _961081] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _961079) = _961081), _961079 = hAPP(c_Int_Onat, _961081), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _961081))], (7935 ^ _775212) ^ [_902640, _902642, _902644] : [class_Groups_Oab__group__add(_902640), -(hAPP(c_Groups_Ouminus__class_Ouminus(_902640), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902640), _902642), _902644)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902640), hAPP(c_Groups_Ouminus__class_Ouminus(_902640), _902642)), hAPP(c_Groups_Ouminus__class_Ouminus(_902640), _902644)))], (22784 ^ _775212) ^ [_1169070, _1169072, _1169074, _1169076, _1169078, _1169080] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1169070, _1169072), _1169072, _1169074), hAPP(hAPP(c_COMBB(_1169076, tc_fun(_1169072, _1169074), tc_prod(_1169070, _1169072)), _1169078), hAPP(hAPP(c_COMBB(_1169070, _1169076, tc_prod(_1169070, _1169072)), _1169080), c_Product__Type_Ofst(_1169070, _1169072)))), c_Product__Type_Osnd(_1169070, _1169072)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1169070, _1169072, _1169074), hAPP(hAPP(c_COMBB(_1169076, tc_fun(_1169072, _1169074), _1169070), _1169078), _1169080)))], (42248 ^ _775212) ^ [_1592067, _1592069, _1592071, _1592073, _1592075, _1592077] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592067, tc_fun(_1592069, tc_fun(_1592071, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1592067, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1592069, _1592071), tc_HOL_Obool), tc_fun(_1592069, tc_fun(_1592071, tc_HOL_Obool)), _1592067), hAPP(c_COMBC(_1592069, tc_fun(tc_prod(_1592069, _1592071), tc_HOL_Obool), tc_fun(_1592071, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1592071, tc_fun(tc_fun(tc_prod(_1592069, _1592071), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1592069, _1592071), tc_HOL_Obool), tc_fun(_1592071, tc_HOL_Obool)), _1592069), c_COMBC(_1592071, tc_fun(tc_prod(_1592069, _1592071), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1592071, tc_prod(_1592069, _1592071)), tc_fun(_1592071, tc_fun(tc_fun(tc_prod(_1592069, _1592071), tc_HOL_Obool), tc_HOL_Obool)), _1592069), hAPP(c_COMBB(tc_prod(_1592069, _1592071), tc_fun(tc_fun(tc_prod(_1592069, _1592071), tc_HOL_Obool), tc_HOL_Obool), _1592071), c_member(tc_prod(_1592069, _1592071)))), c_Product__Type_OPair(_1592069, _1592071))))), _1592073)), _1592075), _1592077)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592069, _1592071)), hAPP(hAPP(c_Product__Type_OPair(_1592069, _1592071), _1592075), _1592077)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1592067, tc_fun(tc_prod(_1592069, _1592071), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1592067, tc_HOL_Obool))), _1592073))))], (5997 ^ _775212) ^ [_870343, _870345, _870347, _870349, _870351] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_870343, _870345), _870347, _870349, _870351), 6002 ^ _775212 : [(6005 ^ _775212) ^ [] : [hBOOL(hAPP(_870343, _870347))], (6003 ^ _775212) ^ [] : [-(_870351 = _870347)]], 6006 ^ _775212 : [(6012 ^ _775212) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_870343, _870345), 6008 ^ [_870343, _870345, _870347, _870349, _870351], _870349, _870351))], (6010 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_870345, _870347, _870349, 6008 ^ [_870343, _870345, _870347, _870349, _870351]))], (6007 ^ _775212) ^ [] : [-(hBOOL(hAPP(_870343, _870347)))]]], (12177 ^ _775212) ^ [_975445, _975447, _975449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975445), _975447)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975445), _975449))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _975445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975447), _975449)))], (16459 ^ _775212) ^ [_1054997, _1054999, _1055001] : [class_Rings_Oordered__ring__abs(_1054997), -(hAPP(c_Groups_Oabs__class_Oabs(_1054997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054997), _1054999), _1055001)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054997), hAPP(c_Groups_Oabs__class_Oabs(_1054997), _1054999)), hAPP(c_Groups_Oabs__class_Oabs(_1054997), _1055001))), 16466 ^ _775212 : [(16469 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054997), _1054999), c_Groups_Ozero__class_Ozero(_1054997)))], (16467 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054997), c_Groups_Ozero__class_Ozero(_1054997)), _1054999))]], 16470 ^ _775212 : [(16473 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054997), _1055001), c_Groups_Ozero__class_Ozero(_1054997)))], (16471 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054997), c_Groups_Ozero__class_Ozero(_1054997)), _1055001))]]], (44913 ^ _775212) ^ [_1662683, _1662685, _1662687] : [44915 ^ _775212 : [(44918 ^ _775212) ^ [] : [hBOOL(hAPP(_1662687, 44914 ^ [_1662683, _1662685, _1662687]))], (44916 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1662683), 44914 ^ [_1662683, _1662685, _1662687]), hAPP(c_List_Oset(_1662683), _1662685))))]], 44919 ^ _775212 : [(44920 ^ _775212) ^ [_1662867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662867), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662683)), _1662685))), -(hBOOL(hAPP(_1662687, hAPP(hAPP(c_List_Onth(_1662683), _1662685), _1662867))))]]], (12117 ^ _775212) ^ [_974381, _974383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974381), _974383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974381)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974383))))], (16831 ^ _775212) ^ [_1062205, _1062207] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062205))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062205)), _1062207) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062207))], (49157 ^ _775212) ^ [_1758685, _1758687, _1758689] : [hAPP(c_List_Orev(_1758685), _1758687) = hAPP(hAPP(c_List_Olist_OCons(_1758685), _1758689), c_List_Olist_ONil(_1758685)), -(_1758687 = hAPP(hAPP(c_List_Olist_OCons(_1758685), _1758689), c_List_Olist_ONil(_1758685)))], (7621 ^ _775212) ^ [_897072, _897074, _897076] : [class_Rings_Oring__1(_897072), -(hAPP(c_Int_Oring__1__class_Oof__int(_897072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _897074), _897076)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897072), hAPP(c_Int_Oring__1__class_Oof__int(_897072), _897074)), hAPP(c_Int_Oring__1__class_Oof__int(_897072), _897076)))], (13771 ^ _775212) ^ [_1003536, _1003538, _1003540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003536)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1003538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003540), _1003536)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1003538), _1003540)), _1003536))], (42633 ^ _775212) ^ [_1603636, _1603638, _1603640, _1603642] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603636, _1603636)), hAPP(hAPP(c_Product__Type_OPair(_1603636, _1603636), _1603638), _1603640)), c_Transitive__Closure_Ortrancl(_1603636, hAPP(c_Relation_Oconverse(_1603636, _1603636), _1603642)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603636, _1603636)), hAPP(hAPP(c_Product__Type_OPair(_1603636, _1603636), _1603640), _1603638)), c_Transitive__Closure_Ortrancl(_1603636, _1603642))))], (29534 ^ _775212) ^ [_1301077, _1301079, _1301081] : [-(hBOOL(hAPP(hAPP(c_member(_1301077), _1301079), _1301081))), -(hBOOL(hAPP(hAPP(c_member(_1301077), _1301079), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1301077, tc_HOL_Obool)), _1301081))))], (43194 ^ _775212) ^ [_1618232, _1618234, _1618236, _1618238] : [hBOOL(hAPP(hAPP(c_member(_1618232), _1618234), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1618232, tc_HOL_Obool), _1618236))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1618232, tc_HOL_Obool)), _1618238), _1618236)), -(hBOOL(hAPP(hAPP(c_member(_1618232), _1618234), _1618238)))], (29688 ^ _775212) ^ [_1304022, _1304024, _1304026, _1304028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1304022, tc_HOL_Obool)), _1304024), _1304026)), hBOOL(hAPP(hAPP(c_member(_1304022), _1304028), _1304024)), -(hBOOL(hAPP(hAPP(c_member(_1304022), _1304028), _1304026)))], (47498 ^ _775212) ^ [_1722708, _1722710, _1722712] : [hBOOL(hAPP(c_List_Olistsp(_1722708, _1722710), _1722712)), 47501 ^ _775212 : [(47502 ^ _775212) ^ [_1722797] : [hBOOL(hAPP(hAPP(c_member(_1722708), _1722797), hAPP(c_List_Oset(_1722708), _1722712))), -(hBOOL(hAPP(_1722710, _1722797)))]]], (14633 ^ _775212) ^ [_1019992, _1019994, _1019996, _1019998, _1020000, _1020002] : [class_Rings_Oring(_1019992), 14636 ^ _775212 : [(14643 ^ _775212) ^ [] : [_1019998 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019992), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1019992), _1020000), _1019994)), _1019996)), _1020002), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019992), _1019994), _1019996)), _1019998) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019992), _1020000), _1019996)), _1020002))], (14637 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019992), _1019994), _1019996)), _1019998) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019992), _1020000), _1019996)), _1020002), -(_1019998 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019992), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1019992), _1020000), _1019994)), _1019996)), _1020002))]]], (51711 ^ _775212) ^ [_1814859, _1814861] : [c_Relation_Oantisym(_1814859, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1814859, _1814859), tc_HOL_Obool)), _1814861), c_Relation_OId(_1814859))), -(c_Relation_Oantisym(_1814859, _1814861))], (45469 ^ _775212) ^ [_1677572, _1677574, _1677576, _1677578, _1677580] : [-(hAPP(hAPP(c_List_Ozip(_1677572, _1677574), _1677576), hAPP(hAPP(c_List_Olist_OCons(_1677574), _1677578), _1677580)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1677572, _1677574)), _1677572, c_List_Olist_ONil(tc_prod(_1677572, _1677574)), hAPP(hAPP(c_COMBC(_1677572, tc_fun(tc_List_Olist(_1677572), tc_List_Olist(tc_prod(_1677572, _1677574))), tc_fun(tc_List_Olist(_1677572), tc_List_Olist(tc_prod(_1677572, _1677574)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1677572, _1677574)), tc_List_Olist(tc_prod(_1677572, _1677574))), tc_fun(tc_fun(tc_List_Olist(_1677572), tc_List_Olist(tc_prod(_1677572, _1677574))), tc_fun(tc_List_Olist(_1677572), tc_List_Olist(tc_prod(_1677572, _1677574)))), _1677572), c_COMBB(tc_List_Olist(tc_prod(_1677572, _1677574)), tc_List_Olist(tc_prod(_1677572, _1677574)), tc_List_Olist(_1677572))), hAPP(hAPP(c_COMBB(tc_prod(_1677572, _1677574), tc_fun(tc_List_Olist(tc_prod(_1677572, _1677574)), tc_List_Olist(tc_prod(_1677572, _1677574))), _1677572), c_List_Olist_OCons(tc_prod(_1677572, _1677574))), hAPP(hAPP(c_COMBC(_1677572, _1677574, tc_prod(_1677572, _1677574)), c_Product__Type_OPair(_1677572, _1677574)), _1677578)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677572), tc_List_Olist(_1677574), tc_List_Olist(tc_prod(_1677572, _1677574))), c_List_Ozip(_1677572, _1677574)), _1677580))), _1677576))], (7947 ^ _775212) ^ [_902918, _902920, _902922] : [class_Groups_Ogroup__add(_902918), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902918), _902920), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902918), hAPP(c_Groups_Ouminus__class_Ouminus(_902918), _902920)), _902922)) = _902922)], (14881 ^ _775212) ^ [_1024499, _1024501] : [14882 ^ _775212 : [(14885 ^ _775212) ^ [] : [_1024501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14883 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024499))]], -(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), _1024499), _1024501))))], (39713 ^ _775212) ^ [_1535304, _1535306, _1535308, _1535310] : [c_Wellfounded_Owf(_1535304, _1535306), -(c_Wellfounded_Owf(_1535308, hAPP(hAPP(c_Relation_Oinv__image(_1535304, _1535308), _1535306), _1535310)))], (15103 ^ _775212) ^ [_1028679, _1028681] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028679), hAPP(c_Nat_OSuc, _1028681)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028679), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1028681))], (15109 ^ _775212) ^ [_1028804, _1028806] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028804), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1028806), _1028804)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028806), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028806, _1028804)))], (17411 ^ _775212) ^ [_1070922] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1070922) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070922), c_Int_OPls)))], (2630 ^ _775212) ^ [_813965, _813967, _813969, _813971, _813973, _813975, _813977, _813979] : [-(c_Random__Sequence_ORandom(_813979, _813975, _813971, _813967) = c_Random__Sequence_ORandom(_813977, _813973, _813969, _813965)), _813979 = _813977, _813975 = _813973, _813971 = _813969, _813967 = _813965], (5835 ^ _775212) ^ [_867476] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _867476)], (17911 ^ _775212) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (34819 ^ _775212) ^ [_1414558, _1414560, _1414562, _1414564, _1414566] : [class_Lattices_Olattice(_1414558), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414560, _1414558)), _1414562), _1414564), _1414566) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1414558), hAPP(_1414562, _1414566)), hAPP(_1414564, _1414566)))], (23754 ^ _775212) ^ [_1188064, _1188066] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1188064, _1188066) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1188064), hAPP(c_Code__Numeral_Onat__of, _1188066))))], (22372 ^ _775212) ^ [_1161129, _1161131] : [_1161129 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1161129, _1161131) = 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)))], (40454 ^ _775212) ^ [_1552246, _1552248, _1552250, _1552252, _1552254, _1552256] : [-(hAPP(hAPP(c_Fun_Ocomp(_1552246, _1552248, _1552250, _1552252), _1552254), _1552256) = hAPP(_1552252, hAPP(_1552254, _1552256)))], (24544 ^ _775212) ^ [_1201339, _1201341, _1201343, _1201345] : [class_Rings_Ocomm__semiring__1(_1201339), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1201339), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201339), _1201341), _1201343)), _1201345)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1201339), _1201343), _1201345)))], (5532 ^ _775212) ^ [_859600, _859602, _859604, _859606, _859608, _859610] : [-(c_COMBB(_859610, _859606, _859602) = c_COMBB(_859608, _859604, _859600)), _859610 = _859608, _859606 = _859604, _859602 = _859600], (29200 ^ _775212) ^ [_1294163, _1294165] : [29201 ^ _775212 : [(29204 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1294163), _1294165)))], (29202 ^ _775212) ^ [] : [_1294165 = c_Orderings_Obot__class_Obot(tc_fun(_1294163, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1294163), _1294165) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24340 ^ _775212) ^ [_1197748, _1197750] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197748), _1197750)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197750), _1197748))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197750), _1197748)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1197748), _1197750)))], (31677 ^ _775212) ^ [_1348503, _1348505, _1348507] : [class_Rings_Oring__1(_1348503), hBOOL(hAPP(hAPP(c_member(_1348503), _1348505), c_Int_Oring__1__class_OInts(_1348503))), -(hBOOL(hAPP(hAPP(c_member(_1348503), hAPP(hAPP(c_Power_Opower__class_Opower(_1348503), _1348505), _1348507)), c_Int_Oring__1__class_OInts(_1348503))))], (8788 ^ _775212) ^ [_917730, _917732] : [class_Rings_Oring__1(_917730), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _917732)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917730), hAPP(c_Int_Onat, _917732)) = hAPP(c_Int_Oring__1__class_Oof__int(_917730), _917732))], (34483 ^ _775212) ^ [_1407834, _1407836, _1407838, _1407840] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407834, tc_HOL_Obool)), _1407836), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407834, tc_HOL_Obool)), _1407838), _1407840)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407834, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407834, tc_HOL_Obool)), _1407836), _1407838)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407834, tc_HOL_Obool)), _1407836), _1407840)))], (30280 ^ _775212) ^ [_1318678, _1318680, _1318682, _1318684] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318678, tc_fun(_1318680, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1318678, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1318680, tc_HOL_Obool), tc_fun(_1318680, tc_HOL_Obool), _1318678), hAPP(c_COMBC(_1318680, tc_fun(_1318680, tc_HOL_Obool), tc_HOL_Obool), c_member(_1318680))), _1318682)), _1318684)), -(hBOOL(hAPP(hAPP(c_member(_1318680), _1318684), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318678, tc_fun(_1318680, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1318678, tc_HOL_Obool))), _1318682))))], (4128 ^ _775212) ^ [_837878, _837880] : [_837880 = _837878, -(c_Finite__Set_Ocard(_837880) = c_Finite__Set_Ocard(_837878))], (6653 ^ _775212) ^ [_880888, _880890, _880892, _880894] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_880888), 6656 ^ _775212 : [(6663 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880888), _880890), _880894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880888), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880888), _880890), _880892)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880888), _880894), _880892))))], (6657 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880888), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880888), _880890), _880892)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880888), _880894), _880892))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880888), _880890), _880894)))]]], (41342 ^ _775212) ^ [_1572268, _1572270, _1572272, _1572274] : [class_Lattices_Osemilattice__sup(_1572268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572268), _1572270)), hBOOL(hAPP(hAPP(c_member(_1572268), _1572272), _1572270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1572268), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1572268), _1572272), _1572274)), hAPP(hAPP(c_Finite__Set_Ofold(_1572268, _1572268, c_Lattices_Osemilattice__sup__class_Osup(_1572268)), _1572274), _1572270))))], (35575 ^ _775212) ^ [_1432177, _1432179, _1432181] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1432177), _1432179)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432177), _1432181)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432177, tc_HOL_Obool)), _1432179), _1432181) = c_Orderings_Obot__class_Obot(tc_fun(_1432177, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1432177), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1432177, tc_HOL_Obool)), _1432179), _1432181)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1432177), _1432179)), hAPP(c_Finite__Set_Ocard(_1432177), _1432181)))], (37860 ^ _775212) ^ [_1483015, _1483017, _1483019, _1483021, _1483023] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1483015, _1483017), _1483019), hAPP(hAPP(c_COMBS(_1483015, tc_fun(_1483017, tc_HOL_Obool), tc_fun(_1483017, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483017, tc_HOL_Obool), tc_fun(tc_fun(_1483017, tc_HOL_Obool), tc_fun(_1483017, tc_HOL_Obool)), _1483015), c_Groups_Ominus__class_Ominus(tc_fun(_1483017, tc_HOL_Obool))), _1483021)), _1483023)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1483015, _1483017), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1483015, _1483017), _1483019), _1483021)), hAPP(hAPP(c_Product__Type_OSigma(_1483015, _1483017), _1483019), _1483023)))], (46346 ^ _775212) ^ [_1698649, _1698651, _1698653, _1698655] : [-(hAPP(c_List_Orotate1(_1698649), c_List_Olist_ONil(_1698649)) = c_List_Olist_ONil(_1698649))], (52425 ^ _775212) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (28197 ^ _775212) ^ [_1275006, _1275008] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1275006, 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(_1275006, tc_HOL_Obool)), tc_fun(_1275006, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1275006, tc_HOL_Obool)), tc_fun(_1275006, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1275006, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1275008)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1275006, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1275008))], (14963 ^ _775212) ^ [_1025914, _1025916, _1025918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025914), _1025918)), _1025916)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025914), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025916), _1025918))))], (30815 ^ _775212) ^ [_1331675, _1331677] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1331675), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1331677)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1331677), _1331675)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1331675), _1331677)))], (47993 ^ _775212) ^ [_1733646, _1733648, _1733650, _1733652] : [-(c_List_Oremdups(_1733646, hAPP(hAPP(c_List_Omap(_1733648, _1733646), _1733650), c_List_Oremdups(_1733648, _1733652))) = c_List_Oremdups(_1733646, hAPP(hAPP(c_List_Omap(_1733648, _1733646), _1733650), _1733652)))], (24736 ^ _775212) ^ [_1204824, _1204826, _1204828] : [class_Divides_Oring__div(_1204824), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204824), _1204826), _1204828)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204824), hAPP(c_Groups_Ouminus__class_Ouminus(_1204824), _1204828)), _1204826) = hAPP(c_Groups_Ouminus__class_Ouminus(_1204824), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204824), _1204828), _1204826)))], (3142 ^ _775212) ^ [_822411, _822413, _822415, _822417] : [-(c_FunDef_Orp__inv__image(_822417, _822413) = c_FunDef_Orp__inv__image(_822415, _822411)), _822417 = _822415, _822413 = _822411], (9739 ^ _775212) ^ [_932689, _932691, _932693] : [9740 ^ _775212 : [(9743 ^ _775212) ^ [] : [_932689 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9741 ^ _775212) ^ [] : [_932691 = _932693]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932689), _932691) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932689), _932693))], (16773 ^ _775212) ^ [_1061213] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061213) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1061213)))], (40015 ^ _775212) ^ [_1541737, _1541739, _1541741, _1541743] : [c_Wellfounded_Owf(_1541737, _1541739), c_Fun_Oinj__on(_1541737, _1541741, _1541743, c_Orderings_Otop__class_Otop(tc_fun(_1541737, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1541741, hAPP(c_Set_Oimage(tc_prod(_1541737, _1541737), tc_prod(_1541741, _1541741), c_Product__Type_Omap__pair(_1541737, _1541741, _1541737, _1541741, _1541743, _1541743)), _1541739)))], (14351 ^ _775212) ^ [_1014682] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014682), _1014682) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52369 ^ _775212) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (39303 ^ _775212) ^ [_1520271, _1520273, _1520275] : [class_Lattices_Odistrib__lattice(_1520271), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520271), _1520273)), -(_1520273 = c_Orderings_Obot__class_Obot(tc_fun(_1520271, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520271), _1520275)), -(_1520275 = c_Orderings_Obot__class_Obot(tc_fun(_1520271, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1520271), c_Big__Operators_Olattice__class_OSup__fin(_1520271, _1520273)), c_Big__Operators_Olattice__class_OSup__fin(_1520271, _1520275)) = c_Big__Operators_Olattice__class_OSup__fin(_1520271, hAPP(c_Set_OCollect(_1520271), hAPP(hAPP(c_COMBB(tc_fun(_1520271, tc_HOL_Obool), tc_HOL_Obool, _1520271), c_HOL_OEx(_1520271)), hAPP(hAPP(c_COMBB(tc_fun(_1520271, tc_fun(_1520271, tc_HOL_Obool)), tc_fun(_1520271, tc_HOL_Obool), _1520271), hAPP(c_COMBB(tc_fun(_1520271, tc_HOL_Obool), tc_HOL_Obool, _1520271), c_HOL_OEx(_1520271))), hAPP(hAPP(c_COMBC(_1520271, tc_fun(_1520271, tc_fun(_1520271, tc_HOL_Obool)), tc_fun(_1520271, tc_fun(_1520271, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1520271, tc_fun(tc_fun(_1520271, tc_HOL_Obool), tc_fun(_1520271, tc_HOL_Obool))), tc_fun(tc_fun(_1520271, tc_fun(_1520271, tc_HOL_Obool)), tc_fun(_1520271, tc_fun(_1520271, tc_HOL_Obool))), _1520271), c_COMBS(_1520271, tc_fun(_1520271, tc_HOL_Obool), tc_fun(_1520271, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1520271, tc_fun(_1520271, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1520271, tc_fun(tc_fun(_1520271, tc_HOL_Obool), tc_fun(_1520271, tc_HOL_Obool))), _1520271), hAPP(c_COMBB(tc_fun(_1520271, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1520271, tc_HOL_Obool), tc_fun(_1520271, tc_HOL_Obool)), _1520271), c_COMBS(_1520271, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1520271, tc_fun(_1520271, tc_HOL_Obool)), tc_fun(_1520271, tc_fun(_1520271, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1520271), hAPP(c_COMBB(tc_fun(_1520271, tc_HOL_Obool), tc_fun(_1520271, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1520271), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520271), c_fconj))), hAPP(hAPP(c_COMBC(_1520271, tc_fun(_1520271, tc_fun(_1520271, _1520271)), tc_fun(_1520271, tc_fun(_1520271, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1520271, _1520271), tc_fun(_1520271, tc_HOL_Obool)), tc_fun(tc_fun(_1520271, tc_fun(_1520271, _1520271)), tc_fun(_1520271, tc_fun(_1520271, tc_HOL_Obool))), _1520271), c_COMBB(tc_fun(_1520271, _1520271), tc_fun(_1520271, tc_HOL_Obool), _1520271)), hAPP(hAPP(c_COMBB(tc_fun(_1520271, tc_HOL_Obool), tc_fun(tc_fun(_1520271, _1520271), tc_fun(_1520271, tc_HOL_Obool)), _1520271), c_COMBB(_1520271, tc_HOL_Obool, _1520271)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1520271)))))), hAPP(hAPP(c_COMBC(_1520271, tc_fun(_1520271, tc_HOL_Obool), tc_fun(_1520271, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1520271, tc_HOL_Obool), tc_fun(_1520271, tc_HOL_Obool)), _1520271), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1520271)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520271), c_fconj), hAPP(hAPP(c_COMBC(_1520271, tc_fun(_1520271, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520271)), _1520273)))), hAPP(hAPP(c_COMBC(_1520271, tc_fun(_1520271, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520271)), _1520275))))))))], (40133 ^ _775212) ^ [_1544618, _1544620] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1544618, _1544620), 40134 ^ [_1544618, _1544620])), -(c_Wellfounded_OwfP(_1544618, _1544620))], (18467 ^ _775212) ^ [_1088898, _1088900] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1088898)), c_Int_OBit1(_1088900)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1088898)), _1088900)))], (45532 ^ _775212) ^ [_1679296, _1679298] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1679296, _1679298) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1679296, _1679298)))], (16437 ^ _775212) ^ [_1054582, _1054584] : [class_Rings_Olinordered__idom(_1054582), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054582), c_Groups_Osgn__class_Osgn(_1054582, _1054584)), hAPP(c_Groups_Oabs__class_Oabs(_1054582), _1054584)) = _1054584)], (17067 ^ _775212) ^ [_1065665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1065665)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1065665) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (50697 ^ _775212) ^ [_1791972, _1791974, _1791976] : [c_List_Oreplicate(_1791972, _1791974, _1791976) = c_List_Olist_ONil(_1791972), -(_1791974 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18901 ^ _775212) ^ [_1096879, _1096881] : [class_Int_Onumber__ring(_1096879), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096879), hAPP(c_Int_Onumber__class_Onumber__of(_1096879), 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)))), _1096881))) = hAPP(c_Int_Onumber__class_Onumber__of(_1096879), c_Int_OMin))], (43541 ^ _775212) ^ [_1626033, _1626035, _1626037] : [class_Complete__Lattice_Ocomplete__lattice(_1626033), -(c_Complete__Lattice_OSup__class_OSup(_1626033, hAPP(hAPP(c_Set_Oinsert(_1626033), _1626035), _1626037)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1626033), _1626035), c_Complete__Lattice_OSup__class_OSup(_1626033, _1626037)))], (25106 ^ _775212) ^ [_1212021, _1212023, _1212025] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212021), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1212023), _1212025))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212021), _1212025)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1212021), _1212023)))], (7405 ^ _775212) ^ [_893103, _893105, _893107] : [c_Com_Ocom_OLocal(_893103, _893105, _893107) = c_Com_Ocom_OSKIP], (12508 ^ _775212) ^ [_981232, _981234, _981236, _981238] : [class_Divides_Osemiring__div(_981232), -(c_Divides_Odiv__class_Omod(_981232, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981232), _981234), _981236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981232), _981234), _981238)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981232), _981234), c_Divides_Odiv__class_Omod(_981232, _981236, _981238)))], (19371 ^ _775212) ^ [_1105390, _1105392, _1105394, _1105396] : [class_Fields_Olinordered__field(_1105390), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105390), _1105392), _1105394)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105390), _1105396), c_Groups_Ozero__class_Ozero(_1105390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105390), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105390), _1105394), _1105396)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105390), _1105392), _1105396))))], (42773 ^ _775212) ^ [_1607916, _1607918, _1607920, _1607922, _1607924, _1607926, _1607928] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607916, tc_fun(_1607918, tc_fun(_1607920, tc_HOL_Obool))), _1607922), _1607924), _1607926), _1607928)), 42776 ^ _775212 : [(42777 ^ _775212) ^ [_1608044] : [hBOOL(hAPP(hAPP(c_member(_1607916), _1608044), _1607922)), -(hBOOL(hAPP(hAPP(hAPP(_1607924, _1608044), _1607926), _1607928)))]]], (37910 ^ _775212) ^ [_1484374, _1484376, _1484378] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1484374, _1484376), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1484374, _1484376), _1484378), hAPP(c_COMBK(tc_fun(_1484376, tc_HOL_Obool), _1484374), c_Orderings_Otop__class_Otop(tc_fun(_1484376, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1484374, _1484376), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1484374, tc_HOL_Obool)), _1484378)), hAPP(c_COMBK(tc_fun(_1484376, tc_HOL_Obool), _1484374), c_Orderings_Otop__class_Otop(tc_fun(_1484376, tc_HOL_Obool)))))], (15653 ^ _775212) ^ [_1039921, _1039923, _1039925, _1039927] : [class_Rings_Olinordered__semidom(_1039921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039923), _1039925)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039921), c_Groups_Ozero__class_Ozero(_1039921)), _1039927)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039921), _1039927), c_Groups_Oone__class_Oone(_1039921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039921), hAPP(hAPP(c_Power_Opower__class_Opower(_1039921), _1039927), _1039925)), hAPP(hAPP(c_Power_Opower__class_Opower(_1039921), _1039927), _1039923))))], (52209 ^ _775212) ^ [_1823610, _1823612] : [-(class_Enum_Oenum(tc_fun(_1823610, _1823612))), class_Enum_Oenum(_1823610), class_Enum_Oenum(_1823612)], (40291 ^ _775212) ^ [_1548890, _1548892] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548890, _1548890)), _1548892)), c_Wellfounded_Oacyclic(_1548890, _1548892), -(c_Wellfounded_Owf(_1548890, _1548892))], (24490 ^ _775212) ^ [_1200366, _1200368, _1200370, _1200372] : [class_Rings_Ocomm__semiring__1(_1200366), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1200366), _1200368), _1200370)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1200366), _1200368), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200366), _1200370), _1200372))))], (3898 ^ _775212) ^ [_834357, _834359, _834361, _834363] : [-(c_Nat_Ocompow(_834363, _834359) = c_Nat_Ocompow(_834361, _834357)), _834363 = _834361, _834359 = _834357], (44216 ^ _775212) ^ [_1643397, _1643399, _1643401, _1643403] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1643397), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1643399), _1643401)))), -(hAPP(c_Random_Opick(_1643399, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1643399)), _1643401), _1643403)), _1643397) = hAPP(c_Random_Opick(_1643399, _1643403), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1643397), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1643399), _1643401))))], (17643 ^ _775212) ^ [_1074805, _1074807] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1074805)))), _1074807) = 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)))), _1074805)), _1074807))], (44612 ^ _775212) ^ [_1655272, _1655274, _1655276] : [_1655272 = _1655274, 44615 ^ _775212 : [(44618 ^ _775212) ^ [_1655420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655420), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655276)), _1655272))), -(hAPP(hAPP(c_List_Onth(_1655276), _1655272), _1655420) = hAPP(hAPP(c_List_Onth(_1655276), _1655274), _1655420))], (44616 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655276)), _1655272) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655276)), _1655274))]]], (34193 ^ _775212) ^ [_1401441, _1401443, _1401445, _1401447] : [c_Equiv__Relations_Oequiv(_1401441, _1401443, _1401445), hBOOL(hAPP(hAPP(c_member(_1401441), _1401447), _1401443)), -(hBOOL(hAPP(hAPP(c_member(_1401441), _1401447), hAPP(c_Relation_OImage(_1401441, _1401441, _1401445), hAPP(hAPP(c_Set_Oinsert(_1401441), _1401447), c_Orderings_Obot__class_Obot(tc_fun(_1401441, tc_HOL_Obool)))))))], (35207 ^ _775212) ^ [_1423817, _1423819, _1423821] : [class_Orderings_Oorder(_1423817), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423817, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1423817), _1423819)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1423817, _1423819), _1423821)) = c_Orderings_Obot__class_Obot(tc_fun(_1423817, tc_HOL_Obool)))], (8665 ^ _775212) ^ [_915666, _915668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _915666)), hAPP(c_Int_Onat, _915668))), 8668 ^ _775212 : [(8671 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _915666), _915668)))], (8669 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _915668)))]]], (46642 ^ _775212) ^ [_1704774, _1704776, _1704778] : [hBOOL(hAPP(c_List_Odistinct(_1704774), hAPP(hAPP(c_List_Oappend(_1704774), _1704776), _1704778))), 46645 ^ _775212 : [(46650 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1704774, tc_HOL_Obool)), hAPP(c_List_Oset(_1704774), _1704776)), hAPP(c_List_Oset(_1704774), _1704778)) = c_Orderings_Obot__class_Obot(tc_fun(_1704774, tc_HOL_Obool)))], (46648 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1704774), _1704778)))], (46646 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1704774), _1704776)))]]], (39253 ^ _775212) ^ [_1518200, _1518202, _1518204] : [class_Lattices_Odistrib__lattice(_1518200), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518200), _1518202)), -(_1518202 = c_Orderings_Obot__class_Obot(tc_fun(_1518200, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518200), _1518204)), -(_1518204 = c_Orderings_Obot__class_Obot(tc_fun(_1518200, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1518200), c_Big__Operators_Olattice__class_OInf__fin(_1518200, _1518202)), c_Big__Operators_Olattice__class_OInf__fin(_1518200, _1518204)) = c_Big__Operators_Olattice__class_OInf__fin(_1518200, hAPP(c_Set_OCollect(_1518200), hAPP(hAPP(c_COMBB(tc_fun(_1518200, tc_HOL_Obool), tc_HOL_Obool, _1518200), c_HOL_OEx(_1518200)), hAPP(hAPP(c_COMBB(tc_fun(_1518200, tc_fun(_1518200, tc_HOL_Obool)), tc_fun(_1518200, tc_HOL_Obool), _1518200), hAPP(c_COMBB(tc_fun(_1518200, tc_HOL_Obool), tc_HOL_Obool, _1518200), c_HOL_OEx(_1518200))), hAPP(hAPP(c_COMBC(_1518200, tc_fun(_1518200, tc_fun(_1518200, tc_HOL_Obool)), tc_fun(_1518200, tc_fun(_1518200, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1518200, tc_fun(tc_fun(_1518200, tc_HOL_Obool), tc_fun(_1518200, tc_HOL_Obool))), tc_fun(tc_fun(_1518200, tc_fun(_1518200, tc_HOL_Obool)), tc_fun(_1518200, tc_fun(_1518200, tc_HOL_Obool))), _1518200), c_COMBS(_1518200, tc_fun(_1518200, tc_HOL_Obool), tc_fun(_1518200, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1518200, tc_fun(_1518200, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1518200, tc_fun(tc_fun(_1518200, tc_HOL_Obool), tc_fun(_1518200, tc_HOL_Obool))), _1518200), hAPP(c_COMBB(tc_fun(_1518200, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1518200, tc_HOL_Obool), tc_fun(_1518200, tc_HOL_Obool)), _1518200), c_COMBS(_1518200, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1518200, tc_fun(_1518200, tc_HOL_Obool)), tc_fun(_1518200, tc_fun(_1518200, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1518200), hAPP(c_COMBB(tc_fun(_1518200, tc_HOL_Obool), tc_fun(_1518200, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1518200), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1518200), c_fconj))), hAPP(hAPP(c_COMBC(_1518200, tc_fun(_1518200, tc_fun(_1518200, _1518200)), tc_fun(_1518200, tc_fun(_1518200, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1518200, _1518200), tc_fun(_1518200, tc_HOL_Obool)), tc_fun(tc_fun(_1518200, tc_fun(_1518200, _1518200)), tc_fun(_1518200, tc_fun(_1518200, tc_HOL_Obool))), _1518200), c_COMBB(tc_fun(_1518200, _1518200), tc_fun(_1518200, tc_HOL_Obool), _1518200)), hAPP(hAPP(c_COMBB(tc_fun(_1518200, tc_HOL_Obool), tc_fun(tc_fun(_1518200, _1518200), tc_fun(_1518200, tc_HOL_Obool)), _1518200), c_COMBB(_1518200, tc_HOL_Obool, _1518200)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1518200)))))), hAPP(hAPP(c_COMBC(_1518200, tc_fun(_1518200, tc_HOL_Obool), tc_fun(_1518200, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1518200, tc_HOL_Obool), tc_fun(_1518200, tc_HOL_Obool)), _1518200), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1518200)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1518200), c_fconj), hAPP(hAPP(c_COMBC(_1518200, tc_fun(_1518200, tc_HOL_Obool), tc_HOL_Obool), c_member(_1518200)), _1518202)))), hAPP(hAPP(c_COMBC(_1518200, tc_fun(_1518200, tc_HOL_Obool), tc_HOL_Obool), c_member(_1518200)), _1518204))))))))], (10005 ^ _775212) ^ [_937432, _937434] : [class_Rings_Olinordered__semidom(_937432), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937432), _937434), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937432), _937434), c_Groups_Oone__class_Oone(_937432)))))], (11702 ^ _775212) ^ [_967351, _967353] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967351), _967353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967353)), _967351)))], (9767 ^ _775212) ^ [_933103] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _933103) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17613 ^ _775212) ^ [_1074243, _1074245] : [class_Int_Onumber__ring(_1074243), 17616 ^ _775212 : [(17623 ^ _775212) ^ [] : [c_Int_Oiszero(_1074243, hAPP(c_Int_Onumber__class_Onumber__of(_1074243), 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), _1074245)))), -(c_Groups_Oone__class_Oone(_1074243) = hAPP(c_Int_Onumber__class_Onumber__of(_1074243), _1074245))], (17617 ^ _775212) ^ [] : [c_Groups_Oone__class_Oone(_1074243) = hAPP(c_Int_Onumber__class_Onumber__of(_1074243), _1074245), -(c_Int_Oiszero(_1074243, hAPP(c_Int_Onumber__class_Onumber__of(_1074243), 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), _1074245)))))]]], (27803 ^ _775212) ^ [_1267104, _1267106, _1267108, _1267110, _1267112] : [27805 ^ _775212 : [(27808 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267104, tc_HOL_Obool)), hAPP(_1267110, 27804 ^ [_1267104, _1267106, _1267108, _1267110, _1267112])), _1267112))], (27806 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1267106), 27804 ^ [_1267104, _1267106, _1267108, _1267110, _1267112]), _1267108)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267104, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267106, tc_fun(_1267104, tc_HOL_Obool)), _1267108), _1267110)), _1267112)))], (22092 ^ _775212) ^ [_1154457, _1154459, _1154461, _1154463] : [hAPP(c_Product__Type_Ofst(_1154457, _1154459), _1154461) = hAPP(c_Product__Type_Ofst(_1154457, _1154459), _1154463), hAPP(c_Product__Type_Osnd(_1154457, _1154459), _1154461) = hAPP(c_Product__Type_Osnd(_1154457, _1154459), _1154463), -(_1154461 = _1154463)], (39817 ^ _775212) ^ [_1537173, _1537175] : [-(hAPP(c_Relation_ODomain(_1537173, _1537173), c_Relation_OId__on(_1537173, _1537175)) = _1537175)], (45184 ^ _775212) ^ [_1669789, _1669791, _1669793, _1669795] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1669789, _1669791))), hAPP(hAPP(c_List_Ozip(_1669789, _1669791), _1669793), _1669795)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669789)), _1669793)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669791)), _1669795)))], (35783 ^ _775212) ^ [_1436190, _1436192, _1436194] : [class_Orderings_Olinorder(_1436190), hBOOL(hAPP(c_Finite__Set_Ofinite(_1436190), _1436192)), -(_1436192 = c_Orderings_Obot__class_Obot(tc_fun(_1436190, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1436190), _1436194)), -(_1436194 = c_Orderings_Obot__class_Obot(tc_fun(_1436190, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1436190, tc_HOL_Obool)), _1436192), _1436194) = c_Orderings_Obot__class_Obot(tc_fun(_1436190, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1436190, c_Orderings_Oord__class_Omax(_1436190), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1436190, tc_HOL_Obool)), _1436192), _1436194)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1436190), c_Big__Operators_Olattice_OSup__fin(_1436190, c_Orderings_Oord__class_Omax(_1436190), _1436192)), c_Big__Operators_Olattice_OSup__fin(_1436190, c_Orderings_Oord__class_Omax(_1436190), _1436194)))], (51767 ^ _775212) ^ [_1815995, _1815997] : [c_Relation_Osym(_1815995, _1815997), -(hAPP(c_Relation_Oconverse(_1815995, _1815995), _1815997) = _1815997)], (41991 ^ _775212) ^ [_1586378, _1586380, _1586382, _1586384, _1586386] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586378, _1586378)), hAPP(hAPP(c_Product__Type_OPair(_1586378, _1586378), _1586380), _1586382)), c_Transitive__Closure_Ortrancl(_1586378, _1586384))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586378, _1586378)), hAPP(hAPP(c_Product__Type_OPair(_1586378, _1586378), _1586382), _1586386)), c_Transitive__Closure_Otrancl(_1586378, _1586384))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586378, _1586378)), hAPP(hAPP(c_Product__Type_OPair(_1586378, _1586378), _1586380), _1586386)), c_Transitive__Closure_Otrancl(_1586378, _1586384))))], (17891 ^ _775212) ^ [_1078942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1078942)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078942), c_Int_OPls)))], (44248 ^ _775212) ^ [_1644286, _1644288, _1644290, _1644292] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644286), tc_List_Olist(_1644286))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644286), tc_List_Olist(_1644286)), _1644288), _1644290)), c_List_Olex(_1644286, _1644292))), 44251 ^ _775212 : [(44254 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644286)), _1644288) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644286)), _1644290))], (44252 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644286), tc_List_Olist(_1644286))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644286), tc_List_Olist(_1644286)), _1644288), _1644290)), c_List_Olexord(_1644286, _1644292))))]]], (16725 ^ _775212) ^ [_1060475, _1060477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060475)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060477))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1060475), _1060477)))], (21270 ^ _775212) ^ [_1139583, _1139585, _1139587] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1139583, _1139585), _1139587)), 21273 ^ _775212 : [(21274 ^ _775212) ^ [_1139668] : [hBOOL(hAPP(hAPP(_1139585, _1139668), _1139587)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1139583, _1139585), _1139668)))]]], (4202 ^ _775212) ^ [_839017, _839019] : [_839019 = _839017, -(c_Int_Onumber__class_Onumber__of(_839019) = c_Int_Onumber__class_Onumber__of(_839017))], (47166 ^ _775212) ^ [_1715495, _1715497, _1715499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715495), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715497)), _1715499))), -(hAPP(hAPP(c_List_Otake(_1715497), _1715495), c_List_Obutlast(_1715497, _1715499)) = hAPP(hAPP(c_List_Otake(_1715497), _1715495), _1715499))], (47480 ^ _775212) ^ [_1722350] : [class_Orderings_Olinorder(_1722350), -(c_Finite__Set_Ofun__left__comm(_1722350, tc_List_Olist(_1722350), c_List_Olinorder__class_Oinsort__key(_1722350, _1722350, c_COMBI(_1722350))))], (22132 ^ _775212) ^ [_1155273, _1155275, _1155277, _1155279, _1155281] : [class_Groups_Ominus(_1155273), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1155275, _1155273)), _1155277), _1155279), _1155281) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1155273), hAPP(_1155277, _1155281)), hAPP(_1155279, _1155281)))], (28107 ^ _775212) ^ [_1273143, _1273145, _1273147, _1273149] : [hAPP(c_Set_Oimage(_1273143, _1273145, _1273147), c_Orderings_Otop__class_Otop(tc_fun(_1273143, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1273145, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273145, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1273145, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1273143, _1273145, _1273147), _1273149))), hAPP(c_Set_Oimage(_1273143, _1273145, _1273147), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1273143, tc_HOL_Obool)), _1273149)))))], (49209 ^ _775212) ^ [_1759906, _1759908, _1759910] : [hAPP(c_List_Orev(_1759906), _1759908) = hAPP(c_List_Orev(_1759906), _1759910), -(_1759908 = _1759910)], (26385 ^ _775212) ^ [_1238564, _1238566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1238564), _1238566)), -(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)), _1238564)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238566))))], (10603 ^ _775212) ^ [_948197, _948199] : [class_Rings_Olinordered__semidom(_948197), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948197), c_Groups_Ozero__class_Ozero(_948197)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_948197), _948199))))], (35003 ^ _775212) ^ [_1419070, _1419072] : [class_Lattices_Oboolean__algebra(_1419070), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419070), hAPP(c_Groups_Ouminus__class_Ouminus(_1419070), _1419072)), _1419072) = c_Orderings_Obot__class_Obot(_1419070))], (8778 ^ _775212) ^ [_917603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _917603)), -(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, _917603))))], (29580 ^ _775212) ^ [_1302075, _1302077] : [29581 ^ _775212 : [(29582 ^ _775212) ^ [_1302128] : [hBOOL(hAPP(hAPP(c_member(_1302075), _1302128), _1302077))]], _1302077 = c_Orderings_Obot__class_Obot(tc_fun(_1302075, tc_HOL_Obool))], (30214 ^ _775212) ^ [_1316652, _1316654] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1316652), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1316654), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 30221 ^ _775212 : [(30228 ^ _775212) ^ [] : [_1316652 = _1316654, -(hAPP(c_Code__Numeral_Oof__nat, _1316652) = hAPP(c_Code__Numeral_Oof__nat, _1316654))], (30222 ^ _775212) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1316652) = hAPP(c_Code__Numeral_Oof__nat, _1316654), -(_1316652 = _1316654)]]], (43392 ^ _775212) ^ [_1622587, _1622589, _1622591] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1622587, tc_HOL_Obool)), _1622589), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1622587, tc_HOL_Obool), _1622591)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1622587, tc_HOL_Obool), tc_fun(_1622587, tc_HOL_Obool)), _1622591), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1622587, tc_HOL_Obool)), _1622589)))], (21463 ^ _775212) ^ [_1142834, _1142836, _1142838] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1142834, _1142834), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1142836), _1142838))), -(_1142834 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1142836 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22750 ^ _775212) ^ [_1168315, _1168317, _1168319, _1168321, _1168323, _1168325] : [hAPP(_1168321, hAPP(c_Product__Type_Osnd(_1168319, _1168315), _1168323)) = hAPP(_1168325, hAPP(c_Product__Type_Osnd(_1168319, _1168315), _1168323)), -(hAPP(c_Product__Type_Oapsnd(_1168315, _1168317, _1168319, _1168321), _1168323) = hAPP(c_Product__Type_Oapsnd(_1168315, _1168317, _1168319, _1168325), _1168323))], (50975 ^ _775212) ^ [_1797719, _1797721, _1797723, _1797725] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1797719, _1797721), c_Lazy__Sequence_Olazy__sequence_OInsert(_1797719, _1797723, _1797725)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1797721, _1797723)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1797719, _1797721), _1797725))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43408 ^ _775212) ^ [_1623248, _1623250, _1623252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1623248, tc_HOL_Obool), tc_HOL_Obool)), _1623250), _1623252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1623248, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623248, tc_HOL_Obool), _1623250)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623248, tc_HOL_Obool), _1623252))))], (15025 ^ _775212) ^ [_1027170, _1027172, _1027174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027170), _1027172)), 15028 ^ _775212 : [(15035 ^ _775212) ^ [] : [_1027172 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027174), _1027170), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027172), _1027170) = _1027174)], (15029 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027172), _1027170) = _1027174, -(_1027172 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027174), _1027170))]]], (12761 ^ _775212) ^ [_985714, _985716] : [class_Lattices_Oab__semigroup__idem__mult(_985714), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985714), _985716), _985716) = _985716)], (49748 ^ _775212) ^ [_1771278, _1771280, _1771282, _1771284] : [_1771278 = _1771280, -(hAPP(c_List_OremoveAll(_1771282, _1771278), hAPP(hAPP(c_List_Olist_OCons(_1771282), _1771280), _1771284)) = hAPP(c_List_OremoveAll(_1771282, _1771278), _1771284))], (46534 ^ _775212) ^ [_1702360, _1702362, _1702364] : [-(hBOOL(hAPP(c_List_Odistinct(_1702360), hAPP(hAPP(c_List_Olist_OCons(_1702360), _1702362), _1702364)))), -(hBOOL(hAPP(hAPP(c_member(_1702360), _1702362), hAPP(c_List_Oset(_1702360), _1702364)))), hBOOL(hAPP(c_List_Odistinct(_1702360), _1702364))], (992 ^ _775212) ^ [_790300, _790302, _790304, _790306] : [-(c_Relation_Osym(_790304, _790300)), c_Relation_Osym(_790306, _790302), _790306 = _790304, _790302 = _790300], (8491 ^ _775212) ^ [_912711, _912713, _912715, _912717] : [class_Rings_Olinordered__ring__strict(_912711), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912711), _912713), _912715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912711), _912717), c_Groups_Ozero__class_Ozero(_912711))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912711), _912715), _912717)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912711), _912713), _912717))))], (5775 ^ _775212) ^ [_866303, _866305, _866307, _866309, _866311, _866313] : [-(c_Com_Ocom_OCond(_866303, _866305, _866307) = c_Com_Ocom_OCond(_866309, _866311, _866313)), _866303 = _866309, _866305 = _866311, _866307 = _866313], (34977 ^ _775212) ^ [_1418240, _1418242, _1418244, _1418246, _1418248] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418240, tc_HOL_Obool)), _1418242), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418244, tc_fun(_1418240, tc_HOL_Obool)), _1418246), _1418248)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418244, tc_fun(_1418240, tc_HOL_Obool)), _1418246), hAPP(hAPP(c_COMBB(tc_fun(_1418240, tc_HOL_Obool), tc_fun(_1418240, tc_HOL_Obool), _1418244), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418240, tc_HOL_Obool)), _1418242)), _1418248)))], (4778 ^ _775212) ^ [_847999, _848001, _848003, _848005] : [-(c_List_Ofilter(_848005, _848001) = c_List_Ofilter(_848003, _847999)), _848005 = _848003, _848001 = _847999], (9939 ^ _775212) ^ [_936206, _936208] : [class_Rings_Olinordered__idom(_936206), 9942 ^ _775212 : [(9949 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _936208), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936206), hAPP(c_Int_Oring__1__class_Oof__int(_936206), _936208)), c_Groups_Ozero__class_Ozero(_936206))))], (9943 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936206), hAPP(c_Int_Oring__1__class_Oof__int(_936206), _936208)), c_Groups_Ozero__class_Ozero(_936206))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _936208), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (40446 ^ _775212) ^ [_1552075, _1552077] : [40447 ^ _775212 : [(40448 ^ _775212) ^ [_1552121] : [hBOOL(hAPP(_1552075, _1552121))]], -(hBOOL(hAPP(_1552075, c_Hilbert__Choice_OEps(_1552077, _1552075))))], (21691 ^ _775212) ^ [_1146838, _1146840, _1146842] : [_1146838 = _1146840, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1146842, tc_HOL_Obool)), _1146840), _1146838)))], (30674 ^ _775212) ^ [_1328585, _1328587, _1328589, _1328591, _1328593] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1328585, _1328587)), hAPP(hAPP(c_Product__Type_OPair(_1328585, _1328587), _1328591), _1328593)), _1328589)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1328585, _1328587, _1328589), _1328591), _1328593)))], (22886 ^ _775212) ^ [_1171243, _1171245, _1171247, _1171249] : [class_Orderings_Olinorder(_1171243), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171243), _1171245), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171243), _1171247), _1171249)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171243), _1171247), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171243), _1171245), _1171249)))], (42429 ^ _775212) ^ [_1597648, _1597650, _1597652, _1597654, _1597656] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597648, tc_fun(_1597650, tc_HOL_Obool)), _1597652), hAPP(hAPP(c_COMBB(tc_fun(_1597650, tc_HOL_Obool), tc_fun(_1597650, tc_HOL_Obool), _1597648), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597650, tc_HOL_Obool)), _1597654)), _1597656)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597650, tc_HOL_Obool)), _1597654), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597648, tc_fun(_1597650, tc_HOL_Obool)), _1597652), _1597656)))], (12416 ^ _775212) ^ [_979370, _979372] : [class_Divides_Osemiring__div(_979370), -(c_Divides_Odiv__class_Omod(_979370, c_Groups_Ozero__class_Ozero(_979370), _979372) = c_Groups_Ozero__class_Ozero(_979370))], (46268 ^ _775212) ^ [_1696675, _1696677, _1696679, _1696681] : [-(hAPP(hAPP(c_List_Oappend(_1696675), _1696677), _1696679) = _1696681), _1696677 = hAPP(hAPP(c_List_Otake(_1696675), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696675)), _1696677)), _1696681), _1696679 = hAPP(hAPP(c_List_Odrop(_1696675), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696675)), _1696677)), _1696681)], (46402 ^ _775212) ^ [_1700137, _1700139, _1700141, _1700143] : [-(_1700137 = c_List_Olist_ONil(_1700139)), -(hAPP(c_List_Ohd(_1700141), hAPP(hAPP(c_List_Omap(_1700139, _1700141), _1700143), _1700137)) = hAPP(_1700143, hAPP(c_List_Ohd(_1700139), _1700137)))], (26509 ^ _775212) ^ [_1241102, _1241104, _1241106] : [class_Orderings_Olinorder(_1241102), 26512 ^ _775212 : [(26519 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241102), _1241106), _1241104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241102, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1241102), _1241104)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1241102), _1241106))))], (26513 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241102, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1241102), _1241104)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1241102), _1241106))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241102), _1241106), _1241104)))]]], (47240 ^ _775212) ^ [_1717002, _1717004, _1717006, _1717008] : [-(_1717002 = _1717004), -(c_List_Oremove1(_1717006, _1717002, hAPP(hAPP(c_List_Olist_OCons(_1717006), _1717004), _1717008)) = hAPP(hAPP(c_List_Olist_OCons(_1717006), _1717004), c_List_Oremove1(_1717006, _1717002, _1717008)))], (5352 ^ _775212) ^ [_856876, _856878] : [_856878 = _856876, -(c_Lattices_Osemilattice__inf__class_Oinf(_856878) = c_Lattices_Osemilattice__inf__class_Oinf(_856876))], (11294 ^ _775212) ^ [_960634] : [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)), _960634)), _960634)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _960634), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8643 ^ _775212) ^ [_915291, _915293] : [class_Rings_Oring__1(_915291), -(hAPP(c_Int_Oring__1__class_Oof__int(_915291), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _915293)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_915291), _915293))], (37832 ^ _775212) ^ [_1481997, _1481999, _1482001, _1482003, _1482005] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1481997, _1481999, hAPP(hAPP(c_Set_Oinsert(_1481997), _1482001), _1482003)), _1482005)), 37837 ^ _775212 : [(37842 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1481997), 37835 ^ [_1481997, _1481999, _1482001, _1482003, _1482005]), 37836 ^ [_1481997, _1481999, _1482001, _1482003, _1482005]))], (37840 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1481997, _1481997, _1481999, 37835 ^ [_1481997, _1481999, _1482001, _1482003, _1482005], 37836 ^ [_1481997, _1481999, _1482001, _1482003, _1482005]), _1482005)))], (37838 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1481997), _1482001), _1482003) = hAPP(hAPP(c_Set_Oinsert(_1481997), 37835 ^ [_1481997, _1481999, _1482001, _1482003, _1482005]), 37836 ^ [_1481997, _1481999, _1482001, _1482003, _1482005]))]]], (19453 ^ _775212) ^ [_1106775, _1106777, _1106779, _1106781] : [class_Fields_Ofield__inverse__zero(_1106775), 19456 ^ _775212 : [(19457 ^ _775212) ^ [] : [_1106777 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106775), _1106779), _1106781), 19460 ^ _775212 : [(19467 ^ _775212) ^ [] : [_1106781 = c_Groups_Ozero__class_Ozero(_1106775), -(_1106777 = c_Groups_Ozero__class_Ozero(_1106775))], (19461 ^ _775212) ^ [] : [-(_1106781 = c_Groups_Ozero__class_Ozero(_1106775)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106775), _1106777), _1106781) = _1106779)]]], (19473 ^ _775212) ^ [] : [-(_1106777 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106775), _1106779), _1106781)), 19476 ^ _775212 : [(19479 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106775), _1106777), _1106781) = _1106779], (19477 ^ _775212) ^ [] : [_1106781 = c_Groups_Ozero__class_Ozero(_1106775)]], 19480 ^ _775212 : [(19483 ^ _775212) ^ [] : [_1106777 = c_Groups_Ozero__class_Ozero(_1106775)], (19481 ^ _775212) ^ [] : [-(_1106781 = c_Groups_Ozero__class_Ozero(_1106775))]]]]], (7495 ^ _775212) ^ [] : [-(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)))], (21799 ^ _775212) ^ [_1148960, _1148962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1148962), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1148960, _1148962) = 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), _1148960), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1148962)))))], (33485 ^ _775212) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (28644 ^ _775212) ^ [_1283912, _1283914, _1283916] : [c_Orderings_Obot__class_Obot(tc_fun(_1283912, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_1283912), _1283914), _1283916)], (29360 ^ _775212) ^ [_1297558, _1297560] : [-(c_Set_Othe__elem(_1297558, _1297560) = c_HOL_OThe(_1297558, hAPP(hAPP(c_COMBB(tc_fun(_1297558, tc_HOL_Obool), tc_HOL_Obool, _1297558), hAPP(c_fequal, _1297560)), hAPP(hAPP(c_COMBC(_1297558, tc_fun(_1297558, tc_HOL_Obool), tc_fun(_1297558, tc_HOL_Obool)), c_Set_Oinsert(_1297558)), c_Orderings_Obot__class_Obot(tc_fun(_1297558, tc_HOL_Obool))))))], (10647 ^ _775212) ^ [_949030, _949032, _949034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949030), _949032)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949030), _949034))), 10650 ^ _775212 : [(10653 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949032), _949034)))], (10651 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _949030)))]]], (16685 ^ _775212) ^ [_1059763, _1059765, _1059767] : [class_Int_Onumber__ring(_1059763), 16688 ^ _775212 : [(16695 ^ _775212) ^ [] : [c_Int_Oiszero(_1059763, hAPP(c_Int_Onumber__class_Onumber__of(_1059763), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1059765), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1059767)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1059763), _1059765) = hAPP(c_Int_Onumber__class_Onumber__of(_1059763), _1059767))], (16689 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1059763), _1059765) = hAPP(c_Int_Onumber__class_Onumber__of(_1059763), _1059767), -(c_Int_Oiszero(_1059763, hAPP(c_Int_Onumber__class_Onumber__of(_1059763), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1059765), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1059767)))))]]], (15635 ^ _775212) ^ [_1039582, _1039584, _1039586, _1039588] : [class_Rings_Olinordered__semidom(_1039582), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1039584), _1039586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039582), c_Groups_Ozero__class_Ozero(_1039582)), _1039588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039582), _1039588), c_Groups_Oone__class_Oone(_1039582))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039582), hAPP(hAPP(c_Power_Opower__class_Opower(_1039582), _1039588), _1039586)), hAPP(hAPP(c_Power_Opower__class_Opower(_1039582), _1039588), _1039584))))], (31741 ^ _775212) ^ [_1349526, _1349528] : [class_Orderings_Olinorder(_1349526), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349526), _1349528)), -(_1349528 = c_Orderings_Obot__class_Obot(tc_fun(_1349526, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1349526), c_Big__Operators_Olinorder__class_OMax(_1349526, _1349528)), _1349528)))], (15209 ^ _775212) ^ [_1031256, _1031258, _1031260, _1031262] : [class_Rings_Olinordered__semidom(_1031256), hAPP(hAPP(c_Power_Opower__class_Opower(_1031256), _1031258), hAPP(c_Nat_OSuc, _1031260)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1031256), _1031262), hAPP(c_Nat_OSuc, _1031260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1031256), c_Groups_Ozero__class_Ozero(_1031256)), _1031258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1031256), c_Groups_Ozero__class_Ozero(_1031256)), _1031262)), -(_1031258 = _1031262)], (19385 ^ _775212) ^ [_1105659, _1105661, _1105663, _1105665] : [class_Rings_Odivision__ring(_1105659), -(_1105661 = c_Groups_Ozero__class_Ozero(_1105659)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105659), _1105663), _1105661) = _1105665, -(_1105663 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105659), _1105665), _1105661))], (49397 ^ _775212) ^ [_1763829, _1763831, _1763833] : [49399 ^ _775212 : [(49402 ^ _775212) ^ [] : [hBOOL(hAPP(_1763831, 49398 ^ [_1763829, _1763831, _1763833]))], (49400 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763829), 49398 ^ [_1763829, _1763831, _1763833]), hAPP(c_List_Oset(_1763829), _1763833))))]], -(c_List_OtakeWhile(_1763829, _1763831, _1763833) = _1763833)], (27891 ^ _775212) ^ [_1269206] : [27893 ^ _775212 : [(27896 ^ _775212) ^ [_1269316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27892 ^ [_1269206, _1269316]), _1269316))], (27894 ^ _775212) ^ [_1269282] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27892 ^ [_1269206, _1269282]), _1269206)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1269206)))], (48072 ^ _775212) ^ [_1735188, _1735190] : [48074 ^ _775212 : [(48077 ^ _775212) ^ [] : [48073 ^ [_1735188, _1735190] = c_List_Olist_ONil(_1735188)], (48075 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1735188)), 48073 ^ [_1735188, _1735190]), hAPP(c_List_Oset(tc_List_Olist(_1735188)), _1735190))))]], -(c_List_Oconcat(_1735188, _1735190) = c_List_Olist_ONil(_1735188))], (38903 ^ _775212) ^ [_1506886, _1506888, _1506890] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506886), hAPP(c_Set_OCollect(_1506886), hAPP(hAPP(c_COMBS(_1506886, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506886), c_fdisj), _1506888)), _1506890)))), 38906 ^ _775212 : [(38909 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506886), hAPP(c_Set_OCollect(_1506886), _1506890))))], (38907 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506886), hAPP(c_Set_OCollect(_1506886), _1506888))))]]], (36863 ^ _775212) ^ [_1460058, _1460060, _1460062, _1460064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1460058), hAPP(c_Set_Oimage(_1460060, _1460058, _1460062), _1460064))), hAPP(c_Finite__Set_Ocard(_1460060), _1460064))), c_Fun_Oinj__on(_1460060, _1460058, _1460062, _1460064)], (1114 ^ _775212) ^ [_791993, _791995] : [-(class_Groups_Olinordered__ab__group__add(_791993)), _791995 = _791993, class_Groups_Olinordered__ab__group__add(_791995)], (19433 ^ _775212) ^ [_1106447, _1106449, _1106451, _1106453] : [class_Rings_Odivision__ring(_1106447), -(_1106449 = c_Groups_Ozero__class_Ozero(_1106447)), 19440 ^ _775212 : [(19447 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106447), _1106451), _1106449) = _1106453, -(_1106451 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106447), _1106453), _1106449))], (19441 ^ _775212) ^ [] : [_1106451 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106447), _1106453), _1106449), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106447), _1106451), _1106449) = _1106453)]]], (48236 ^ _775212) ^ [_1739633, _1739635, _1739637, _1739639] : [-(hAPP(c_List_Ofilter(_1739633, _1739635), hAPP(c_List_Ofilter(_1739633, _1739637), _1739639)) = hAPP(c_List_Ofilter(_1739633, hAPP(hAPP(c_COMBS(_1739633, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1739633), c_fconj), _1739637)), _1739635)), _1739639))], (28546 ^ _775212) ^ [_1281698, _1281700, _1281702, _1281704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281698, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1281698, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28547 ^ [_1281698, _1281700, _1281702, _1281704])), _1281700)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1281698, 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), 28547 ^ [_1281698, _1281700, _1281702, _1281704]), _1281702))), _1281704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281698, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1281698, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1281700)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1281698, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1281704))))], (29248 ^ _775212) ^ [_1295087] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1295087)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1295087)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1295087)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (36369 ^ _775212) ^ [_1450111, _1450113] : [c_Equiv__Relations_Oequivp(_1450111, hAPP(hAPP(c_COMBC(_1450111, tc_fun(tc_prod(_1450111, _1450111), tc_HOL_Obool), tc_fun(_1450111, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450111, tc_fun(tc_fun(tc_prod(_1450111, _1450111), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1450111, _1450111), tc_HOL_Obool), tc_fun(_1450111, tc_HOL_Obool)), _1450111), c_COMBC(_1450111, tc_fun(tc_prod(_1450111, _1450111), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450111, tc_prod(_1450111, _1450111)), tc_fun(_1450111, tc_fun(tc_fun(tc_prod(_1450111, _1450111), tc_HOL_Obool), tc_HOL_Obool)), _1450111), hAPP(c_COMBB(tc_prod(_1450111, _1450111), tc_fun(tc_fun(tc_prod(_1450111, _1450111), tc_HOL_Obool), tc_HOL_Obool), _1450111), c_member(tc_prod(_1450111, _1450111)))), c_Product__Type_OPair(_1450111, _1450111)))), _1450113)), -(c_Equiv__Relations_Oequiv(_1450111, c_Orderings_Otop__class_Otop(tc_fun(_1450111, tc_HOL_Obool)), _1450113))], (52225 ^ _775212) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (9865 ^ _775212) ^ [_934855, _934857, _934859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _934855), _934857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _934859), _934855)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _934859), _934857))))], (46041 ^ _775212) ^ [_1690598, _1690600, _1690602, _1690604] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690598), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690600)), _1690602)))), -(hAPP(hAPP(c_List_Onth(_1690600), hAPP(hAPP(c_List_Oappend(_1690600), _1690602), _1690604)), _1690598) = hAPP(hAPP(c_List_Onth(_1690600), _1690604), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1690598), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690600)), _1690602))))], (9955 ^ _775212) ^ [_936468, _936470, _936472, _936474, _936476, _936478] : [class_Rings_Olinordered__semiring__1__strict(_936468), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936468), _936470), _936472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936468), _936474), _936472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936468), c_Groups_Ozero__class_Ozero(_936468)), _936476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936468), c_Groups_Ozero__class_Ozero(_936468)), _936478)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936468), _936476), _936478) = c_Groups_Oone__class_Oone(_936468), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936468), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936468), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936468), _936476), _936470)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936468), _936478), _936474))), _936472)))], (45188 ^ _775212) ^ [_1669924, _1669926, _1669928] : [hAPP(hAPP(c_List_Olist_OCons(_1669924), _1669926), _1669928) = c_List_Olist_ONil(_1669924)], (42195 ^ _775212) ^ [_1591036, _1591038, _1591040, _1591042, _1591044] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591036, tc_fun(_1591038, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1591036, tc_HOL_Obool)), _1591040), _1591042)), _1591044) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1591038, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591036, tc_fun(_1591038, tc_HOL_Obool)), _1591040), _1591044)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1591036, tc_fun(_1591038, tc_HOL_Obool)), _1591042), _1591044)))], (51653 ^ _775212) ^ [_1813639, _1813641] : [-(c_Relation_Oantisym(_1813639, c_Relation_OId__on(_1813639, _1813641)))], (43029 ^ _775212) ^ [_1614091, _1614093] : [-(c_Relation_Ototal__on(_1614091, c_Orderings_Obot__class_Obot(tc_fun(_1614091, tc_HOL_Obool)), _1614093))], (29208 ^ _775212) ^ [_1294307, _1294309] : [class_Orderings_Oorder(_1294307), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1294307, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1294307), _1294309), c_Orderings_Obot__class_Obot(tc_fun(_1294307, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1294307), _1294309)) = hAPP(hAPP(c_Set_Oinsert(_1294307), _1294309), c_Orderings_Obot__class_Obot(tc_fun(_1294307, tc_HOL_Obool))))], (40063 ^ _775212) ^ [_1543150, _1543152, _1543154, _1543156] : [40064 ^ _775212 : [(40065 ^ _775212) ^ [_1543204] : [hBOOL(hAPP(hAPP(_1543154, _1543156), _1543204))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1543150, _1543152, _1543154), _1543156)))], (15882 ^ _775212) ^ [_1044204, _1044206, _1044208] : [class_Fields_Olinordered__field(_1044204), 15888 ^ _775212 : [(15891 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044204), _1044206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044204), _1044208), 15887 ^ [_1044204, _1044206, _1044208])))], (15889 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044204), c_Groups_Ozero__class_Ozero(_1044204)), 15887 ^ [_1044204, _1044206, _1044208])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044204), _1044206), _1044208)))], (11724 ^ _775212) ^ [_967635, _967637] : [11725 ^ _775212 : [(11728 ^ _775212) ^ [] : [_967635 = hAPP(c_Nat_OSuc, _967637)], (11726 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967635), _967637))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967635), hAPP(c_Nat_OSuc, _967637))))], (25440 ^ _775212) ^ [_1218065, _1218067, _1218069, _1218071] : [class_Orderings_Oorder(_1218065), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1218065, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1218067), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218065), hAPP(_1218067, _1218069)), hAPP(_1218067, _1218071)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218069), _1218071)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218071), _1218069)))], (41827 ^ _775212) ^ [_1582351, _1582353, _1582355] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582351, _1582351)), hAPP(hAPP(c_Product__Type_OPair(_1582351, _1582351), _1582353), _1582353)), c_Transitive__Closure_Ortrancl(_1582351, _1582355))))], (50397 ^ _775212) ^ [_1785576, _1785578, _1785580, _1785582] : [50398 ^ _775212 : [(50401 ^ _775212) ^ [] : [c_List_Olist__ex(_1785576, _1785578, _1785582)], (50399 ^ _775212) ^ [] : [hBOOL(hAPP(_1785578, _1785580))]], -(c_List_Olist__ex(_1785576, _1785578, hAPP(hAPP(c_List_Olist_OCons(_1785576), _1785580), _1785582)))], (7360 ^ _775212) ^ [_892087, _892089, _892091, _892093, _892095, _892097] : [-(c_Com_Ocom_OLocal(_892087, _892089, _892091) = c_Com_Ocom_OLocal(_892093, _892095, _892097)), _892087 = _892093, _892089 = _892095, _892091 = _892097], (28048 ^ _775212) ^ [_1271949] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1271949)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1271949)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1271949)))], (9775 ^ _775212) ^ [_933258, _933260, _933262] : [_933260 = _933262, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _933258)), _933260) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _933258)), _933262))], (47734 ^ _775212) ^ [_1727625, _1727627, _1727629, _1727631, _1727633, _1727635] : [c_List_Olist__all2(_1727625, _1727627, _1727629, _1727631, _1727633), -(c_List_Olist__all2(_1727625, _1727627, _1727629, hAPP(hAPP(c_List_Otake(_1727625), _1727635), _1727631), hAPP(hAPP(c_List_Otake(_1727627), _1727635), _1727633)))], (52359 ^ _775212) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (41841 ^ _775212) ^ [_1582681, _1582683, _1582685, _1582687, _1582689] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582681, _1582681)), hAPP(hAPP(c_Product__Type_OPair(_1582681, _1582681), _1582683), _1582685)), _1582687)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1582681, _1582681)), hAPP(hAPP(c_Product__Type_OPair(_1582681, _1582681), _1582685), _1582689)), c_Transitive__Closure_Ortrancl(_1582681, _1582687))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582681, _1582681)), hAPP(hAPP(c_Product__Type_OPair(_1582681, _1582681), _1582683), _1582689)), c_Transitive__Closure_Ortrancl(_1582681, _1582687))))], (42155 ^ _775212) ^ [_1590014, _1590016, _1590018, _1590020, _1590022, _1590024, _1590026, _1590028] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590014, tc_fun(_1590016, tc_fun(_1590018, tc_HOL_Obool))), _1590020), _1590022), _1590024), _1590026)), hBOOL(hAPP(hAPP(c_member(_1590014), _1590028), _1590020)), -(hBOOL(hAPP(hAPP(hAPP(_1590022, _1590028), _1590024), _1590026)))], (24030 ^ _775212) ^ [_1192748, _1192750] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192748), _1192750))), 24031 ^ _775212 : [(24032 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192748), _1192750)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192750), _1192748)))], (24038 ^ _775212) ^ [] : [_1192748 = _1192750]]], (39791 ^ _775212) ^ [_1536734, _1536736, _1536738] : [c_Wellfounded_Owf(_1536734, _1536736), hBOOL(hAPP(hAPP(c_member(tc_prod(_1536734, _1536734)), hAPP(hAPP(c_Product__Type_OPair(_1536734, _1536734), _1536738), _1536738)), _1536736))], (3526 ^ _775212) ^ [_828507, _828509] : [_828509 = _828507, -(c_New__Random__Sequence_Opos__single(_828509) = c_New__Random__Sequence_Opos__single(_828507))], (33431 ^ _775212) ^ [] : [-(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)))], (8107 ^ _775212) ^ [_905821, _905823, _905825, _905827] : [class_Rings_Ocomm__semiring__1(_905821), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905821), _905823), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905821), _905825), _905827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905821), _905823), _905825)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905821), _905823), _905827)))], (2730 ^ _775212) ^ [_815511, _815513] : [_815513 = _815511, -(c_Code__Numeral_OSuc__code__numeral(_815513) = c_Code__Numeral_OSuc__code__numeral(_815511))], (51281 ^ _775212) ^ [_1804711, _1804713, _1804715] : [c_List_Olist__ex(_1804711, _1804715, _1804713), 51285 ^ _775212 : [(51288 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1804715, 51284 ^ [_1804711, _1804713, _1804715])))], (51286 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804711), 51284 ^ [_1804711, _1804713, _1804715]), hAPP(c_List_Oset(_1804711), _1804713))))]]], (52179 ^ _775212) ^ [_1823215, _1823217] : [class_Orderings_Otop(_1823215), -(class_Orderings_Otop(tc_fun(_1823217, _1823215)))], (21853 ^ _775212) ^ [_1149979, _1149981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1149979), 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)), _1149981)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1149979, _1149981) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1149979, _1149981)))], (30112 ^ _775212) ^ [_1314917, _1314919, _1314921] : [class_Orderings_Oord(_1314917), 30115 ^ _775212 : [(30122 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314917), _1314919), _1314921)), -(hBOOL(hAPP(hAPP(c_member(_1314917), _1314919), hAPP(c_SetInterval_Oord__class_OlessThan(_1314917), _1314921))))], (30116 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1314917), _1314919), hAPP(c_SetInterval_Oord__class_OlessThan(_1314917), _1314921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314917), _1314919), _1314921)))]]], (33801 ^ _775212) ^ [_1391946, _1391948, _1391950, _1391952, _1391954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1391946, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1391948, _1391946, _1391950), _1391952)), _1391954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1391946, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1391948, tc_HOL_Obool), tc_fun(_1391946, tc_HOL_Obool), c_Set_Oimage(_1391948, _1391946, _1391950)), hAPP(c_Set_OPow(_1391948), _1391952))), hAPP(c_Set_OPow(_1391946), _1391954))))], (28235 ^ _775212) ^ [_1275870, _1275872, _1275874] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1275870), _1275872)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1275870), hAPP(hAPP(c_Set_Oinsert(_1275870), _1275874), _1275872))))], (6352 ^ _775212) ^ [_875601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _875601)), -(_875601 = hAPP(c_Nat_OSuc, 6355 ^ [_875601]))], (13262 ^ _775212) ^ [_995174, _995176] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _995174), _995176)), _995174)))], (25004 ^ _775212) ^ [_1210091, _1210093, _1210095, _1210097] : [class_Divides_Osemiring__div(_1210091), -(_1210093 = c_Groups_Ozero__class_Ozero(_1210091)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1210091), _1210093), _1210095)), 25015 ^ _775212 : [(25022 ^ _775212) ^ [] : [_1210095 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210091), _1210097), _1210093), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210091), _1210095), _1210093) = _1210097)], (25016 ^ _775212) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210091), _1210095), _1210093) = _1210097, -(_1210095 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210091), _1210097), _1210093))]]], (27654 ^ _775212) ^ [_1263246, _1263248] : [class_Orderings_Olinorder(_1263246), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1263246, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1263246), _1263248)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1263246), _1263248))], (22728 ^ _775212) ^ [_1167688, _1167690, _1167692, _1167694, _1167696, _1167698] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1167688, _1167690, _1167692), _1167694), hAPP(hAPP(c_Product__Type_OPair(_1167688, _1167690), _1167696), _1167698)) = hAPP(hAPP(_1167694, _1167696), _1167698))], (27602 ^ _775212) ^ [_1262328, _1262330, _1262332, _1262334, _1262336] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1262328, tc_fun(_1262330, tc_HOL_Obool)), _1262332), _1262334), _1262336))), 27603 ^ _775212 : [(27604 ^ _775212) ^ [_1262400] : [hBOOL(hAPP(hAPP(c_member(_1262328), _1262400), _1262332)), hBOOL(hAPP(hAPP(_1262334, _1262400), _1262336))]]], (39029 ^ _775212) ^ [_1509616, _1509618] : [-(hAPP(c_Set_OCollect(_1509616), hAPP(hAPP(c_COMBC(_1509616, _1509616, tc_HOL_Obool), c_fequal), _1509618)) = hAPP(hAPP(c_Set_Oinsert(_1509616), _1509618), c_Orderings_Obot__class_Obot(tc_fun(_1509616, tc_HOL_Obool))))], (24378 ^ _775212) ^ [_1198425, _1198427, _1198429, _1198431] : [class_Rings_Ocomm__semiring__1(_1198425), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1198425), _1198427), _1198429)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1198425), hAPP(hAPP(c_Power_Opower__class_Opower(_1198425), _1198427), _1198431)), hAPP(hAPP(c_Power_Opower__class_Opower(_1198425), _1198429), _1198431))))], (10129 ^ _775212) ^ [_939704, _939706] : [class_Groups_Olinordered__ab__group__add(_939704), 10132 ^ _775212 : [(10139 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939704), _939706), c_Groups_Ozero__class_Ozero(_939704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939704), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939704), _939706), _939706)), c_Groups_Ozero__class_Ozero(_939704))))], (10133 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939704), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939704), _939706), _939706)), c_Groups_Ozero__class_Ozero(_939704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939704), _939706), c_Groups_Ozero__class_Ozero(_939704))))]]], (41448 ^ _775212) ^ [_1574271, _1574273, _1574275] : [class_Orderings_Olinorder(_1574271), hBOOL(hAPP(c_Finite__Set_Ofinite(_1574271), _1574273)), -(c_Big__Operators_Olattice_OInf__fin(_1574271, c_Orderings_Oord__class_Omin(_1574271), hAPP(hAPP(c_Set_Oinsert(_1574271), _1574275), _1574273)) = hAPP(hAPP(c_Finite__Set_Ofold(_1574271, _1574271, c_Orderings_Oord__class_Omin(_1574271)), _1574275), _1574273))], (40431 ^ _775212) ^ [_1551817, _1551819] : [-(c_Hilbert__Choice_OEps(_1551817, hAPP(hAPP(c_COMBC(_1551817, _1551817, tc_HOL_Obool), c_fequal), _1551819)) = _1551819)], (50326 ^ _775212) ^ [_1784335, _1784337, _1784339] : [-(c_List_Olist__ex(_1784335, _1784337, _1784339)), 50327 ^ _775212 : [(50328 ^ _775212) ^ [_1784400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1784400), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784335)), _1784339))), hBOOL(hAPP(_1784337, hAPP(hAPP(c_List_Onth(_1784335), _1784339), _1784400)))]]], (48819 ^ _775212) ^ [_1751834, _1751836, _1751838, _1751840, _1751842] : [class_Orderings_Olinorder(_1751834), c_List_Olinorder__class_Osorted(_1751834, hAPP(hAPP(c_List_Omap(_1751836, _1751834), _1751838), _1751840)), -(c_List_Olinorder__class_Osorted(_1751834, hAPP(hAPP(c_List_Omap(_1751836, _1751834), _1751838), c_List_Oremove1(_1751836, _1751842, _1751840))))], (2690 ^ _775212) ^ [_814891, _814893] : [_814893 = _814891, -(c_DSequence_Osingle(_814893) = c_DSequence_Osingle(_814891))], (30825 ^ _775212) ^ [_1331862, _1331864] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1331862), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1331864))), 30828 ^ _775212 : [(30831 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1331864), _1331862))], (30829 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1331862), _1331864)))]]], (15907 ^ _775212) ^ [_1044722, _1044724, _1044726] : [class_Int_Onumber(_1044722), 15910 ^ _775212 : [(15917 ^ _775212) ^ [] : [_1044726 = hAPP(c_Int_Onumber__class_Onumber__of(_1044722), _1044724), -(hAPP(c_Int_Onumber__class_Onumber__of(_1044722), _1044724) = _1044726)], (15911 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1044722), _1044724) = _1044726, -(_1044726 = hAPP(c_Int_Onumber__class_Onumber__of(_1044722), _1044724))]]], (52291 ^ _775212) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (27858 ^ _775212) ^ [_1268568] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1268568))))], (41219 ^ _775212) ^ [_1569713, _1569715, _1569717, _1569719] : [-(hAPP(c_Finite__Set_Ofold__image(_1569713, _1569715, _1569717), _1569719) = c_Finite__Set_Ofold(_1569715, _1569713, hAPP(hAPP(c_COMBB(_1569713, tc_fun(_1569713, _1569713), _1569715), _1569717), _1569719)))], (21335 ^ _775212) ^ [_1140627, _1140629, _1140631] : [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), _1140627), _1140629))), -(hBOOL(hAPP(hAPP(_1140631, _1140627), _1140629))), 21342 ^ _775212 : [(21345 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(_1140631, 21340 ^ [_1140627, _1140629, _1140631]), 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)))), 21341 ^ [_1140627, _1140629, _1140631])))), -(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), 21340 ^ [_1140627, _1140629, _1140631]), 21341 ^ [_1140627, _1140629, _1140631])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 21341 ^ [_1140627, _1140629, _1140631]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21355 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1140631, 21340 ^ [_1140627, _1140629, _1140631]), 21341 ^ [_1140627, _1140629, _1140631]))], (21343 ^ _775212) ^ [] : [-(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), 21340 ^ [_1140627, _1140629, _1140631]), 21341 ^ [_1140627, _1140629, _1140631]))))]]], (37880 ^ _775212) ^ [_1483532, _1483534, _1483536, _1483538] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1483532, _1483534)), hAPP(hAPP(c_Product__Type_OSigma(_1483532, _1483534), _1483536), hAPP(c_COMBK(tc_fun(_1483534, tc_HOL_Obool), _1483532), _1483538))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1483532), _1483536)), hAPP(c_Finite__Set_Ocard(_1483534), _1483538)))], (38936 ^ _775212) ^ [_1507578, _1507580] : [c_Orderings_Obot__class_Obot(tc_fun(_1507578, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1507578), _1507580), 38939 ^ _775212 : [(38940 ^ _775212) ^ [_1507663] : [hBOOL(hAPP(_1507580, _1507663))]]], (32844 ^ _775212) ^ [_1370968, _1370970, _1370972, _1370974, _1370976, _1370978] : [-(_1370968 = _1370970), -(hAPP(c_Fun_Ofun__upd(_1370972, _1370974, _1370976, _1370970, _1370978), _1370968) = hAPP(_1370976, _1370968))], (38895 ^ _775212) ^ [_1506670, _1506672, _1506674, _1506676] : [-(hAPP(c_Set_Ovimage(_1506670, _1506672, _1506674), hAPP(c_Set_OCollect(_1506672), _1506676)) = hAPP(c_Set_OCollect(_1506670), hAPP(hAPP(c_COMBB(_1506672, tc_HOL_Obool, _1506670), _1506676), _1506674)))], (28652 ^ _775212) ^ [_1284094, _1284096, _1284098] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284094, tc_HOL_Obool)), _1284096), _1284098) = c_Orderings_Obot__class_Obot(tc_fun(_1284094, tc_HOL_Obool)), 28655 ^ _775212 : [(28658 ^ _775212) ^ [] : [-(_1284098 = c_Orderings_Obot__class_Obot(tc_fun(_1284094, tc_HOL_Obool)))], (28656 ^ _775212) ^ [] : [-(_1284096 = c_Orderings_Obot__class_Obot(tc_fun(_1284094, tc_HOL_Obool)))]]], (5829 ^ _775212) ^ [_867371] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _867371)], (20921 ^ _775212) ^ [_1133065, _1133067, _1133069, _1133071] : [class_Fields_Olinordered__field__inverse__zero(_1133065), class_Int_Onumber(_1133065), 20928 ^ _775212 : [(20929 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133065), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133065), _1133067), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069))), _1133071)), 20932 ^ _775212 : [(20939 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133065), c_Groups_Ozero__class_Ozero(_1133065)), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069)))), 20942 ^ _775212 : [(20949 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133065), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069)), c_Groups_Ozero__class_Ozero(_1133065)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133065), c_Groups_Ozero__class_Ozero(_1133065)), _1133071)))], (20943 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133065), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069)), c_Groups_Ozero__class_Ozero(_1133065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133065), _1133071), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069))), _1133067)))]]], (20933 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133065), c_Groups_Ozero__class_Ozero(_1133065)), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133065), _1133067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133065), _1133071), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069)))))]]], (20955 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133065), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133065), _1133067), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069))), _1133071))), 20958 ^ _775212 : [(20961 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133065), _1133067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133065), _1133071), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069))))], (20959 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133065), c_Groups_Ozero__class_Ozero(_1133065)), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069))))]], 20962 ^ _775212 : [(20965 ^ _775212) ^ [] : [20966 ^ _775212 : [(20969 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133065), _1133071), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069))), _1133067))], (20967 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133065), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069)), c_Groups_Ozero__class_Ozero(_1133065))))]], 20970 ^ _775212 : [(20973 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133065), c_Groups_Ozero__class_Ozero(_1133065)), _1133071))], (20971 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133065), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069)), c_Groups_Ozero__class_Ozero(_1133065)))]]], (20963 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133065), c_Groups_Ozero__class_Ozero(_1133065)), hAPP(c_Int_Onumber__class_Onumber__of(_1133065), _1133069)))]]]]], (36881 ^ _775212) ^ [_1460392, _1460394, _1460396, _1460398, _1460400, _1460402] : [c_Fun_Oinj__on(_1460392, _1460394, _1460396, _1460398), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1460394, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1460392, _1460394, _1460396), _1460398)), _1460400)), c_Fun_Oinj__on(_1460394, _1460392, _1460402, _1460400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1460392, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1460394, _1460392, _1460402), _1460400)), _1460398)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460392), _1460398)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460394), _1460400)), -(hAPP(c_Finite__Set_Ocard(_1460392), _1460398) = hAPP(c_Finite__Set_Ocard(_1460394), _1460400))], (24874 ^ _775212) ^ [_1207350, _1207352, _1207354] : [class_Rings_Odvd(_1207350), class_Rings_Osemiring__0(_1207350), 24881 ^ _775212 : [(24891 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1207352, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207350), _1207354), 24898 ^ [_1207350, _1207352, _1207354])))), 24892 ^ _775212 : [(24893 ^ _775212) ^ [_1207679] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207350), _1207354), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207350), _1207679), c_Groups_Ozero__class_Ozero(_1207350)))), hBOOL(hAPP(_1207352, _1207679))]]], (24882 ^ _775212) ^ [] : [24883 ^ _775212 : [(24884 ^ _775212) ^ [_1207542] : [hBOOL(hAPP(_1207352, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207350), _1207354), _1207542)))]], 24886 ^ _775212 : [(24889 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1207352, 24885 ^ [_1207350, _1207352, _1207354])))], (24887 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207350), _1207354), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207350), 24885 ^ [_1207350, _1207352, _1207354]), c_Groups_Ozero__class_Ozero(_1207350)))))]]]]], (21899 ^ _775212) ^ [_1150750, _1150752, _1150754] : [-(hAPP(hAPP(c_Product__Type_OPair(_1150750, _1150752), hAPP(c_Product__Type_Ofst(_1150750, _1150752), _1150754)), hAPP(c_Product__Type_Osnd(_1150750, _1150752), _1150754)) = _1150754)], (37517 ^ _775212) ^ [_1474302, _1474304, _1474306, _1474308] : [-(hBOOL(hAPP(hAPP(c_member(_1474302), _1474304), _1474306))), -(hAPP(c_Set_Ovimage(_1474308, _1474302, hAPP(c_COMBK(_1474302, _1474308), _1474304)), _1474306) = c_Orderings_Obot__class_Obot(tc_fun(_1474308, tc_HOL_Obool)))], (52509 ^ _775212) ^ [_1826376, _1826378] : [-(class_Finite__Set_Ofinite(tc_sum(_1826376, _1826378))), class_Finite__Set_Ofinite(_1826376), class_Finite__Set_Ofinite(_1826378)], (42495 ^ _775212) ^ [_1599995, _1599997, _1599999, _1600001, _1600003] : [-(_1599995 = c_Orderings_Obot__class_Obot(tc_fun(_1599997, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599999, tc_HOL_Obool)), _1600001), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599997, tc_fun(_1599999, tc_HOL_Obool)), _1599995), _1600003)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599997, tc_fun(_1599999, tc_HOL_Obool)), _1599995), hAPP(hAPP(c_COMBB(tc_fun(_1599999, tc_HOL_Obool), tc_fun(_1599999, tc_HOL_Obool), _1599997), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599999, tc_HOL_Obool)), _1600001)), _1600003)))], (9619 ^ _775212) ^ [_930526, _930528] : [class_Rings_Ocomm__semiring__1(_930526), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930526), c_Groups_Oone__class_Oone(_930526)), _930528) = _930528)], (40401 ^ _775212) ^ [_1551312, _1551314, _1551316] : [40402 ^ _775212 : [(40403 ^ _775212) ^ [_1551366] : [hBOOL(hAPP(_1551312, _1551366))]], _1551314 = c_Hilbert__Choice_OEps(_1551316, _1551312), -(hBOOL(hAPP(_1551312, _1551314)))], (17933 ^ _775212) ^ [] : [-(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)))))], (45238 ^ _775212) ^ [_1670865, _1670867, _1670869, _1670871, _1670873, _1670875, _1670877, _1670879] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1670865, _1670867), _1670869), _1670871), hAPP(hAPP(c_List_Ozip(_1670865, _1670867), hAPP(hAPP(c_List_Omap(_1670873, _1670865), _1670875), _1670877)), _1670879)) = hAPP(hAPP(c_List_Omap(tc_prod(_1670873, _1670867), _1670869), hAPP(c_Product__Type_Oprod_Oprod__case(_1670873, _1670867, _1670869), hAPP(hAPP(c_COMBB(tc_fun(_1670867, tc_prod(_1670865, _1670867)), tc_fun(_1670867, _1670869), _1670873), hAPP(c_COMBB(tc_prod(_1670865, _1670867), _1670869, _1670867), _1670871)), hAPP(hAPP(c_COMBB(_1670865, tc_fun(_1670867, tc_prod(_1670865, _1670867)), _1670873), c_Product__Type_OPair(_1670865, _1670867)), _1670875)))), hAPP(hAPP(c_List_Ozip(_1670873, _1670867), _1670877), _1670879)))], (44210 ^ _775212) ^ [_1643254, _1643256, _1643258, _1643260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1643254), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1643256), _1643258))), -(hAPP(c_Random_Opick(_1643256, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1643256)), _1643258), _1643260)), _1643254) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1643256), _1643258))], (2696 ^ _775212) ^ [_814976, _814978, _814980, _814982, _814984, _814986, _814988, _814990] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_814990, _814986, _814982, _814978) = c_New__Random__Sequence_Opos__not__random__dseq(_814988, _814984, _814980, _814976)), _814990 = _814988, _814986 = _814984, _814982 = _814980, _814978 = _814976], (40456 ^ _775212) ^ [_1552296, _1552298, _1552300, _1552302, _1552304, _1552306, _1552308, _1552310, _1552312] : [hAPP(c_Fun_Ocomp(_1552296, _1552298, _1552300, _1552302), _1552304) = hAPP(c_Fun_Ocomp(_1552306, _1552298, _1552300, _1552308), _1552310), -(hAPP(_1552302, hAPP(_1552304, _1552312)) = hAPP(_1552308, hAPP(_1552310, _1552312)))], (44750 ^ _775212) ^ [_1658977, _1658979, _1658981] : [-(hAPP(c_List_Oset(_1658977), hAPP(hAPP(c_List_Olist_OCons(_1658977), _1658979), _1658981)) = hAPP(hAPP(c_Set_Oinsert(_1658977), _1658979), hAPP(c_List_Oset(_1658977), _1658981)))], (36996 ^ _775212) ^ [_1462991, _1462993, _1462995, _1462997] : [c_Fun_Oinj__on(_1462991, tc_fun(tc_fun(_1462991, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1462991, tc_fun(tc_prod(_1462991, _1462991), tc_HOL_Obool), tc_fun(tc_fun(_1462991, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1462991, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1462991, _1462991), tc_HOL_Obool), tc_fun(tc_fun(_1462991, tc_HOL_Obool), tc_HOL_Obool)), _1462991), c_Equiv__Relations_Oquotient(_1462991)), hAPP(hAPP(c_COMBC(_1462991, tc_fun(_1462991, tc_HOL_Obool), tc_fun(_1462991, tc_HOL_Obool)), c_Set_Oinsert(_1462991)), c_Orderings_Obot__class_Obot(tc_fun(_1462991, tc_HOL_Obool))))), _1462993), _1462995), hBOOL(hAPP(hAPP(c_member(_1462991), _1462997), _1462995)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462991), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1462991, tc_HOL_Obool)), _1462995), hAPP(hAPP(c_Set_Oinsert(_1462991), _1462997), c_Orderings_Obot__class_Obot(tc_fun(_1462991, tc_HOL_Obool))))), _1462993) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1462991, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462991), _1462995), _1462993)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462991), hAPP(hAPP(c_Set_Oinsert(_1462991), _1462997), c_Orderings_Obot__class_Obot(tc_fun(_1462991, tc_HOL_Obool)))), _1462993)))], (22396 ^ _775212) ^ [_1161630, _1161632] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161630)), hAPP(c_Nat_OSuc, _1161632)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1161630))), 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)), _1161632)))))], (42609 ^ _775212) ^ [_1603085, _1603087, _1603089, _1603091, _1603093] : [_1603085 = c_Orderings_Obot__class_Obot(tc_fun(_1603087, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1603089, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603087, tc_fun(_1603089, tc_HOL_Obool)), _1603085), _1603091)), _1603093) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1603089, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1603089, tc_HOL_Obool))), _1603093))], (44851 ^ _775212) ^ [_1661305, _1661307, _1661309, _1661311, _1661313, _1661315, _1661317] : [hAPP(hAPP(c_List_Omap(_1661305, _1661307), _1661309), _1661311) = hAPP(hAPP(c_List_Omap(_1661313, _1661307), _1661315), _1661317), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661305)), _1661311) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661313)), _1661317))], (5186 ^ _775212) ^ [_854319, _854321] : [_854321 = _854319, -(c_Set_OBex(_854321) = c_Set_OBex(_854319))], (42832 ^ _775212) ^ [_1609242, _1609244] : [-(c_Relation_Orefl__on(_1609242, c_Orderings_Otop__class_Otop(tc_fun(_1609242, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1609242, _1609242), tc_HOL_Obool)), _1609244), c_Relation_OId(_1609242))))], (49742 ^ _775212) ^ [_1771203, _1771205, _1771207, _1771209] : [-(hBOOL(hAPP(_1771203, _1771205))), -(hAPP(c_List_OremoveAll(_1771207, _1771205), hAPP(c_List_Ofilter(_1771207, _1771203), _1771209)) = hAPP(c_List_Ofilter(_1771207, _1771203), _1771209))], (47977 ^ _775212) ^ [_1733327, _1733329] : [-(hAPP(c_List_Oset(_1733327), c_List_Oremdups(_1733327, _1733329)) = hAPP(c_List_Oset(_1733327), _1733329))], (39460 ^ _775212) ^ [_1526435, _1526437] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526435), _1526437)), -(_1526437 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1526435, 39464 ^ [_1526435, _1526437]), 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)), 39463 ^ [_1526435, _1526437]))))], (50113 ^ _775212) ^ [_1779521, _1779523, _1779525, _1779527] : [50115 ^ _775212 : [(50118 ^ _775212) ^ [] : [hBOOL(hAPP(_1779525, 50114 ^ [_1779521, _1779523, _1779525, _1779527]))], (50116 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779521), 50114 ^ [_1779521, _1779523, _1779525, _1779527]), hAPP(c_List_Oset(_1779521), _1779523))))]], -(c_List_OtakeWhile(_1779521, _1779525, hAPP(hAPP(c_List_Oappend(_1779521), _1779523), _1779527)) = hAPP(hAPP(c_List_Oappend(_1779521), _1779523), c_List_OtakeWhile(_1779521, _1779525, _1779527)))], (50715 ^ _775212) ^ [_1792257, _1792259, _1792261] : [_1792259 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1792257) = c_List_Oreplicate(_1792257, _1792259, _1792261))], (42431 ^ _775212) ^ [_1597738, _1597740, _1597742, _1597744, _1597746] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597738, tc_fun(_1597740, tc_HOL_Obool)), _1597742), hAPP(hAPP(c_COMBC(_1597738, tc_fun(_1597740, tc_HOL_Obool), tc_fun(_1597740, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1597740, tc_HOL_Obool), tc_fun(tc_fun(_1597740, tc_HOL_Obool), tc_fun(_1597740, tc_HOL_Obool)), _1597738), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597740, tc_HOL_Obool))), _1597744)), _1597746)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597740, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597738, tc_fun(_1597740, tc_HOL_Obool)), _1597742), _1597744)), _1597746))], (17531 ^ _775212) ^ [_1072849, _1072851] : [class_Int_Onumber__ring(_1072849), class_Rings_Olinordered__idom(_1072849), 17538 ^ _775212 : [(17545 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1072851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072849), c_Groups_Ozero__class_Ozero(_1072849)), hAPP(c_Int_Onumber__class_Onumber__of(_1072849), _1072851))))], (17539 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072849), c_Groups_Ozero__class_Ozero(_1072849)), hAPP(c_Int_Onumber__class_Onumber__of(_1072849), _1072851))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1072851)))]]], (49849 ^ _775212) ^ [_1773368, _1773370, _1773372, _1773374, _1773376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1773368, _1773370)), hAPP(_1773368, _1773372))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773374, _1773374)), hAPP(hAPP(c_Product__Type_OPair(_1773374, _1773374), _1773370), _1773372)), c_List_Omeasures(_1773374, _1773376))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773374, _1773374)), hAPP(hAPP(c_Product__Type_OPair(_1773374, _1773374), _1773370), _1773372)), c_List_Omeasures(_1773374, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1773374, tc_Nat_Onat)), _1773368), _1773376)))))], (41002 ^ _775212) ^ [_1564985, _1564987, _1564989] : [41004 ^ _775212 : [(41007 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1564985), 41003 ^ [_1564985, _1564987, _1564989]), c_Wellfounded_Oacc(_1564985, _1564989)))], (41005 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564985, _1564985)), hAPP(hAPP(c_Product__Type_OPair(_1564985, _1564985), 41003 ^ [_1564985, _1564987, _1564989]), _1564987)), _1564989)))]], -(hBOOL(hAPP(hAPP(c_member(_1564985), _1564987), c_Wellfounded_Oacc(_1564985, _1564989))))], (17387 ^ _775212) ^ [_1070566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070566), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1070566)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16269 ^ _775212) ^ [_1051110, _1051112, _1051114] : [class_Int_Onumber(_1051110), class_Orderings_Olinorder(_1051110), 16276 ^ _775212 : [(16283 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051110), hAPP(c_Int_Onumber__class_Onumber__of(_1051110), _1051114)), hAPP(c_Int_Onumber__class_Onumber__of(_1051110), _1051112)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051110), hAPP(c_Int_Onumber__class_Onumber__of(_1051110), _1051112)), hAPP(c_Int_Onumber__class_Onumber__of(_1051110), _1051114))))], (16277 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051110), hAPP(c_Int_Onumber__class_Onumber__of(_1051110), _1051112)), hAPP(c_Int_Onumber__class_Onumber__of(_1051110), _1051114))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051110), hAPP(c_Int_Onumber__class_Onumber__of(_1051110), _1051114)), hAPP(c_Int_Onumber__class_Onumber__of(_1051110), _1051112)))]]], (18547 ^ _775212) ^ [_1090280] : [class_Rings_Osemiring__1(_1090280), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1090280), c_Groups_Oone__class_Oone(_1090280)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1090280))], (43447 ^ _775212) ^ [_1623966, _1623968] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623966, tc_HOL_Obool), hAPP(c_Set_OPow(_1623966), _1623968)) = _1623968)], (52157 ^ _775212) ^ [_1822928, _1822930] : [-(class_Finite__Set_Ofinite(tc_fun(_1822928, _1822930))), class_Finite__Set_Ofinite(_1822928), class_Finite__Set_Ofinite(_1822930)], (29949 ^ _775212) ^ [_1309037, _1309039, _1309041, _1309043, _1309045, _1309047] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309037, tc_fun(_1309039, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1309037, tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_fun(_1309039, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1309039, tc_fun(tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_fun(_1309039, tc_HOL_Obool)), _1309037), c_COMBC(_1309039, tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1309039, tc_prod(_1309037, _1309039)), tc_fun(_1309039, tc_fun(tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_HOL_Obool)), _1309037), hAPP(c_COMBB(tc_prod(_1309037, _1309039), tc_fun(tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_HOL_Obool), _1309039), c_member(tc_prod(_1309037, _1309039)))), c_Product__Type_OPair(_1309037, _1309039)))), _1309041)), hAPP(hAPP(c_COMBC(_1309037, tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_fun(_1309039, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1309039, tc_fun(tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_fun(_1309039, tc_HOL_Obool)), _1309037), c_COMBC(_1309039, tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1309039, tc_prod(_1309037, _1309039)), tc_fun(_1309039, tc_fun(tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_HOL_Obool)), _1309037), hAPP(c_COMBB(tc_prod(_1309037, _1309039), tc_fun(tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool), tc_HOL_Obool), _1309039), c_member(tc_prod(_1309037, _1309039)))), c_Product__Type_OPair(_1309037, _1309039)))), _1309043)), _1309045), _1309047)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1309037, _1309039)), hAPP(hAPP(c_Product__Type_OPair(_1309037, _1309039), _1309045), _1309047)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1309037, _1309039), tc_HOL_Obool)), _1309041), _1309043))))], (14693 ^ _775212) ^ [_1021239, _1021241, _1021243] : [class_Rings_Olinordered__semidom(_1021239), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021239), c_Groups_Ozero__class_Ozero(_1021239)), _1021241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021239), c_Groups_Ozero__class_Ozero(_1021239)), hAPP(hAPP(c_Power_Opower__class_Opower(_1021239), _1021241), _1021243))))], (25575 ^ _775212) ^ [_1220895, _1220897, _1220899] : [class_Groups_Ocomm__monoid__add(_1220895), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220895), _1220897), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220899))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220895), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220895), _1220897), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1220899))), hAPP(_1220897, _1220899)))], (47174 ^ _775212) ^ [_1715684, _1715686] : [-(c_List_Obutlast(_1715684, _1715686) = hAPP(hAPP(c_List_Otake(_1715684), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715684)), _1715686)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1715686))], (29354 ^ _775212) ^ [_1297381, _1297383, _1297385] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1297381), _1297383)), -(hAPP(c_Finite__Set_Ocard(_1297381), hAPP(hAPP(c_Set_Oinsert(_1297381), _1297385), _1297383)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1297381), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1297381, tc_HOL_Obool)), _1297383), hAPP(hAPP(c_Set_Oinsert(_1297381), _1297385), c_Orderings_Obot__class_Obot(tc_fun(_1297381, tc_HOL_Obool)))))))], (2742 ^ _775212) ^ [_815681, _815683, _815685, _815687, _815689, _815691, _815693, _815695] : [-(c_Product__Type_Ocurry(_815695, _815691, _815687, _815683) = c_Product__Type_Ocurry(_815693, _815689, _815685, _815681)), _815695 = _815693, _815691 = _815689, _815687 = _815685, _815683 = _815681], (48009 ^ _775212) ^ [_1733942, _1733944] : [c_List_Oremdups(_1733942, _1733944) = c_List_Olist_ONil(_1733942), -(_1733944 = c_List_Olist_ONil(_1733942))], (52375 ^ _775212) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (30268 ^ _775212) ^ [_1318305, _1318307, _1318309, _1318311, _1318313, _1318315] : [hBOOL(hAPP(hAPP(c_member(_1318305), _1318307), _1318309)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318305, tc_fun(_1318311, tc_HOL_Obool)), _1318309), hAPP(hAPP(c_COMBB(tc_fun(_1318311, tc_HOL_Obool), tc_fun(_1318311, tc_HOL_Obool), _1318305), hAPP(c_Set_Oinsert(_1318311), _1318313)), _1318315)) = hAPP(hAPP(c_Set_Oinsert(_1318311), _1318313), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318305, tc_fun(_1318311, tc_HOL_Obool)), _1318309), _1318315)))], (46867 ^ _775212) ^ [_1709432, _1709434, _1709436] : [class_Lattices_Olattice(_1709432), -(c_Big__Operators_Olattice__class_OInf__fin(_1709432, hAPP(c_List_Oset(_1709432), hAPP(hAPP(c_List_Olist_OCons(_1709432), _1709434), _1709436))) = hAPP(c_List_Ofoldl(_1709432, _1709432, c_Lattices_Osemilattice__inf__class_Oinf(_1709432), _1709434), _1709436))], (20085 ^ _775212) ^ [_1117864, _1117866, _1117868, _1117870] : [class_Fields_Ofield__inverse__zero(_1117864), -(_1117866 = c_Groups_Ozero__class_Ozero(_1117864)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117864), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117864), _1117868), _1117866)), _1117870) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117864), _1117868), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117864), _1117870), _1117866))), _1117866))], (18153 ^ _775212) ^ [_1083500] : [c_Int_OBit0(_1083500) = c_Int_OPls, -(_1083500 = c_Int_OPls)], (45736 ^ _775212) ^ [_1683838, _1683840, _1683842] : [_1683838 = _1683840, -(_1683838 = hAPP(hAPP(c_List_Oappend(_1683842), c_List_Olist_ONil(_1683842)), _1683840))], (34521 ^ _775212) ^ [_1408920, _1408922, _1408924, _1408926] : [class_Lattices_Odistrib__lattice(_1408920), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408920), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408920), _1408922), _1408924)), _1408926) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1408920), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408920), _1408922), _1408926)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1408920), _1408924), _1408926)))], (33608 ^ _775212) ^ [_1387656, _1387658, _1387660, _1387662] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1387656, _1387656)), hAPP(hAPP(c_Product__Type_OPair(_1387656, _1387656), _1387658), _1387660)), c_Relation_OId__on(_1387656, _1387662))), 33611 ^ _775212 : [(33614 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1387656), _1387658), _1387662)))], (33612 ^ _775212) ^ [] : [-(_1387658 = _1387660)]]], (12404 ^ _775212) ^ [_979176, _979178, _979180] : [class_Divides_Osemiring__div(_979176), -(c_Divides_Odiv__class_Omod(_979176, c_Divides_Odiv__class_Omod(_979176, _979178, _979180), _979180) = c_Divides_Odiv__class_Omod(_979176, _979178, _979180))], (43658 ^ _775212) ^ [_1628622, _1628624, _1628626] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1628622, tc_HOL_Obool)), _1628624)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628622), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1628622, tc_HOL_Obool), _1628624))), 43668 ^ _775212 : [(43671 ^ _775212) ^ [] : [hAPP(c_Finite__Set_Ocard(_1628622), 43667 ^ [_1628622, _1628624, _1628626]) = _1628626], (43669 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1628622, tc_HOL_Obool)), 43667 ^ [_1628622, _1628624, _1628626]), _1628624)))]], 43675 ^ _775212 : [(43679 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1628622, tc_HOL_Obool)), 43677 ^ [_1628622, _1628624, _1628626]), _1628624)))], (43681 ^ _775212) ^ [] : [43674 ^ [_1628622, _1628624, _1628626] = 43677 ^ [_1628622, _1628624, _1628626]], (43683 ^ _775212) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628622, tc_HOL_Obool)), 43674 ^ [_1628622, _1628624, _1628626]), 43677 ^ [_1628622, _1628624, _1628626]) = c_Orderings_Obot__class_Obot(tc_fun(_1628622, tc_HOL_Obool))], (43676 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1628622, tc_HOL_Obool)), 43674 ^ [_1628622, _1628624, _1628626]), _1628624)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1628626), hAPP(c_Finite__Set_Ocard(tc_fun(_1628622, tc_HOL_Obool)), _1628624)) = hAPP(c_Finite__Set_Ocard(_1628622), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1628622, tc_HOL_Obool), _1628624)))], (5326 ^ _775212) ^ [_856493, _856495, _856497, _856499] : [-(c_Product__Type_OPair(_856499, _856495) = c_Product__Type_OPair(_856497, _856493)), _856499 = _856497, _856495 = _856493], (38979 ^ _775212) ^ [_1508356, _1508358, _1508360] : [-(hAPP(hAPP(c_Set_Oinsert(_1508356), _1508358), _1508360) = hAPP(c_Set_OCollect(_1508356), hAPP(hAPP(c_COMBS(_1508356, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508356), c_fdisj), hAPP(hAPP(c_COMBC(_1508356, _1508356, tc_HOL_Obool), c_fequal), _1508358))), hAPP(hAPP(c_COMBC(_1508356, tc_fun(_1508356, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508356)), _1508360))))], (1874 ^ _775212) ^ [_801493, _801495] : [-(class_Int_Onumber(_801493)), _801495 = _801493, class_Int_Onumber(_801495)], (8994 ^ _775212) ^ [_921008, _921010, _921012] : [class_Orderings_Oorder(_921008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921008), _921010), _921012)), 9001 ^ _775212 : [(9008 ^ _775212) ^ [] : [_921012 = _921010, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921008), _921012), _921010)))], (9002 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921008), _921012), _921010)), -(_921012 = _921010)]]], (17903 ^ _775212) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (44624 ^ _775212) ^ [_1655559, _1655561, _1655563] : [-(_1655559 = _1655561), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655563)), _1655559) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655563)), _1655561), 44630 ^ _775212 : [(44633 ^ _775212) ^ [] : [hAPP(hAPP(c_List_Onth(_1655563), _1655559), 44629 ^ [_1655559, _1655561, _1655563]) = hAPP(hAPP(c_List_Onth(_1655563), _1655561), 44629 ^ [_1655559, _1655561, _1655563])], (44631 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44629 ^ [_1655559, _1655561, _1655563]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655563)), _1655559))))]]], (6064 ^ _775212) ^ [_871321] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871321), hAPP(c_Nat_OSuc, _871321))))], (31345 ^ _775212) ^ [_1342448, _1342450, _1342452] : [class_Rings_Osemiring__1(_1342448), hBOOL(hAPP(hAPP(c_member(_1342448), _1342450), c_Nat_Osemiring__1__class_ONats(_1342448))), hBOOL(hAPP(hAPP(c_member(_1342448), _1342452), c_Nat_Osemiring__1__class_ONats(_1342448))), -(hBOOL(hAPP(hAPP(c_member(_1342448), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1342448), _1342450), _1342452)), c_Nat_Osemiring__1__class_ONats(_1342448))))], (46498 ^ _775212) ^ [_1701712] : [-(hAPP(c_List_Otl(_1701712), c_List_Olist_ONil(_1701712)) = c_List_Olist_ONil(_1701712))], (39361 ^ _775212) ^ [_1522985, _1522987, _1522989, _1522991] : [-(c_Nitpick_Oprod(_1522985, _1522987, _1522989, _1522991) = hAPP(c_Set_OCollect(tc_prod(_1522985, _1522987)), hAPP(c_Product__Type_Oprod_Oprod__case(_1522985, _1522987, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1522985, tc_fun(_1522987, tc_HOL_Obool), tc_fun(_1522987, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1522987, tc_HOL_Obool), tc_fun(_1522987, tc_HOL_Obool)), _1522985), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1522987)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522985), c_fconj), hAPP(hAPP(c_COMBC(_1522985, tc_fun(_1522985, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522985)), _1522989)))), hAPP(hAPP(c_COMBC(_1522987, tc_fun(_1522987, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522987)), _1522991)))))], (35075 ^ _775212) ^ [_1420578, _1420580, _1420582, _1420584, _1420586] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1420578, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1420580, _1420578, _1420582), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420580, tc_HOL_Obool)), _1420584), _1420586))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420578, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1420580, _1420578, _1420582), _1420584)), hAPP(c_Set_Oimage(_1420580, _1420578, _1420582), _1420586)))))], (16189 ^ _775212) ^ [_1049666, _1049668, _1049670] : [class_Groups_Oordered__ab__group__add__abs(_1049666), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049666), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049666), hAPP(c_Groups_Oabs__class_Oabs(_1049666), _1049668)), hAPP(c_Groups_Oabs__class_Oabs(_1049666), _1049670))), hAPP(c_Groups_Oabs__class_Oabs(_1049666), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049666), _1049670), _1049668)))))], (46931 ^ _775212) ^ [_1711016, _1711018, _1711020] : [46932 ^ _775212 : [(46933 ^ _775212) ^ [_1711105, _1711107] : [_1711018 = hAPP(hAPP(c_List_Olist_OCons(_1711016), _1711107), _1711105)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711016), tc_List_Olist(_1711016))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711016), tc_List_Olist(_1711016)), c_List_Olist_ONil(_1711016)), _1711018)), c_List_Olexord(_1711016, _1711020))))], (4750 ^ _775212) ^ [_847595, _847597, _847599, _847601] : [-(c_List_Olast(_847601, _847597) = c_List_Olast(_847599, _847595)), _847601 = _847599, _847597 = _847595], (25965 ^ _775212) ^ [_1229730, _1229732, _1229734, _1229736] : [class_Groups_Ocomm__monoid__add(_1229730), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1229732), _1229734)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1229730), _1229736), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1229732), _1229734)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229730), hAPP(_1229736, _1229732)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1229730), _1229736), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1229732)), _1229734))))], (17931 ^ _775212) ^ [_1079504] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1079504))) = 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)))), _1079504))], (44720 ^ _775212) ^ [_1658071, _1658073, _1658075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658071), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658073)), _1658075))), -(hAPP(c_Random_Opick(_1658073, hAPP(hAPP(c_List_Omap(_1658073, tc_prod(tc_Code__Numeral_Ocode__numeral, _1658073)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1658073), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1658075)), hAPP(c_Code__Numeral_Oof__nat, _1658071)) = hAPP(hAPP(c_List_Onth(_1658073), _1658075), _1658071))], (32437 ^ _775212) ^ [_1362875, _1362877, _1362879] : [class_Orderings_Olinorder(_1362875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362875), _1362877)), -(_1362879 = c_Orderings_Obot__class_Obot(tc_fun(_1362875, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1362875, tc_HOL_Obool)), _1362879), _1362877)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362875), c_Big__Operators_Olattice_OSup__fin(_1362875, c_Orderings_Oord__class_Omax(_1362875), _1362879)), c_Big__Operators_Olattice_OSup__fin(_1362875, c_Orderings_Oord__class_Omax(_1362875), _1362877)) = c_Big__Operators_Olattice_OSup__fin(_1362875, c_Orderings_Oord__class_Omax(_1362875), _1362877))], (28536 ^ _775212) ^ [_1281538, _1281540] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1281538, _1281540)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1281538, _1281540), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1281540), c_Orderings_Otop__class_Otop(tc_fun(_1281540, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281538), c_Orderings_Otop__class_Otop(tc_fun(_1281538, tc_HOL_Obool)))))], (13272 ^ _775212) ^ [_995359, _995361] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _995359), _995361) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _995359, _995361)), _995361))], (40938 ^ _775212) ^ [_1563365, _1563367, _1563369, _1563371, _1563373, _1563375, _1563377, _1563379] : [class_Groups_Ocomm__monoid__mult(_1563365), c_Fun_Oinj__on(_1563367, _1563369, _1563371, _1563373), _1563375 = hAPP(c_Set_Oimage(_1563367, _1563369, _1563371), _1563373), 40952 ^ _775212 : [(40955 ^ _775212) ^ [] : [hAPP(_1563377, 40951 ^ [_1563365, _1563367, _1563369, _1563371, _1563373, _1563375, _1563377, _1563379]) = hAPP(hAPP(c_Fun_Ocomp(_1563369, _1563365, _1563367, _1563379), _1563371), 40951 ^ [_1563365, _1563367, _1563369, _1563371, _1563373, _1563375, _1563377, _1563379])], (40953 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1563367), 40951 ^ [_1563365, _1563367, _1563369, _1563371, _1563373, _1563375, _1563377, _1563379]), _1563373)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1563369, _1563365), _1563379), _1563375) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1563367, _1563365), _1563377), _1563373))], (41654 ^ _775212) ^ [_1578439, _1578441, _1578443, _1578445] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578439, _1578439)), _1578441), c_Transitive__Closure_Otrancl(_1578439, _1578443))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578439, _1578439), tc_HOL_Obool)), _1578443), _1578445)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578439, _1578439)), _1578441), c_Transitive__Closure_Otrancl(_1578439, _1578445))))], (42291 ^ _775212) ^ [_1593808, _1593810, _1593812] : [-(hAPP(c_Relation_Oconverse(_1593808, _1593810), hAPP(c_Relation_Oconverse(_1593810, _1593808), _1593812)) = _1593812)], (16793 ^ _775212) ^ [_1061565, _1061567, _1061569, _1061571] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1061565, _1061567), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1061569), _1061571))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1061565), _1061567) = _1061569)], (12556 ^ _775212) ^ [_982244] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _982244) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27307 ^ _775212) ^ [_1256277, _1256279, _1256281] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256277, tc_HOL_Obool)), _1256279), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256277, tc_HOL_Obool)), _1256281), _1256279))))], (21509 ^ _775212) ^ [_1143418, _1143420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143418)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143420)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1143418, _1143420), c_Divides_OposDivAlg(_1143418, _1143420))))], (18587 ^ _775212) ^ [_1090980] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1090980)), 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, _1090980, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (21633 ^ _775212) ^ [_1145644, _1145646] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1145644), _1145646) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1145644, _1145646)))], (44405 ^ _775212) ^ [_1649170, _1649172] : [-(c_List_Olistrel(_1649170, c_Transitive__Closure_Ortrancl(_1649170, _1649172)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1649170), c_List_Olistrel1(_1649170, _1649172)))], (48468 ^ _775212) ^ [_1745624, _1745626] : [c_List_Oupt(_1745624, _1745626) = c_List_Olist_ONil(tc_Nat_Onat), -(_1745626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1745626), _1745624)))], (52663 ^ _775212) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (36026 ^ _775212) ^ [_1443156, _1443158, _1443160, _1443162, _1443164, _1443166] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443156, tc_fun(_1443158, tc_HOL_Obool))), _1443160), _1443162), _1443164), _1443166)), -(hBOOL(hAPP(hAPP(_1443162, _1443164), _1443166)))], (11342 ^ _775212) ^ [_961361, _961363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _961361)), 11345 ^ _775212 : [(11354 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _961361), _961363) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _961361 = c_Groups_Oone__class_Oone(tc_Int_Oint), _961363 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (11346 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _961361), _961363) = c_Groups_Oone__class_Oone(tc_Int_Oint), 11349 ^ _775212 : [(11352 ^ _775212) ^ [] : [-(_961363 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (11350 ^ _775212) ^ [] : [-(_961361 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (46885 ^ _775212) ^ [_1709819, _1709821, _1709823] : [class_Orderings_Olinorder(_1709819), -(c_Big__Operators_Olattice_OInf__fin(_1709819, c_Orderings_Oord__class_Omin(_1709819), hAPP(c_List_Oset(_1709819), hAPP(hAPP(c_List_Olist_OCons(_1709819), _1709821), _1709823))) = hAPP(c_List_Ofoldl(_1709819, _1709819, c_Orderings_Oord__class_Omin(_1709819), _1709821), _1709823))], (46432 ^ _775212) ^ [_1700487, _1700489] : [-(_1700487 = c_List_Olist_ONil(_1700489)), -(hAPP(c_List_Ohd(_1700489), _1700487) = hAPP(hAPP(c_List_Onth(_1700489), _1700487), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18527 ^ _775212) ^ [] : [-(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))))], (52691 ^ _775212) ^ [_1828462, _1828464] : [_1828462 = _1828464, -(hBOOL(hAPP(hAPP(c_fequal, _1828462), _1828464)))], (3464 ^ _775212) ^ [_827522, _827524] : [_827524 = _827522, -(c_New__Random__Sequence_Oneg__single(_827524) = c_New__Random__Sequence_Oneg__single(_827522))], (52347 ^ _775212) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (39898 ^ _775212) ^ [_1538839, _1538841, _1538843, _1538845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1538839, _1538841), tc_HOL_Obool)), _1538843), _1538845)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1538839, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1538839, _1538841), _1538843)), hAPP(c_Relation_ODomain(_1538839, _1538841), _1538845))))], (5082 ^ _775212) ^ [_852725, _852727] : [_852727 = _852725, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_852727) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_852725))], (8689 ^ _775212) ^ [_916088, _916090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _916088)), _916090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916088), hAPP(c_Int_Onat, _916090))))], (41732 ^ _775212) ^ [_1580254, _1580256, _1580258, _1580260, _1580262, _1580264] : [c_Finite__Set_Ofun__left__comm(_1580254, _1580256, _1580258), -(hAPP(hAPP(_1580258, _1580260), hAPP(hAPP(_1580258, _1580262), _1580264)) = hAPP(hAPP(_1580258, _1580262), hAPP(hAPP(_1580258, _1580260), _1580264)))], (18023 ^ _775212) ^ [_1080934, _1080936] : [class_Int_Onumber__ring(_1080934), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080934), hAPP(c_Int_Onumber__class_Onumber__of(_1080934), _1080936)), c_Groups_Oone__class_Oone(_1080934)) = hAPP(c_Int_Onumber__class_Onumber__of(_1080934), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1080936), c_Int_OBit1(c_Int_OPls))))], (14359 ^ _775212) ^ [_1014823, _1014825] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1014823)), hAPP(c_Nat_OSuc, _1014825)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014823), _1014825))], (21161 ^ _775212) ^ [_1137700, _1137702] : [21162 ^ _775212 : [(21165 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137702), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21163 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137700), _1137702))]], -(c_Divides_OposDivAlg(_1137700, _1137702) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137700))], (40089 ^ _775212) ^ [_1543579, _1543581, _1543583, _1543585] : [40091 ^ _775212 : [(40094 ^ _775212) ^ [] : [c_Wellfounded_Owf(_1543581, hAPP(_1543583, 40090 ^ [_1543579, _1543581, _1543583, _1543585]))], (40092 ^ _775212) ^ [] : [-(hBOOL(hAPP(_1543579, 40090 ^ [_1543579, _1543581, _1543583, _1543585])))]], -(c_Wellfounded_Owf(tc_prod(_1543585, _1543581), c_Recdef_Osame__fst(_1543585, _1543581, _1543579, _1543583)))], (30018 ^ _775212) ^ [_1312854, _1312856, _1312858, _1312860, _1312862] : [-(hBOOL(hAPP(hAPP(c_member(_1312854), _1312856), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312858, tc_fun(_1312854, tc_HOL_Obool)), _1312860), _1312862)))), 30019 ^ _775212 : [(30020 ^ _775212) ^ [_1312936] : [hBOOL(hAPP(hAPP(c_member(_1312858), _1312936), _1312860)), hBOOL(hAPP(hAPP(c_member(_1312854), _1312856), hAPP(_1312862, _1312936)))]]], (30668 ^ _775212) ^ [_1328450, _1328452, _1328454, _1328456, _1328458] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1328450, _1328452, _1328454), _1328456), _1328458)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1328450, _1328452)), hAPP(hAPP(c_Product__Type_OPair(_1328450, _1328452), _1328456), _1328458)), _1328454)))], (40756 ^ _775212) ^ [] : [-(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))], (10815 ^ _775212) ^ [_951896] : [10816 ^ _775212 : [(10817 ^ _775212) ^ [_951953] : [hBOOL(hAPP(_951896, _951953))]], 10819 ^ _775212 : [(10822 ^ _775212) ^ [] : [-(hBOOL(hAPP(_951896, hAPP(c_Int_Onat, 10818 ^ [_951896]))))], (10820 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10818 ^ [_951896])))]]], (43396 ^ _775212) ^ [_1622737, _1622739, _1622741, _1622743] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1622737, tc_HOL_Obool), tc_fun(_1622739, tc_HOL_Obool)), _1622741), hAPP(hAPP(c_COMBC(tc_fun(_1622737, tc_HOL_Obool), tc_fun(_1622737, tc_fun(_1622739, tc_HOL_Obool)), tc_fun(_1622739, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1622737, tc_fun(_1622739, tc_HOL_Obool))), _1622743)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1622737, tc_fun(_1622739, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1622737, tc_HOL_Obool), _1622741)), _1622743))], (16953 ^ _775212) ^ [_1064012] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1064012)), -(hAPP(c_Int_Onat, _1064012) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2084 ^ _775212) ^ [_805316, _805318] : [_805318 = _805316, -(c_Int_Osucc(_805318) = c_Int_Osucc(_805316))], (27690 ^ _775212) ^ [_1264079, _1264081, _1264083, _1264085, _1264087] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1264079, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1264081, tc_fun(_1264079, tc_HOL_Obool)), _1264083), _1264085)), _1264087) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1264081, tc_fun(_1264079, tc_HOL_Obool)), _1264083), hAPP(hAPP(c_COMBC(_1264081, tc_fun(_1264079, tc_HOL_Obool), tc_fun(_1264079, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1264079, tc_HOL_Obool), tc_fun(tc_fun(_1264079, tc_HOL_Obool), tc_fun(_1264079, tc_HOL_Obool)), _1264081), c_Groups_Ominus__class_Ominus(tc_fun(_1264079, tc_HOL_Obool))), _1264085)), _1264087)))], (31575 ^ _775212) ^ [_1346751, _1346753] : [class_Groups_Olinordered__ab__group__add(_1346751), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346751), _1346753)), -(_1346753 = c_Orderings_Obot__class_Obot(tc_fun(_1346751, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1346751), c_Big__Operators_Olinorder__class_OMin(_1346751, _1346753)) = c_Big__Operators_Olinorder__class_OMax(_1346751, hAPP(c_Set_Oimage(_1346751, _1346751, c_Groups_Ouminus__class_Ouminus(_1346751)), _1346753)))], (46746 ^ _775212) ^ [_1706892, _1706894, _1706896, _1706898, _1706900, _1706902, _1706904] : [-(hAPP(c_List_Ofoldl(_1706892, _1706894, _1706896, _1706898), hAPP(hAPP(c_List_Omap(_1706900, _1706894), _1706902), _1706904)) = hAPP(c_List_Ofoldl(_1706892, _1706900, hAPP(hAPP(c_COMBC(_1706892, tc_fun(_1706900, _1706894), tc_fun(_1706900, _1706892)), hAPP(hAPP(c_COMBB(tc_fun(_1706894, _1706892), tc_fun(tc_fun(_1706900, _1706894), tc_fun(_1706900, _1706892)), _1706892), c_COMBB(_1706894, _1706892, _1706900)), _1706896)), _1706902), _1706898), _1706904))], (52477 ^ _775212) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (16701 ^ _775212) ^ [_1060046] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060046) = _1060046)], (40698 ^ _775212) ^ [_1558025, _1558027, _1558029, _1558031, _1558033, _1558035, _1558037] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1558025, _1558027, _1558029), hAPP(c_Fun_Ocomp(_1558031, tc_fun(_1558027, _1558029), _1558025, _1558033), _1558035)), _1558037) = hAPP(hAPP(_1558033, hAPP(_1558035, hAPP(c_Product__Type_Ofst(_1558025, _1558027), _1558037))), hAPP(c_Product__Type_Osnd(_1558025, _1558027), _1558037)))], (16377 ^ _775212) ^ [_1053246, _1053248, _1053250, _1053252] : [class_Int_Onumber__ring(_1053246), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053246), hAPP(c_Int_Onumber__class_Onumber__of(_1053246), _1053248)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053246), hAPP(c_Int_Onumber__class_Onumber__of(_1053246), _1053250)), _1053252)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053246), hAPP(c_Int_Onumber__class_Onumber__of(_1053246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1053248), _1053250))), _1053252))], (8061 ^ _775212) ^ [_904733, _904735, _904737, _904739, _904741] : [class_Rings_Osemiring(_904733), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904733), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904733), _904735), _904737)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904733), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904733), _904739), _904737)), _904741)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904733), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904733), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904733), _904735), _904739)), _904737)), _904741))], (35261 ^ _775212) ^ [_1425064, _1425066, _1425068] : [class_Orderings_Oorder(_1425064), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425064, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1425064, _1425066), _1425068)), hAPP(c_SetInterval_Oord__class_OatLeast(_1425064), _1425068)) = c_Orderings_Obot__class_Obot(tc_fun(_1425064, tc_HOL_Obool)))], (41221 ^ _775212) ^ [_1569766, _1569768] : [c_Wellfounded_Owf(_1569766, _1569768), -(c_Wellfounded_Owf(_1569766, c_Transitive__Closure_Otrancl(_1569766, _1569768)))], (14025 ^ _775212) ^ [_1008473, _1008475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1008473)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1008473), _1008475)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1008475), _1008473) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1008475), _1008473)), _1008473)))], (6779 ^ _775212) ^ [_883206, _883208] : [class_Groups_Olinordered__ab__group__add(_883206), 6782 ^ _775212 : [(6789 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883206), _883208), c_Groups_Ozero__class_Ozero(_883206))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883206), _883208), _883208)), c_Groups_Ozero__class_Ozero(_883206))))], (6783 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883206), _883208), _883208)), c_Groups_Ozero__class_Ozero(_883206))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883206), _883208), c_Groups_Ozero__class_Ozero(_883206))))]]], (12715 ^ _775212) ^ [_984948, _984950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _984948)), 12718 ^ _775212 : [(12721 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _984950, _984948)), _984948)))], (12719 ^ _775212) ^ [] : [-(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, _984950, _984948))))]]], (46143 ^ _775212) ^ [_1693528] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1693528)), -(c_List_Onat__list(_1693528))], (6144 ^ _775212) ^ [_872356] : [-(_872356 = 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)), _872356)))], (43304 ^ _775212) ^ [_1620482] : [class_Complete__Lattice_Ocomplete__lattice(_1620482), -(c_Complete__Lattice_OInf__class_OInf(_1620482, c_Orderings_Obot__class_Obot(tc_fun(_1620482, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1620482))], (45977 ^ _775212) ^ [_1689076, _1689078, _1689080, _1689082, _1689084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1689076, tc_HOL_Obool)), hAPP(c_List_Oset(_1689076), _1689078)), _1689080)), hBOOL(hAPP(hAPP(c_member(_1689076), _1689082), _1689080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1689076, tc_HOL_Obool)), hAPP(c_List_Oset(_1689076), hAPP(hAPP(c_List_Olist__update(_1689076, _1689078), _1689084), _1689082))), _1689080)))], (46454 ^ _775212) ^ [_1700823, _1700825, _1700827] : [hBOOL(hAPP(c_List_Odistinct(_1700823), _1700825)), -(hBOOL(hAPP(c_List_Odistinct(_1700823), hAPP(hAPP(c_List_Odrop(_1700823), _1700827), _1700825))))], (12745 ^ _775212) ^ [_985446, _985448] : [class_Rings_Olinordered__idom(_985446), 12748 ^ _775212 : [(12755 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985446), c_Groups_Ozero__class_Ozero(_985446)), _985448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985446), c_Groups_Ozero__class_Ozero(_985446)), c_Groups_Osgn__class_Osgn(_985446, _985448))))], (12749 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985446), c_Groups_Ozero__class_Ozero(_985446)), c_Groups_Osgn__class_Osgn(_985446, _985448))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985446), c_Groups_Ozero__class_Ozero(_985446)), _985448)))]]], (6326 ^ _775212) ^ [_875123, _875125] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_875123, _875125)) = 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(_875123)), c_Com_Ocom_Ocom__size(_875125))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (46788 ^ _775212) ^ [_1707878, _1707880, _1707882] : [-(hAPP(c_List_Orotate1(_1707878), hAPP(c_List_Orotate(_1707878, _1707880), _1707882)) = hAPP(c_List_Orotate(_1707878, _1707880), hAPP(c_List_Orotate1(_1707878), _1707882)))], (44381 ^ _775212) ^ [_1648458, _1648460, _1648462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1648458, _1648458), tc_HOL_Obool)), _1648460), _1648462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1648458), tc_List_Olist(_1648458)), tc_HOL_Obool)), c_List_Olistrel(_1648458, _1648460)), c_List_Olistrel(_1648458, _1648462))))], (14439 ^ _775212) ^ [_1016319, _1016321, _1016323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016319), _1016321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016319), _1016323)), 14446 ^ _775212 : [(14453 ^ _775212) ^ [] : [_1016321 = _1016323, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016321), _1016319) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016323), _1016319))], (14447 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016321), _1016319) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016323), _1016319), -(_1016321 = _1016323)]]], (23012 ^ _775212) ^ [_1173567, _1173569, _1173571, _1173573] : [class_Orderings_Olinorder(_1173567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173567), _1173569), _1173571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173567), _1173569), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173567), _1173571), _1173573))))], (36000 ^ _775212) ^ [] : [-(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))], (40714 ^ _775212) ^ [_1558427, _1558429, _1558431, _1558433, _1558435, _1558437] : [c_Finite__Set_Ofolding(_1558427, _1558429, _1558431, _1558433), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558427), _1558435)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558427), _1558437)), -(hAPP(c_Fun_Ocomp(_1558429, _1558429, _1558429, hAPP(_1558433, _1558437)), hAPP(_1558433, _1558435)) = hAPP(c_Fun_Ocomp(_1558429, _1558429, _1558429, hAPP(_1558433, _1558435)), hAPP(_1558433, _1558437)))], (26030 ^ _775212) ^ [_1231123, _1231125] : [26032 ^ _775212 : [(26035 ^ _775212) ^ [] : [hBOOL(hAPP(_1231125, 26031 ^ [_1231123, _1231125]))], (26033 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26031 ^ [_1231123, _1231125]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1231123))))]], 26036 ^ _775212 : [(26037 ^ _775212) ^ [_1231278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1231278), _1231123)), -(hBOOL(hAPP(_1231125, _1231278)))]]], (36076 ^ _775212) ^ [_1444310, _1444312, _1444314, _1444316, _1444318] : [class_Groups_Ocomm__monoid__add(_1444310), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444312), _1444314)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444312), _1444316)), 36090 ^ _775212 : [(36093 ^ _775212) ^ [] : [hAPP(_1444318, 36089 ^ [_1444310, _1444312, _1444314, _1444316, _1444318]) = c_Groups_Ozero__class_Ozero(_1444310)], (36091 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1444312), 36089 ^ [_1444310, _1444312, _1444314, _1444316, _1444318]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444312, tc_HOL_Obool)), _1444314), _1444316))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444312, _1444310), _1444318), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1444312, tc_HOL_Obool)), _1444314), _1444316)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1444310), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444312, _1444310), _1444318), _1444314)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444312, _1444310), _1444318), _1444316)))], (39275 ^ _775212) ^ [_1519299, _1519301, _1519303] : [class_Lattices_Odistrib__lattice(_1519299), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519299), _1519301)), -(_1519301 = c_Orderings_Obot__class_Obot(tc_fun(_1519299, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1519299), _1519303), c_Big__Operators_Olattice__class_OInf__fin(_1519299, _1519301)) = c_Big__Operators_Olattice__class_OInf__fin(_1519299, hAPP(c_Set_OCollect(_1519299), hAPP(hAPP(c_COMBB(tc_fun(_1519299, tc_HOL_Obool), tc_HOL_Obool, _1519299), c_HOL_OEx(_1519299)), hAPP(hAPP(c_COMBC(_1519299, tc_fun(_1519299, tc_HOL_Obool), tc_fun(_1519299, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519299, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1519299, tc_HOL_Obool), tc_fun(_1519299, tc_HOL_Obool)), _1519299), c_COMBS(_1519299, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519299, tc_HOL_Obool), tc_fun(_1519299, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1519299), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519299), c_fconj)), hAPP(hAPP(c_COMBC(_1519299, tc_fun(_1519299, _1519299), tc_fun(_1519299, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519299, tc_HOL_Obool), tc_fun(tc_fun(_1519299, _1519299), tc_fun(_1519299, tc_HOL_Obool)), _1519299), c_COMBB(_1519299, tc_HOL_Obool, _1519299)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1519299), _1519303))))), hAPP(hAPP(c_COMBC(_1519299, tc_fun(_1519299, tc_HOL_Obool), tc_HOL_Obool), c_member(_1519299)), _1519301))))))], (42531 ^ _775212) ^ [_1600836, _1600838, _1600840, _1600842] : [-(hAPP(c_Set_OCollect(_1600836), hAPP(hAPP(c_COMBB(tc_fun(_1600838, tc_HOL_Obool), tc_HOL_Obool, _1600836), c_HOL_OAll(_1600838)), hAPP(hAPP(c_COMBB(tc_fun(_1600838, tc_HOL_Obool), tc_fun(_1600838, tc_HOL_Obool), _1600836), hAPP(c_COMBS(_1600838, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1600838), c_fimplies), hAPP(hAPP(c_COMBC(_1600838, tc_fun(_1600838, tc_HOL_Obool), tc_HOL_Obool), c_member(_1600838)), _1600840)))), _1600842))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600838, tc_fun(_1600836, tc_HOL_Obool)), _1600840), hAPP(hAPP(c_COMBB(tc_fun(_1600836, tc_HOL_Obool), tc_fun(_1600836, tc_HOL_Obool), _1600838), c_Set_OCollect(_1600836)), hAPP(c_COMBC(_1600836, _1600838, tc_HOL_Obool), _1600842))))], (13477 ^ _775212) ^ [_998812, _998814, _998816] : [class_Divides_Osemiring__div(_998812), -(_998814 = c_Groups_Ozero__class_Ozero(_998812)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_998812), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998812), _998814), _998816)), _998814) = _998816)], (14311 ^ _775212) ^ [_1013836, _1013838, _1013840, _1013842] : [class_Divides_Oring__div(_1013836), -(c_Divides_Odiv__class_Omod(_1013836, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1013836), _1013838), _1013840), _1013842) = c_Divides_Odiv__class_Omod(_1013836, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1013836), _1013838), c_Divides_Odiv__class_Omod(_1013836, _1013840, _1013842)), _1013842))], (52637 ^ _775212) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (52271 ^ _775212) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (21885 ^ _775212) ^ [_1150478, _1150480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150480)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1150478, _1150480) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1150478, _1150480)))], (29486 ^ _775212) ^ [_1300167, _1300169] : [-(hBOOL(hAPP(hAPP(c_member(_1300167), _1300169), c_Orderings_Otop__class_Otop(tc_fun(_1300167, tc_HOL_Obool)))))], (19487 ^ _775212) ^ [_1107269, _1107271, _1107273, _1107275] : [class_Fields_Ofield__inverse__zero(_1107269), 19490 ^ _775212 : [(19491 ^ _775212) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107269), _1107271), _1107273) = _1107275, 19494 ^ _775212 : [(19501 ^ _775212) ^ [] : [_1107273 = c_Groups_Ozero__class_Ozero(_1107269), -(_1107275 = c_Groups_Ozero__class_Ozero(_1107269))], (19495 ^ _775212) ^ [] : [-(_1107273 = c_Groups_Ozero__class_Ozero(_1107269)), -(_1107271 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107269), _1107275), _1107273))]]], (19507 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107269), _1107271), _1107273) = _1107275), 19510 ^ _775212 : [(19513 ^ _775212) ^ [] : [_1107271 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107269), _1107275), _1107273)], (19511 ^ _775212) ^ [] : [_1107273 = c_Groups_Ozero__class_Ozero(_1107269)]], 19514 ^ _775212 : [(19517 ^ _775212) ^ [] : [_1107275 = c_Groups_Ozero__class_Ozero(_1107269)], (19515 ^ _775212) ^ [] : [-(_1107273 = c_Groups_Ozero__class_Ozero(_1107269))]]]]], (45076 ^ _775212) ^ [_1667681, _1667683] : [c_Orderings_Obot__class_Obot(tc_fun(_1667681, tc_HOL_Obool)) = hAPP(c_List_Oset(_1667681), _1667683), -(_1667683 = c_List_Olist_ONil(_1667681))], (45913 ^ _775212) ^ [_1687523, _1687525, _1687527, _1687529] : [_1687525 = _1687529, -(hAPP(hAPP(c_List_Oappend(_1687523), _1687525), _1687527) = hAPP(hAPP(c_List_Oappend(_1687523), _1687529), _1687527))], (44716 ^ _775212) ^ [_1657970, _1657972, _1657974, _1657976] : [-(hAPP(hAPP(c_List_Otake(_1657970), _1657972), hAPP(hAPP(c_List_Otake(_1657970), _1657974), _1657976)) = hAPP(hAPP(c_List_Otake(_1657970), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1657972), _1657974)), _1657976))], (25100 ^ _775212) ^ [_1211867, _1211869, _1211871, _1211873, _1211875] : [-(hAPP(c_New__DSequence_Oneg__bind(_1211867, _1211869, _1211871, _1211873), _1211875) = c_Lazy__Sequence_Ohb__bind(_1211867, _1211869, hAPP(_1211871, _1211875), hAPP(hAPP(c_COMBC(_1211867, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1211869))), _1211873), _1211875)))], (25380 ^ _775212) ^ [_1216847, _1216849] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216847)), _1216849)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216847), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1216849)))))], (37687 ^ _775212) ^ [_1478616, _1478618, _1478620, _1478622] : [hBOOL(hAPP(hAPP(c_member(_1478616), _1478618), c_Wellfounded_Oacc(_1478616, _1478620))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1478616, _1478616)), hAPP(hAPP(c_Product__Type_OPair(_1478616, _1478616), _1478622), _1478618)), _1478620)), -(hBOOL(hAPP(hAPP(c_member(_1478616), _1478622), c_Wellfounded_Oacc(_1478616, _1478620))))], (20887 ^ _775212) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (39059 ^ _775212) ^ [_1510404, _1510406] : [-(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), _1510404)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1510406))))))], (41919 ^ _775212) ^ [_1584655, _1584657] : [-(c_Transitive__Closure_Otrancl(_1584655, _1584657) = hAPP(hAPP(c_Relation_Orel__comp(_1584655, _1584655, _1584655), c_Transitive__Closure_Ortrancl(_1584655, _1584657)), _1584657))], (52377 ^ _775212) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (12691 ^ _775212) ^ [_984543, _984545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984543), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 12694 ^ _775212 : [(12697 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984543), c_Divides_Odiv__class_Omod(tc_Int_Oint, _984545, _984543))))], (12695 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _984545, _984543)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (7787 ^ _775212) ^ [_900212, _900214, _900216, _900218] : [class_Groups_Oab__semigroup__mult(_900212), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_900212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_900212), _900214), _900216)), _900218) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_900212), _900214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_900212), _900216), _900218)))], (34429 ^ _775212) ^ [_1406729, _1406731, _1406733] : [34430 ^ _775212 : [(34433 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1406729), _1406733))], (34431 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1406729), _1406731))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1406729), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406729, tc_HOL_Obool)), _1406731), _1406733))))], (4932 ^ _775212) ^ [_850410, _850412, _850414, _850416, _850418, _850420] : [-(c_Lazy__Sequence_Oanamorph(_850420, _850416, _850412) = c_Lazy__Sequence_Oanamorph(_850418, _850414, _850410)), _850420 = _850418, _850416 = _850414, _850412 = _850410], (52289 ^ _775212) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (51663 ^ _775212) ^ [_1813792, _1813794] : [c_Relation_Oantisym(_1813792, _1813794), -(c_Relation_Oantisym(_1813792, hAPP(c_Relation_Oconverse(_1813792, _1813792), _1813794)))], (40377 ^ _775212) ^ [_1550633, _1550635, _1550637, _1550639, _1550641, _1550643] : [hBOOL(hAPP(hAPP(c_member(_1550633), _1550635), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550637, _1550639, tc_fun(_1550633, tc_HOL_Obool)), _1550641), _1550643))), 40382 ^ _775212 : [(40385 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550633), _1550635), hAPP(hAPP(_1550641, 40380 ^ [_1550633, _1550635, _1550637, _1550639, _1550641, _1550643]), 40381 ^ [_1550633, _1550635, _1550637, _1550639, _1550641, _1550643]))))], (40383 ^ _775212) ^ [] : [-(_1550643 = hAPP(hAPP(c_Product__Type_OPair(_1550637, _1550639), 40380 ^ [_1550633, _1550635, _1550637, _1550639, _1550641, _1550643]), 40381 ^ [_1550633, _1550635, _1550637, _1550639, _1550641, _1550643]))]]], (51541 ^ _775212) ^ [_1811733, _1811735] : [-(c_Equiv__Relations_Oequivp(_1811733, _1811735)), c_Predicate_Oreflp(_1811733, _1811735), c_Predicate_Osymp(_1811733, _1811735), c_Predicate_Otransp(_1811733, _1811735)], (13288 ^ _775212) ^ [_995688, _995690] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _995688)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _995690)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _995688), _995690))], (7374 ^ _775212) ^ [_892325, _892327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _892325), _892327)), -(_892327 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _892325), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 7377 ^ [_892325, _892327]))))], (32529 ^ _775212) ^ [_1364546, _1364548] : [class_Orderings_Olinorder(_1364546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364546), _1364548)), -(_1364548 = c_Orderings_Obot__class_Obot(tc_fun(_1364546, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1364546), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364546), 32542 ^ [_1364546, _1364548]), 32543 ^ [_1364546, _1364548])), hAPP(hAPP(c_Set_Oinsert(_1364546), 32542 ^ [_1364546, _1364548]), hAPP(hAPP(c_Set_Oinsert(_1364546), 32543 ^ [_1364546, _1364548]), c_Orderings_Obot__class_Obot(tc_fun(_1364546, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1364546), c_Big__Operators_Olattice_OSup__fin(_1364546, c_Orderings_Oord__class_Omax(_1364546), _1364548)), _1364548)))], (22786 ^ _775212) ^ [_1169171, _1169173, _1169175, _1169177, _1169179] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1169171, _1169173, _1169175), _1169177), _1169179) = hAPP(hAPP(_1169177, hAPP(c_Product__Type_Ofst(_1169171, _1169173), _1169179)), hAPP(c_Product__Type_Osnd(_1169171, _1169173), _1169179)))], (32993 ^ _775212) ^ [_1373613, _1373615, _1373617, _1373619] : [class_Groups_Ocomm__monoid__mult(_1373613), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1373615), _1373617))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1373615, _1373613), _1373619), _1373617) = c_Groups_Oone__class_Oone(_1373613))], (43547 ^ _775212) ^ [_1626154] : [class_Complete__Lattice_Ocomplete__lattice(_1626154), -(c_Complete__Lattice_OSup__class_OSup(_1626154, c_Orderings_Otop__class_Otop(tc_fun(_1626154, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1626154))], (47965 ^ _775212) ^ [_1733121, _1733123] : [hBOOL(hAPP(c_List_Odistinct(_1733121), _1733123)), -(c_List_Oremdups(_1733121, _1733123) = _1733123)], (31142 ^ _775212) ^ [_1338205, _1338207, _1338209, _1338211] : [c_Finite__Set_Ofolding__one(_1338205, _1338207, _1338209), -(hAPP(_1338209, hAPP(hAPP(c_Set_Oinsert(_1338205), _1338211), c_Orderings_Obot__class_Obot(tc_fun(_1338205, tc_HOL_Obool)))) = _1338211)], (6671 ^ _775212) ^ [_881221] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _881221), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _881221)], (31713 ^ _775212) ^ [_1349119, _1349121, _1349123] : [class_Orderings_Olinorder(_1349119), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349119), _1349121)), hBOOL(hAPP(hAPP(c_member(_1349119), _1349123), _1349121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349119), _1349123), c_Big__Operators_Olinorder__class_OMax(_1349119, _1349121))))], (33419 ^ _775212) ^ [_1382379] : [-(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)), _1382379), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (32983 ^ _775212) ^ [_1373489, _1373491, _1373493, _1373495] : [class_Groups_Ocomm__monoid__mult(_1373489), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1373491), _1373493))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1373491, _1373489), _1373495), _1373493) = c_Groups_Oone__class_Oone(_1373489))], (13447 ^ _775212) ^ [_998294, _998296] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _998294, _998296)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _998294), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _998296)))], (40526 ^ _775212) ^ [_1554151, _1554153, _1554155, _1554157, _1554159, _1554161] : [c_Fun_Oinj__on(_1554151, _1554153, hAPP(c_Fun_Ocomp(_1554155, _1554153, _1554151, _1554157), _1554159), _1554161), -(c_Fun_Oinj__on(_1554155, _1554153, _1554157, hAPP(c_Set_Oimage(_1554151, _1554155, _1554159), _1554161)))], (17317 ^ _775212) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36429 ^ _775212) ^ [_1451503, _1451505, _1451507, _1451509] : [c_Fun_Oinj__on(_1451503, _1451505, _1451507, c_Orderings_Otop__class_Otop(tc_fun(_1451503, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1451503, tc_fun(_1451509, _1451505), hAPP(hAPP(c_COMBB(_1451505, tc_fun(_1451509, _1451505), _1451503), c_COMBK(_1451505, _1451509)), _1451507), c_Orderings_Otop__class_Otop(tc_fun(_1451503, tc_HOL_Obool))))], (28688 ^ _775212) ^ [_1284809, _1284811, _1284813] : [class_Orderings_Obot(_1284809), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1284811, _1284809)), _1284813) = c_Orderings_Obot__class_Obot(_1284809))], (20351 ^ _775212) ^ [_1122348, _1122350] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122348), _1122350), hAPP(c_Int_Onumber__class_Onumber__of(_1122348), c_Int_OBit1(c_Int_OPls))) = _1122350), class_Fields_Ofield(_1122348), class_Int_Onumber__ring(_1122348)], (16023 ^ _775212) ^ [_1046700, _1046702] : [class_Groups_Oordered__ab__group__add__abs(_1046700), -(hAPP(c_Groups_Oabs__class_Oabs(_1046700), hAPP(c_Groups_Ouminus__class_Ouminus(_1046700), _1046702)) = hAPP(c_Groups_Oabs__class_Oabs(_1046700), _1046702))], (13675 ^ _775212) ^ [_1001928, _1001930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001928), _1001930)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1001928), _1001930) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17319 ^ _775212) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (8079 ^ _775212) ^ [_905244, _905246, _905248, _905250] : [class_Rings_Ocomm__semiring(_905244), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905244), _905246), _905248)), _905250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905244), _905246), _905250)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905244), _905248), _905250)))], (29216 ^ _775212) ^ [_1294556] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1294556), hAPP(c_Nat_OSuc, _1294556)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1294556), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (52267 ^ _775212) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (30262 ^ _775212) ^ [_1317816, _1317818, _1317820, _1317822, _1317824, _1317826] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1317818, _1317820)), hAPP(hAPP(c_Product__Type_OPair(_1317818, _1317820), _1317824), _1317826)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1317816, tc_fun(tc_prod(_1317818, _1317820), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1317816, tc_HOL_Obool))), _1317822))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1317816, tc_fun(_1317818, tc_fun(_1317820, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1317816, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1317818, _1317820), tc_HOL_Obool), tc_fun(_1317818, tc_fun(_1317820, tc_HOL_Obool)), _1317816), hAPP(c_COMBC(_1317818, tc_fun(tc_prod(_1317818, _1317820), tc_HOL_Obool), tc_fun(_1317820, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317820, tc_fun(tc_fun(tc_prod(_1317818, _1317820), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1317818, _1317820), tc_HOL_Obool), tc_fun(_1317820, tc_HOL_Obool)), _1317818), c_COMBC(_1317820, tc_fun(tc_prod(_1317818, _1317820), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317820, tc_prod(_1317818, _1317820)), tc_fun(_1317820, tc_fun(tc_fun(tc_prod(_1317818, _1317820), tc_HOL_Obool), tc_HOL_Obool)), _1317818), hAPP(c_COMBB(tc_prod(_1317818, _1317820), tc_fun(tc_fun(tc_prod(_1317818, _1317820), tc_HOL_Obool), tc_HOL_Obool), _1317820), c_member(tc_prod(_1317818, _1317820)))), c_Product__Type_OPair(_1317818, _1317820))))), _1317822)), _1317824), _1317826)))], (34833 ^ _775212) ^ [_1414913, _1414915, _1414917, _1414919] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414913, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414913, tc_HOL_Obool)), _1414915), _1414917)), _1414919) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414913, tc_HOL_Obool)), _1414915), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414913, tc_HOL_Obool)), _1414917), _1414919)))], (45088 ^ _775212) ^ [_1667896, _1667898] : [hAPP(c_List_Oset(_1667896), _1667898) = c_Orderings_Obot__class_Obot(tc_fun(_1667896, tc_HOL_Obool)), -(_1667898 = c_List_Olist_ONil(_1667896))], (41102 ^ _775212) ^ [_1567329, _1567331, _1567333, _1567335, _1567337, _1567339] : [class_Rings_Ocomm__semiring__1(_1567329), hBOOL(hAPP(c_Finite__Set_Ofinite(_1567331), _1567333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1567331, tc_HOL_Obool)), _1567335), _1567333)), 41116 ^ _775212 : [(41119 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1567329), hAPP(_1567337, 41115 ^ [_1567329, _1567331, _1567333, _1567335, _1567337, _1567339])), hAPP(_1567339, 41115 ^ [_1567329, _1567331, _1567333, _1567335, _1567337, _1567339])))], (41117 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1567331), 41115 ^ [_1567329, _1567331, _1567333, _1567335, _1567337, _1567339]), _1567335)))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1567329), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1567331, _1567329), _1567337), _1567335)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1567331, _1567329), _1567339), _1567333))))], (51511 ^ _775212) ^ [_1811257, _1811259] : [c_Relation_Otrans(_1811257, hAPP(c_Set_OCollect(tc_prod(_1811257, _1811257)), hAPP(c_Product__Type_Oprod_Oprod__case(_1811257, _1811257, tc_HOL_Obool), _1811259))), -(c_Predicate_Otransp(_1811257, _1811259))], (52221 ^ _775212) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (27001 ^ _775212) ^ [_1250479, _1250481, _1250483, _1250485] : [27005 ^ _775212 : [(27008 ^ _775212) ^ [] : [hBOOL(hAPP(_1250485, 27004 ^ [_1250479, _1250481, _1250483, _1250485]))], (27006 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1250479), 27004 ^ [_1250479, _1250481, _1250483, _1250485]), _1250481)))]], 27010 ^ _775212 : [(27013 ^ _775212) ^ [] : [hBOOL(hAPP(_1250485, 27009 ^ [_1250479, _1250481, _1250483, _1250485]))], (27011 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1250479), 27009 ^ [_1250479, _1250481, _1250483, _1250485]), _1250483)))]], 27014 ^ _775212 : [(27015 ^ _775212) ^ [_1250812] : [hBOOL(hAPP(hAPP(c_member(_1250479), _1250812), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1250479, tc_HOL_Obool)), _1250481), _1250483))), -(hBOOL(hAPP(_1250485, _1250812)))]]], (44304 ^ _775212) ^ [_1645975, _1645977, _1645979, _1645981, _1645983] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645975), tc_List_Olist(_1645975))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645975), tc_List_Olist(_1645975)), _1645977), _1645979)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1645975), c_List_Olistrel1(_1645975, _1645981)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645975), tc_List_Olist(_1645975))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645975), tc_List_Olist(_1645975)), hAPP(hAPP(c_List_Olist_OCons(_1645975), _1645983), _1645977)), hAPP(hAPP(c_List_Olist_OCons(_1645975), _1645983), _1645979))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1645975), c_List_Olistrel1(_1645975, _1645981)))))], (48560 ^ _775212) ^ [_1747255, _1747257] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1747255, _1747257) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1747255), _1747257)))], (34457 ^ _775212) ^ [_1407391, _1407393, _1407395] : [34459 ^ _775212 : [(34465 ^ _775212) ^ [] : [-(34458 ^ [_1407391, _1407393, _1407395] = 34461 ^ [_1407391, _1407393, _1407395])], (34463 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1407391), 34461 ^ [_1407391, _1407393, _1407395]), _1407395)))], (34460 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1407391), 34458 ^ [_1407391, _1407393, _1407395]), _1407393)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407391, tc_HOL_Obool)), _1407393), _1407395) = c_Orderings_Obot__class_Obot(tc_fun(_1407391, tc_HOL_Obool)))], (50996 ^ _775212) ^ [_1798498, _1798500, _1798502] : [hBOOL(hAPP(hAPP(c_member(_1798498), _1798500), hAPP(c_List_Oset(_1798498), _1798502))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1798498), _1798502), _1798500)))], (13787 ^ _775212) ^ [_1003962, _1003964, _1003966, _1003968] : [class_Divides_Osemiring__div(_1003962), -(_1003964 = c_Groups_Ozero__class_Ozero(_1003962)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1003962), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003962), _1003966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003962), _1003968), _1003964))), _1003964) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003962), _1003968), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1003962), _1003966), _1003964)))], (49105 ^ _775212) ^ [_1757703, _1757705] : [-(c_Fun_Oinj__on(tc_List_Olist(_1757703), tc_List_Olist(_1757703), c_List_Orev(_1757703), _1757705))], (43096 ^ _775212) ^ [_1615801, _1615803, _1615805] : [c_Relation_Ototal__on(_1615801, _1615803, _1615805), 43099 ^ _775212 : [(43100 ^ _775212) ^ [_1615945] : [hBOOL(hAPP(hAPP(c_member(_1615801), _1615945), _1615803)), 43103 ^ _775212 : [(43104 ^ _775212) ^ [_1616085] : [hBOOL(hAPP(hAPP(c_member(_1615801), _1616085), _1615803)), -(_1615945 = _1616085), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615801, _1615801)), hAPP(hAPP(c_Product__Type_OPair(_1615801, _1615801), _1615945), _1616085)), _1615805))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615801, _1615801)), hAPP(hAPP(c_Product__Type_OPair(_1615801, _1615801), _1616085), _1615945)), _1615805)))]]]]], (52057 ^ _775212) ^ [_1821251, _1821253, _1821255] : [c_Fun_Oinj__on(_1821251, _1821253, _1821255, c_Orderings_Otop__class_Otop(tc_fun(_1821251, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1821253, _1821251, _1821251, c_Hilbert__Choice_Oinv__into(_1821251, _1821253, c_Orderings_Otop__class_Otop(tc_fun(_1821251, tc_HOL_Obool)), _1821255)), _1821255) = c_Fun_Oid(_1821251))], (51569 ^ _775212) ^ [_1812097, _1812099, _1812101, _1812103] : [c_Predicate_Osymp(_1812097, _1812099), hBOOL(hAPP(hAPP(_1812099, _1812101), _1812103)), -(hBOOL(hAPP(hAPP(_1812099, _1812103), _1812101)))], (49247 ^ _775212) ^ [_1760635, _1760637, _1760639, _1760641] : [hAPP(c_List_Orev(_1760635), _1760637) = hAPP(hAPP(c_List_Olist_OCons(_1760635), _1760639), _1760641), -(_1760637 = hAPP(hAPP(c_List_Oappend(_1760635), hAPP(c_List_Orev(_1760635), _1760641)), hAPP(hAPP(c_List_Olist_OCons(_1760635), _1760639), c_List_Olist_ONil(_1760635))))], (9993 ^ _775212) ^ [_937195] : [class_Rings_Olinordered__semidom(_937195), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937195), c_Groups_Oone__class_Oone(_937195)), c_Groups_Ozero__class_Ozero(_937195)))], (41590 ^ _775212) ^ [_1576889, _1576891, _1576893] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576889, _1576889)), _1576891), _1576893)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576889, _1576889)), _1576891), c_Transitive__Closure_Otrancl(_1576889, _1576893))))], (51290 ^ _775212) ^ [_1804871, _1804873, _1804875, _1804877] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1804871, tc_fun(_1804873, tc_HOL_Obool)), _1804875), _1804877) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1804873, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1804873, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1804871, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1804873, tc_HOL_Obool)), c_HOL_OEx(_1804871)), hAPP(hAPP(c_COMBB(tc_fun(_1804871, tc_HOL_Obool), tc_fun(_1804871, tc_HOL_Obool), tc_fun(_1804873, tc_HOL_Obool)), hAPP(c_COMBS(_1804871, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1804871), c_fconj), hAPP(hAPP(c_COMBC(_1804871, tc_fun(_1804871, tc_HOL_Obool), tc_HOL_Obool), c_member(_1804871)), _1804875)))), hAPP(hAPP(c_COMBC(tc_fun(_1804873, tc_HOL_Obool), tc_fun(_1804871, tc_fun(_1804873, tc_HOL_Obool)), tc_fun(_1804871, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1804873, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1804871, tc_fun(_1804873, tc_HOL_Obool)), tc_fun(_1804871, tc_HOL_Obool)), tc_fun(_1804873, tc_HOL_Obool)), c_COMBB(tc_fun(_1804873, tc_HOL_Obool), tc_HOL_Obool, _1804871)), c_fequal)), _1804877))))))], (40387 ^ _775212) ^ [_1550902, _1550904, _1550906, _1550908, _1550910, _1550912] : [-(hAPP(c_Set_Ovimage(_1550902, tc_prod(_1550904, _1550906), _1550908), hAPP(hAPP(c_Product__Type_OSigma(_1550904, _1550906), _1550910), hAPP(c_COMBK(tc_fun(_1550906, tc_HOL_Obool), _1550904), _1550912))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1550902, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1550902, _1550904, hAPP(c_Fun_Ocomp(tc_prod(_1550904, _1550906), _1550904, _1550902, c_Product__Type_Ofst(_1550904, _1550906)), _1550908)), _1550910)), hAPP(c_Set_Ovimage(_1550902, _1550906, hAPP(c_Fun_Ocomp(tc_prod(_1550904, _1550906), _1550906, _1550902, c_Product__Type_Osnd(_1550904, _1550906)), _1550908)), _1550912)))], (24692 ^ _775212) ^ [_1203916, _1203918, _1203920] : [class_Divides_Osemiring__div(_1203916), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1203916), _1203918), _1203920)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1203916), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1203916), _1203920), _1203918)), _1203918) = _1203920)], (29979 ^ _775212) ^ [_1311660, _1311662, _1311664, _1311666] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1311660, _1311662)), hAPP(hAPP(c_Product__Type_OPair(_1311660, _1311662), _1311664), _1311666)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1311660, _1311662), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1311660, tc_fun(_1311662, tc_HOL_Obool))), _1311664), _1311666)))], (14901 ^ _775212) ^ [_1024853, _1024855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1024853), _1024855)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024853), _1024855)))], (22756 ^ _775212) ^ [_1168470, _1168472, _1168474] : [class_Int_Onumber(_1168470), class_Orderings_Oord(_1168470), 22763 ^ _775212 : [(22770 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168470), hAPP(c_Int_Onumber__class_Onumber__of(_1168470), _1168472)), hAPP(c_Int_Onumber__class_Onumber__of(_1168470), _1168474)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1168470), hAPP(c_Int_Onumber__class_Onumber__of(_1168470), _1168472)), hAPP(c_Int_Onumber__class_Onumber__of(_1168470), _1168474)) = hAPP(c_Int_Onumber__class_Onumber__of(_1168470), _1168474))], (22764 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168470), hAPP(c_Int_Onumber__class_Onumber__of(_1168470), _1168472)), hAPP(c_Int_Onumber__class_Onumber__of(_1168470), _1168474))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1168470), hAPP(c_Int_Onumber__class_Onumber__of(_1168470), _1168472)), hAPP(c_Int_Onumber__class_Onumber__of(_1168470), _1168474)) = hAPP(c_Int_Onumber__class_Onumber__of(_1168470), _1168472))]]], (3374 ^ _775212) ^ [_826063, _826065] : [_826065 = _826063, -(c_Nitpick_Onum(_826065) = c_Nitpick_Onum(_826063))], (44732 ^ _775212) ^ [_1658547, _1658549] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1658547), hAPP(c_List_Oset(_1658547), _1658549))))], (49235 ^ _775212) ^ [_1760351, _1760353] : [class_Groups_Ocomm__monoid__add(_1760351), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1760351), hAPP(c_List_Orev(_1760351), _1760353)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1760351), _1760353))], (17333 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (42958 ^ _775212) ^ [_1612273, _1612275, _1612277, _1612279, _1612281] : [c_Relation_Osingle__valued(_1612273, _1612275, hAPP(c_Relation_Oconverse(_1612275, _1612273), _1612277)), -(hAPP(c_Relation_OImage(_1612275, _1612273, _1612277), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1612275, tc_HOL_Obool)), _1612279), _1612281)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1612273, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1612275, _1612273, _1612277), _1612279)), hAPP(c_Relation_OImage(_1612275, _1612273, _1612277), _1612281)))], (9233 ^ _775212) ^ [_924802, _924804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _924802), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _924804), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _924802), _924804)))], (34809 ^ _775212) ^ [_1414429] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1414429) = c_Orderings_Oord__class_Omin(_1414429)), class_Lattices_Osemilattice__inf(_1414429), class_Orderings_Olinorder(_1414429)], (21179 ^ _775212) ^ [_1137910, _1137912] : [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), _1137910))), 21182 ^ _775212 : [(21189 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137912)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137910)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137912), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137910)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137910)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137912), 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), _1137910)))))], (21183 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137912)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137910))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137912), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137910)) = 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), _1137912)))]]], (1174 ^ _775212) ^ [_792743, _792745] : [-(class_Rings_Oordered__ring__abs(_792743)), _792745 = _792743, class_Rings_Oordered__ring__abs(_792745)], (37920 ^ _775212) ^ [_1484826, _1484828, _1484830, _1484832, _1484834] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1484826, _1484828), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484826, tc_HOL_Obool)), _1484830), _1484832)), hAPP(c_COMBK(tc_fun(_1484828, tc_HOL_Obool), _1484826), _1484834)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1484826, _1484828), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1484826, _1484828), _1484830), hAPP(c_COMBK(tc_fun(_1484828, tc_HOL_Obool), _1484826), _1484834))), hAPP(hAPP(c_Product__Type_OSigma(_1484826, _1484828), _1484832), hAPP(c_COMBK(tc_fun(_1484828, tc_HOL_Obool), _1484826), _1484834))))], (24632 ^ _775212) ^ [_1202820, _1202822, _1202824] : [class_Divides_Osemiring__div(_1202820), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1202820), _1202822), _1202824)), -(c_Divides_Odiv__class_Omod(_1202820, _1202824, _1202822) = c_Groups_Ozero__class_Ozero(_1202820))], (22466 ^ _775212) ^ [_1162986, _1162988, _1162990, _1162992] : [class_Orderings_Olinorder(_1162986), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162986), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162986), _1162988), _1162990)), _1162992) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162986), _1162988), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162986), _1162990), _1162992)))], (39115 ^ _775212) ^ [_1512704, _1512706] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1512704))), -(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)), _1512704))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1512706)))) = 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)), _1512704))), 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, _1512706))))))], (5384 ^ _775212) ^ [_857352, _857354] : [_857354 = _857352, -(c_HOL_OEx(_857354) = c_HOL_OEx(_857352))], (48256 ^ _775212) ^ [_1739949, _1739951, _1739953, _1739955, _1739957] : [-(hAPP(c_List_Ofilter(_1739949, _1739951), hAPP(hAPP(c_List_Omap(_1739953, _1739949), _1739955), _1739957)) = hAPP(hAPP(c_List_Omap(_1739953, _1739949), _1739955), hAPP(c_List_Ofilter(_1739953, hAPP(c_Fun_Ocomp(_1739949, tc_HOL_Obool, _1739953, _1739951), _1739955)), _1739957)))], (42242 ^ _775212) ^ [_1591943, _1591945, _1591947] : [c_Relation_Orefl__on(_1591943, _1591945, _1591947), -(c_Relation_Orefl__on(_1591943, _1591945, hAPP(c_Relation_Oconverse(_1591943, _1591943), _1591947)))], (15424 ^ _775212) ^ [_1035280, _1035282, _1035284] : [-(hBOOL(hAPP(_1035280, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035282), _1035284)))), 15427 ^ _775212 : [(15430 ^ _775212) ^ [] : [hBOOL(hAPP(_1035280, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15428 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035282), _1035284)))]], 15432 ^ _775212 : [(15435 ^ _775212) ^ [] : [hBOOL(hAPP(_1035280, 15431 ^ [_1035280, _1035282, _1035284]))], (15433 ^ _775212) ^ [] : [-(_1035282 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035284), 15431 ^ [_1035280, _1035282, _1035284]))]]], (23904 ^ _775212) ^ [_1190660, _1190662, _1190664] : [class_Rings_Olinordered__idom(_1190660), 23907 ^ _775212 : [(23914 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1190660), _1190662), _1190664)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1190660), hAPP(c_Groups_Oabs__class_Oabs(_1190660), _1190662)), _1190664)))], (23908 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1190660), hAPP(c_Groups_Oabs__class_Oabs(_1190660), _1190662)), _1190664)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1190660), _1190662), _1190664)))]]], (45094 ^ _775212) ^ [_1667993, _1667995] : [_1667995 = c_List_Olist_ONil(_1667993), -(hAPP(c_List_Oset(_1667993), _1667995) = c_Orderings_Obot__class_Obot(tc_fun(_1667993, tc_HOL_Obool)))], (27551 ^ _775212) ^ [_1261265, _1261267, _1261269, _1261271] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1261265, _1261267)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1261269, _1261271)))), 27552 ^ _775212 : [(27555 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1261269), _1261265)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1261267), _1261271))], (27553 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1261265), _1261267)))]]], (24008 ^ _775212) ^ [_1192392, _1192394] : [-(_1192392 = _1192394), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192392), _1192394)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1192394), _1192392))], (18627 ^ _775212) ^ [_1091718, _1091720] : [class_Rings_Olinordered__idom(_1091718), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091718), c_Groups_Ozero__class_Ozero(_1091718)), hAPP(hAPP(c_Power_Opower__class_Opower(_1091718), _1091720), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (30428 ^ _775212) ^ [_1323042, _1323044, _1323046, _1323048] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1323042, tc_HOL_Obool)), _1323044), hAPP(hAPP(c_Set_Oinsert(_1323042), _1323046), _1323048)))), 30431 ^ _775212 : [(30434 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1323042, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323042, tc_HOL_Obool)), _1323044), hAPP(hAPP(c_Set_Oinsert(_1323042), _1323046), c_Orderings_Obot__class_Obot(tc_fun(_1323042, tc_HOL_Obool))))), _1323048))], (30432 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1323042), _1323046), _1323044)))]], 30435 ^ _775212 : [(30438 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1323042, tc_HOL_Obool)), _1323044), _1323048))], (30436 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1323042), _1323046), _1323044))]]], (23286 ^ _775212) ^ [_1179128, _1179130] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1179128), hAPP(c_Nat_OSuc, _1179130)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1179130), 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)), _1179130)), _1179128))], (45106 ^ _775212) ^ [_1668220, _1668222, _1668224, _1668226] : [_1668226 = c_List_Olist_ONil(_1668220), -(hAPP(hAPP(c_List_Omap(_1668220, _1668222), _1668224), _1668226) = c_List_Olist_ONil(_1668222))], (3300 ^ _775212) ^ [_824854, _824856, _824858, _824860, _824862, _824864] : [-(c_Predicate_ORangeP(_824864, _824860, _824856) = c_Predicate_ORangeP(_824862, _824858, _824854)), _824864 = _824862, _824860 = _824858, _824856 = _824854], (43557 ^ _775212) ^ [_1626450, _1626452, _1626454] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1626450, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1626450, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1626450, tc_HOL_Obool), tc_HOL_Obool)), _1626452), _1626454))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1626450, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1626450, tc_HOL_Obool), _1626452)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1626450, tc_HOL_Obool), _1626454)))))], (26909 ^ _775212) ^ [_1248378, _1248380, _1248382, _1248384, _1248386] : [-(hAPP(c_Set_Oimage(_1248378, _1248380, _1248382), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248378, tc_HOL_Obool)), _1248384), _1248386)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248380, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1248378, _1248380, _1248382), _1248384)), hAPP(c_Set_Oimage(_1248378, _1248380, _1248382), _1248386)))], (6829 ^ _775212) ^ [_884103] : [class_Rings_Osemiring__1(_884103), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_884103), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_884103))], (9669 ^ _775212) ^ [_931477, _931479, _931481, _931483] : [class_Groups_Oordered__ab__semigroup__add(_931477), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931477), _931479), _931481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931477), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931477), _931479), _931483)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931477), _931481), _931483))))], (49780 ^ _775212) ^ [_1771871, _1771873, _1771875] : [-(hBOOL(hAPP(hAPP(c_member(_1771871), _1771873), hAPP(c_List_Oset(_1771871), _1771875)))), -(c_List_Oinsert(_1771871, _1771873, _1771875) = hAPP(hAPP(c_List_Olist_OCons(_1771871), _1771873), _1771875))], (37006 ^ _775212) ^ [] : [-(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))], (37044 ^ _775212) ^ [_1464261, _1464263, _1464265, _1464267, _1464269] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1464261, _1464263, _1464265), _1464267), _1464269), c_Orderings_Obot__class_Obot(tc_fun(_1464263, tc_HOL_Obool))) = _1464269)], (46678 ^ _775212) ^ [_1705521, _1705523, _1705525] : [-(hAPP(c_List_Otl(_1705521), hAPP(hAPP(c_List_Otake(_1705521), _1705523), _1705525)) = hAPP(hAPP(c_List_Otake(_1705521), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1705523), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1705521), _1705525)))], (50721 ^ _775212) ^ [_1792350, _1792352] : [-(c_List_Oreplicate(_1792350, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1792352) = c_List_Olist_ONil(_1792350))], (44610 ^ _775212) ^ [_1655211, _1655213, _1655215] : [-(hAPP(hAPP(c_List_Onth(_1655211), hAPP(hAPP(c_List_Olist_OCons(_1655211), _1655213), _1655215)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1655213)], (51791 ^ _775212) ^ [_1816357, _1816359] : [-(c_Relation_Osym(_1816357, c_Relation_OId__on(_1816357, _1816359)))], (46444 ^ _775212) ^ [_1700605, _1700607, _1700609, _1700611] : [hBOOL(hAPP(c_List_Odistinct(_1700605), _1700607)), -(hBOOL(hAPP(hAPP(c_member(_1700605), _1700609), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1700605, tc_HOL_Obool)), hAPP(c_List_Oset(_1700605), _1700607)), hAPP(hAPP(c_Set_Oinsert(_1700605), hAPP(hAPP(c_List_Onth(_1700605), _1700607), _1700611)), c_Orderings_Obot__class_Obot(tc_fun(_1700605, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1700605), hAPP(hAPP(c_List_Olist__update(_1700605, _1700607), _1700611), _1700609))))], (41295 ^ _775212) ^ [_1571324, _1571326] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571324, _1571324)), hAPP(hAPP(c_Product__Type_OPair(_1571324, _1571324), 41296 ^ [_1571324, _1571326]), 41296 ^ [_1571324, _1571326])), c_Transitive__Closure_Otrancl(_1571324, _1571326)))), -(c_Wellfounded_Oacyclic(_1571324, _1571326))], (49197 ^ _775212) ^ [_1759660, _1759662, _1759664, _1759666, _1759668] : [c_List_Olist__all2(_1759660, _1759662, _1759664, hAPP(c_List_Orev(_1759660), _1759666), hAPP(c_List_Orev(_1759662), _1759668)), -(c_List_Olist__all2(_1759660, _1759662, _1759664, _1759666, _1759668))], (44893 ^ _775212) ^ [_1662227, _1662229, _1662231] : [c_Fun_Oinj__on(tc_List_Olist(_1662227), tc_List_Olist(_1662229), hAPP(c_List_Omap(_1662227, _1662229), _1662231), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1662227), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1662227, _1662229, _1662231, c_Orderings_Otop__class_Otop(tc_fun(_1662227, tc_HOL_Obool))))], (17471 ^ _775212) ^ [_1071916, _1071918] : [class_Int_Onumber__ring(_1071916), class_Rings_Olinordered__idom(_1071916), 17478 ^ _775212 : [(17485 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071918), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071916), hAPP(c_Int_Onumber__class_Onumber__of(_1071916), _1071918)), c_Groups_Ozero__class_Ozero(_1071916))))], (17479 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071916), hAPP(c_Int_Onumber__class_Onumber__of(_1071916), _1071918)), c_Groups_Ozero__class_Ozero(_1071916))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071918), c_Int_OPls)))]]], (44174 ^ _775212) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5420 ^ _775212) ^ [_857908, _857910] : [_857910 = _857908, -(c_Orderings_Oord__class_Oless__eq(_857910) = c_Orderings_Oord__class_Oless__eq(_857908))], (50051 ^ _775212) ^ [_1778154, _1778156, _1778158, _1778160, _1778162] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778154)), _1778156) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778158)), _1778160), 50057 ^ _775212 : [(50060 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(_1778162, hAPP(hAPP(c_List_Onth(_1778154), _1778156), 50056 ^ [_1778154, _1778156, _1778158, _1778160, _1778162])), hAPP(hAPP(c_List_Onth(_1778158), _1778160), 50056 ^ [_1778154, _1778156, _1778158, _1778160, _1778162])))], (50058 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50056 ^ [_1778154, _1778156, _1778158, _1778160, _1778162]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778154)), _1778156))))]], -(c_List_Olist__all2(_1778154, _1778158, _1778162, _1778156, _1778160))], (44748 ^ _775212) ^ [_1658912, _1658914, _1658916, _1658918, _1658920] : [-(hAPP(hAPP(c_List_Otake(_1658912), _1658914), hAPP(hAPP(c_List_Omap(_1658916, _1658912), _1658918), _1658920)) = hAPP(hAPP(c_List_Omap(_1658916, _1658912), _1658918), hAPP(hAPP(c_List_Otake(_1658916), _1658914), _1658920)))], (7250 ^ _775212) ^ [_890400, _890402, _890404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890400), _890402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890400), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _890402), _890404))))], (41370 ^ _775212) ^ [_1572802, _1572804, _1572806, _1572808] : [class_Orderings_Olinorder(_1572802), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572802), _1572804)), hBOOL(hAPP(hAPP(c_member(_1572802), _1572806), _1572804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1572802), hAPP(hAPP(c_Finite__Set_Ofold(_1572802, _1572802, c_Orderings_Oord__class_Omin(_1572802)), _1572808), _1572804)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1572802), _1572806), _1572808))))], (44096 ^ _775212) ^ [_1639441, _1639443] : [-(c_List_Olenlex(_1639441, _1639443) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1639441)), tc_List_Olist(_1639441)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1639441), c_Wellfounded_Oless__than, c_List_Olex(_1639441, _1639443))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1639441), tc_List_Olist(_1639441), tc_prod(tc_Nat_Onat, tc_List_Olist(_1639441))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1639441), tc_prod(tc_Nat_Onat, tc_List_Olist(_1639441))), tc_List_Olist(_1639441)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1639441))), c_Nat_Osize__class_Osize(tc_List_Olist(_1639441)))), c_COMBI(tc_List_Olist(_1639441)))))], (48097 ^ _775212) ^ [_1735716, _1735718, _1735720, _1735722] : [class_Orderings_Olinorder(_1735716), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735718)), c_List_Olinorder__class_Osort__key(_1735718, _1735716, _1735720, _1735722)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735718)), _1735722))], (37952 ^ _775212) ^ [_1485894, _1485896, _1485898, _1485900, _1485902, _1485904] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1485894, _1485896)), hAPP(hAPP(c_Product__Type_OPair(_1485894, _1485896), _1485898), _1485900)), hAPP(hAPP(c_Product__Type_OSigma(_1485894, _1485896), _1485902), _1485904))), 37955 ^ _775212 : [(37958 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1485896), _1485900), hAPP(_1485904, _1485898))))], (37956 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1485894), _1485898), _1485902)))]]], (31589 ^ _775212) ^ [_1346951, _1346953] : [class_Orderings_Olinorder(_1346951), -(c_Big__Operators_Olinorder__class_OMin(_1346951, hAPP(hAPP(c_Set_Oinsert(_1346951), _1346953), c_Orderings_Obot__class_Obot(tc_fun(_1346951, tc_HOL_Obool)))) = _1346953)], (19049 ^ _775212) ^ [_1099741, _1099743] : [class_Rings_Odivision__ring(_1099741), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099741), _1099743), c_Groups_Oone__class_Oone(_1099741)) = _1099743)], (17047 ^ _775212) ^ [_1065343] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1065343), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1065343))], (33841 ^ _775212) ^ [_1392982, _1392984, _1392986, _1392988, _1392990] : [c_Finite__Set_Ofolding__one__idem(_1392982, _1392984, _1392986), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392982), _1392988)), -(_1392988 = c_Orderings_Obot__class_Obot(tc_fun(_1392982, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392982), _1392990)), -(_1392990 = c_Orderings_Obot__class_Obot(tc_fun(_1392982, tc_HOL_Obool))), -(hAPP(_1392986, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392982, tc_HOL_Obool)), _1392988), _1392990)) = hAPP(hAPP(_1392984, hAPP(_1392986, _1392988)), hAPP(_1392986, _1392990)))], (51456 ^ _775212) ^ [_1808856, _1808858, _1808860, _1808862] : [class_Complete__Lattice_Ocomplete__lattice(_1808856), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1808858, _1808856), _1808860), _1808862) = c_Complete__Lattice_OSup__class_OSup(_1808856, hAPP(c_Set_OCollect(_1808856), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1808858, _1808856), tc_HOL_Obool), tc_HOL_Obool, _1808856), c_HOL_OEx(tc_fun(_1808858, _1808856))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1808858, _1808856), tc_HOL_Obool), tc_fun(tc_fun(_1808858, _1808856), tc_HOL_Obool), _1808856), hAPP(c_COMBS(tc_fun(_1808858, _1808856), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1808858, _1808856)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1808858, _1808856), tc_fun(tc_fun(_1808858, _1808856), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1808858, _1808856))), _1808860)))), hAPP(hAPP(c_COMBC(_1808856, tc_fun(tc_fun(_1808858, _1808856), _1808856), tc_fun(tc_fun(_1808858, _1808856), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1808856, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1808858, _1808856), _1808856), tc_fun(tc_fun(_1808858, _1808856), tc_HOL_Obool)), _1808856), c_COMBB(_1808856, tc_HOL_Obool, tc_fun(_1808858, _1808856))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1808858, _1808856), _1808858, _1808856), c_COMBI(tc_fun(_1808858, _1808856))), _1808862)))))))], (1684 ^ _775212) ^ [_799118, _799120] : [-(class_Rings_Ocomm__semiring__1(_799118)), _799120 = _799118, class_Rings_Ocomm__semiring__1(_799120)], (44018 ^ _775212) ^ [_1637571, _1637573, _1637575, _1637577, _1637579, _1637581] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637571, _1637573)), _1637575), hAPP(hAPP(c_Relation_Orel__comp(_1637571, _1637577, _1637573), _1637579), _1637581))), 44024 ^ _775212 : [(44029 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637577, _1637573)), hAPP(hAPP(c_Product__Type_OPair(_1637577, _1637573), 44022 ^ [_1637571, _1637573, _1637575, _1637577, _1637579, _1637581]), 44023 ^ [_1637571, _1637573, _1637575, _1637577, _1637579, _1637581])), _1637581)))], (44027 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637571, _1637577)), hAPP(hAPP(c_Product__Type_OPair(_1637571, _1637577), 44021 ^ [_1637571, _1637573, _1637575, _1637577, _1637579, _1637581]), 44022 ^ [_1637571, _1637573, _1637575, _1637577, _1637579, _1637581])), _1637579)))], (44025 ^ _775212) ^ [] : [-(_1637575 = hAPP(hAPP(c_Product__Type_OPair(_1637571, _1637573), 44021 ^ [_1637571, _1637573, _1637575, _1637577, _1637579, _1637581]), 44023 ^ [_1637571, _1637573, _1637575, _1637577, _1637579, _1637581]))]]], (42818 ^ _775212) ^ [_1608948, _1608950] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1608948, _1608948), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1608948, _1608950)), c_Relation_OId(_1608948)) = c_Transitive__Closure_Ortrancl(_1608948, _1608950))], (1244 ^ _775212) ^ [_793618, _793620] : [-(class_Divides_Oring__div(_793618)), _793620 = _793618, class_Divides_Oring__div(_793620)], (38008 ^ _775212) ^ [_1487371, _1487373, _1487375, _1487377, _1487379, _1487381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1487371, _1487373), tc_HOL_Obool)), _1487375), hAPP(hAPP(c_Product__Type_OSigma(_1487371, _1487373), _1487377), hAPP(c_COMBK(tc_fun(_1487373, tc_HOL_Obool), _1487371), _1487379)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1487373, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1487371, _1487373, _1487375), _1487381)), _1487379)))], (52285 ^ _775212) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (51080 ^ _775212) ^ [_1800253, _1800255, _1800257, _1800259] : [class_Groups_Ocomm__monoid__add(_1800253), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1800255, tc_HOL_Obool)), _1800257)), 51090 ^ _775212 : [(51093 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1800255), 51089 ^ [_1800253, _1800255, _1800257, _1800259]))], (51091 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1800255, tc_HOL_Obool)), 51089 ^ [_1800253, _1800255, _1800257, _1800259]), _1800257)))]], 51097 ^ _775212 : [(51101 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1800255, tc_HOL_Obool)), 51099 ^ [_1800253, _1800255, _1800257, _1800259]), _1800257)))], (51098 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1800255, tc_HOL_Obool)), 51096 ^ [_1800253, _1800255, _1800257, _1800259]), _1800257)))], (51110 ^ _775212) ^ [] : [hAPP(_1800259, 51104 ^ [_1800253, _1800255, _1800257, _1800259]) = c_Groups_Ozero__class_Ozero(_1800253)], (51106 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1800255), 51104 ^ [_1800253, _1800255, _1800257, _1800259]), 51096 ^ [_1800253, _1800255, _1800257, _1800259])))], (51108 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1800255), 51104 ^ [_1800253, _1800255, _1800257, _1800259]), 51099 ^ [_1800253, _1800255, _1800257, _1800259])))], (51103 ^ _775212) ^ [] : [51096 ^ [_1800253, _1800255, _1800257, _1800259] = 51099 ^ [_1800253, _1800255, _1800257, _1800259]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1800255, _1800253), _1800259), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1800255, tc_HOL_Obool), _1800257)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1800255, tc_HOL_Obool), _1800253), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1800255, _1800253), _1800259)), _1800257))], (45461 ^ _775212) ^ [_1677297, _1677299, _1677301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1677297), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1677299), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1677299)), _1677301)))), -(hBOOL(hAPP(hAPP(c_member(_1677299), hAPP(c_Random_Opick(_1677299, _1677301), _1677297)), hAPP(c_List_Oset(_1677299), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1677299), _1677299), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1677299)), _1677301)))))], (22398 ^ _775212) ^ [_1161696, _1161698] : [22399 ^ _775212 : [(22402 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161698), _1161696))], (22400 ^ _775212) ^ [] : [_1161696 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1161698, _1161696) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161698))], (50453 ^ _775212) ^ [_1786999, _1787001, _1787003] : [50454 ^ _775212 : [(50455 ^ _775212) ^ [_1787076, _1787078] : [_1787003 = hAPP(hAPP(c_List_Oappend(_1786999), _1787078), hAPP(hAPP(c_List_Olist_OCons(_1786999), _1787001), _1787076))]], -(hBOOL(hAPP(hAPP(c_member(_1786999), _1787001), hAPP(c_List_Oset(_1786999), _1787003))))], (48510 ^ _775212) ^ [_1746369, _1746371] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1746369)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1746371)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1746369), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1746371)) = c_List_Olist_ONil(tc_Nat_Onat))], (24426 ^ _775212) ^ [_1199275, _1199277, _1199279, _1199281] : [class_Divides_Osemiring__div(_1199275), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199275), _1199277), _1199279)), 24433 ^ _775212 : [(24440 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199275), _1199277), _1199281)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199275), _1199277), c_Divides_Odiv__class_Omod(_1199275, _1199281, _1199279))))], (24434 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199275), _1199277), c_Divides_Odiv__class_Omod(_1199275, _1199281, _1199279))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1199275), _1199277), _1199281)))]]], (42115 ^ _775212) ^ [_1589178, _1589180, _1589182, _1589184, _1589186, _1589188] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1589178, tc_fun(_1589180, tc_HOL_Obool)), _1589182), _1589184), _1589186)), hBOOL(hAPP(hAPP(c_member(_1589178), _1589188), _1589182)), -(hBOOL(hAPP(hAPP(_1589184, _1589188), _1589186)))], (48352 ^ _775212) ^ [_1742333, _1742335, _1742337, _1742339] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1742333)), c_List_Otranspose__rel(_1742333)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1742333)), hAPP(hAPP(c_List_Olist_OCons(_1742333), _1742335), _1742337)), _1742339))), -(c_List_Otranspose(_1742333, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1742333)), hAPP(hAPP(c_List_Olist_OCons(_1742333), _1742335), _1742337)), _1742339)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1742333)), hAPP(hAPP(c_List_Olist_OCons(_1742333), _1742335), c_List_Oconcat(_1742333, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1742333), tc_List_Olist(_1742333)), c_List_Olist_Olist__case(tc_List_Olist(_1742333), _1742333, c_List_Olist_ONil(_1742333), hAPP(hAPP(c_COMBB(tc_List_Olist(_1742333), tc_fun(tc_List_Olist(_1742333), tc_List_Olist(_1742333)), _1742333), c_COMBK(tc_List_Olist(_1742333), tc_List_Olist(_1742333))), hAPP(hAPP(c_COMBC(_1742333, tc_List_Olist(_1742333), tc_List_Olist(_1742333)), c_List_Olist_OCons(_1742333)), c_List_Olist_ONil(_1742333))))), _1742339)))), c_List_Otranspose(_1742333, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1742333)), _1742337), c_List_Oconcat(tc_List_Olist(_1742333), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1742333), tc_List_Olist(tc_List_Olist(_1742333))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1742333)), _1742333, c_List_Olist_ONil(tc_List_Olist(_1742333)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1742333), tc_List_Olist(tc_List_Olist(_1742333))), _1742333), hAPP(hAPP(c_COMBC(tc_List_Olist(_1742333), tc_List_Olist(tc_List_Olist(_1742333)), tc_List_Olist(tc_List_Olist(_1742333))), c_List_Olist_OCons(tc_List_Olist(_1742333))), c_List_Olist_ONil(tc_List_Olist(_1742333)))))), _1742339))))))], (29540 ^ _775212) ^ [_1301137, _1301139, _1301141, _1301143, _1301145, _1301147] : [hBOOL(hAPP(hAPP(c_member(_1301137), _1301139), _1301141)), hBOOL(hAPP(hAPP(_1301143, _1301139), _1301145)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1301137, tc_fun(_1301147, tc_HOL_Obool)), _1301141), _1301143), _1301145)))], (45782 ^ _775212) ^ [_1684696, _1684698, _1684700] : [hAPP(hAPP(c_List_Oappend(_1684696), _1684698), _1684700) = c_List_Olist_ONil(_1684696), 45785 ^ _775212 : [(45788 ^ _775212) ^ [] : [-(_1684700 = c_List_Olist_ONil(_1684696))], (45786 ^ _775212) ^ [] : [-(_1684698 = c_List_Olist_ONil(_1684696))]]], (7833 ^ _775212) ^ [_901010, _901012] : [class_Groups_Ogroup__add(_901010), 7836 ^ _775212 : [(7843 ^ _775212) ^ [] : [_901012 = c_Groups_Ozero__class_Ozero(_901010), -(hAPP(c_Groups_Ouminus__class_Ouminus(_901010), _901012) = c_Groups_Ozero__class_Ozero(_901010))], (7837 ^ _775212) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_901010), _901012) = c_Groups_Ozero__class_Ozero(_901010), -(_901012 = c_Groups_Ozero__class_Ozero(_901010))]]], (41241 ^ _775212) ^ [_1570132, _1570134, _1570136] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1570132), _1570134)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1570132, tc_HOL_Obool)), _1570134), _1570136) = hAPP(hAPP(c_Finite__Set_Ofold(_1570132, tc_fun(_1570132, tc_HOL_Obool), c_Set_Oinsert(_1570132)), _1570136), _1570134))], (39373 ^ _775212) ^ [_1523335, _1523337] : [c_Relation_Orefl__on(_1523335, c_Orderings_Otop__class_Otop(tc_fun(_1523335, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1523335, _1523335)), hAPP(c_Product__Type_Oprod_Oprod__case(_1523335, _1523335, tc_HOL_Obool), _1523337))), -(c_Predicate_Oreflp(_1523335, _1523337))], (29214 ^ _775212) ^ [_1294466, _1294468, _1294470, _1294472] : [-(hAPP(c_Set_Oimage(_1294466, _1294468, _1294470), _1294472) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294466, tc_fun(_1294468, tc_HOL_Obool)), _1294472), hAPP(hAPP(c_COMBC(_1294466, tc_fun(_1294468, tc_HOL_Obool), tc_fun(_1294468, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1294468, tc_fun(tc_fun(_1294468, tc_HOL_Obool), tc_fun(_1294468, tc_HOL_Obool)), _1294466), c_Set_Oinsert(_1294468)), _1294470)), c_Orderings_Obot__class_Obot(tc_fun(_1294468, tc_HOL_Obool)))))], (37707 ^ _775212) ^ [_1479086, _1479088, _1479090, _1479092, _1479094] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1479086, _1479086, _1479088, _1479090, _1479092), _1479094)), -(hBOOL(hAPP(hAPP(c_member(_1479086), _1479090), _1479092))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1479086, _1479088, hAPP(hAPP(c_Set_Oinsert(_1479086), _1479090), _1479092)), _1479094)))], (8627 ^ _775212) ^ [_915014, _915016, _915018] : [class_Rings_Olinordered__idom(_915014), 8630 ^ _775212 : [(8637 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _915016), _915018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915014), hAPP(c_Int_Oring__1__class_Oof__int(_915014), _915016)), hAPP(c_Int_Oring__1__class_Oof__int(_915014), _915018))))], (8631 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915014), hAPP(c_Int_Oring__1__class_Oof__int(_915014), _915016)), hAPP(c_Int_Oring__1__class_Oof__int(_915014), _915018))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _915016), _915018)))]]], (10928 ^ _775212) ^ [_953896, _953898, _953900, _953902] : [class_Groups_Oordered__comm__monoid__add(_953896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953896), c_Groups_Ozero__class_Ozero(_953896)), _953898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953896), _953900), _953902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953896), _953900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953896), _953898), _953902))))], (46182 ^ _775212) ^ [_1694618, _1694620] : [-(hAPP(c_List_Oset(_1694618), hAPP(c_List_Orotate1(_1694618), _1694620)) = hAPP(c_List_Oset(_1694618), _1694620))], (5680 ^ _775212) ^ [_864761, _864763, _864765, _864767] : [-(c_Com_Ocom_OSemi(_864761, _864763) = c_Com_Ocom_OSemi(_864765, _864767)), _864761 = _864765, _864763 = _864767], (24144 ^ _775212) ^ [_1194553, _1194555] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194553), _1194555)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194555), _1194553)), -(_1194553 = _1194555)], (50663 ^ _775212) ^ [_1791333, _1791335, _1791337] : [-(c_List_Osplice(_1791333, hAPP(hAPP(c_List_Olist_OCons(_1791333), _1791335), _1791337), c_List_Olist_ONil(_1791333)) = hAPP(hAPP(c_List_Olist_OCons(_1791333), _1791335), _1791337))], (37918 ^ _775212) ^ [_1484711, _1484713, _1484715, _1484717, _1484719] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1484711, _1484713), _1484715), hAPP(hAPP(c_COMBS(_1484711, tc_fun(_1484713, tc_HOL_Obool), tc_fun(_1484713, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484713, tc_HOL_Obool), tc_fun(tc_fun(_1484713, tc_HOL_Obool), tc_fun(_1484713, tc_HOL_Obool)), _1484711), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484713, tc_HOL_Obool))), _1484717)), _1484719)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1484711, _1484713), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1484711, _1484713), _1484715), _1484717)), hAPP(hAPP(c_Product__Type_OSigma(_1484711, _1484713), _1484715), _1484719)))], (46280 ^ _775212) ^ [_1696981, _1696983, _1696985, _1696987] : [_1696981 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1696983), _1696981), hAPP(hAPP(c_List_Olist_OCons(_1696983), _1696985), _1696987)) = hAPP(hAPP(c_List_Olist_OCons(_1696983), _1696985), _1696987))], (13701 ^ _775212) ^ [_1002339, _1002341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002339), 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)), _1002341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1002339), _1002341)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (3914 ^ _775212) ^ [_834591, _834593, _834595, _834597] : [-(c_Big__Operators_Olattice__class_OSup__fin(_834597, _834593) = c_Big__Operators_Olattice__class_OSup__fin(_834595, _834591)), _834597 = _834595, _834593 = _834591], (52367 ^ _775212) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (19097 ^ _775212) ^ [_1100674] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1100674)))], (15485 ^ _775212) ^ [_1036686, _1036688, _1036690, _1036692, _1036694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036686), _1036688)), 15488 ^ _775212 : [(15495 ^ _775212) ^ [] : [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), _1036688), _1036686)), _1036690)), _1036692) = _1036694, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036688), _1036690)), _1036692) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036686), _1036690)), _1036694))], (15489 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036688), _1036690)), _1036692) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036686), _1036690)), _1036694), -(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), _1036688), _1036686)), _1036690)), _1036692) = _1036694)]]], (17329 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (52127 ^ _775212) ^ [_1822533, _1822535] : [class_Lattices_Olattice(_1822533), -(class_Lattices_Osemilattice__sup(tc_fun(_1822535, _1822533)))], (50387 ^ _775212) ^ [_1785462, _1785464, _1785466, _1785468] : [c_List_Olist__ex(_1785462, _1785464, hAPP(hAPP(c_List_Olist_OCons(_1785462), _1785466), _1785468)), -(hBOOL(hAPP(_1785464, _1785466))), -(c_List_Olist__ex(_1785462, _1785464, _1785468))], (41666 ^ _775212) ^ [_1578709, _1578711, _1578713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578709, _1578709), tc_HOL_Obool)), _1578711), hAPP(hAPP(c_Product__Type_OSigma(_1578709, _1578709), _1578713), hAPP(c_COMBK(tc_fun(_1578709, tc_HOL_Obool), _1578709), _1578713)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578709, _1578709), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1578709, _1578711)), hAPP(hAPP(c_Product__Type_OSigma(_1578709, _1578709), _1578713), hAPP(c_COMBK(tc_fun(_1578709, tc_HOL_Obool), _1578709), _1578713)))))], (38110 ^ _775212) ^ [_1490322, _1490324, _1490326, _1490328] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490322), _1490324)), 38116 ^ _775212 : [(38119 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490326), hAPP(_1490328, 38115 ^ [_1490322, _1490324, _1490326, _1490328])))], (38117 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490322), 38115 ^ [_1490322, _1490324, _1490326, _1490328]), _1490324)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1490322, _1490326)), hAPP(hAPP(c_Product__Type_OSigma(_1490322, _1490326), _1490324), _1490328))))], (17701 ^ _775212) ^ [_1075877, _1075879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075877), _1075879)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1075877)), c_Int_OBit1(_1075879))))], (8015 ^ _775212) ^ [_903945, _903947] : [class_Rings_Omult__zero(_903945), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903945), _903947), c_Groups_Ozero__class_Ozero(_903945)) = c_Groups_Ozero__class_Ozero(_903945))], (16591 ^ _775212) ^ [_1057517, _1057519] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1057517), _1057519))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1057517))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1057519))))], (18093 ^ _775212) ^ [_1082428, _1082430] : [c_Int_OBit0(_1082428) = c_Int_OBit0(_1082430), -(_1082428 = _1082430)], (35615 ^ _775212) ^ [_1432953, _1432955, _1432957] : [class_Lattices_Olattice(_1432953), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432953), _1432955)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432953), _1432957)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432953, tc_HOL_Obool)), _1432955), _1432957) = c_Orderings_Obot__class_Obot(tc_fun(_1432953, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1432953), c_Big__Operators_Olattice__class_OSup__fin(_1432953, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1432953, tc_HOL_Obool)), _1432955), _1432957))), c_Big__Operators_Olattice__class_OSup__fin(_1432953, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432953, tc_HOL_Obool)), _1432955), _1432957))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1432953), c_Big__Operators_Olattice__class_OSup__fin(_1432953, _1432955)), c_Big__Operators_Olattice__class_OSup__fin(_1432953, _1432957)))], (37421 ^ _775212) ^ [_1471996, _1471998, _1472000, _1472002, _1472004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471996, tc_HOL_Obool)), _1471998), _1472000)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472002, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1472002, _1471996, _1472004), _1471998)), hAPP(c_Set_Ovimage(_1472002, _1471996, _1472004), _1472000))))], (9471 ^ _775212) ^ [_928343, _928345, _928347] : [class_Orderings_Olinorder(_928343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928343), _928345), _928347)), 9478 ^ _775212 : [(9485 ^ _775212) ^ [] : [_928345 = _928347, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928343), _928345), _928347))], (9479 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928343), _928345), _928347))), -(_928345 = _928347)]]], (28660 ^ _775212) ^ [_1284247, _1284249, _1284251] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284247, tc_HOL_Obool)), _1284249), _1284251) = c_Orderings_Obot__class_Obot(tc_fun(_1284247, tc_HOL_Obool))), _1284249 = c_Orderings_Obot__class_Obot(tc_fun(_1284247, tc_HOL_Obool)), _1284251 = c_Orderings_Obot__class_Obot(tc_fun(_1284247, tc_HOL_Obool))], (18245 ^ _775212) ^ [_1085021, _1085023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085021)), c_Int_OBit1(_1085023))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085021), _1085023)))], (27916 ^ _775212) ^ [_1269760, _1269762, _1269764] : [class_Orderings_Otop(_1269760), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1269762, _1269760)), _1269764) = c_Orderings_Otop__class_Otop(_1269760))], (19219 ^ _775212) ^ [_1102652, _1102654, _1102656, _1102658] : [class_Fields_Olinordered__field__inverse__zero(_1102652), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102652), _1102654), _1102656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102652), _1102658), c_Groups_Ozero__class_Ozero(_1102652))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102652), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102652), _1102656), _1102658)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102652), _1102654), _1102658))))], (5809 ^ _775212) ^ [_866893, _866895, _866897, _866899, _866901] : [c_Com_Ocom_OWhile(_866893, _866895) = c_Com_Ocom_OCond(_866897, _866899, _866901)], (49365 ^ _775212) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (23774 ^ _775212) ^ [_1188397, _1188399] : [_1188397 = _1188399, -(hAPP(c_Code__Numeral_Onat__of, _1188397) = hAPP(c_Code__Numeral_Onat__of, _1188399))], (41879 ^ _775212) ^ [_1583671, _1583673, _1583675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583671, _1583671), tc_HOL_Obool)), _1583673), _1583675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583671, _1583671), tc_HOL_Obool)), _1583675), c_Transitive__Closure_Ortrancl(_1583671, _1583673))), -(c_Transitive__Closure_Ortrancl(_1583671, _1583675) = c_Transitive__Closure_Ortrancl(_1583671, _1583673))], (9275 ^ _775212) ^ [_925522, _925524, _925526] : [class_Orderings_Olinorder(_925522), 9278 ^ _775212 : [(9285 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925522), _925526), _925524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925522), _925524), _925526))], (9279 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925522), _925524), _925526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925522), _925526), _925524)))]]], (14497 ^ _775212) ^ [_1017368, _1017370, _1017372] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017368), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1017370), _1017372)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017368), _1017370)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017368), _1017372)))], (39809 ^ _775212) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (10597 ^ _775212) ^ [_948094, _948096] : [class_Rings_Olinordered__semidom(_948094), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948094), c_Groups_Ozero__class_Ozero(_948094)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_948094), _948096))))], (35507 ^ _775212) ^ [_1430631, _1430633, _1430635, _1430637, _1430639] : [class_Groups_Ocomm__monoid__add(_1430631), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430633), _1430635)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430633), _1430637)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430633, tc_HOL_Obool)), _1430635), _1430637) = c_Orderings_Obot__class_Obot(tc_fun(_1430633, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430633, _1430631), _1430639), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430633, tc_HOL_Obool)), _1430635), _1430637)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1430631), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430633, _1430631), _1430639), _1430635)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430633, _1430631), _1430639), _1430637)))], (8605 ^ _775212) ^ [_914701, _914703] : [class_Int_Oring__char__0(_914701), 8608 ^ _775212 : [(8615 ^ _775212) ^ [] : [_914703 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_914701) = hAPP(c_Int_Oring__1__class_Oof__int(_914701), _914703))], (8609 ^ _775212) ^ [] : [c_Groups_Ozero__class_Ozero(_914701) = hAPP(c_Int_Oring__1__class_Oof__int(_914701), _914703), -(_914703 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (39599 ^ _775212) ^ [_1530937, _1530939, _1530941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530937, _1530937), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530937, _1530937, _1530937), _1530939), _1530941)), _1530939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1530937, tc_HOL_Obool), tc_fun(_1530937, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1530937, tc_HOL_Obool), tc_fun(_1530937, tc_HOL_Obool), tc_fun(_1530937, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1530937, _1530939)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1530937, tc_HOL_Obool), tc_fun(_1530937, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1530937, _1530941)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1530937, tc_HOL_Obool), tc_fun(_1530937, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1530937, tc_HOL_Obool), tc_fun(_1530937, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1530937, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1530937, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1530937, tc_HOL_Obool), tc_fun(_1530937, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1530937, _1530939))))], (37890 ^ _775212) ^ [_1483927, _1483929, _1483931, _1483933] : [hAPP(hAPP(c_Product__Type_OSigma(_1483927, _1483929), _1483931), hAPP(c_COMBK(tc_fun(_1483929, tc_HOL_Obool), _1483927), _1483933)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1483927, _1483929), tc_HOL_Obool)), -(_1483931 = c_Orderings_Obot__class_Obot(tc_fun(_1483927, tc_HOL_Obool))), -(_1483933 = c_Orderings_Obot__class_Obot(tc_fun(_1483929, tc_HOL_Obool)))], (47060 ^ _775212) ^ [_1713212, _1713214, _1713216] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1713212)), _1713214), c_List_Olists(_1713212, _1713216)))), 47061 ^ _775212 : [(47064 ^ _775212) ^ [_1713340, _1713342] : [_1713214 = hAPP(hAPP(c_List_Olist_OCons(_1713212), _1713342), _1713340), hBOOL(hAPP(hAPP(c_member(_1713212), _1713342), _1713216)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1713212)), _1713340), c_List_Olists(_1713212, _1713216)))], (47062 ^ _775212) ^ [] : [_1713214 = c_List_Olist_ONil(_1713212)]]], (44067 ^ _775212) ^ [_1638794, _1638796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 44068 ^ [_1638794, _1638796]), hAPP(_1638794, 44068 ^ [_1638794, _1638796]))), -(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)), _1638794)), _1638796)))))], (23560 ^ _775212) ^ [_1184147, _1184149, _1184151, _1184153, _1184155, _1184157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1184147, tc_fun(_1184149, tc_HOL_Obool))), _1184151), _1184153)), hBOOL(hAPP(hAPP(_1184151, _1184155), _1184157)), -(hBOOL(hAPP(hAPP(_1184153, _1184155), _1184157)))], (22916 ^ _775212) ^ [_1171854, _1171856] : [class_Orderings_Olinorder(_1171854), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1171854), _1171856), _1171856) = _1171856)], (22780 ^ _775212) ^ [_1168952, _1168954, _1168956, _1168958, _1168960] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1168952, _1168954, _1168956), _1168958), _1168960) = hAPP(hAPP(_1168958, hAPP(c_Product__Type_Ofst(_1168952, _1168954), _1168960)), hAPP(c_Product__Type_Osnd(_1168952, _1168954), _1168960)))], (19801 ^ _775212) ^ [_1112589, _1112591, _1112593, _1112595] : [class_Fields_Olinordered__field__inverse__zero(_1112589), 19804 ^ _775212 : [(19805 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), _1112591), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112589), _1112593), _1112595))), 19808 ^ _775212 : [(19815 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), c_Groups_Ozero__class_Ozero(_1112589)), _1112595))), 19818 ^ _775212 : [(19825 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), _1112595), c_Groups_Ozero__class_Ozero(_1112589)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), _1112591), c_Groups_Ozero__class_Ozero(_1112589))))], (19819 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), _1112595), c_Groups_Ozero__class_Ozero(_1112589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), _1112593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112589), _1112591), _1112595))))]]], (19809 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), c_Groups_Ozero__class_Ozero(_1112589)), _1112595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112589), _1112591), _1112595)), _1112593)))]]], (19831 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), _1112591), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112589), _1112593), _1112595)))), 19834 ^ _775212 : [(19837 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112589), _1112591), _1112595)), _1112593))], (19835 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), c_Groups_Ozero__class_Ozero(_1112589)), _1112595)))]], 19838 ^ _775212 : [(19841 ^ _775212) ^ [] : [19842 ^ _775212 : [(19845 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), _1112593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112589), _1112591), _1112595)))], (19843 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), _1112595), c_Groups_Ozero__class_Ozero(_1112589))))]], 19846 ^ _775212 : [(19849 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), _1112591), c_Groups_Ozero__class_Ozero(_1112589)))], (19847 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), _1112595), c_Groups_Ozero__class_Ozero(_1112589)))]]], (19839 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112589), c_Groups_Ozero__class_Ozero(_1112589)), _1112595))]]]]], (1644 ^ _775212) ^ [_798618, _798620] : [-(class_Groups_Oab__semigroup__add(_798618)), _798620 = _798618, class_Groups_Oab__semigroup__add(_798620)], (28852 ^ _775212) ^ [_1287971, _1287973, _1287975] : [-(hAPP(hAPP(c_Set_Oinsert(_1287971), _1287973), _1287975) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287971, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1287971), _1287973), c_Orderings_Obot__class_Obot(tc_fun(_1287971, tc_HOL_Obool)))), _1287975))], (1544 ^ _775212) ^ [_797368, _797370] : [-(class_Groups_Oordered__ab__semigroup__add(_797368)), _797370 = _797368, class_Groups_Oordered__ab__semigroup__add(_797370)], (22604 ^ _775212) ^ [_1165382, _1165384, _1165386, _1165388] : [class_Orderings_Olinorder(_1165382), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165382), _1165384), _1165386)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165382), _1165384), _1165388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165382), _1165384), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165382), _1165386), _1165388))))], (1184 ^ _775212) ^ [_792868, _792870] : [-(class_Rings_Olinordered__ring(_792868)), _792870 = _792868, class_Rings_Olinordered__ring(_792870)], (52589 ^ _775212) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (44423 ^ _775212) ^ [_1649633, _1649635, _1649637, _1649639] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649633), tc_List_Olist(_1649633))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649633), tc_List_Olist(_1649633)), _1649635), _1649637)), c_List_Olistrel(_1649633, _1649639))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649633), tc_List_Olist(_1649633))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649633), tc_List_Olist(_1649633)), _1649635), _1649637)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1649633), c_List_Olistrel1(_1649633, _1649639)))))], (50538 ^ _775212) ^ [_1788755, _1788757, _1788759, _1788761] : [-(c_List_Olist__all(_1788755, _1788757, hAPP(hAPP(c_List_Oappend(_1788755), _1788759), _1788761))), c_List_Olist__all(_1788755, _1788757, _1788759), c_List_Olist__all(_1788755, _1788757, _1788761)], (30757 ^ _775212) ^ [_1330325, _1330327, _1330329] : [_1330325 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1330327, _1330327), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1330327, _1330327), tc_HOL_Obool)), _1330325), _1330329)))], (2760 ^ _775212) ^ [_815982, _815984, _815986, _815988, _815990, _815992, _815994, _815996, _815998, _816000, _816002, _816004, _816006, _816008] : [-(c_New__Random__Sequence_Opos__decr__bind(_816008, _816004, _816000, _815996, _815992, _815988, _815984) = c_New__Random__Sequence_Opos__decr__bind(_816006, _816002, _815998, _815994, _815990, _815986, _815982)), _816008 = _816006, _816004 = _816002, _816000 = _815998, _815996 = _815994, _815992 = _815990, _815988 = _815986, _815984 = _815982], (44292 ^ _775212) ^ [_1645589, _1645591, _1645593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1645589, _1645589), tc_HOL_Obool)), _1645591), _1645593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1645589), tc_List_Olist(_1645589)), tc_HOL_Obool)), c_List_Olistrel1(_1645589, _1645591)), c_List_Olistrel1(_1645589, _1645593))))], (46988 ^ _775212) ^ [_1712132, _1712134, _1712136] : [-(_1712132 = c_List_Olist_ONil(_1712134)), -(c_List_Olast(_1712134, hAPP(hAPP(c_List_Olist_OCons(_1712134), _1712136), _1712132)) = c_List_Olast(_1712134, _1712132))], (52557 ^ _775212) ^ [_1826991, _1826993] : [-(class_Finite__Set_Ofinite(tc_prod(_1826991, _1826993))), class_Finite__Set_Ofinite(_1826991), class_Finite__Set_Ofinite(_1826993)], (34719 ^ _775212) ^ [_1412786, _1412788, _1412790] : [class_Lattices_Olattice(_1412786), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412786), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1412786), _1412788), _1412790)), _1412788)))], (17977 ^ _775212) ^ [_1080194, _1080196] : [class_Int_Onumber__ring(_1080194), class_Rings_Olinordered__idom(_1080194), 17984 ^ _775212 : [(17991 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1080196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080194), c_Groups_Oone__class_Oone(_1080194)), hAPP(c_Int_Onumber__class_Onumber__of(_1080194), _1080196))))], (17985 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080194), c_Groups_Oone__class_Oone(_1080194)), hAPP(c_Int_Onumber__class_Onumber__of(_1080194), _1080196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1080196)))]]], (32349 ^ _775212) ^ [_1361063, _1361065] : [-(c_Sum__Type_OPlus(_1361063, _1361065, c_Orderings_Otop__class_Otop(tc_fun(_1361063, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1361065, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1361063, _1361065), tc_HOL_Obool)))], (30879 ^ _775212) ^ [_1332895, _1332897, _1332899, _1332901] : [hBOOL(hAPP(hAPP(c_member(_1332895), _1332897), c_SetInterval_Oord_OlessThan(_1332895, _1332899, _1332901))), -(hBOOL(hAPP(hAPP(_1332899, _1332897), _1332901)))], (4400 ^ _775212) ^ [_842142, _842144] : [_842144 = _842142, -(c_List_Oreturn__list(_842144) = c_List_Oreturn__list(_842142))], (37052 ^ _775212) ^ [] : [-(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))))], (43216 ^ _775212) ^ [_1618693, _1618695, _1618697] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1618693, tc_HOL_Obool)), _1618695), _1618697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1618693, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1618693, tc_HOL_Obool), _1618697)), _1618695)))], (27940 ^ _775212) ^ [_1270137, _1270139, _1270141, _1270143] : [-(hAPP(hAPP(c_Set_Oinsert(_1270137), _1270139), hAPP(hAPP(c_Set_Oinsert(_1270137), _1270141), _1270143)) = hAPP(hAPP(c_Set_Oinsert(_1270137), _1270141), hAPP(hAPP(c_Set_Oinsert(_1270137), _1270139), _1270143)))], (12669 ^ _775212) ^ [_984205, _984207] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _984205), _984207) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _984205, _984207) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (43844 ^ _775212) ^ [_1633603, _1633605, _1633607, _1633609] : [class_Lattices_Osemilattice__inf(_1633603), hBOOL(hAPP(c_Finite__Set_Ofinite(_1633603), _1633605)), 43854 ^ _775212 : [(43857 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1633603), _1633607), 43853 ^ [_1633603, _1633605, _1633607, _1633609]))], (43855 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633603), 43853 ^ [_1633603, _1633605, _1633607, _1633609]), _1633605)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1633603), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1633603), _1633607), _1633609)), hAPP(hAPP(c_Finite__Set_Ofold(_1633603, _1633603, c_Lattices_Osemilattice__inf__class_Oinf(_1633603)), _1633609), _1633605))))], (42293 ^ _775212) ^ [_1593847, _1593849, _1593851, _1593853, _1593855] : [-(hAPP(c_Relation_Oconverse(_1593847, _1593849), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593851, tc_fun(tc_prod(_1593847, _1593849), tc_HOL_Obool)), _1593853), _1593855)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593851, tc_fun(tc_prod(_1593849, _1593847), tc_HOL_Obool)), _1593853), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1593847, _1593849), tc_HOL_Obool), tc_fun(tc_prod(_1593849, _1593847), tc_HOL_Obool), _1593851), c_Relation_Oconverse(_1593847, _1593849)), _1593855)))], (28836 ^ _775212) ^ [_1287688, _1287690, _1287692] : [class_Groups_Ocomm__monoid__add(_1287688), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1287690, _1287688), _1287692), c_Orderings_Obot__class_Obot(tc_fun(_1287690, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1287688))], (46748 ^ _775212) ^ [_1706994, _1706996, _1706998, _1707000] : [class_Groups_Osemigroup__add(_1706994), -(hAPP(c_List_Ofoldl(_1706994, _1706994, c_Groups_Oplus__class_Oplus(_1706994), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1706994), _1706996), _1706998)), _1707000) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1706994), _1706996), hAPP(c_List_Ofoldl(_1706994, _1706994, c_Groups_Oplus__class_Oplus(_1706994), _1706998), _1707000)))], (19019 ^ _775212) ^ [_1099004, _1099006] : [class_Rings_Odivision__ring(_1099004), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099004), c_Groups_Ozero__class_Ozero(_1099004)), _1099006) = c_Groups_Ozero__class_Ozero(_1099004))], (2328 ^ _775212) ^ [_809130, _809132] : [_809132 = _809130, -(c_Nitpick_Oone__frac(_809132) = c_Nitpick_Oone__frac(_809130))], (52025 ^ _775212) ^ [_1820483, _1820485, _1820487, _1820489, _1820491] : [c_Equiv__Relations_Opart__equivp(_1820483, _1820485), hBOOL(hAPP(hAPP(_1820485, _1820487), _1820489)), hBOOL(hAPP(hAPP(_1820485, _1820489), _1820491)), -(hBOOL(hAPP(hAPP(_1820485, _1820487), _1820491)))], (12073 ^ _775212) ^ [_973608, _973610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973608), _973610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973608)), _973610)))], (23674 ^ _775212) ^ [_1186767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1186767)), _1186767 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22730 ^ _775212) ^ [_1167746, _1167748, _1167750, _1167752, _1167754, _1167756] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1167746, _1167748, _1167750), _1167752), hAPP(hAPP(c_Product__Type_OPair(_1167746, _1167748), _1167754), _1167756)) = hAPP(hAPP(_1167752, _1167754), _1167756))], (46218 ^ _775212) ^ [_1695465, _1695467] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695465)), hAPP(c_List_Orotate1(_1695465), _1695467)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695465)), _1695467))], (40660 ^ _775212) ^ [_1557006, _1557008, _1557010, _1557012, _1557014, _1557016] : [c_Finite__Set_Ofolding(_1557006, _1557008, _1557010, _1557012), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557006), _1557014)), hBOOL(hAPP(hAPP(c_member(_1557006), _1557016), _1557014)), -(hAPP(_1557012, _1557014) = hAPP(c_Fun_Ocomp(_1557008, _1557008, _1557008, hAPP(_1557012, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1557006, tc_HOL_Obool)), _1557014), hAPP(hAPP(c_Set_Oinsert(_1557006), _1557016), c_Orderings_Obot__class_Obot(tc_fun(_1557006, tc_HOL_Obool)))))), hAPP(_1557010, _1557016)))], (13797 ^ _775212) ^ [_1004140, _1004142, _1004144, _1004146] : [class_Divides_Osemiring__div(_1004140), -(_1004142 = c_Groups_Ozero__class_Ozero(_1004140)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1004140), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004140), _1004144), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004140), _1004142), _1004146))), _1004142) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004140), _1004146), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1004140), _1004144), _1004142)))], (39928 ^ _775212) ^ [_1539540, _1539542, _1539544] : [c_Wellfounded_Owf(_1539540, _1539542), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1539540, tc_HOL_Obool)), _1539544), hAPP(c_Relation_OImage(_1539540, _1539540, _1539542), _1539544))), -(_1539544 = c_Orderings_Obot__class_Obot(tc_fun(_1539540, tc_HOL_Obool)))], (10579 ^ _775212) ^ [_947840, _947842] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _947840), _947842) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10582 ^ _775212 : [(10585 ^ _775212) ^ [] : [-(_947842 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10583 ^ _775212) ^ [] : [-(_947840 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (45706 ^ _775212) ^ [_1683148, _1683150, _1683152, _1683154, _1683156] : [-(_1683148 = _1683150), -(hAPP(hAPP(c_List_Onth(_1683152), hAPP(hAPP(c_List_Olist__update(_1683152, _1683154), _1683148), _1683156)), _1683150) = hAPP(hAPP(c_List_Onth(_1683152), _1683154), _1683150))], (43398 ^ _775212) ^ [_1622827, _1622829, _1622831, _1622833] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1622827, tc_fun(_1622829, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1622827, tc_HOL_Obool), _1622831)), _1622833) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1622827, tc_HOL_Obool), tc_fun(_1622829, tc_HOL_Obool)), _1622831), hAPP(hAPP(c_COMBC(tc_fun(_1622827, tc_HOL_Obool), tc_fun(_1622827, tc_fun(_1622829, tc_HOL_Obool)), tc_fun(_1622829, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1622827, tc_fun(_1622829, tc_HOL_Obool))), _1622833)))], (51761 ^ _775212) ^ [_1815889, _1815891] : [c_Relation_Osym(_1815889, _1815891), -(c_Relation_Osym(_1815889, hAPP(c_Relation_Oconverse(_1815889, _1815889), _1815891)))], (12675 ^ _775212) ^ [_984295, _984297] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _984295, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _984297)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _984295, _984297) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (49593 ^ _775212) ^ [_1767887, _1767889, _1767891, _1767893, _1767895] : [-(c_List_OdropWhile(_1767887, _1767889, _1767891) = hAPP(hAPP(c_List_Olist_OCons(_1767887), _1767893), _1767895)), _1767891 = hAPP(hAPP(c_List_Oappend(_1767887), c_List_OtakeWhile(_1767887, _1767889, _1767891)), hAPP(hAPP(c_List_Olist_OCons(_1767887), _1767893), _1767895)), -(hBOOL(hAPP(_1767889, _1767893)))], (34191 ^ _775212) ^ [] : [-(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))], (23580 ^ _775212) ^ [_1184529, _1184531, _1184533] : [-(c_HOL_OThe(tc_prod(_1184529, _1184531), hAPP(c_Product__Type_Oprod_Oprod__case(_1184529, _1184531, tc_HOL_Obool), _1184533)) = c_HOL_OThe(tc_prod(_1184529, _1184531), hAPP(hAPP(c_COMBS(tc_prod(_1184529, _1184531), _1184531, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1184529, tc_fun(_1184531, tc_HOL_Obool), tc_prod(_1184529, _1184531)), _1184533), c_Product__Type_Ofst(_1184529, _1184531))), c_Product__Type_Osnd(_1184529, _1184531))))], (1624 ^ _775212) ^ [_798368, _798370] : [-(class_Groups_Oab__semigroup__mult(_798368)), _798370 = _798368, class_Groups_Oab__semigroup__mult(_798370)], (17823 ^ _775212) ^ [_1077836] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1077836)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077836))))], (1884 ^ _775212) ^ [_801618, _801620] : [-(class_Groups_Oone(_801618)), _801620 = _801618, class_Groups_Oone(_801620)], (52645 ^ _775212) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (34099 ^ _775212) ^ [_1399088, _1399090, _1399092] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399088), _1399090), _1399092) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399088, tc_fun(tc_fun(_1399088, tc_HOL_Obool), tc_HOL_Obool)), _1399090), hAPP(hAPP(c_COMBC(_1399088, tc_fun(tc_fun(_1399088, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1399088, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1399088, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1399088, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1399088, tc_HOL_Obool), tc_HOL_Obool)), _1399088), c_Set_Oinsert(tc_fun(_1399088, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1399088, tc_HOL_Obool), tc_fun(_1399088, tc_HOL_Obool), _1399088), c_Relation_OImage(_1399088, _1399088, _1399092)), hAPP(hAPP(c_COMBC(_1399088, tc_fun(_1399088, tc_HOL_Obool), tc_fun(_1399088, tc_HOL_Obool)), c_Set_Oinsert(_1399088)), c_Orderings_Obot__class_Obot(tc_fun(_1399088, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399088, tc_HOL_Obool), tc_HOL_Obool)))))], (724 ^ _775212) ^ [_786336, _786338, _786340, _786342, _786344, _786346] : [-(c_Finite__Set_Ofun__left__comm(_786344, _786340, _786336)), c_Finite__Set_Ofun__left__comm(_786346, _786342, _786338), _786346 = _786344, _786342 = _786340, _786338 = _786336], (2266 ^ _775212) ^ [_808215, _808217, _808219, _808221] : [-(c_Divides_Opdivmod(_808221, _808217) = c_Divides_Opdivmod(_808219, _808215)), _808221 = _808219, _808217 = _808215], (2736 ^ _775212) ^ [_815596, _815598] : [_815598 = _815596, -(c_Lazy__Sequence_Ohit__bound(_815598) = c_Lazy__Sequence_Ohit__bound(_815596))], (45662 ^ _775212) ^ [_1682051, _1682053, _1682055, _1682057, _1682059] : [-(hAPP(hAPP(c_List_Oappend(_1682051), _1682053), hAPP(hAPP(c_List_Olist_OCons(_1682051), _1682055), c_List_Olist_ONil(_1682051))) = hAPP(hAPP(c_List_Oappend(_1682051), _1682057), hAPP(hAPP(c_List_Olist_OCons(_1682051), _1682059), c_List_Olist_ONil(_1682051)))), _1682053 = _1682057, _1682055 = _1682059], (17591 ^ _775212) ^ [_1073855, _1073857] : [class_Int_Onumber__ring(_1073855), -(hAPP(c_Int_Onumber__class_Onumber__of(_1073855), c_Int_Opred(_1073857)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073855), hAPP(c_Groups_Ouminus__class_Ouminus(_1073855), c_Groups_Oone__class_Oone(_1073855))), hAPP(c_Int_Onumber__class_Onumber__of(_1073855), _1073857)))], (37862 ^ _775212) ^ [_1483130, _1483132, _1483134, _1483136, _1483138, _1483140] : [hBOOL(hAPP(hAPP(c_member(_1483130), _1483132), _1483134)), 37865 ^ _775212 : [(37872 ^ _775212) ^ [] : [_1483138 = _1483140, -(hAPP(hAPP(c_Product__Type_OSigma(_1483136, _1483130), _1483138), hAPP(c_COMBK(tc_fun(_1483130, tc_HOL_Obool), _1483136), _1483134)) = hAPP(hAPP(c_Product__Type_OSigma(_1483136, _1483130), _1483140), hAPP(c_COMBK(tc_fun(_1483130, tc_HOL_Obool), _1483136), _1483134)))], (37866 ^ _775212) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1483136, _1483130), _1483138), hAPP(c_COMBK(tc_fun(_1483130, tc_HOL_Obool), _1483136), _1483134)) = hAPP(hAPP(c_Product__Type_OSigma(_1483136, _1483130), _1483140), hAPP(c_COMBK(tc_fun(_1483130, tc_HOL_Obool), _1483136), _1483134)), -(_1483138 = _1483140)]]], (9561 ^ _775212) ^ [_929585, _929587, _929589, _929591] : [class_Orderings_Opreorder(_929585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929585), _929587), _929589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929585), _929589), _929591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929585), _929587), _929591)))], (48226 ^ _775212) ^ [_1739339, _1739341, _1739343] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739339)), hAPP(c_List_Ofilter(_1739339, _1739341), _1739343))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739339)), hAPP(c_List_Ofilter(_1739339, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1739339), c_fNot), _1739341)), _1739343))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739339)), _1739343))], (47130 ^ _775212) ^ [_1714832] : [-(c_List_Obutlast(_1714832, c_List_Olist_ONil(_1714832)) = c_List_Olist_ONil(_1714832))], (47406 ^ _775212) ^ [_1720748, _1720750, _1720752, _1720754] : [-(hBOOL(hAPP(c_List_Olistsp(_1720748, _1720750), hAPP(hAPP(c_List_Olist_OCons(_1720748), _1720752), _1720754)))), hBOOL(hAPP(_1720750, _1720752)), hBOOL(hAPP(c_List_Olistsp(_1720748, _1720750), _1720754))], (28769 ^ _775212) ^ [_1286456, _1286458, _1286460, _1286462] : [-(_1286456 = c_Orderings_Obot__class_Obot(tc_fun(_1286458, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1286458, tc_fun(_1286460, tc_HOL_Obool)), _1286456), hAPP(c_COMBK(tc_fun(_1286460, tc_HOL_Obool), _1286458), _1286462)) = _1286462)], (31138 ^ _775212) ^ [_1338129, _1338131, _1338133, _1338135] : [-(c_Nitpick_Ofold__graph_H(_1338129, _1338131, _1338133, _1338135, c_Orderings_Obot__class_Obot(tc_fun(_1338129, tc_HOL_Obool)), _1338135))], (42260 ^ _775212) ^ [_1593063, _1593065, _1593067, _1593069, _1593071] : [hBOOL(hAPP(hAPP(c_member(_1593063), _1593065), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593067, tc_fun(_1593063, tc_HOL_Obool)), _1593069), _1593071))), 42263 ^ _775212 : [(42264 ^ _775212) ^ [_1593187] : [hBOOL(hAPP(hAPP(c_member(_1593067), _1593187), _1593069)), -(hBOOL(hAPP(hAPP(c_member(_1593063), _1593065), hAPP(_1593071, _1593187))))]]], (25679 ^ _775212) ^ [_1223811, _1223813, _1223815] : [-(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), _1223811)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1223813))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1223815))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223815), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1223811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1223811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223815), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1223813)))))], (49820 ^ _775212) ^ [_1772555, _1772557, _1772559] : [-(c_List_Omaps(_1772555, _1772557, _1772559, c_List_Olist_ONil(_1772555)) = c_List_Olist_ONil(_1772557))], (28289 ^ _775212) ^ [_1276749, _1276751, _1276753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276749, tc_HOL_Obool)), _1276751), _1276753)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276749), _1276753)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1276749), _1276751)))], (17511 ^ _775212) ^ [_1072535, _1072537] : [class_Int_Onumber__ring(_1072535), class_Rings_Olinordered__idom(_1072535), 17518 ^ _775212 : [(17525 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072537), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072535), hAPP(c_Int_Onumber__class_Onumber__of(_1072535), _1072537)), c_Groups_Ozero__class_Ozero(_1072535))))], (17519 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072535), hAPP(c_Int_Onumber__class_Onumber__of(_1072535), _1072537)), c_Groups_Ozero__class_Ozero(_1072535))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072537), c_Int_OPls)))]]], (44760 ^ _775212) ^ [_1659234, _1659236, _1659238, _1659240, _1659242] : [hAPP(hAPP(c_List_Omap(_1659234, _1659236), _1659238), _1659240) = hAPP(hAPP(c_List_Omap(_1659234, _1659236), _1659238), _1659242), c_Fun_Oinj__on(_1659234, _1659236, _1659238, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659234, tc_HOL_Obool)), hAPP(c_List_Oset(_1659234), _1659240)), hAPP(c_List_Oset(_1659234), _1659242))), -(_1659240 = _1659242)], (23630 ^ _775212) ^ [_1185558, _1185560, _1185562, _1185564] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1185558, _1185560)), c_Nitpick_Opair__box_OPairBox(_1185558, _1185560, _1185562, _1185564)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37944 ^ _775212) ^ [_1485549, _1485551, _1485553, _1485555, _1485557] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1485549, _1485551), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485549, tc_HOL_Obool)), _1485553), _1485555)), hAPP(c_COMBK(tc_fun(_1485551, tc_HOL_Obool), _1485549), _1485557)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1485549, _1485551), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1485549, _1485551), _1485553), hAPP(c_COMBK(tc_fun(_1485551, tc_HOL_Obool), _1485549), _1485557))), hAPP(hAPP(c_Product__Type_OSigma(_1485549, _1485551), _1485555), hAPP(c_COMBK(tc_fun(_1485551, tc_HOL_Obool), _1485549), _1485557))))], (35189 ^ _775212) ^ [_1423360, _1423362, _1423364, _1423366, _1423368] : [class_Orderings_Olinorder(_1423360), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423360, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1423360, _1423362, _1423364)), c_SetInterval_Oord__class_OatLeastAtMost(_1423360, _1423366, _1423368)) = c_SetInterval_Oord__class_OatLeastAtMost(_1423360, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1423360), _1423362), _1423366), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1423360), _1423364), _1423368)))], (39367 ^ _775212) ^ [_1523220, _1523222] : [c_Predicate_Oreflp(_1523220, _1523222), -(c_Relation_Orefl__on(_1523220, c_Orderings_Otop__class_Otop(tc_fun(_1523220, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1523220, _1523220)), hAPP(c_Product__Type_Oprod_Oprod__case(_1523220, _1523220, tc_HOL_Obool), _1523222))))], (48829 ^ _775212) ^ [_1752017, _1752019, _1752021, _1752023, _1752025] : [class_Orderings_Olinorder(_1752017), c_List_Olinorder__class_Osorted(_1752017, hAPP(hAPP(c_List_Omap(_1752019, _1752017), _1752021), _1752023)), -(c_List_Olinorder__class_Osorted(_1752017, hAPP(hAPP(c_List_Omap(_1752019, _1752017), _1752021), c_List_Olinorder__class_Oinsort__insert__key(_1752019, _1752017, _1752021, _1752025, _1752023))))], (5629 ^ _775212) ^ [_863885, _863887] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _863885, _863887, _863885))], (41851 ^ _775212) ^ [_1582948, _1582950, _1582952, _1582954, _1582956] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582948, _1582948)), hAPP(hAPP(c_Product__Type_OPair(_1582948, _1582948), _1582950), _1582952)), c_Transitive__Closure_Ortrancl(_1582948, _1582954))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1582948, _1582948)), hAPP(hAPP(c_Product__Type_OPair(_1582948, _1582948), _1582952), _1582956)), _1582954)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582948, _1582948)), hAPP(hAPP(c_Product__Type_OPair(_1582948, _1582948), _1582950), _1582956)), c_Transitive__Closure_Ortrancl(_1582948, _1582954))))], (20311 ^ _775212) ^ [_1121626, _1121628, _1121630] : [class_Fields_Olinordered__field(_1121626), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121626), _1121628), _1121630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121626), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121626), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121626), _1121628), _1121630)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121626), c_Groups_Oone__class_Oone(_1121626)), c_Groups_Oone__class_Oone(_1121626)))), _1121630)))], (27955 ^ _775212) ^ [_1270448] : [27957 ^ _775212 : [(27960 ^ _775212) ^ [_1270558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27956 ^ [_1270448, _1270558]), _1270558))], (27958 ^ _775212) ^ [_1270524] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27956 ^ [_1270448, _1270524]), _1270448)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1270448)))], (23584 ^ _775212) ^ [_1184684, _1184686, _1184688, _1184690, _1184692, _1184694] : [c_Nitpick_Opair__box_OPairBox(_1184684, _1184686, _1184688, _1184690) = c_Nitpick_Opair__box_OPairBox(_1184684, _1184686, _1184692, _1184694), 23587 ^ _775212 : [(23590 ^ _775212) ^ [] : [-(_1184690 = _1184694)], (23588 ^ _775212) ^ [] : [-(_1184688 = _1184692)]]], (7451 ^ _775212) ^ [_893950, _893952, _893954, _893956, _893958] : [class_Rings_Ocomm__semiring__1(_893950), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893950), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893950), _893952), _893954)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893950), _893956), _893958)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893950), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893950), _893952), _893956)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893950), _893954), _893958)))], (33875 ^ _775212) ^ [_1393579, _1393581, _1393583, _1393585, _1393587] : [c_Finite__Set_Ofolding__one__idem(_1393579, _1393581, _1393583), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393579), _1393585)), hBOOL(hAPP(hAPP(c_member(_1393579), _1393587), _1393585)), -(hAPP(hAPP(_1393581, _1393587), hAPP(_1393583, _1393585)) = hAPP(_1393583, _1393585))], (4006 ^ _775212) ^ [_835999, _836001, _836003, _836005] : [-(c_List_Olists(_836005, _836001) = c_List_Olists(_836003, _835999)), _836005 = _836003, _836001 = _835999], (22182 ^ _775212) ^ [_1156395, _1156397] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1156395))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1156397)), hAPP(c_Int_Onat, _1156395)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1156397), _1156395)), 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)))], (33791 ^ _775212) ^ [_1391629, _1391631] : [hAPP(c_Set_OPow(_1391629), _1391631) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1391629, tc_HOL_Obool), tc_HOL_Obool))], (36459 ^ _775212) ^ [_1452036, _1452038, _1452040] : [c_Equiv__Relations_Oequivp(_1452036, _1452038), -(hBOOL(hAPP(hAPP(_1452038, _1452040), _1452040)))], (49440 ^ _775212) ^ [_1764680] : [-(c_List_Oreturn__list(_1764680) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1764680))], (47905 ^ _775212) ^ [_1731707, _1731709] : [-(c_Enum_On__lists(_1731707, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1731709) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1731707)), c_List_Olist_ONil(_1731707)), c_List_Olist_ONil(tc_List_Olist(_1731707))))], (39035 ^ _775212) ^ [_1509818, _1509820] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1509818), hAPP(c_Set_OCollect(_1509818), _1509820))), 39038 ^ _775212 : [(39045 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1509818), c_Orderings_Otop__class_Otop(tc_fun(_1509818, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1509818), hAPP(c_Set_OCollect(_1509818), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1509818), c_fNot), _1509820)))))], (39039 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1509818), hAPP(c_Set_OCollect(_1509818), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1509818), c_fNot), _1509820)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1509818), c_Orderings_Otop__class_Otop(tc_fun(_1509818, tc_HOL_Obool)))))]]], (4850 ^ _775212) ^ [_849071, _849073, _849075, _849077, _849079, _849081] : [-(c_List_Oreplicate(_849081, _849077, _849073) = c_List_Oreplicate(_849079, _849075, _849071)), _849081 = _849079, _849077 = _849075, _849073 = _849071], (4298 ^ _775212) ^ [_840553, _840555, _840557, _840559] : [-(c_List_Orotate(_840559, _840555) = c_List_Orotate(_840557, _840553)), _840559 = _840557, _840555 = _840553], (29728 ^ _775212) ^ [_1304829, _1304831, _1304833, _1304835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1304829, tc_HOL_Obool)), _1304831), _1304833)), hBOOL(hAPP(hAPP(c_member(_1304829), _1304835), _1304831)), -(hBOOL(hAPP(hAPP(c_member(_1304829), _1304835), _1304833)))], (29070 ^ _775212) ^ [_1291557, _1291559, _1291561, _1291563, _1291565] : [_1291557 = c_Orderings_Obot__class_Obot(tc_fun(_1291559, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291559, tc_fun(_1291561, tc_HOL_Obool)), _1291557), hAPP(hAPP(c_COMBB(tc_fun(_1291561, tc_HOL_Obool), tc_fun(_1291561, tc_HOL_Obool), _1291559), hAPP(c_Set_Oinsert(_1291561), _1291563)), _1291565)) = c_Orderings_Obot__class_Obot(tc_fun(_1291561, tc_HOL_Obool)))], (6429 ^ _775212) ^ [_876919, _876921, _876923, _876925] : [class_Groups_Ocancel__semigroup__add(_876919), 6432 ^ _775212 : [(6439 ^ _775212) ^ [] : [_876923 = _876925, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876919), _876921), _876923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876919), _876921), _876925))], (6433 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876919), _876921), _876923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_876919), _876921), _876925), -(_876923 = _876925)]]], (14427 ^ _775212) ^ [_1016085, _1016087, _1016089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016085), _1016087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016085), _1016089)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016087), _1016089))))], (18589 ^ _775212) ^ [_1091017] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1091017))), 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), _1091017), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (450 ^ _775212) ^ [_782113, _782115, _782117, _782119] : [-(c_Wellfounded_OwfP(_782117, _782113)), c_Wellfounded_OwfP(_782119, _782115), _782119 = _782117, _782115 = _782113], (51608 ^ _775212) ^ [_1812806, _1812808, _1812810, _1812812] : [-(c_Wellfounded_Omax__extp(_1812806, _1812808, _1812810, _1812812)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1812806), _1812810)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1812806), _1812812)), -(_1812812 = c_Orderings_Obot__class_Obot(tc_fun(_1812806, tc_HOL_Obool))), 51622 ^ _775212 : [(51625 ^ _775212) ^ [_1813151] : [hBOOL(hAPP(hAPP(c_member(_1812806), _1813151), _1812812)), hBOOL(hAPP(hAPP(_1812808, 51621 ^ [_1812806, _1812808, _1812810, _1812812]), _1813151))], (51623 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1812806), 51621 ^ [_1812806, _1812808, _1812810, _1812812]), _1812810)))]]], (36225 ^ _775212) ^ [_1447264, _1447266, _1447268] : [class_Lattices_Olattice(_1447264), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447264), _1447266)), -(_1447266 = c_Orderings_Obot__class_Obot(tc_fun(_1447264, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447264), _1447268)), -(_1447268 = c_Orderings_Obot__class_Obot(tc_fun(_1447264, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1447264, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1447264, tc_HOL_Obool)), _1447266), _1447268)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1447264), c_Big__Operators_Olattice__class_OInf__fin(_1447264, _1447266)), c_Big__Operators_Olattice__class_OInf__fin(_1447264, _1447268)))], (7483 ^ _775212) ^ [_894563, _894565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894563)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _894565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894563), _894565)))], (52669 ^ _775212) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (8235 ^ _775212) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5881 ^ _775212) ^ [_868301, _868303, _868305, _868307, _868309] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_868301, _868303), _868305, _868307, _868309)), 5882 ^ _775212 : [(5889 ^ _775212) ^ [] : [hBOOL(hAPP(_868301, _868305)), 5892 ^ _775212 : [(5893 ^ _775212) ^ [_868511] : [c_Natural_Oevaln(_868303, _868305, _868307, _868511), c_Natural_Oevaln(c_Com_Ocom_OWhile(_868301, _868303), _868511, _868307, _868309)]]], (5883 ^ _775212) ^ [] : [_868309 = _868305, -(hBOOL(hAPP(_868301, _868305)))]]], (10037 ^ _775212) ^ [_938086, _938088] : [class_Rings_Ocomm__semiring__1(_938086), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938086), _938088), _938088) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938086), c_Groups_Oone__class_Oone(_938086)), c_Groups_Oone__class_Oone(_938086))), _938088))], (34065 ^ _775212) ^ [_1398020, _1398022, _1398024, _1398026] : [-(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), _1398020), _1398022)), 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), _1398024), _1398026)), 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), _1398020), _1398024)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398022), _1398026))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (17239 ^ _775212) ^ [_1068475, _1068477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068475), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068475)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068477)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26803 ^ _775212) ^ [_1246307, _1246309, _1246311, _1246313] : [class_Orderings_Olinorder(_1246307), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246307), _1246309), _1246311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246307), _1246311), _1246313)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1246307, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1246307, _1246309, _1246311)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1246307, _1246311, _1246313)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1246307, _1246309), _1246313))], (18591 ^ _775212) ^ [_1091061, _1091063] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1091061)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1091063))) = 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), _1091061), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091063))))], (46630 ^ _775212) ^ [_1704493, _1704495] : [class_Groups_Ocomm__monoid__add(_1704493), hBOOL(hAPP(c_List_Odistinct(_1704493), _1704495)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1704493), _1704495) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1704493, _1704493), c_COMBI(_1704493)), hAPP(c_List_Oset(_1704493), _1704495)))], (34203 ^ _775212) ^ [_1401648, _1401650, _1401652, _1401654, _1401656] : [c_Equiv__Relations_Oequiv(_1401648, _1401650, _1401652), hBOOL(hAPP(hAPP(c_member(tc_prod(_1401648, _1401648)), hAPP(hAPP(c_Product__Type_OPair(_1401648, _1401648), _1401654), _1401656)), _1401652)), -(hAPP(c_Relation_OImage(_1401648, _1401648, _1401652), hAPP(hAPP(c_Set_Oinsert(_1401648), _1401654), c_Orderings_Obot__class_Obot(tc_fun(_1401648, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1401648, _1401648, _1401652), hAPP(hAPP(c_Set_Oinsert(_1401648), _1401656), c_Orderings_Obot__class_Obot(tc_fun(_1401648, tc_HOL_Obool)))))], (32289 ^ _775212) ^ [_1359877, _1359879, _1359881] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1359877, tc_HOL_Obool), tc_fun(_1359877, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1359877, tc_HOL_Obool), tc_fun(_1359877, tc_HOL_Obool)), _1359879), _1359881)), c_Wellfounded_Ofinite__psubset(_1359877)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1359877, tc_HOL_Obool)), _1359879), _1359881)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359877), _1359881))], (46286 ^ _775212) ^ [_1697104, _1697106, _1697108, _1697110] : [-(_1697104 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1697106), _1697104), hAPP(hAPP(c_List_Olist_OCons(_1697106), _1697108), _1697110)) = hAPP(hAPP(c_List_Odrop(_1697106), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1697104), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1697110))], (8567 ^ _775212) ^ [_914094, _914096] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914094)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _914096)), _914094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _914096 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19521 ^ _775212) ^ [_1107763, _1107765, _1107767, _1107769] : [class_Fields_Ofield__inverse__zero(_1107763), -(_1107765 = c_Groups_Ozero__class_Ozero(_1107763)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107763), _1107767), _1107765)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107763), _1107769), _1107765)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107763), _1107767), _1107769))], (8401 ^ _775212) ^ [_911013, _911015, _911017, _911019] : [class_Rings_Olinordered__ring__strict(_911013), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911013), _911015), c_Groups_Ozero__class_Ozero(_911013))), 8408 ^ _775212 : [(8415 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911013), _911019), _911017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911013), _911015), _911017)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911013), _911015), _911019))))], (8409 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911013), _911015), _911017)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911013), _911015), _911019))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911013), _911019), _911017)))]]], (28642 ^ _775212) ^ [_1283857, _1283859, _1283861] : [hAPP(hAPP(c_Set_Oinsert(_1283857), _1283859), _1283861) = c_Orderings_Obot__class_Obot(tc_fun(_1283857, tc_HOL_Obool))], (41269 ^ _775212) ^ [_1570735, _1570737, _1570739, _1570741] : [class_Orderings_Olinorder(_1570735), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570735), _1570737)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1570735, _1570735, c_Orderings_Oord__class_Omin(_1570735)), _1570739), hAPP(hAPP(c_Set_Oinsert(_1570735), _1570741), _1570737)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1570735), _1570741), hAPP(hAPP(c_Finite__Set_Ofold(_1570735, _1570735, c_Orderings_Oord__class_Omin(_1570735)), _1570739), _1570737)))], (52651 ^ _775212) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (23404 ^ _775212) ^ [_1181074, _1181076] : [-(c_Nitpick_Oint__lcm(_1181074, _1181076) = 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), _1181074)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1181076)))))], (52735 ^ _775212) ^ [_1829017, _1829019] : [hBOOL(_1829017), -(hBOOL(hAPP(hAPP(c_fdisj, _1829017), _1829019)))], (42533 ^ _775212) ^ [_1600970, _1600972, _1600974, _1600976, _1600978] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600970, tc_fun(_1600972, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1600970), _1600974), _1600976)), _1600978) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1600972, tc_HOL_Obool)), hAPP(_1600978, _1600974)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600970, tc_fun(_1600972, tc_HOL_Obool)), _1600976), _1600978)))], (29939 ^ _775212) ^ [_1308823, _1308825, _1308827, _1308829, _1308831] : [-(hBOOL(hAPP(hAPP(c_member(_1308823), _1308825), c_SetInterval_Oord_OatLeastAtMost(_1308823, _1308827, _1308829, _1308831)))), hBOOL(hAPP(hAPP(_1308827, _1308829), _1308825)), hBOOL(hAPP(hAPP(_1308827, _1308825), _1308831))], (22041 ^ _775212) ^ [_1153443, _1153445, _1153447, _1153449, _1153451, _1153453] : [hAPP(hAPP(c_Product__Type_OPair(_1153443, _1153445), _1153447), _1153449) = hAPP(hAPP(c_Product__Type_OPair(_1153443, _1153445), _1153451), _1153453), 22044 ^ _775212 : [(22047 ^ _775212) ^ [] : [-(_1153449 = _1153453)], (22045 ^ _775212) ^ [] : [-(_1153447 = _1153451)]]], (20517 ^ _775212) ^ [_1125458, _1125460, _1125462, _1125464] : [class_Fields_Olinordered__field__inverse__zero(_1125458), 20520 ^ _775212 : [(20521 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125458), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125458), _1125460), _1125462)), _1125464)), 20524 ^ _775212 : [(20531 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125458), c_Groups_Ozero__class_Ozero(_1125458)), _1125462))), 20534 ^ _775212 : [(20541 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125458), _1125462), c_Groups_Ozero__class_Ozero(_1125458)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125458), c_Groups_Ozero__class_Ozero(_1125458)), _1125464)))], (20535 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125458), _1125462), c_Groups_Ozero__class_Ozero(_1125458))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125458), _1125464), _1125462)), _1125460)))]]], (20525 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125458), c_Groups_Ozero__class_Ozero(_1125458)), _1125462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125458), _1125460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125458), _1125464), _1125462))))]]], (20547 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125458), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125458), _1125460), _1125462)), _1125464))), 20550 ^ _775212 : [(20553 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125458), _1125460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125458), _1125464), _1125462)))], (20551 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125458), c_Groups_Ozero__class_Ozero(_1125458)), _1125462)))]], 20554 ^ _775212 : [(20557 ^ _775212) ^ [] : [20558 ^ _775212 : [(20561 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125458), _1125464), _1125462)), _1125460))], (20559 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125458), _1125462), c_Groups_Ozero__class_Ozero(_1125458))))]], 20562 ^ _775212 : [(20565 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125458), c_Groups_Ozero__class_Ozero(_1125458)), _1125464))], (20563 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125458), _1125462), c_Groups_Ozero__class_Ozero(_1125458)))]]], (20555 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125458), c_Groups_Ozero__class_Ozero(_1125458)), _1125462))]]]]], (46047 ^ _775212) ^ [_1690689, _1690691, _1690693, _1690695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690689), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690691)), _1690693))), -(hBOOL(hAPP(hAPP(c_member(_1690691), _1690695), hAPP(c_List_Oset(_1690691), hAPP(hAPP(c_List_Olist__update(_1690691, _1690693), _1690689), _1690695)))))], (15069 ^ _775212) ^ [_1027966, _1027968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027966), _1027968)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027966), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027968), _1027966)) = _1027968)], (52363 ^ _775212) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (40168 ^ _775212) ^ [_1545619, _1545621] : [c_Wellfounded_OwfP(_1545619, _1545621), -(c_Wellfounded_Oacyclic(_1545619, hAPP(c_Set_OCollect(tc_prod(_1545619, _1545619)), hAPP(c_Product__Type_Oprod_Oprod__case(_1545619, _1545619, tc_HOL_Obool), _1545621))))], (38299 ^ _775212) ^ [_1495307] : [-(c_Relation_Orefl__on(_1495307, c_Orderings_Obot__class_Obot(tc_fun(_1495307, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1495307, _1495307), tc_HOL_Obool))))], (46762 ^ _775212) ^ [_1707335, _1707337, _1707339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1707335), _1707337)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1707335), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1707337), _1707339))))], (18585 ^ _775212) ^ [] : [-(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))))], (13370 ^ _775212) ^ [_997029, _997031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _997029)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _997031, _997029)), _997029)))], (42105 ^ _775212) ^ [_1588963, _1588965, _1588967, _1588969] : [class_Complete__Lattice_Ocomplete__lattice(_1588963), hBOOL(hAPP(c_Finite__Set_Ofinite(_1588965), _1588967)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1588965, _1588963), _1588967), _1588969) = hAPP(hAPP(c_Finite__Set_Ofold(_1588965, _1588963, hAPP(hAPP(c_COMBB(_1588963, tc_fun(_1588963, _1588963), _1588965), c_Lattices_Osemilattice__inf__class_Oinf(_1588963)), _1588969)), c_Orderings_Otop__class_Otop(_1588963)), _1588967))], (28395 ^ _775212) ^ [_1278757, _1278759, _1278761, _1278763] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278757), _1278759)), 28398 ^ _775212 : [(28399 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278761), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278757, tc_fun(_1278761, tc_HOL_Obool)), _1278759), _1278763))), 28402 ^ _775212 : [(28403 ^ _775212) ^ [_1278941] : [hBOOL(hAPP(hAPP(c_member(_1278757), _1278941), _1278759)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1278761), hAPP(_1278763, _1278941))))]]], (28409 ^ _775212) ^ [] : [28411 ^ _775212 : [(28414 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278761), hAPP(_1278763, 28410 ^ [_1278757, _1278759, _1278761, _1278763])))], (28412 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1278757), 28410 ^ [_1278757, _1278759, _1278761, _1278763]), _1278759)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1278761), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278757, tc_fun(_1278761, tc_HOL_Obool)), _1278759), _1278763))))]]], (43451 ^ _775212) ^ [_1624065, _1624067, _1624069] : [class_Complete__Lattice_Ocomplete__lattice(_1624065), 43454 ^ _775212 : [(43455 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1624065), c_Complete__Lattice_OSup__class_OSup(_1624065, _1624067)), _1624069)), 43458 ^ _775212 : [(43459 ^ _775212) ^ [_1624223] : [hBOOL(hAPP(hAPP(c_member(_1624065), _1624223), _1624067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1624065), _1624223), _1624069)))]]], (43465 ^ _775212) ^ [] : [43467 ^ _775212 : [(43470 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1624065), 43466 ^ [_1624065, _1624067, _1624069]), _1624069))], (43468 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1624065), 43466 ^ [_1624065, _1624067, _1624069]), _1624067)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1624065), c_Complete__Lattice_OSup__class_OSup(_1624065, _1624067)), _1624069)))]]], (40247 ^ _775212) ^ [_1547717, _1547719, _1547721] : [40249 ^ _775212 : [(40252 ^ _775212) ^ [] : [hBOOL(hAPP(_1547719, 40248 ^ [_1547717, _1547719, _1547721]))], (40250 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547717), 40248 ^ [_1547717, _1547719, _1547721]), _1547721)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1547717, _1547719), _1547721)))], (16059 ^ _775212) ^ [_1047311, _1047313] : [class_Int_Onumber__ring(_1047311), -(hAPP(c_Int_Onumber__class_Onumber__of(_1047311), _1047313) = hAPP(c_Int_Oring__1__class_Oof__int(_1047311), _1047313))], (47218 ^ _775212) ^ [_1716476, _1716478, _1716480, _1716482, _1716484] : [class_Groups_Ocomm__monoid__add(_1716476), hBOOL(hAPP(hAPP(c_member(_1716478), _1716480), hAPP(c_List_Oset(_1716478), _1716482))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1716476), hAPP(hAPP(c_List_Omap(_1716478, _1716476), _1716484), _1716482)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1716476), hAPP(_1716484, _1716480)), hAPP(c_List_Omonoid__add__class_Olistsum(_1716476), hAPP(hAPP(c_List_Omap(_1716478, _1716476), _1716484), c_List_Oremove1(_1716478, _1716480, _1716482)))))], (25030 ^ _775212) ^ [_1210530, _1210532, _1210534, _1210536] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1210530, _1210532, _1210534), c_Product__Type_Ocurry(_1210530, _1210532, _1210534, _1210536)) = _1210536)], (49774 ^ _775212) ^ [_1771712, _1771714, _1771716, _1771718, _1771720] : [c_Fun_Oinj__on(_1771712, _1771714, _1771716, c_Orderings_Otop__class_Otop(tc_fun(_1771712, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1771712, _1771714), _1771716), hAPP(c_List_OremoveAll(_1771712, _1771718), _1771720)) = hAPP(c_List_OremoveAll(_1771714, hAPP(_1771716, _1771718)), hAPP(hAPP(c_List_Omap(_1771712, _1771714), _1771716), _1771720)))], (17301 ^ _775212) ^ [_1069326, _1069328] : [class_Int_Onumber__ring(_1069326), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069326), _1069328), hAPP(c_Int_Onumber__class_Onumber__of(_1069326), c_Int_OPls)) = _1069328)], (44849 ^ _775212) ^ [_1661253, _1661255, _1661257, _1661259] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661253)), hAPP(hAPP(c_List_Omap(_1661255, _1661253), _1661257), _1661259)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661255)), _1661259))], (22744 ^ _775212) ^ [_1168166, _1168168, _1168170, _1168172, _1168174, _1168176] : [hAPP(c_Product__Type_Oapsnd(_1168166, _1168168, _1168170, _1168172), _1168174) = hAPP(c_Product__Type_Oapsnd(_1168166, _1168168, _1168170, _1168176), _1168174), -(hAPP(_1168172, hAPP(c_Product__Type_Osnd(_1168170, _1168166), _1168174)) = hAPP(_1168176, hAPP(c_Product__Type_Osnd(_1168170, _1168166), _1168174)))], (42165 ^ _775212) ^ [_1590237, _1590239, _1590241, _1590243, _1590245, _1590247, _1590249, _1590251] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590237, tc_fun(_1590239, tc_fun(_1590241, tc_HOL_Obool))), _1590243), _1590245), _1590247), _1590249)), -(hBOOL(hAPP(hAPP(hAPP(_1590245, _1590251), _1590247), _1590249))), hBOOL(hAPP(hAPP(c_member(_1590237), _1590251), _1590243))], (14951 ^ _775212) ^ [_1025724, _1025726] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025724), _1025726))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025726), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025724), _1025726)) = _1025724)], (13437 ^ _775212) ^ [_998076, _998078] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _998076, _998078)), _998078) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (39438 ^ _775212) ^ [_1525991, _1525993] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1525991, _1525993, tc_prod(_1525991, _1525993)), c_Product__Type_OPair(_1525991, _1525993)) = c_Fun_Oid(tc_prod(_1525991, _1525993)))], (44463 ^ _775212) ^ [_1651349, _1651351, _1651353, _1651355, _1651357, _1651359] : [hBOOL(hAPP(hAPP(_1651349, _1651351), _1651353)), c_List_Olistrelp(_1651355, _1651349, _1651357, _1651359), -(c_List_Olistrelp(_1651355, _1651349, hAPP(hAPP(c_List_Olist_OCons(_1651355), _1651351), _1651357), hAPP(hAPP(c_List_Olist_OCons(_1651355), _1651353), _1651359)))], (37046 ^ _775212) ^ [_1464310] : [class_Nat_Osemiring__char__0(_1464310), -(c_Fun_Oinj__on(tc_Nat_Onat, _1464310, c_Nat_Osemiring__1__class_Oof__nat(_1464310), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (40542 ^ _775212) ^ [_1554461, _1554463, _1554465, _1554467, _1554469, _1554471] : [c_Fun_Oinj__on(_1554461, _1554463, _1554465, _1554467), 40545 ^ _775212 : [(40552 ^ _775212) ^ [] : [c_Fun_Oinj__on(_1554461, _1554469, hAPP(c_Fun_Ocomp(_1554463, _1554469, _1554461, _1554471), _1554465), _1554467), -(c_Fun_Oinj__on(_1554463, _1554469, _1554471, hAPP(c_Set_Oimage(_1554461, _1554463, _1554465), _1554467)))], (40546 ^ _775212) ^ [] : [c_Fun_Oinj__on(_1554463, _1554469, _1554471, hAPP(c_Set_Oimage(_1554461, _1554463, _1554465), _1554467)), -(c_Fun_Oinj__on(_1554461, _1554469, hAPP(c_Fun_Ocomp(_1554463, _1554469, _1554461, _1554471), _1554465), _1554467))]]], (45726 ^ _775212) ^ [_1683549, _1683551, _1683553, _1683555, _1683557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1683549), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683551)), _1683553))), -(hAPP(hAPP(c_List_Olist__update(_1683551, hAPP(hAPP(c_List_Oappend(_1683551), _1683553), _1683555)), _1683549), _1683557) = hAPP(hAPP(c_List_Oappend(_1683551), hAPP(hAPP(c_List_Olist__update(_1683551, _1683553), _1683549), _1683557)), _1683555))], (52567 ^ _775212) ^ [_1827120, _1827122] : [-(class_Enum_Oenum(tc_prod(_1827120, _1827122))), class_Enum_Oenum(_1827120), class_Enum_Oenum(_1827122)], (5625 ^ _775212) ^ [_863785, _863787, _863789, _863791, _863793] : [-(hAPP(hAPP(c_Power_Opower_Opower(_863785, _863787, _863789), _863791), hAPP(c_Nat_OSuc, _863793)) = hAPP(hAPP(_863789, _863791), hAPP(hAPP(c_Power_Opower_Opower(_863785, _863787, _863789), _863791), _863793)))], (29764 ^ _775212) ^ [_1305537, _1305539, _1305541] : [_1305539 = _1305541, -(hAPP(hAPP(c_COMBC(_1305537, tc_fun(_1305537, tc_HOL_Obool), tc_HOL_Obool), c_member(_1305537)), _1305539) = hAPP(hAPP(c_COMBC(_1305537, tc_fun(_1305537, tc_HOL_Obool), tc_HOL_Obool), c_member(_1305537)), _1305541))], (28345 ^ _775212) ^ [_1277863] : [class_Finite__Set_Ofinite(_1277863), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1277863), c_Orderings_Otop__class_Otop(tc_fun(_1277863, tc_HOL_Obool)))))], (44608 ^ _775212) ^ [_1655155, _1655157, _1655159, _1655161] : [-(hAPP(hAPP(c_List_Onth(_1655155), hAPP(hAPP(c_List_Olist_OCons(_1655155), _1655157), _1655159)), hAPP(c_Nat_OSuc, _1655161)) = hAPP(hAPP(c_List_Onth(_1655155), _1655159), _1655161))], (52321 ^ _775212) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (22454 ^ _775212) ^ [_1162700, _1162702, _1162704, _1162706] : [class_Orderings_Olinorder(_1162700), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162700), _1162702), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162700), _1162704), _1162706)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162700), _1162704), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162700), _1162702), _1162706)))], (29614 ^ _775212) ^ [_1302613, _1302615, _1302617, _1302619] : [-(hBOOL(hAPP(hAPP(c_member(_1302613), _1302615), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1302613, tc_HOL_Obool)), _1302617), _1302619)))), hBOOL(hAPP(hAPP(c_member(_1302613), _1302615), _1302617)), -(hBOOL(hAPP(hAPP(c_member(_1302613), _1302615), _1302619)))], (43384 ^ _775212) ^ [_1622349, _1622351] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1622349, tc_HOL_Obool), _1622351) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1622349, tc_HOL_Obool), tc_fun(_1622349, tc_HOL_Obool)), _1622351), c_COMBI(tc_fun(_1622349, tc_HOL_Obool))))], (18263 ^ _775212) ^ [_1085324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1085324)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1085324))))], (1854 ^ _775212) ^ [_801243, _801245] : [-(class_Power_Opower(_801243)), _801245 = _801243, class_Power_Opower(_801245)], (39611 ^ _775212) ^ [_1531680, _1531682, _1531684, _1531686] : [hBOOL(hAPP(hAPP(c_member(_1531682), _1531686), hAPP(c_Relation_ORange(_1531680, _1531682), _1531684))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1531680, _1531682, hAPP(hAPP(c_COMBC(_1531680, tc_fun(tc_prod(_1531680, _1531682), tc_HOL_Obool), tc_fun(_1531682, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531682, tc_fun(tc_fun(tc_prod(_1531680, _1531682), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1531680, _1531682), tc_HOL_Obool), tc_fun(_1531682, tc_HOL_Obool)), _1531680), c_COMBC(_1531682, tc_fun(tc_prod(_1531680, _1531682), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531682, tc_prod(_1531680, _1531682)), tc_fun(_1531682, tc_fun(tc_fun(tc_prod(_1531680, _1531682), tc_HOL_Obool), tc_HOL_Obool)), _1531680), hAPP(c_COMBB(tc_prod(_1531680, _1531682), tc_fun(tc_fun(tc_prod(_1531680, _1531682), tc_HOL_Obool), tc_HOL_Obool), _1531682), c_member(tc_prod(_1531680, _1531682)))), c_Product__Type_OPair(_1531680, _1531682)))), _1531684)), _1531686)))], (11524 ^ _775212) ^ [_964355, _964357, _964359, _964361, _964363, _964365] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _964355), _964357)), _964359) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _964361), _964363)), _964365), 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), _964361), _964363)), _964365))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _964365), _964361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _964359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _964361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _964361), _964355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _964357), _964363)))], (38170 ^ _775212) ^ [_1491900, _1491902, _1491904, _1491906, _1491908] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1491900, _1491902)), _1491904), hAPP(hAPP(c_Product__Type_OSigma(_1491900, _1491902), _1491906), _1491908))), 38174 ^ _775212 : [(38180 ^ _775212) ^ [] : [-(_1491904 = hAPP(hAPP(c_Product__Type_OPair(_1491900, _1491902), 38173 ^ [_1491900, _1491902, _1491904, _1491906, _1491908]), 38176 ^ [_1491900, _1491902, _1491904, _1491906, _1491908]))], (38178 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491902), 38176 ^ [_1491900, _1491902, _1491904, _1491906, _1491908]), hAPP(_1491908, 38173 ^ [_1491900, _1491902, _1491904, _1491906, _1491908]))))], (38175 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491900), 38173 ^ [_1491900, _1491902, _1491904, _1491906, _1491908]), _1491906)))]]], (22820 ^ _775212) ^ [_1169849, _1169851] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169849)), hAPP(c_Nat_OSuc, _1169851)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1169849))), 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, _1169851))), 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)), _1169851)))))], (2612 ^ _775212) ^ [_813664, _813666, _813668, _813670, _813672, _813674, _813676, _813678] : [-(c_Nitpick_Opair__box_OPairBox(_813678, _813674, _813670, _813666) = c_Nitpick_Opair__box_OPairBox(_813676, _813672, _813668, _813664)), _813678 = _813676, _813674 = _813672, _813670 = _813668, _813666 = _813664], (9845 ^ _775212) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (316 ^ _775212) ^ [_779990, _779992, _779994, _779996, _779998, _780000, _780002, _780004, _780006, _780008] : [-(c_Typedef_Otype__definition(_780006, _780002, _779998, _779994, _779990)), c_Typedef_Otype__definition(_780008, _780004, _780000, _779996, _779992), _780008 = _780006, _780004 = _780002, _780000 = _779998, _779996 = _779994, _779992 = _779990], (39743 ^ _775212) ^ [_1535841, _1535843] : [c_Wellfounded_Owf(_1535841, hAPP(hAPP(c_Relation_Orel__comp(_1535841, _1535841, _1535841), _1535843), _1535843)), -(c_Wellfounded_Owf(_1535841, _1535843))], (18727 ^ _775212) ^ [_1093293, _1093295, _1093297] : [class_Rings_Oring__1(_1093293), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1093293), hAPP(c_Groups_Ouminus__class_Ouminus(_1093293), _1093295)), 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)))), _1093297)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1093293), _1093295), 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)))), _1093297)))], (47118 ^ _775212) ^ [_1714548, _1714550, _1714552] : [-(hAPP(hAPP(c_List_Odrop(_1714548), _1714550), c_List_Obutlast(_1714548, _1714552)) = c_List_Obutlast(_1714548, hAPP(hAPP(c_List_Odrop(_1714548), _1714550), _1714552)))], (40488 ^ _775212) ^ [_1553115, _1553117, _1553119, _1553121, _1553123, _1553125, _1553127] : [-(hAPP(c_Fun_Ocomp(_1553115, _1553117, _1553119, _1553121), c_Fun_Ofun__upd(_1553119, _1553115, _1553123, _1553125, _1553127)) = c_Fun_Ofun__upd(_1553119, _1553117, hAPP(c_Fun_Ocomp(_1553115, _1553117, _1553119, _1553121), _1553123), _1553125, hAPP(_1553121, _1553127)))], (9257 ^ _775212) ^ [_925249, _925251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _925249), _925251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _925249), c_Groups_Oone__class_Oone(tc_Int_Oint))), _925251)))], (33241 ^ _775212) ^ [_1378844, _1378846, _1378848, _1378850, _1378852, _1378854] : [class_Groups_Oordered__ab__group__add(_1378844), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378846), _1378848)), 33251 ^ _775212 : [(33254 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1378844), c_Groups_Ozero__class_Ozero(_1378844)), hAPP(_1378850, 33250 ^ [_1378844, _1378846, _1378848, _1378850, _1378852, _1378854])))], (33252 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1378846), 33250 ^ [_1378844, _1378846, _1378848, _1378850, _1378852, _1378854]), _1378848)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1378846, _1378844), _1378850), _1378848) = _1378852, hBOOL(hAPP(hAPP(c_member(_1378846), _1378854), _1378848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1378844), hAPP(_1378850, _1378854)), _1378852)))], (29344 ^ _775212) ^ [_1297172, _1297174, _1297176] : [class_Orderings_Olinorder(_1297172), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297172), _1297174), _1297176)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297172, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1297172, _1297174, _1297176)), hAPP(hAPP(c_Set_Oinsert(_1297172), _1297176), c_Orderings_Obot__class_Obot(tc_fun(_1297172, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1297172, _1297174, _1297176))], (31971 ^ _775212) ^ [_1353249, _1353251, _1353253] : [class_Orderings_Olinorder(_1353249), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353249), _1353251)), -(_1353251 = c_Orderings_Obot__class_Obot(tc_fun(_1353249, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353249), _1353253)), -(_1353253 = c_Orderings_Obot__class_Obot(tc_fun(_1353249, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1353249, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353249, tc_HOL_Obool)), _1353251), _1353253)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1353249), c_Big__Operators_Olinorder__class_OMin(_1353249, _1353251)), c_Big__Operators_Olinorder__class_OMin(_1353249, _1353253)))], (650 ^ _775212) ^ [_785271, _785273, _785275, _785277] : [-(c_FunDef_Ois__measure(_785275, _785271)), c_FunDef_Ois__measure(_785277, _785273), _785277 = _785275, _785273 = _785271], (27864 ^ _775212) ^ [_1268657, _1268659] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1268657, _1268659))))], (41923 ^ _775212) ^ [_1584730, _1584732] : [-(c_Transitive__Closure_Ortrancl(_1584730, c_Transitive__Closure_Otrancl(_1584730, _1584732)) = c_Transitive__Closure_Ortrancl(_1584730, _1584732))], (42420 ^ _775212) ^ [_1597385, _1597387, _1597389, _1597391, _1597393] : [42422 ^ _775212 : [(42425 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597385, tc_HOL_Obool)), _1597387), hAPP(_1597393, 42421 ^ [_1597385, _1597387, _1597389, _1597391, _1597393])))], (42423 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1597389), 42421 ^ [_1597385, _1597387, _1597389, _1597391, _1597393]), _1597391)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597385, tc_HOL_Obool)), _1597387), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1597389, tc_fun(_1597385, tc_HOL_Obool)), _1597391), _1597393))))], (52389 ^ _775212) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (1980 ^ _775212) ^ [_803738, _803740, _803742, _803744] : [-(c_Com_Ocom_OWhile(_803744, _803740) = c_Com_Ocom_OWhile(_803742, _803738)), _803744 = _803742, _803740 = _803738], (20075 ^ _775212) ^ [_1117686, _1117688, _1117690, _1117692] : [class_Fields_Ofield(_1117686), -(_1117688 = c_Groups_Ozero__class_Ozero(_1117686)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117686), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117686), _1117690), _1117688)), _1117692) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117686), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117686), _1117690), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117686), _1117688), _1117692))), _1117688))], (7683 ^ _775212) ^ [_898324, _898326, _898328] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _898324), _898326)), _898328) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _898324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _898326), _898328)))], (4870 ^ _775212) ^ [_849377, _849379, _849381, _849383, _849385, _849387, _849389, _849391, _849393, _849395] : [-(c_Predicate_Opred__comp(_849395, _849391, _849387, _849383, _849379) = c_Predicate_Opred__comp(_849393, _849389, _849385, _849381, _849377)), _849395 = _849393, _849391 = _849389, _849387 = _849385, _849383 = _849381, _849379 = _849377], (3542 ^ _775212) ^ [_828741, _828743, _828745, _828747] : [-(c_Wellfounded_Omax__ext(_828747, _828743) = c_Wellfounded_Omax__ext(_828745, _828741)), _828747 = _828745, _828743 = _828741], (16731 ^ _775212) ^ [_1060580, _1060582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1060580), _1060582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060580)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060582))))], (32838 ^ _775212) ^ [_1370871, _1370873, _1370875, _1370877, _1370879, _1370881] : [_1370871 = _1370873, -(hAPP(c_Fun_Ofun__upd(_1370875, _1370877, _1370879, _1370873, _1370881), _1370871) = _1370881)], (8850 ^ _775212) ^ [_918719, _918721] : [class_Orderings_Opreorder(_918719), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918719), _918721), _918721)))], (32916 ^ _775212) ^ [_1372259, _1372261, _1372263, _1372265] : [class_Fields_Olinordered__field(_1372259), -(hAPP(c_Groups_Oabs__class_Oabs(_1372259), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1372261, _1372259), _1372263), _1372265)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1372261, _1372259), hAPP(hAPP(c_COMBB(_1372259, _1372259, _1372261), c_Groups_Oabs__class_Oabs(_1372259)), _1372263)), _1372265))], (12502 ^ _775212) ^ [_981089, _981091, _981093, _981095] : [class_Divides_Osemiring__div(_981089), -(c_Divides_Odiv__class_Omod(_981089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981089), _981091), _981093), _981095) = c_Divides_Odiv__class_Omod(_981089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981089), c_Divides_Odiv__class_Omod(_981089, _981091, _981095)), c_Divides_Odiv__class_Omod(_981089, _981093, _981095)), _981095))], (22424 ^ _775212) ^ [_1162089, _1162091, _1162093] : [class_Orderings_Olinorder(_1162089), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162089), _1162091), _1162093) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162089), _1162093), _1162091))], (52385 ^ _775212) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (2434 ^ _775212) ^ [_810775, _810777, _810779, _810781] : [-(c_Nitpick_Oinverse__frac(_810781, _810777) = c_Nitpick_Oinverse__frac(_810779, _810775)), _810781 = _810779, _810777 = _810775], (12827 ^ _775212) ^ [_986804, _986806] : [class_Rings_Olinordered__idom(_986804), 12830 ^ _775212 : [(12837 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986804), c_Groups_Ozero__class_Ozero(_986804)), _986806)), -(c_Groups_Osgn__class_Osgn(_986804, _986806) = c_Groups_Oone__class_Oone(_986804))], (12831 ^ _775212) ^ [] : [c_Groups_Osgn__class_Osgn(_986804, _986806) = c_Groups_Oone__class_Oone(_986804), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986804), c_Groups_Ozero__class_Ozero(_986804)), _986806)))]]], (14383 ^ _775212) ^ [_1015224, _1015226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015224), _1015226)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1015224, _1015226) = _1015224)], (37443 ^ _775212) ^ [_1472484, _1472486, _1472488, _1472490, _1472492, _1472494] : [-(hAPP(c_Set_Ovimage(_1472484, _1472486, _1472488), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1472490, tc_fun(_1472486, tc_HOL_Obool)), _1472492), _1472494)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1472490, tc_fun(_1472484, tc_HOL_Obool)), _1472492), hAPP(hAPP(c_COMBB(tc_fun(_1472486, tc_HOL_Obool), tc_fun(_1472484, tc_HOL_Obool), _1472490), c_Set_Ovimage(_1472484, _1472486, _1472488)), _1472494)))], (40452 ^ _775212) ^ [_1552179, _1552181, _1552183, _1552185, _1552187, _1552189, _1552191] : [-(hAPP(c_Fun_Ocomp(_1552179, _1552181, _1552183, _1552185), hAPP(c_Fun_Ocomp(_1552187, _1552179, _1552183, _1552189), _1552191)) = hAPP(c_Fun_Ocomp(_1552187, _1552181, _1552183, hAPP(c_Fun_Ocomp(_1552179, _1552181, _1552187, _1552185), _1552189)), _1552191))], (18287 ^ _775212) ^ [_1085737, _1085739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085737), _1085739)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1085737)), c_Int_OBit0(_1085739))))], (35057 ^ _775212) ^ [_1420159, _1420161, _1420163, _1420165] : [-(hBOOL(hAPP(hAPP(c_member(_1420159), _1420161), _1420163))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420159, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1420159), _1420161), _1420165)), _1420163) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420159, tc_HOL_Obool)), _1420165), _1420163))], (13326 ^ _775212) ^ [_996369] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _996369), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _996369)], (30316 ^ _775212) ^ [_1320677, _1320679, _1320681] : [-(hBOOL(hAPP(hAPP(c_member(_1320677), _1320679), _1320681))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320677, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1320677), _1320679), _1320681)), hAPP(hAPP(c_Set_Oinsert(_1320677), _1320679), c_Orderings_Obot__class_Obot(tc_fun(_1320677, tc_HOL_Obool)))) = _1320681)], (14141 ^ _775212) ^ [_1010721, _1010723] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1010721), _1010723)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1010721)), _1010723))], (8541 ^ _775212) ^ [_913624, _913626, _913628, _913630, _913632, _913634] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_913624), -(_913626 = c_Groups_Ozero__class_Ozero(_913624)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913624), _913628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913624), _913626), _913632)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913624), _913630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913624), _913626), _913634)), _913628 = _913630, -(_913632 = _913634)], (48127 ^ _775212) ^ [_1736251, _1736253] : [-(hAPP(c_List_Oset(_1736251), c_List_Oconcat(_1736251, _1736253)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1736251), tc_fun(_1736251, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1736251)), _1736253)), c_List_Oset(_1736251)))], (8589 ^ _775212) ^ [_914475, _914477] : [class_Int_Oring__char__0(_914475), 8592 ^ _775212 : [(8599 ^ _775212) ^ [] : [_914477 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_914475), _914477) = c_Groups_Ozero__class_Ozero(_914475))], (8593 ^ _775212) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_914475), _914477) = c_Groups_Ozero__class_Ozero(_914475), -(_914477 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (32733 ^ _775212) ^ [_1368455, _1368457] : [class_Orderings_Olinorder(_1368455), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368455), _1368457)), -(_1368457 = c_Orderings_Obot__class_Obot(tc_fun(_1368455, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1368455), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1368455), 32746 ^ [_1368455, _1368457]), 32747 ^ [_1368455, _1368457])), hAPP(hAPP(c_Set_Oinsert(_1368455), 32746 ^ [_1368455, _1368457]), hAPP(hAPP(c_Set_Oinsert(_1368455), 32747 ^ [_1368455, _1368457]), c_Orderings_Obot__class_Obot(tc_fun(_1368455, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1368455), c_Big__Operators_Olattice_OInf__fin(_1368455, c_Orderings_Oord__class_Omin(_1368455), _1368457)), _1368457)))], (6823 ^ _775212) ^ [_883999, _884001] : [class_Rings_Olinordered__semidom(_883999), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883999), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_883999), _884001)), c_Groups_Ozero__class_Ozero(_883999)))], (43043 ^ _775212) ^ [_1614328, _1614330, _1614332] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614328, _1614328)), hAPP(hAPP(c_Product__Type_OPair(_1614328, _1614328), _1614330), _1614330)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1614328, _1614328), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1614332))))], (22726 ^ _775212) ^ [_1167631, _1167633, _1167635] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1167631), _1167633)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1167635), _1167633)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1167631), _1167635)), _1167633))], (28672 ^ _775212) ^ [_1284475, _1284477] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1284475, tc_HOL_Obool)), _1284477), c_Orderings_Obot__class_Obot(tc_fun(_1284475, tc_HOL_Obool))) = _1284477)], (47758 ^ _775212) ^ [_1728109, _1728111, _1728113, _1728115, _1728117, _1728119, _1728121] : [c_List_Olist__all2(_1728115, _1728111, hAPP(hAPP(c_COMBB(_1728109, tc_fun(_1728111, tc_HOL_Obool), _1728115), _1728113), _1728117), _1728119, _1728121), -(c_List_Olist__all2(_1728109, _1728111, _1728113, hAPP(hAPP(c_List_Omap(_1728115, _1728109), _1728117), _1728119), _1728121))], (42001 ^ _775212) ^ [_1586650, _1586652, _1586654, _1586656] : [-(hBOOL(hAPP(hAPP(c_member(_1586650), _1586652), hAPP(c_Relation_ODomain(_1586650, _1586650), _1586654)))), 42004 ^ _775212 : [(42011 ^ _775212) ^ [] : [_1586652 = _1586656, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586650, _1586650)), hAPP(hAPP(c_Product__Type_OPair(_1586650, _1586650), _1586652), _1586656)), c_Transitive__Closure_Ortrancl(_1586650, _1586654))))], (42005 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586650, _1586650)), hAPP(hAPP(c_Product__Type_OPair(_1586650, _1586650), _1586652), _1586656)), c_Transitive__Closure_Ortrancl(_1586650, _1586654))), -(_1586652 = _1586656)]]], (26665 ^ _775212) ^ [_1243789] : [c_Nat__Transfer_Onat__set(_1243789), 26668 ^ _775212 : [(26669 ^ _775212) ^ [_1243855] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1243855), _1243789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243855)))]]], (14939 ^ _775212) ^ [_1025528, _1025530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025528), _1025530)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025528), _1025530) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11054 ^ _775212) ^ [_956257, _956259, _956261, _956263] : [class_Rings_Olinordered__semiring(_956257), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956257), _956259), _956261)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956257), _956263), _956261))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956257), c_Groups_Ozero__class_Ozero(_956257)), _956261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956257), _956259), _956263)))], (28824 ^ _775212) ^ [_1287484, _1287486] : [class_Lattices_Obounded__lattice__bot(_1287484), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287484), c_Orderings_Obot__class_Obot(_1287484)), _1287486) = _1287486)], (19677 ^ _775212) ^ [_1110265] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1110265) = 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), _1110265), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (52617 ^ _775212) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (23172 ^ _775212) ^ [_1176379] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176379) = _1176379)], (47728 ^ _775212) ^ [_1727528, _1727530, _1727532, _1727534] : [_1727534 = c_List_Olist_ONil(_1727530), -(c_List_Olist__all2(_1727528, _1727530, _1727532, c_List_Olist_ONil(_1727528), _1727534))], (45584 ^ _775212) ^ [_1680274, _1680276, _1680278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680274), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1680276))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1680276), _1680274), _1680278)) = 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), _1680276)), _1680278)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1680276), _1680274)))], (14655 ^ _775212) ^ [_1020494, _1020496, _1020498] : [class_Rings_Ocomm__ring__1(_1020494), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1020494), _1020496), _1020498) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020494), _1020496), hAPP(c_Groups_Ouminus__class_Ouminus(_1020494), _1020498)))], (47030 ^ _775212) ^ [_1712674, _1712676, _1712678] : [-(c_List_Olast(_1712674, hAPP(hAPP(c_List_Oappend(_1712674), _1712676), hAPP(hAPP(c_List_Olist_OCons(_1712674), _1712678), c_List_Olist_ONil(_1712674)))) = _1712678)], (8810 ^ _775212) ^ [_918109, _918111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _918109)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _918111)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918109), _918111)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _918109)), hAPP(c_Int_Onat, _918111)))], (52245 ^ _775212) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (28914 ^ _775212) ^ [_1289064, _1289066, _1289068] : [class_Orderings_Oorder(_1289064), 28917 ^ _775212 : [(28924 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289064), _1289066), _1289068))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1289064, _1289066), _1289068) = c_Orderings_Obot__class_Obot(tc_fun(_1289064, tc_HOL_Obool)))], (28918 ^ _775212) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1289064, _1289066), _1289068) = c_Orderings_Obot__class_Obot(tc_fun(_1289064, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289064), _1289066), _1289068))]]], (15107 ^ _775212) ^ [_1028757, _1028759] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028757, _1028759) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1028757), _1028759)), _1028759)))], (51332 ^ _775212) ^ [_1805954, _1805956, _1805958, _1805960] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805954), _1805956)), 51335 ^ _775212 : [(51336 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805958), hAPP(c_Set_OCollect(_1805958), hAPP(hAPP(c_COMBB(tc_fun(_1805954, tc_HOL_Obool), tc_HOL_Obool, _1805958), c_HOL_OEx(_1805954)), hAPP(hAPP(c_COMBB(tc_fun(_1805954, tc_HOL_Obool), tc_fun(_1805954, tc_HOL_Obool), _1805958), hAPP(c_COMBS(_1805954, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1805954), c_fconj), hAPP(hAPP(c_COMBC(_1805954, tc_fun(_1805954, tc_HOL_Obool), tc_HOL_Obool), c_member(_1805954)), _1805956)))), _1805960))))), 51339 ^ _775212 : [(51340 ^ _775212) ^ [_1806262] : [hBOOL(hAPP(hAPP(c_member(_1805954), _1806262), _1805956)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1805958), hAPP(c_Set_OCollect(_1805958), hAPP(hAPP(c_COMBC(_1805958, _1805954, tc_HOL_Obool), _1805960), _1806262)))))]]], (51346 ^ _775212) ^ [] : [51348 ^ _775212 : [(51351 ^ _775212) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805958), hAPP(c_Set_OCollect(_1805958), hAPP(hAPP(c_COMBC(_1805958, _1805954, tc_HOL_Obool), _1805960), 51347 ^ [_1805954, _1805956, _1805958, _1805960]))))], (51349 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805954), 51347 ^ [_1805954, _1805956, _1805958, _1805960]), _1805956)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1805958), hAPP(c_Set_OCollect(_1805958), hAPP(hAPP(c_COMBB(tc_fun(_1805954, tc_HOL_Obool), tc_HOL_Obool, _1805958), c_HOL_OEx(_1805954)), hAPP(hAPP(c_COMBB(tc_fun(_1805954, tc_HOL_Obool), tc_fun(_1805954, tc_HOL_Obool), _1805958), hAPP(c_COMBS(_1805954, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1805954), c_fconj), hAPP(hAPP(c_COMBC(_1805954, tc_fun(_1805954, tc_HOL_Obool), tc_HOL_Obool), c_member(_1805954)), _1805956)))), _1805960))))))]]], (43956 ^ _775212) ^ [_1636204, _1636206, _1636208, _1636210, _1636212, _1636214, _1636216, _1636218] : [c_Finite__Set_Ofolding__image__simple__idem(_1636204, _1636206, _1636208, _1636210, _1636212, _1636214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1636206), _1636216)), hBOOL(hAPP(hAPP(c_member(_1636206), _1636218), _1636216)), -(hAPP(hAPP(_1636208, hAPP(_1636212, _1636218)), hAPP(_1636214, _1636216)) = hAPP(_1636214, _1636216))], (4958 ^ _775212) ^ [_850801, _850803] : [_850803 = _850801, -(c_List_Olist_OCons(_850803) = c_List_Olist_OCons(_850801))], (45210 ^ _775212) ^ [_1670323, _1670325, _1670327] : [45211 ^ _775212 : [(45214 ^ _775212) ^ [] : [_1670327 = c_List_Olist_ONil(_1670323)], (45212 ^ _775212) ^ [] : [_1670325 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1670323), _1670325), _1670327) = c_List_Olist_ONil(_1670323))], (33992 ^ _775212) ^ [_1396053, _1396055, _1396057, _1396059, _1396061, _1396063] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1396053, _1396055), tc_HOL_Obool)), _1396057), _1396059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1396053, tc_HOL_Obool)), _1396061), _1396063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1396055, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1396053, _1396055, _1396057), _1396061)), hAPP(c_Relation_OImage(_1396053, _1396055, _1396059), _1396063))))], (6287 ^ _775212) ^ [_874489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _874489), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_874489 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23712 ^ _775212) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (13298 ^ _775212) ^ [_995873, _995875] : [class_Divides_Osemiring__div(_995873), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_995873), c_Groups_Ozero__class_Ozero(_995873)), _995875) = c_Groups_Ozero__class_Ozero(_995873))], (47517 ^ _775212) ^ [_1723096, _1723098, _1723100, _1723102, _1723104] : [class_Orderings_Olinorder(_1723096), -(hAPP(c_List_Oset(_1723098), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1723098, _1723096, _1723100), _1723102), _1723104)) = hAPP(hAPP(c_Set_Oinsert(_1723098), _1723102), hAPP(c_List_Oset(_1723098), _1723104)))], (52611 ^ _775212) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (39659 ^ _775212) ^ [_1533944, _1533946, _1533948, _1533950] : [39660 ^ _775212 : [(39661 ^ _775212) ^ [_1533998] : [hBOOL(hAPP(hAPP(_1533948, _1533998), _1533950))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1533944, _1533946, _1533948), _1533950)))], (52327 ^ _775212) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (22138 ^ _775212) ^ [_1155410, _1155412, _1155414, _1155416] : [class_Groups_Ouminus(_1155410), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1155412, _1155410)), _1155414), _1155416) = hAPP(c_Groups_Ouminus__class_Ouminus(_1155410), hAPP(_1155414, _1155416)))], (47857 ^ _775212) ^ [_1730584, _1730586, _1730588, _1730590] : [hBOOL(hAPP(c_List_Odistinct(_1730584), _1730586)), hBOOL(hAPP(c_List_Odistinct(_1730588), _1730590)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1730584, _1730588)), c_Enum_Oproduct(_1730584, _1730588, _1730586, _1730590))))], (25438 ^ _775212) ^ [_1217948, _1217950, _1217952, _1217954, _1217956, _1217958, _1217960] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1217948, _1217950, _1217952, _1217954), _1217956), _1217958), _1217960) = c_New__DSequence_Opos__bind(_1217948, _1217950, hAPP(hAPP(hAPP(_1217952, _1217956), _1217958), _1217960), hAPP(hAPP(c_COMBC(_1217948, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1217950))), hAPP(hAPP(c_COMBC(_1217948, 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(_1217950)))), hAPP(hAPP(c_COMBC(_1217948, 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(_1217950))))), _1217954), _1217956)), _1217958)), _1217960)))], (50917 ^ _775212) ^ [_1796178, _1796180, _1796182, _1796184, _1796186] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1796178, _1796180, hAPP(hAPP(c_COMBC(_1796178, tc_fun(tc_prod(_1796178, _1796180), tc_HOL_Obool), tc_fun(_1796180, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1796180, tc_fun(tc_fun(tc_prod(_1796178, _1796180), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1796178, _1796180), tc_HOL_Obool), tc_fun(_1796180, tc_HOL_Obool)), _1796178), c_COMBC(_1796180, tc_fun(tc_prod(_1796178, _1796180), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1796180, tc_prod(_1796178, _1796180)), tc_fun(_1796180, tc_fun(tc_fun(tc_prod(_1796178, _1796180), tc_HOL_Obool), tc_HOL_Obool)), _1796178), hAPP(c_COMBB(tc_prod(_1796178, _1796180), tc_fun(tc_fun(tc_prod(_1796178, _1796180), tc_HOL_Obool), tc_HOL_Obool), _1796180), c_member(tc_prod(_1796178, _1796180)))), c_Product__Type_OPair(_1796178, _1796180)))), _1796182)), _1796184), _1796186)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1796180, _1796178)), hAPP(hAPP(c_Product__Type_OPair(_1796180, _1796178), _1796184), _1796186)), hAPP(c_Relation_Oconverse(_1796178, _1796180), _1796182))))], (49273 ^ _775212) ^ [_1761096, _1761098] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1761096), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1761096))), c_List_Otranspose(_1761096, _1761098)))))], (45927 ^ _775212) ^ [_1687772, _1687774, _1687776, _1687778, _1687780, _1687782] : [hAPP(hAPP(c_List_Oappend(_1687772), _1687774), _1687776) = _1687778, _1687780 = hAPP(hAPP(c_List_Oappend(_1687772), _1687776), _1687782), -(hAPP(hAPP(c_List_Oappend(_1687772), _1687774), _1687780) = hAPP(hAPP(c_List_Oappend(_1687772), _1687778), _1687782))], (39412 ^ _775212) ^ [_1525520, _1525522] : [-(hAPP(c_Fun_Oid(_1525520), _1525522) = _1525522)], (190 ^ _775212) ^ [_777955, _777957, _777959, _777961, _777963, _777965, _777967, _777969, _777971, _777973, _777975, _777977] : [-(c_Nitpick_Ofold__graph_H(_777975, _777971, _777967, _777963, _777959, _777955)), c_Nitpick_Ofold__graph_H(_777977, _777973, _777969, _777965, _777961, _777957), _777977 = _777975, _777973 = _777971, _777969 = _777967, _777965 = _777963, _777961 = _777959, _777957 = _777955], (43765 ^ _775212) ^ [_1631515, _1631517, _1631519, _1631521, _1631523] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631515, _1631515)), hAPP(hAPP(c_Product__Type_OPair(_1631515, _1631515), _1631517), _1631519)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631515, _1631515), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1631521)), _1631523))), 43769 ^ _775212 : [(43772 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631515, _1631515)), hAPP(hAPP(c_Product__Type_OPair(_1631515, _1631515), 43768 ^ [_1631515, _1631517, _1631519, _1631521, _1631523]), _1631519)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631515, _1631515), tc_HOL_Obool), _1631521), _1631523))))], (43770 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631515, _1631515)), hAPP(hAPP(c_Product__Type_OPair(_1631515, _1631515), _1631517), 43768 ^ [_1631515, _1631517, _1631519, _1631521, _1631523])), _1631523)))]]], (24100 ^ _775212) ^ [_1193857, _1193859] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193857), _1193859)), 24105 ^ _775212 : [(24108 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193859), _1193857))], (24106 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1193857), _1193859)))]], -(_1193857 = _1193859)], (47740 ^ _775212) ^ [_1727772, _1727774, _1727776] : [_1727772 = _1727774, -(c_List_Olist__all2(_1727776, _1727776, c_fequal, _1727772, _1727774))], (5757 ^ _775212) ^ [_866048, _866050, _866052, _866054] : [-(hBOOL(hAPP(_866048, _866050))), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_866048, _866052), _866050, _866054, _866050))], (41835 ^ _775212) ^ [_1582569, _1582571] : [-(hAPP(c_Relation_ODomain(_1582569, _1582569), c_Transitive__Closure_Ortrancl(_1582569, _1582571)) = c_Orderings_Otop__class_Otop(tc_fun(_1582569, tc_HOL_Obool)))], (10881 ^ _775212) ^ [_953038, _953040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _953038), _953040)), -(_953040 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _953038), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 10884 ^ [_953038, _953040])))], (22632 ^ _775212) ^ [_1165902, _1165904, _1165906, _1165908] : [class_Orderings_Olinorder(_1165902), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165902), _1165904), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165902), _1165906), _1165908))), 22639 ^ _775212 : [(22642 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165902), _1165904), _1165908)))], (22640 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165902), _1165904), _1165906)))]]], (13258 ^ _775212) ^ [_995038, _995040, _995042] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _995038, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995040), _995042)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995040), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _995038), _995040), _995042))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _995038, _995040)))], (3908 ^ _775212) ^ [_834506, _834508] : [_834508 = _834506, -(c_List_Orotate1(_834508) = c_List_Orotate1(_834506))], (16547 ^ _775212) ^ [_1056734, _1056736] : [16548 ^ _775212 : [(16551 ^ _775212) ^ [] : [_1056736 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16549 ^ _775212) ^ [] : [-(_1056734 = 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), _1056734)), _1056736))))], (46574 ^ _775212) ^ [_1703267, _1703269] : [46576 ^ _775212 : [(46580 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46578 ^ [_1703267, _1703269]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703267)), _1703269))))], (46582 ^ _775212) ^ [] : [46575 ^ [_1703267, _1703269] = 46578 ^ [_1703267, _1703269]], (46584 ^ _775212) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1703267), _1703269), 46575 ^ [_1703267, _1703269]) = hAPP(hAPP(c_List_Onth(_1703267), _1703269), 46578 ^ [_1703267, _1703269]))], (46577 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46575 ^ [_1703267, _1703269]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703267)), _1703269))))]], -(hBOOL(hAPP(c_List_Odistinct(_1703267), _1703269)))], (37066 ^ _775212) ^ [_1464664, _1464666, _1464668, _1464670, _1464672, _1464674] : [c_Fun_Oinj__on(_1464664, _1464666, _1464668, _1464670), hAPP(_1464668, _1464672) = _1464674, hBOOL(hAPP(hAPP(c_member(_1464664), _1464672), _1464670)), -(hAPP(c_Fun_Othe__inv__into(_1464664, _1464666, _1464670, _1464668), _1464674) = _1464672)], (6142 ^ _775212) ^ [_872322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872322), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21539 ^ _775212) ^ [_1144108, _1144110, _1144112, _1144114] : [_1144108 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1144110), _1144112)), _1144114), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1144108, _1144110), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1144112), _1144114)))), 21546 ^ _775212 : [(21549 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144114)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1144114), _1144110))], (21547 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144110)))]], 21554 ^ _775212 : [(21557 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1144110), _1144114)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1144114), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21555 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144110))]]], (28986 ^ _775212) ^ [_1290193, _1290195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290193, tc_HOL_Obool)), _1290195), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1290193, tc_HOL_Obool)), _1290195))), -(_1290195 = c_Orderings_Obot__class_Obot(tc_fun(_1290193, tc_HOL_Obool)))], (32025 ^ _775212) ^ [_1354133, _1354135, _1354137] : [class_Lattices_Olattice(_1354133), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354133), _1354135)), -(hBOOL(hAPP(hAPP(c_member(_1354133), _1354137), _1354135))), -(_1354135 = c_Orderings_Obot__class_Obot(tc_fun(_1354133, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1354133, hAPP(hAPP(c_Set_Oinsert(_1354133), _1354137), _1354135)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1354133), _1354137), c_Big__Operators_Olattice__class_OSup__fin(_1354133, _1354135)))], (21819 ^ _775212) ^ [_1149332, _1149334] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1149332), _1149334)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1149332), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1149334)))], (22258 ^ _775212) ^ [_1158104, _1158106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158104)), hAPP(c_Nat_OSuc, _1158106))), -(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(_1158104))), 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)), _1158106)))))], (45995 ^ _775212) ^ [_1689610, _1689612, _1689614, _1689616, _1689618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1689610), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689612)), _1689614))), 45998 ^ _775212 : [(46005 ^ _775212) ^ [] : [-(_1689610 = _1689616), -(hAPP(hAPP(c_List_Onth(_1689612), hAPP(hAPP(c_List_Olist__update(_1689612, _1689614), _1689610), _1689618)), _1689616) = hAPP(hAPP(c_List_Onth(_1689612), _1689614), _1689616))], (45999 ^ _775212) ^ [] : [_1689610 = _1689616, -(hAPP(hAPP(c_List_Onth(_1689612), hAPP(hAPP(c_List_Olist__update(_1689612, _1689614), _1689610), _1689618)), _1689616) = _1689618)]]], (5150 ^ _775212) ^ [_853787, _853789, _853791, _853793] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_853793, _853789) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_853791, _853787)), _853793 = _853791, _853789 = _853787], (28085 ^ _775212) ^ [_1272754] : [-(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)), _1272754))))], (20187 ^ _775212) ^ [_1119611, _1119613, _1119615, _1119617] : [class_Fields_Ofield__inverse__zero(_1119611), class_Int_Onumber(_1119611), 20194 ^ _775212 : [(20195 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1119611), _1119613) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119611), _1119615), _1119617), 20198 ^ _775212 : [(20205 ^ _775212) ^ [] : [_1119617 = c_Groups_Ozero__class_Ozero(_1119611), -(hAPP(c_Int_Onumber__class_Onumber__of(_1119611), _1119613) = c_Groups_Ozero__class_Ozero(_1119611))], (20199 ^ _775212) ^ [] : [-(_1119617 = c_Groups_Ozero__class_Ozero(_1119611)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119611), hAPP(c_Int_Onumber__class_Onumber__of(_1119611), _1119613)), _1119617) = _1119615)]]], (20211 ^ _775212) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1119611), _1119613) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119611), _1119615), _1119617)), 20214 ^ _775212 : [(20217 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119611), hAPP(c_Int_Onumber__class_Onumber__of(_1119611), _1119613)), _1119617) = _1119615], (20215 ^ _775212) ^ [] : [_1119617 = c_Groups_Ozero__class_Ozero(_1119611)]], 20218 ^ _775212 : [(20221 ^ _775212) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1119611), _1119613) = c_Groups_Ozero__class_Ozero(_1119611)], (20219 ^ _775212) ^ [] : [-(_1119617 = c_Groups_Ozero__class_Ozero(_1119611))]]]]], (6795 ^ _775212) ^ [_883489, _883491, _883493] : [class_Groups_Oordered__comm__monoid__add(_883489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883489), c_Groups_Ozero__class_Ozero(_883489)), _883491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883489), c_Groups_Ozero__class_Ozero(_883489)), _883493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883489), c_Groups_Ozero__class_Ozero(_883489)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883489), _883491), _883493))))], (4840 ^ _775212) ^ [_848922, _848924, _848926, _848928] : [-(c_List_Oupt(_848928, _848924) = c_List_Oupt(_848926, _848922)), _848928 = _848926, _848924 = _848922], (8243 ^ _775212) ^ [_908145, _908147, _908149, _908151] : [class_Rings_Olinordered__ring__strict(_908145), 8246 ^ _775212 : [(8261 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908145), _908147), _908149)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908145), _908151), _908149)))), 8262 ^ _775212 : [(8269 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908145), _908149), c_Groups_Ozero__class_Ozero(_908145))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908145), _908151), _908147))], (8263 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908145), c_Groups_Ozero__class_Ozero(_908145)), _908149)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908145), _908147), _908151))]]], (8247 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908145), _908147), _908149)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908145), _908151), _908149))), 8252 ^ _775212 : [(8255 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908145), _908147), _908151)))], (8253 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908145), c_Groups_Ozero__class_Ozero(_908145)), _908149)))]], 8256 ^ _775212 : [(8259 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908145), _908151), _908147)))], (8257 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908145), _908149), c_Groups_Ozero__class_Ozero(_908145))))]]]]], (9601 ^ _775212) ^ [_930241, _930243] : [class_Groups_Ocomm__monoid__mult(_930241), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930241), c_Groups_Oone__class_Oone(_930241)), _930243) = _930243)], (42203 ^ _775212) ^ [_1591225, _1591227] : [c_Wellfounded_Oacyclic(_1591225, _1591227), -(c_Wellfounded_Oacyclic(_1591225, hAPP(c_Relation_Oconverse(_1591225, _1591225), _1591227)))], (1764 ^ _775212) ^ [_800118, _800120] : [-(class_Groups_Omonoid__mult(_800118)), _800120 = _800118, class_Groups_Omonoid__mult(_800120)], (22736 ^ _775212) ^ [_1167934, _1167936, _1167938] : [-(hAPP(c_Product__Type_Ofst(_1167934, _1167936), _1167938) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1167934, _1167936, _1167934), c_COMBK(_1167934, _1167936)), _1167938))], (39564 ^ _775212) ^ [_1529762, _1529764, _1529766, _1529768] : [-(hAPP(c_Relation_ORange(_1529762, _1529764), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529762, _1529764), tc_HOL_Obool)), _1529766), _1529768)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1529764, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1529762, _1529764), _1529766)), hAPP(c_Relation_ORange(_1529762, _1529764), _1529768)))], (23282 ^ _775212) ^ [_1179013, _1179015, _1179017, _1179019, _1179021, _1179023, _1179025] : [-(hAPP(c_Product__Type_Oapsnd(_1179013, _1179015, _1179017, _1179019), hAPP(c_Product__Type_Oapfst(_1179021, _1179017, _1179013, _1179023), _1179025)) = hAPP(c_Product__Type_Oapfst(_1179021, _1179017, _1179015, _1179023), hAPP(c_Product__Type_Oapsnd(_1179013, _1179015, _1179021, _1179019), _1179025)))], (52393 ^ _775212) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (45937 ^ _775212) ^ [_1688002, _1688004, _1688006, _1688008] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688002)), hAPP(hAPP(c_List_Oappend(_1688002), _1688004), _1688006)), c_List_Olists(_1688002, _1688008))), 45940 ^ _775212 : [(45943 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688002)), _1688006), c_List_Olists(_1688002, _1688008))))], (45941 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688002)), _1688004), c_List_Olists(_1688002, _1688008))))]]], (41925 ^ _775212) ^ [_1584785, _1584787, _1584789, _1584791] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584785, _1584785)), hAPP(hAPP(c_Product__Type_OPair(_1584785, _1584785), _1584787), _1584789)), c_Transitive__Closure_Ortrancl(_1584785, _1584791))), -(_1584787 = _1584789), 41932 ^ _775212 : [(41935 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584785, _1584785)), hAPP(hAPP(c_Product__Type_OPair(_1584785, _1584785), _1584787), _1584789)), c_Transitive__Closure_Otrancl(_1584785, _1584791))))], (41933 ^ _775212) ^ [] : [_1584787 = _1584789]]], (15075 ^ _775212) ^ [_1028077, _1028079, _1028081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028077), _1028079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028081), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028079), _1028081)), _1028077))))], (38901 ^ _775212) ^ [_1506838, _1506840] : [-(hAPP(c_Set_OCollect(_1506838), _1506840) = _1506840)], (34053 ^ _775212) ^ [] : [-(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))))))], (43326 ^ _775212) ^ [_1620903, _1620905, _1620907] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620903, tc_HOL_Obool)), _1620905), _1620907) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620903, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1620903, tc_HOL_Obool)), _1620905), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1620903, tc_HOL_Obool)), _1620907), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1620903, tc_HOL_Obool), tc_HOL_Obool))))))], (13254 ^ _775212) ^ [_994946, _994948] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _994946), _994948)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994946)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994948)))], (51946 ^ _775212) ^ [_1818985, _1818987] : [c_Equiv__Relations_Oequivp(_1818985, _1818987), -(c_Equiv__Relations_Opart__equivp(_1818985, _1818987))], (38923 ^ _775212) ^ [_1507398, _1507400] : [hAPP(c_Set_OCollect(_1507398), _1507400) = c_Orderings_Obot__class_Obot(tc_fun(_1507398, tc_HOL_Obool)), 38926 ^ _775212 : [(38927 ^ _775212) ^ [_1507483] : [hBOOL(hAPP(_1507400, _1507483))]]], (11312 ^ _775212) ^ [_960964, _960966] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _960964) = _960966, 11315 ^ _775212 : [(11318 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _960966)))], (11316 ^ _775212) ^ [] : [-(_960964 = hAPP(c_Int_Onat, _960966))]]], (30891 ^ _775212) ^ [_1333119, _1333121, _1333123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333119)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1333121), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1333123)), 30901 ^ _775212 : [(30907 ^ _775212) ^ [] : [-(_1333121 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30903 ^ [_1333119, _1333121, _1333123]), 30900 ^ [_1333119, _1333121, _1333123]))], (30905 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30903 ^ [_1333119, _1333121, _1333123]), _1333123)))], (30902 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30900 ^ [_1333119, _1333121, _1333123]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1333119))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1333121), _1333119) = _1333121)], (52133 ^ _775212) ^ [_1822612, _1822614] : [class_Lattices_Olattice(_1822612), -(class_Lattices_Osemilattice__inf(tc_fun(_1822614, _1822612)))], (41706 ^ _775212) ^ [_1579789, _1579791, _1579793, _1579795, _1579797] : [c_Finite__Set_Ofun__left__comm(_1579789, _1579791, _1579793), -(hAPP(c_Fun_Ocomp(_1579791, _1579791, _1579791, hAPP(_1579793, _1579795)), hAPP(_1579793, _1579797)) = hAPP(c_Fun_Ocomp(_1579791, _1579791, _1579791, hAPP(_1579793, _1579797)), hAPP(_1579793, _1579795)))], (29895 ^ _775212) ^ [_1307961, _1307963, _1307965] : [hBOOL(hAPP(hAPP(c_member(_1307961), _1307963), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1307961, tc_HOL_Obool)), _1307965))), hBOOL(hAPP(hAPP(c_member(_1307961), _1307963), _1307965))], (27099 ^ _775212) ^ [_1252542, _1252544, _1252546, _1252548] : [class_Lattices_Osemilattice__sup(_1252542), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252542), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252542), _1252544), _1252546)), _1252548) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252542), _1252544), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1252542), _1252546), _1252548)))], (20361 ^ _775212) ^ [_1122499, _1122501] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122499), _1122501), hAPP(c_Int_Onumber__class_Onumber__of(_1122499), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1122499), _1122501)), class_Fields_Ofield__inverse__zero(_1122499), class_Int_Onumber__ring(_1122499)], (27447 ^ _775212) ^ [_1259245, _1259247, _1259249] : [class_Orderings_Olinorder(_1259245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259245), _1259247), _1259249)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259245, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1259245), _1259247)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1259245, _1259247), _1259249)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1259245), _1259249))], (27868 ^ _775212) ^ [_1268719, _1268721] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1268719, _1268721))))], (32953 ^ _775212) ^ [_1372941, _1372943, _1372945, _1372947] : [class_Rings_Ocomm__semiring__1(_1372941), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372943), _1372945)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1372943, _1372941), _1372947), _1372945) = c_Groups_Ozero__class_Ozero(_1372941)), 32962 ^ _775212 : [(32963 ^ _775212) ^ [_1373122] : [hBOOL(hAPP(hAPP(c_member(_1372943), _1373122), _1372945)), hAPP(_1372947, _1373122) = c_Groups_Ozero__class_Ozero(_1372941)]]], (9847 ^ _775212) ^ [_934574, _934576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934574), _934576)), 9850 ^ _775212 : [(9853 ^ _775212) ^ [] : [_934574 = _934576], (9851 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _934574), _934576)))]]], (6757 ^ _775212) ^ [_882812, _882814, _882816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882812), _882814)), _882816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882812), _882816)))], (26740 ^ _775212) ^ [_1245127, _1245129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245127)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1245127, _1245129)))], (10249 ^ _775212) ^ [_941814, _941816, _941818] : [class_Rings_Oordered__cancel__semiring(_941814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941814), c_Groups_Ozero__class_Ozero(_941814)), _941816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941814), _941818), c_Groups_Ozero__class_Ozero(_941814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941814), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941814), _941816), _941818)), c_Groups_Ozero__class_Ozero(_941814))))], (6895 ^ _775212) ^ [_885055, _885057] : [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), _885055), _885057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _885055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _885057)))], (12374 ^ _775212) ^ [_978711, _978713, _978715, _978717] : [_978711 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _978713), _978715)), _978717), -(_978713 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _978711, _978713) = _978717), 12381 ^ _775212 : [(12384 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _978717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _978717), _978713))], (12382 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _978713)))]], 12389 ^ _775212 : [(12392 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _978713), _978717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _978717), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (12390 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _978713))]]], (45021 ^ _775212) ^ [_1665305, _1665307, _1665309] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1665305), _1665307)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1665305)), hAPP(c_Set_OCollect(tc_List_Olist(_1665305)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1665305), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1665305)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1665305), tc_fun(_1665305, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1665305, tc_HOL_Obool), tc_fun(tc_fun(_1665305, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1665305)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1665305, tc_HOL_Obool))), c_List_Oset(_1665305))), _1665307))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1665305), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1665305)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1665305)))), _1665309))))))], (39971 ^ _775212) ^ [_1540423, _1540425, _1540427, _1540429, _1540431] : [-(hAPP(c_Relation_ODomain(_1540423, _1540425), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1540423, _1540425)), hAPP(hAPP(c_Product__Type_OPair(_1540423, _1540425), _1540427), _1540429)), _1540431)) = hAPP(hAPP(c_Set_Oinsert(_1540423), _1540427), hAPP(c_Relation_ODomain(_1540423, _1540425), _1540431)))], (16743 ^ _775212) ^ [_1060818] : [class_Rings_Osemiring__1(_1060818), -(c_Int_Oiszero(_1060818, c_Groups_Ozero__class_Ozero(_1060818)))], (42439 ^ _775212) ^ [_1598136, _1598138, _1598140, _1598142, _1598144, _1598146, _1598148] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1598136, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598138, tc_fun(_1598136, tc_HOL_Obool)), _1598140), _1598142)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598144, tc_fun(_1598136, tc_HOL_Obool)), _1598146), _1598148)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598138, tc_fun(_1598136, tc_HOL_Obool)), _1598140), hAPP(hAPP(c_COMBB(tc_fun(_1598144, tc_fun(_1598136, tc_HOL_Obool)), tc_fun(_1598136, tc_HOL_Obool), _1598138), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598144, tc_fun(_1598136, tc_HOL_Obool)), _1598146)), hAPP(hAPP(c_COMBC(_1598138, tc_fun(_1598144, tc_fun(_1598136, tc_HOL_Obool)), tc_fun(_1598144, tc_fun(_1598136, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1598136, tc_HOL_Obool), tc_fun(_1598136, tc_HOL_Obool)), tc_fun(tc_fun(_1598144, tc_fun(_1598136, tc_HOL_Obool)), tc_fun(_1598144, tc_fun(_1598136, tc_HOL_Obool))), _1598138), c_COMBB(tc_fun(_1598136, tc_HOL_Obool), tc_fun(_1598136, tc_HOL_Obool), _1598144)), hAPP(hAPP(c_COMBB(tc_fun(_1598136, tc_HOL_Obool), tc_fun(tc_fun(_1598136, tc_HOL_Obool), tc_fun(_1598136, tc_HOL_Obool)), _1598138), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1598136, tc_HOL_Obool))), _1598142))), _1598148))))], (17671 ^ _775212) ^ [_1075330, _1075332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1075330)), c_Int_OBit1(_1075332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1075330), _1075332)))], (43420 ^ _775212) ^ [_1623506, _1623508, _1623510] : [class_Complete__Lattice_Ocomplete__lattice(_1623506), class_Orderings_Olinorder(_1623506), 43427 ^ _775212 : [(43437 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1623506), _1623508), c_Complete__Lattice_OSup__class_OSup(_1623506, _1623510)))), 43438 ^ _775212 : [(43439 ^ _775212) ^ [_1623812] : [hBOOL(hAPP(hAPP(c_member(_1623506), _1623812), _1623510)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1623506), _1623508), _1623812))]]], (43428 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1623506), _1623508), c_Complete__Lattice_OSup__class_OSup(_1623506, _1623510))), 43432 ^ _775212 : [(43435 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1623506), _1623508), 43431 ^ [_1623506, _1623508, _1623510])))], (43433 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623506), 43431 ^ [_1623506, _1623508, _1623510]), _1623510)))]]]]], (44322 ^ _775212) ^ [_1646599, _1646601, _1646603, _1646605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646599), tc_List_Olist(_1646599))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646599), tc_List_Olist(_1646599)), _1646601), _1646603)), c_List_Olistrel1(_1646599, hAPP(c_Relation_Oconverse(_1646599, _1646599), _1646605)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646599), tc_List_Olist(_1646599))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646599), tc_List_Olist(_1646599)), _1646601), _1646603)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1646599), tc_List_Olist(_1646599)), c_List_Olistrel1(_1646599, _1646605)))))], (23626 ^ _775212) ^ [_1185492, _1185494] : [-(c_Divides_Odivmod__nat(_1185492, _1185494) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1185492, _1185494)))], (23636 ^ _775212) ^ [_1185700, _1185702] : [-(c_HOL_OThe(_1185700, hAPP(hAPP(c_COMBC(_1185700, _1185700, tc_HOL_Obool), c_fequal), _1185702)) = _1185702)], (22264 ^ _775212) ^ [_1158231, _1158233] : [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(_1158231))), 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)), _1158233)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158231)), hAPP(c_Nat_OSuc, _1158233))))], (18931 ^ _775212) ^ [_1097362, _1097364] : [class_Fields_Olinordered__field__inverse__zero(_1097362), class_Int_Onumber__ring(_1097362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097362), c_Groups_Ozero__class_Ozero(_1097362)), _1097364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097362), c_Groups_Ozero__class_Ozero(_1097362)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1097362), _1097364), hAPP(c_Int_Onumber__class_Onumber__of(_1097362), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (42573 ^ _775212) ^ [_1602086, _1602088, _1602090, _1602092, _1602094] : [_1602086 = c_Orderings_Obot__class_Obot(tc_fun(_1602088, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602088, tc_fun(_1602090, tc_HOL_Obool)), _1602086), hAPP(hAPP(c_COMBB(tc_fun(_1602090, tc_HOL_Obool), tc_fun(_1602090, tc_HOL_Obool), _1602088), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602090, tc_HOL_Obool)), _1602092)), _1602094)) = c_Orderings_Otop__class_Otop(tc_fun(_1602090, tc_HOL_Obool)))], (15791 ^ _775212) ^ [_1042522, _1042524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1042522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042524), _1042522))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1042524), _1042522) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042524), _1042522)), _1042522)))], (46792 ^ _775212) ^ [_1707970, _1707972, _1707974] : [-(hAPP(c_List_Orotate(_1707970, _1707972), _1707974) = hAPP(c_List_Orotate(_1707970, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1707972, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707970)), _1707974))), _1707974))], (22394 ^ _775212) ^ [_1161567, _1161569] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1161567)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161569)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1161569))), 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), _1161567)), c_Int_Onat)))))], (38353 ^ _775212) ^ [_1496257, _1496259] : [class_Orderings_Olinorder(_1496257), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496257), _1496259)), -(c_Big__Operators_Olinorder__class_OMin(_1496257, _1496259) = hAPP(c_Finite__Set_Ofold1(_1496257, c_Orderings_Oord__class_Omin(_1496257)), _1496259))], (22528 ^ _775212) ^ [_1164073, _1164075, _1164077, _1164079] : [class_Orderings_Olinorder(_1164073), 22531 ^ _775212 : [(22540 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164073), _1164075), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1164073), _1164077), _1164079)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164073), _1164075), _1164077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164073), _1164075), _1164079))], (22532 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164073), _1164075), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1164073), _1164077), _1164079))), 22535 ^ _775212 : [(22538 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164073), _1164075), _1164079)))], (22536 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164073), _1164075), _1164077)))]]]]], (5668 ^ _775212) ^ [_864557, _864559] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_864557, _864559)], (23850 ^ _775212) ^ [_1189743, _1189745, _1189747, _1189749, _1189751, _1189753] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1189743, _1189745, _1189747, _1189749), _1189751), _1189753) = hAPP(_1189749, hAPP(hAPP(c_Product__Type_OPair(_1189743, _1189745), _1189751), _1189753)))], (42483 ^ _775212) ^ [_1599717, _1599719, _1599721, _1599723, _1599725] : [-(_1599717 = c_Orderings_Obot__class_Obot(tc_fun(_1599719, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599721, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599719, tc_fun(_1599721, tc_HOL_Obool)), _1599717), _1599723)), _1599725) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599719, tc_fun(_1599721, tc_HOL_Obool)), _1599717), hAPP(hAPP(c_COMBC(_1599719, tc_fun(_1599721, tc_HOL_Obool), tc_fun(_1599721, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599721, tc_HOL_Obool), tc_fun(tc_fun(_1599721, tc_HOL_Obool), tc_fun(_1599721, tc_HOL_Obool)), _1599719), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599721, tc_HOL_Obool))), _1599723)), _1599725)))], (27870 ^ _775212) ^ [_1268750, _1268752] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1268750, _1268752))))], (5016 ^ _775212) ^ [_851660, _851662, _851664, _851666] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_851666, _851662) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_851664, _851660)), _851666 = _851664, _851662 = _851660], (19621 ^ _775212) ^ [_1109322, _1109324, _1109326] : [class_Rings_Odivision__ring(_1109322), -(_1109324 = c_Groups_Ozero__class_Ozero(_1109322)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1109322), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109322), _1109326), _1109324)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109322), _1109326), hAPP(c_Groups_Ouminus__class_Ouminus(_1109322), _1109324)))], (25404 ^ _775212) ^ [_1217333, _1217335] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1217333)), _1217335)), 25407 ^ _775212 : [(25414 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217333))), -(_1217335 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25408 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217333)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217333), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217335))))]]], (42561 ^ _775212) ^ [_1601694, _1601696, _1601698, _1601700, _1601702] : [class_Complete__Lattice_Ocomplete__lattice(_1601694), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1601696, tc_HOL_Obool)), _1601698), _1601700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1601694), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601696, _1601694), _1601700), _1601702)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601696, _1601694), _1601698), _1601702))))], (5701 ^ _775212) ^ [_865126, _865128, _865130] : [class_Rings_Osemiring__1(_865126), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_865126, _865128, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _865130) = _865130)], (11975 ^ _775212) ^ [_971976, _971978] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971976), _971978)), _971976 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _971978 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12159 ^ _775212) ^ [_975088, _975090, _975092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975088), _975090)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975092), _975090))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _975090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975088), _975092)))], (29166 ^ _775212) ^ [_1293534, _1293536, _1293538, _1293540, _1293542] : [_1293534 = c_Orderings_Obot__class_Obot(tc_fun(_1293536, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293536, tc_fun(_1293538, tc_HOL_Obool)), _1293534), hAPP(hAPP(c_COMBB(tc_fun(_1293538, tc_HOL_Obool), tc_fun(_1293538, tc_HOL_Obool), _1293536), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293538, tc_HOL_Obool)), _1293540)), _1293542)) = c_Orderings_Obot__class_Obot(tc_fun(_1293538, tc_HOL_Obool)))], (18379 ^ _775212) ^ [_1087296] : [-(c_Int_Osucc(c_Int_OBit0(_1087296)) = c_Int_OBit1(_1087296))], (47563 ^ _775212) ^ [_1724036, _1724038, _1724040] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1724036)), _1724040), c_List_Olists(_1724036, _1724038))), -(hBOOL(hAPP(c_List_Olistsp(_1724036, hAPP(hAPP(c_COMBC(_1724036, tc_fun(_1724036, tc_HOL_Obool), tc_HOL_Obool), c_member(_1724036)), _1724038)), _1724040)))], (16629 ^ _775212) ^ [_1058464, _1058466, _1058468, _1058470, _1058472, _1058474, _1058476] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1058464, _1058466), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1058468), _1058470))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1058472, _1058466), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1058474), _1058476))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1058466)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1058464), _1058472), _1058466), 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), _1058468), _1058474)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1058470), _1058476)), _1058466))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1058470), _1058476), _1058466)))))], (45385 ^ _775212) ^ [_1675211] : [-(c_List_Olistset(_1675211, c_List_Olist_ONil(tc_fun(_1675211, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1675211)), c_List_Olist_ONil(_1675211)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1675211), tc_HOL_Obool))))], (5342 ^ _775212) ^ [_856727, _856729, _856731, _856733] : [-(c_Relation_Oconverse(_856733, _856729) = c_Relation_Oconverse(_856731, _856727)), _856733 = _856731, _856729 = _856727], (8387 ^ _775212) ^ [_910758, _910760, _910762] : [class_Rings_Olinordered__semiring__strict(_910758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910758), c_Groups_Ozero__class_Ozero(_910758)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_910758), _910760), _910762))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910758), c_Groups_Ozero__class_Ozero(_910758)), _910762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910758), c_Groups_Ozero__class_Ozero(_910758)), _910760)))], (10699 ^ _775212) ^ [_950033, _950035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950033)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950035)), -(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), _950033), _950035))))], (33584 ^ _775212) ^ [_1386925, _1386927, _1386929, _1386931] : [-(hAPP(c_Relation_OField(_1386925), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1386925, _1386925)), hAPP(hAPP(c_Product__Type_OPair(_1386925, _1386925), _1386927), _1386929)), _1386931)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386925, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1386925), _1386927), hAPP(hAPP(c_Set_Oinsert(_1386925), _1386929), c_Orderings_Obot__class_Obot(tc_fun(_1386925, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1386925), _1386931)))], (13839 ^ _775212) ^ [_1004980, _1004982, _1004984] : [class_Divides_Osemiring__div(_1004980), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004980), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1004980), _1004982), _1004984)), _1004984)), c_Divides_Odiv__class_Omod(_1004980, _1004982, _1004984)) = _1004982)], (5584 ^ _775212) ^ [_863103, _863105] : [hAPP(_863103, 5585 ^ [_863103, _863105]) = hAPP(_863105, 5585 ^ [_863103, _863105]), -(_863103 = _863105)], (42055 ^ _775212) ^ [_1587851, _1587853, _1587855, _1587857] : [c_Wellfounded_Oacyclic(_1587851, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1587851, _1587851)), hAPP(hAPP(c_Product__Type_OPair(_1587851, _1587851), _1587853), _1587855)), _1587857)), 42058 ^ _775212 : [(42061 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587851, _1587851)), hAPP(hAPP(c_Product__Type_OPair(_1587851, _1587851), _1587855), _1587853)), c_Transitive__Closure_Ortrancl(_1587851, _1587857)))], (42059 ^ _775212) ^ [] : [-(c_Wellfounded_Oacyclic(_1587851, _1587857))]]], (52619 ^ _775212) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (43575 ^ _775212) ^ [_1626856, _1626858] : [class_Complete__Lattice_Ocomplete__lattice(_1626856), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626856), _1626858)), -(_1626858 = c_Orderings_Obot__class_Obot(tc_fun(_1626856, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1626856, _1626858) = c_Complete__Lattice_OSup__class_OSup(_1626856, _1626858))], (31699 ^ _775212) ^ [_1348892, _1348894, _1348896] : [class_Orderings_Olinorder(_1348892), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348892), _1348894)), hBOOL(hAPP(hAPP(c_member(_1348892), _1348896), _1348894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348892), c_Big__Operators_Olinorder__class_OMin(_1348892, _1348894)), _1348896)))], (49418 ^ _775212) ^ [_1764309, _1764311, _1764313, _1764315] : [hBOOL(hAPP(_1764309, _1764311)), -(c_List_OtakeWhile(_1764313, _1764309, hAPP(hAPP(c_List_Olist_OCons(_1764313), _1764311), _1764315)) = hAPP(hAPP(c_List_Olist_OCons(_1764313), _1764311), c_List_OtakeWhile(_1764313, _1764309, _1764315)))], (13507 ^ _775212) ^ [_999264, _999266] : [class_Divides_Osemiring__div(_999264), -(_999266 = c_Groups_Ozero__class_Ozero(_999264)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_999264), _999266), _999266) = c_Groups_Oone__class_Oone(_999264))], (36020 ^ _775212) ^ [_1443023, _1443025, _1443027, _1443029, _1443031, _1443033] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443023, tc_fun(_1443025, tc_HOL_Obool))), _1443027), _1443029), _1443031), _1443033)), -(hBOOL(hAPP(hAPP(_1443027, _1443031), _1443033)))], (29913 ^ _775212) ^ [_1308345, _1308347, _1308349] : [-(hBOOL(hAPP(hAPP(c_member(_1308345), _1308347), _1308349))), -(hBOOL(hAPP(hAPP(c_member(_1308345), _1308347), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308345, tc_HOL_Obool)), _1308349))))], (34485 ^ _775212) ^ [_1407918, _1407920, _1407922, _1407924] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407918, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407918, tc_HOL_Obool)), _1407920), _1407922)), _1407924) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407918, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407918, tc_HOL_Obool)), _1407920), _1407924)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407918, tc_HOL_Obool)), _1407922), _1407924)))], (49081 ^ _775212) ^ [_1756953, _1756955, _1756957] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1756953), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1756953))), _1756955))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1756957), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1756953))), _1756955))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1756953), _1756953), hAPP(hAPP(c_COMBC(tc_List_Olist(_1756953), tc_Nat_Onat, _1756953), c_List_Onth(_1756953)), _1756957)), hAPP(c_List_Ofilter(tc_List_Olist(_1756953), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1756953)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1756957)), c_Nat_Osize__class_Osize(tc_List_Olist(_1756953)))), c_List_Otranspose(_1756953, _1756955))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1756953)), _1756955), _1756957))], (40980 ^ _775212) ^ [_1564368, _1564370, _1564372, _1564374, _1564376, _1564378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564368, tc_HOL_Obool)), _1564370), _1564372)), 40986 ^ _775212 : [(40989 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564374, tc_HOL_Obool)), hAPP(_1564376, 40985 ^ [_1564368, _1564370, _1564372, _1564374, _1564376, _1564378])), hAPP(_1564378, 40985 ^ [_1564368, _1564370, _1564372, _1564374, _1564376, _1564378])))], (40987 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1564368), 40985 ^ [_1564368, _1564370, _1564372, _1564374, _1564376, _1564378]), _1564370)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564368, _1564374), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1564368, _1564374), _1564370), _1564376)), hAPP(hAPP(c_Product__Type_OSigma(_1564368, _1564374), _1564372), _1564378))))], (18613 ^ _775212) ^ [_1091455, _1091457, _1091459] : [class_Rings_Olinordered__semidom(_1091455), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091455), hAPP(hAPP(c_Power_Opower__class_Opower(_1091455), _1091457), 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(_1091455), _1091459), 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(_1091455), c_Groups_Ozero__class_Ozero(_1091455)), _1091459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091455), _1091457), _1091459)))], (34 ^ _775212) ^ [_775665, _775667] : [-(class_Rings_Odivision__ring__inverse__zero(_775665)), _775667 = _775665, class_Rings_Odivision__ring__inverse__zero(_775667)], (18159 ^ _775212) ^ [_1083575] : [_1083575 = c_Int_OPls, -(c_Int_OBit0(_1083575) = c_Int_OPls)], (14957 ^ _775212) ^ [_1025795, _1025797, _1025799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025797), _1025799))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025795), _1025799)), _1025797)))], (44176 ^ _775212) ^ [_1641768, _1641770, _1641772] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641768)), hAPP(hAPP(c_List_Olist_OCons(_1641768), _1641770), _1641772)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641768)), _1641772)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38289 ^ _775212) ^ [_1495113, _1495115] : [-(c_Relation_Orefl__on(_1495113, _1495115, c_Relation_OId__on(_1495113, _1495115)))], (34023 ^ _775212) ^ [_1396834, _1396836, _1396838, _1396840, _1396842] : [-(hBOOL(hAPP(hAPP(c_member(_1396834), _1396836), hAPP(c_Relation_OImage(_1396838, _1396834, _1396840), _1396842)))), 34024 ^ _775212 : [(34025 ^ _775212) ^ [_1396920] : [hBOOL(hAPP(hAPP(c_member(_1396838), _1396920), _1396842)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1396838, _1396834)), hAPP(hAPP(c_Product__Type_OPair(_1396838, _1396834), _1396920), _1396836)), _1396840))]]], (29004 ^ _775212) ^ [_1290548, _1290550, _1290552] : [class_Orderings_Oorder(_1290548), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290548), _1290550), _1290552)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1290548, _1290552, _1290550) = c_Orderings_Obot__class_Obot(tc_fun(_1290548, tc_HOL_Obool)))], (14501 ^ _775212) ^ [_1017482, _1017484, _1017486] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1017482), _1017484)), _1017486) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017482), _1017486)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017484), _1017486)))], (38806 ^ _775212) ^ [_1504759] : [-(c_Finite__Set_Ofun__left__comm__idem(_1504759, tc_fun(_1504759, tc_HOL_Obool), c_Set_Oinsert(_1504759)))], (5709 ^ _775212) ^ [_865252, _865254, _865256, _865258, _865260, _865262] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_865252, _865254, _865256), _865258, _865260, _865262), 5714 ^ _775212 : [(5717 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_865254, _865258, _865260, _865262))], (5715 ^ _775212) ^ [] : [-(hBOOL(hAPP(_865252, _865258)))]], 5718 ^ _775212 : [(5721 ^ _775212) ^ [] : [-(c_Natural_Oevaln(_865256, _865258, _865260, _865262))], (5719 ^ _775212) ^ [] : [hBOOL(hAPP(_865252, _865258))]]], (23782 ^ _775212) ^ [_1188517] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1188517)) = _1188517)], (50623 ^ _775212) ^ [_1790422, _1790424] : [-(c_List_Osplice(_1790422, c_List_Olist_ONil(_1790422), _1790424) = _1790424)], (45846 ^ _775212) ^ [_1685796, _1685798, _1685800, _1685802, _1685804, _1685806] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685796)), _1685798) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685800)), _1685802), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685796)), _1685804) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685800)), _1685806), -(hAPP(hAPP(c_List_Ozip(_1685796, _1685800), hAPP(hAPP(c_List_Oappend(_1685796), _1685798), _1685804)), hAPP(hAPP(c_List_Oappend(_1685800), _1685802), _1685806)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1685796, _1685800)), hAPP(hAPP(c_List_Ozip(_1685796, _1685800), _1685798), _1685802)), hAPP(hAPP(c_List_Ozip(_1685796, _1685800), _1685804), _1685806)))], (38078 ^ _775212) ^ [_1489394, _1489396, _1489398] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1489394), _1489396)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1489394, _1489394), tc_HOL_Obool)), _1489398), hAPP(hAPP(c_Product__Type_OSigma(_1489394, _1489394), _1489396), hAPP(c_COMBK(tc_fun(_1489394, tc_HOL_Obool), _1489394), _1489396)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1489394, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1489394), _1489396), _1489398))))], (4816 ^ _775212) ^ [_848552, _848554, _848556, _848558, _848560, _848562] : [-(c_Predicate_Oconversep(_848562, _848558, _848554) = c_Predicate_Oconversep(_848560, _848556, _848552)), _848562 = _848560, _848558 = _848556, _848554 = _848552], (46744 ^ _775212) ^ [_1706831, _1706833, _1706835, _1706837, _1706839] : [-(hAPP(c_List_Orotate(_1706831, _1706833), hAPP(hAPP(c_List_Omap(_1706835, _1706831), _1706837), _1706839)) = hAPP(hAPP(c_List_Omap(_1706835, _1706831), _1706837), hAPP(c_List_Orotate(_1706835, _1706833), _1706839)))], (48193 ^ _775212) ^ [_1738644, _1738646, _1738648, _1738650, _1738652] : [class_Orderings_Olinorder(_1738644), -(hAPP(c_List_Ofilter(_1738646, _1738648), c_List_Olinorder__class_Osort__key(_1738646, _1738644, _1738650, _1738652)) = c_List_Olinorder__class_Osort__key(_1738646, _1738644, _1738650, hAPP(c_List_Ofilter(_1738646, _1738648), _1738652)))], (39827 ^ _775212) ^ [] : [-(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)))))], (22742 ^ _775212) ^ [_1168085, _1168087, _1168089, _1168091, _1168093] : [-(hAPP(c_Product__Type_Osnd(_1168085, _1168087), hAPP(c_Product__Type_Oapsnd(_1168089, _1168087, _1168085, _1168091), _1168093)) = hAPP(_1168091, hAPP(c_Product__Type_Osnd(_1168085, _1168089), _1168093)))], (42731 ^ _775212) ^ [_1606180, _1606182, _1606184, _1606186, _1606188] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606180, _1606180)), hAPP(hAPP(c_Product__Type_OPair(_1606180, _1606180), hAPP(_1606182, hAPP(c_Nat_OSuc, 42732 ^ [_1606180, _1606182, _1606184, _1606186, _1606188]))), hAPP(_1606182, 42732 ^ [_1606180, _1606182, _1606184, _1606186, _1606188]))), c_Transitive__Closure_Ortrancl(_1606180, _1606184))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606180, _1606180)), hAPP(hAPP(c_Product__Type_OPair(_1606180, _1606180), hAPP(_1606182, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1606186), _1606188))), hAPP(_1606182, _1606186))), c_Transitive__Closure_Ortrancl(_1606180, _1606184))))], (6049 ^ _775212) ^ [_871133] : [-(_871133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_871133 = hAPP(c_Nat_OSuc, 6052 ^ [_871133]))], (52239 ^ _775212) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (15846 ^ _775212) ^ [_1043530, _1043532, _1043534] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1043530, _1043532) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1043534, _1043532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043534), _1043530)), -(_1043530 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043532), 15853 ^ [_1043530, _1043532, _1043534])))], (52445 ^ _775212) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (47128 ^ _775212) ^ [_1714779, _1714781, _1714783, _1714785] : [-(hAPP(hAPP(c_List_Omap(_1714779, _1714781), _1714783), c_List_Obutlast(_1714779, _1714785)) = c_List_Obutlast(_1714781, hAPP(hAPP(c_List_Omap(_1714779, _1714781), _1714783), _1714785)))], (7381 ^ _775212) ^ [_892444, _892446] : [7382 ^ _775212 : [(7383 ^ _775212) ^ [_892500] : [_892446 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _892444), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _892500)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _892444), _892446)))], (27039 ^ _775212) ^ [_1251234, _1251236, _1251238] : [class_Lattices_Olattice(_1251234), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251234), _1251236), _1251238) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1251234), _1251238), _1251236))], (35243 ^ _775212) ^ [_1424619, _1424621, _1424623, _1424625, _1424627] : [class_Orderings_Olinorder(_1424619), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424619, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1424619, _1424621, _1424623)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1424619, _1424625, _1424627)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1424619, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1424619), _1424621), _1424625), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424619), _1424623), _1424627)))], (17467 ^ _775212) ^ [_1071854] : [-(c_Int_Osucc(_1071854) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071854), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38721 ^ _775212) ^ [_1503026, _1503028, _1503030] : [class_Lattices_Oab__semigroup__idem__mult(_1503026), hAPP(_1503028, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1503026), 38726 ^ [_1503026, _1503028, _1503030]), 38727 ^ [_1503026, _1503028, _1503030])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1503026), hAPP(_1503028, 38726 ^ [_1503026, _1503028, _1503030])), hAPP(_1503028, 38727 ^ [_1503026, _1503028, _1503030])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503026), _1503030)), -(_1503030 = c_Orderings_Obot__class_Obot(tc_fun(_1503026, tc_HOL_Obool))), -(hAPP(_1503028, hAPP(c_Finite__Set_Ofold1(_1503026, c_Groups_Otimes__class_Otimes(_1503026)), _1503030)) = hAPP(c_Finite__Set_Ofold1(_1503026, c_Groups_Otimes__class_Otimes(_1503026)), hAPP(c_Set_Oimage(_1503026, _1503026, _1503028), _1503030)))], (47949 ^ _775212) ^ [_1732847, _1732849] : [-(hBOOL(hAPP(c_List_Odistinct(_1732847), c_List_Oremdups(_1732847, _1732849))))], (2180 ^ _775212) ^ [_806860, _806862, _806864, _806866, _806868, _806870, _806872, _806874] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_806874, _806870, _806866, _806862) = c_Nat_Osemiring__1__class_Oof__nat__aux(_806872, _806868, _806864, _806860)), _806874 = _806872, _806870 = _806868, _806866 = _806864, _806862 = _806860], (5990 ^ _775212) ^ [_870183, _870185, _870187, _870189] : [hAPP(_870183, 5991 ^ [_870183, _870185, _870187, _870189]) = hAPP(c_Nat_Onat_Onat__rec(_870185, _870187, _870189), 5991 ^ [_870183, _870185, _870187, _870189]), -(hAPP(_870183, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _870187)], (28763 ^ _775212) ^ [_1286319, _1286321, _1286323, _1286325] : [_1286319 = c_Orderings_Obot__class_Obot(tc_fun(_1286321, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1286321, tc_fun(_1286323, tc_HOL_Obool)), _1286319), hAPP(c_COMBK(tc_fun(_1286323, tc_HOL_Obool), _1286321), _1286325)) = c_Orderings_Obot__class_Obot(tc_fun(_1286323, tc_HOL_Obool)))], (39105 ^ _775212) ^ [_1512325, _1512327, _1512329, _1512331, _1512333, _1512335] : [class_Groups_Ocomm__monoid__add(_1512325), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512327), _1512329)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512327, _1512325), hAPP(hAPP(c_COMBS(_1512327, _1512325, _1512325), hAPP(hAPP(c_COMBS(_1512327, _1512325, tc_fun(_1512325, _1512325)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1512325, tc_fun(_1512325, _1512325)), _1512327), c_If(_1512325)), _1512331)), _1512333)), _1512335)), _1512329) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1512325), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512327, _1512325), _1512333), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1512327, tc_HOL_Obool)), _1512329), hAPP(c_Set_OCollect(_1512327), _1512331)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512327, _1512325), _1512335), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1512327, tc_HOL_Obool)), _1512329), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1512327, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1512327), _1512331))))))], (50815 ^ _775212) ^ [_1794171, _1794173, _1794175, _1794177, _1794179] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1794171, _1794173, _1794175), _1794177), _1794179)), -(hBOOL(hAPP(hAPP(_1794175, _1794179), _1794177)))], (21371 ^ _775212) ^ [_1141261, _1141263, _1141265, _1141267, _1141269] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1141261, _1141263), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1141265), _1141267))), -(_1141263 = 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)), _1141269)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1141261, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1141263), _1141269)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1141265), _1141269)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1141263), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1141265, _1141269))), _1141267)))))], (17275 ^ _775212) ^ [_1068976] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1068976) = _1068976)], (17281 ^ _775212) ^ [_1069057] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1069057), c_Int_OPls) = _1069057)], (33781 ^ _775212) ^ [_1391368, _1391370, _1391372] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1391368, tc_HOL_Obool)), _1391370), hAPP(c_Set_OPow(_1391368), _1391372))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1391368, tc_HOL_Obool)), _1391370), _1391372)))], (16873 ^ _775212) ^ [_1062865, _1062867] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062865)))), 16876 ^ _775212 : [(16883 ^ _775212) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062867)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062865), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062867)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062865), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062867))))], (16877 ^ _775212) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1062867))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062865), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062867)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062865))]]], (47829 ^ _775212) ^ [_1729986, _1729988, _1729990, _1729992, _1729994, _1729996, _1729998, _1730000] : [c_List_Olist__all2(_1729986, _1729988, _1729990, _1729992, _1729994), hBOOL(hAPP(hAPP(_1729990, _1729996), _1729998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730000), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729988)), _1729994))), -(c_List_Olist__all2(_1729986, _1729988, _1729990, hAPP(hAPP(c_List_Olist__update(_1729986, _1729992), _1730000), _1729996), hAPP(hAPP(c_List_Olist__update(_1729988, _1729994), _1730000), _1729998)))], (44821 ^ _775212) ^ [_1660755, _1660757, _1660759, _1660761, _1660763, _1660765] : [-(hBOOL(hAPP(hAPP(c_member(_1660755), _1660757), hAPP(c_List_Oset(_1660755), _1660759)))), -(hAPP(hAPP(c_List_Omap(_1660755, _1660761), c_Fun_Ofun__upd(_1660755, _1660761, _1660763, _1660757, _1660765)), _1660759) = hAPP(hAPP(c_List_Omap(_1660755, _1660761), _1660763), _1660759))], (8311 ^ _775212) ^ [_909357, _909359, _909361, _909363] : [class_Rings_Olinordered__ring__strict(_909357), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909357), c_Groups_Ozero__class_Ozero(_909357)), _909359)), 8318 ^ _775212 : [(8325 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909357), _909361), _909363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909357), _909359), _909361)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909357), _909359), _909363))))], (8319 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909357), _909359), _909361)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909357), _909359), _909363))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909357), _909361), _909363)))]]], (4952 ^ _775212) ^ [_850716, _850718] : [_850718 = _850716, -(c_List_Olist_ONil(_850718) = c_List_Olist_ONil(_850716))], (51294 ^ _775212) ^ [_1805239, _1805241, _1805243, _1805245] : [c_Relation_Otrans(_1805239, _1805241), -(c_Relation_Otrans(_1805243, hAPP(hAPP(c_Relation_Oinv__image(_1805239, _1805243), _1805241), _1805245)))], (22302 ^ _775212) ^ [_1159312, _1159314] : [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), _1159312))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1159314), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1159312))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1159314), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159312))), 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), _1159314))), c_COMBI(tc_Int_Oint))))], (39502 ^ _775212) ^ [_1528025, _1528027, _1528029, _1528031] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1528025, _1528027, _1528029), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528025, _1528027), tc_HOL_Obool))), _1528031) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528025, _1528029), tc_HOL_Obool)))], (52325 ^ _775212) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (5637 ^ _775212) ^ [_863995, _863997, _863999, _864001, _864003, _864005] : [c_Natural_Oevaln(_863995, _863997, _863999, _864001), c_Natural_Oevaln(_864003, _864001, _863999, _864005), -(c_Natural_Oevaln(c_Com_Ocom_OSemi(_863995, _864003), _863997, _863999, _864005))], (46666 ^ _775212) ^ [_1705272, _1705274] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705272)), hAPP(c_List_Otl(_1705272), _1705274)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705272)), _1705274)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (22090 ^ _775212) ^ [_1154413, _1154415, _1154417, _1154419] : [-(hAPP(c_Product__Type_Osnd(_1154413, _1154415), hAPP(hAPP(c_Product__Type_OPair(_1154413, _1154415), _1154417), _1154419)) = _1154419)], (22720 ^ _775212) ^ [_1167530] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1167530) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34847 ^ _775212) ^ [_1415168, _1415170, _1415172] : [class_Lattices_Osemilattice__inf(_1415168), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415168), _1415170), _1415172) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415168), _1415172), _1415170))], (32753 ^ _775212) ^ [_1368926, _1368928, _1368930, _1368932, _1368934, _1368936] : [hBOOL(hAPP(hAPP(c_member(_1368926), _1368928), _1368930)), -(hAPP(c_Set_Oimage(_1368926, _1368932, c_Fun_Ofun__upd(_1368926, _1368932, _1368934, _1368928, _1368936)), _1368930) = hAPP(hAPP(c_Set_Oinsert(_1368932), _1368936), hAPP(c_Set_Oimage(_1368926, _1368932, _1368934), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368926, tc_HOL_Obool)), _1368930), hAPP(hAPP(c_Set_Oinsert(_1368926), _1368928), c_Orderings_Obot__class_Obot(tc_fun(_1368926, tc_HOL_Obool)))))))], (2372 ^ _775212) ^ [_809814, _809816, _809818, _809820] : [-(c_Random_Olog(_809820, _809816) = c_Random_Olog(_809818, _809814)), _809820 = _809818, _809816 = _809814], (10439 ^ _775212) ^ [_945401, _945403, _945405] : [class_Rings_Oordered__cancel__semiring(_945401), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945401), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945401), _945403), _945405)), c_Groups_Ozero__class_Ozero(_945401)))), 10444 ^ _775212 : [(10451 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945401), _945403), c_Groups_Ozero__class_Ozero(_945401))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945401), c_Groups_Ozero__class_Ozero(_945401)), _945405))], (10445 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945401), c_Groups_Ozero__class_Ozero(_945401)), _945403)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945401), _945405), c_Groups_Ozero__class_Ozero(_945401)))]]], (220 ^ _775212) ^ [_778500, _778502] : [-(class_Fields_Olinordered__field(_778500)), _778502 = _778500, class_Fields_Olinordered__field(_778502)], (9221 ^ _775212) ^ [_924623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _924623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _924623)))], (1784 ^ _775212) ^ [_800368, _800370] : [-(class_Rings_Osemiring__1(_800368)), _800370 = _800368, class_Rings_Osemiring__1(_800370)], (30911 ^ _775212) ^ [_1333458, _1333460, _1333462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333458)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1333460), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1333462)), 30921 ^ _775212 : [(30927 ^ _775212) ^ [] : [-(_1333460 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30923 ^ [_1333458, _1333460, _1333462]), 30920 ^ [_1333458, _1333460, _1333462]))], (30925 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30923 ^ [_1333458, _1333460, _1333462]), _1333462)))], (30922 ^ _775212) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30920 ^ [_1333458, _1333460, _1333462]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1333458))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1333460), _1333458) = _1333460)], (8021 ^ _775212) ^ [_904044, _904046] : [class_Rings_Ocomm__semiring__1(_904044), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904044), c_Groups_Ozero__class_Ozero(_904044)), _904046) = c_Groups_Ozero__class_Ozero(_904044))], (34831 ^ _775212) ^ [_1414840, _1414842, _1414844, _1414846] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414840, tc_HOL_Obool)), _1414842), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414840, tc_HOL_Obool)), _1414844), _1414846)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414840, tc_HOL_Obool)), _1414844), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414840, tc_HOL_Obool)), _1414842), _1414846)))], (29516 ^ _775212) ^ [_1300742, _1300744, _1300746, _1300748] : [hBOOL(hAPP(hAPP(c_member(_1300742), _1300744), _1300746)), -(hBOOL(hAPP(hAPP(c_member(_1300742), _1300744), _1300748))), -(hBOOL(hAPP(hAPP(c_member(_1300742), _1300744), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300742, tc_HOL_Obool)), _1300746), _1300748))))], (41418 ^ _775212) ^ [_1573716, _1573718, _1573720] : [class_Lattices_Olattice(_1573716), hBOOL(hAPP(c_Finite__Set_Ofinite(_1573716), _1573718)), -(c_Big__Operators_Olattice__class_OInf__fin(_1573716, hAPP(hAPP(c_Set_Oinsert(_1573716), _1573720), _1573718)) = hAPP(hAPP(c_Finite__Set_Ofold(_1573716, _1573716, c_Lattices_Osemilattice__inf__class_Oinf(_1573716)), _1573720), _1573718))], (14519 ^ _775212) ^ [_1017823, _1017825, _1017827] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1017823), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017825, _1017827)), _1017827) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1017823), _1017825), _1017827))], (41829 ^ _775212) ^ [_1582400, _1582402, _1582404, _1582406] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582400, _1582400)), hAPP(hAPP(c_Product__Type_OPair(_1582400, _1582400), _1582402), _1582404)), c_Transitive__Closure_Otrancl(_1582400, _1582406))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582400, _1582400)), hAPP(hAPP(c_Product__Type_OPair(_1582400, _1582400), _1582402), _1582404)), c_Transitive__Closure_Ortrancl(_1582400, _1582406))))], (50033 ^ _775212) ^ [_1777866] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1777866) = c_Lazy__Sequence_Osmall__lazy_H(_1777866, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1777866)))], (35177 ^ _775212) ^ [_1423080, _1423082, _1423084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423080, tc_HOL_Obool)), _1423082), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1423080, tc_HOL_Obool)), _1423084))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423080, tc_HOL_Obool)), _1423082), _1423084) = c_Orderings_Obot__class_Obot(tc_fun(_1423080, tc_HOL_Obool)))], (15439 ^ _775212) ^ [_1035580, _1035582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1035580), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1035582), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1035580), _1035582)))], (52427 ^ _775212) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (52601 ^ _775212) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (48234 ^ _775212) ^ [_1739569, _1739571, _1739573] : [-(c_List_Opartition(_1739569, _1739571, _1739573) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1739569), tc_List_Olist(_1739569)), hAPP(c_List_Ofilter(_1739569, _1739571), _1739573)), hAPP(c_List_Ofilter(_1739569, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1739569, c_fNot), _1739571)), _1739573)))], (52597 ^ _775212) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (36913 ^ _775212) ^ [_1461088, _1461090, _1461092, _1461094, _1461096] : [c_Fun_Oinj__on(_1461088, _1461090, _1461092, hAPP(hAPP(c_Set_Oinsert(_1461088), _1461094), _1461096)), 36916 ^ _775212 : [(36919 ^ _775212) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1461090), hAPP(_1461092, _1461094)), hAPP(c_Set_Oimage(_1461088, _1461090, _1461092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1461088, tc_HOL_Obool)), _1461096), hAPP(hAPP(c_Set_Oinsert(_1461088), _1461094), c_Orderings_Obot__class_Obot(tc_fun(_1461088, tc_HOL_Obool)))))))], (36917 ^ _775212) ^ [] : [-(c_Fun_Oinj__on(_1461088, _1461090, _1461092, _1461096))]]], (52519 ^ _775212) ^ [_1826505, _1826507] : [-(class_Enum_Oenum(tc_sum(_1826505, _1826507))), class_Enum_Oenum(_1826505), class_Enum_Oenum(_1826507)], (49279 ^ _775212) ^ [_1761263, _1761265, _1761267] : [-(hAPP(c_List_Orev(_1761263), hAPP(hAPP(c_List_Otake(_1761263), _1761265), _1761267)) = hAPP(hAPP(c_List_Odrop(_1761263), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761263)), _1761267)), _1761265)), hAPP(c_List_Orev(_1761263), _1761267)))], (52429 ^ _775212) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (32563 ^ _775212) ^ [_1365194, _1365196, _1365198] : [class_Orderings_Olinorder(_1365194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365194), _1365196)), hBOOL(hAPP(hAPP(c_member(_1365194), _1365198), _1365196)), 32574 ^ _775212 : [(32581 ^ _775212) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365194, tc_HOL_Obool)), _1365196), hAPP(hAPP(c_Set_Oinsert(_1365194), _1365198), c_Orderings_Obot__class_Obot(tc_fun(_1365194, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1365194, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1365194, c_Orderings_Oord__class_Omin(_1365194), _1365196) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365194), _1365198), c_Big__Operators_Olattice_OInf__fin(_1365194, c_Orderings_Oord__class_Omin(_1365194), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365194, tc_HOL_Obool)), _1365196), hAPP(hAPP(c_Set_Oinsert(_1365194), _1365198), c_Orderings_Obot__class_Obot(tc_fun(_1365194, tc_HOL_Obool)))))))], (32575 ^ _775212) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365194, tc_HOL_Obool)), _1365196), hAPP(hAPP(c_Set_Oinsert(_1365194), _1365198), c_Orderings_Obot__class_Obot(tc_fun(_1365194, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1365194, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1365194, c_Orderings_Oord__class_Omin(_1365194), _1365196) = _1365198)]]], (52383 ^ _775212) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (44106 ^ _775212) ^ [_1639684, _1639686, _1639688] : [c_FunDef_Ois__measure(_1639684, _1639686), -(c_FunDef_Ois__measure(tc_prod(_1639688, _1639684), hAPP(hAPP(c_COMBB(_1639684, tc_Nat_Onat, tc_prod(_1639688, _1639684)), _1639686), c_Product__Type_Osnd(_1639688, _1639684))))], (28646 ^ _775212) ^ [_1283961] : [c_Orderings_Otop__class_Otop(tc_fun(_1283961, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1283961, tc_HOL_Obool))], (46588 ^ _775212) ^ [_1703699, _1703701, _1703703, _1703705] : [hBOOL(hAPP(c_List_Odistinct(_1703699), _1703701)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703703), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703699)), _1703701))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703705), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703699)), _1703701))), 46599 ^ _775212 : [(46606 ^ _775212) ^ [] : [_1703703 = _1703705, -(hAPP(hAPP(c_List_Onth(_1703699), _1703701), _1703703) = hAPP(hAPP(c_List_Onth(_1703699), _1703701), _1703705))], (46600 ^ _775212) ^ [] : [hAPP(hAPP(c_List_Onth(_1703699), _1703701), _1703703) = hAPP(hAPP(c_List_Onth(_1703699), _1703701), _1703705), -(_1703703 = _1703705)]]], (50727 ^ _775212) ^ [_1792487, _1792489, _1792491] : [-(hAPP(c_List_Orev(_1792487), c_List_Oreplicate(_1792487, _1792489, _1792491)) = c_List_Oreplicate(_1792487, _1792489, _1792491))], (10795 ^ _775212) ^ [_951533] : [hBOOL(hAPP(_951533, 10796 ^ [_951533])), 10799 ^ _775212 : [(10800 ^ _775212) ^ [_951627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _951627)), -(hBOOL(hAPP(_951533, hAPP(c_Int_Onat, _951627))))]]], (39494 ^ _775212) ^ [_1527659, _1527661, _1527663, _1527665, _1527667, _1527669, _1527671] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527659, _1527661, _1527663), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527665, tc_fun(tc_prod(_1527659, _1527661), tc_HOL_Obool)), _1527667), _1527669)), _1527671) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527665, tc_fun(tc_prod(_1527659, _1527663), tc_HOL_Obool)), _1527667), hAPP(hAPP(c_COMBC(_1527665, tc_fun(tc_prod(_1527661, _1527663), tc_HOL_Obool), tc_fun(tc_prod(_1527659, _1527663), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1527659, _1527661), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1527661, _1527663), tc_HOL_Obool), tc_fun(tc_prod(_1527659, _1527663), tc_HOL_Obool)), _1527665), c_Relation_Orel__comp(_1527659, _1527661, _1527663)), _1527669)), _1527671)))], (51731 ^ _775212) ^ [_1815371, _1815373] : [c_Relation_Osym(_1815371, _1815373), c_Relation_Otrans(_1815371, _1815373), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1815371, _1815371), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1815371, _1815371, _1815371), hAPP(c_Relation_Oconverse(_1815371, _1815371), _1815373)), _1815373)), _1815373)))], (42355 ^ _775212) ^ [_1595599, _1595601, _1595603, _1595605] : [-(hAPP(c_Relation_Oconverse(_1595599, _1595601), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1595599, _1595601), tc_HOL_Obool)), _1595603), _1595605)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1595601, _1595599), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1595599, _1595601), _1595603)), hAPP(c_Relation_Oconverse(_1595599, _1595601), _1595605)))], (32015 ^ _775212) ^ [_1353947, _1353949] : [class_Int_Oring__char__0(_1353947), hBOOL(hAPP(hAPP(c_member(_1353947), _1353949), c_Int_Oring__1__class_OInts(_1353947))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353947), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353947), c_Groups_Oone__class_Oone(_1353947)), _1353949)), _1353949) = c_Groups_Ozero__class_Ozero(_1353947)], (16395 ^ _775212) ^ [_1053685, _1053687, _1053689] : [class_Int_Onumber__ring(_1053685), -(hAPP(c_Int_Onumber__class_Onumber__of(_1053685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1053687), _1053689)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053685), hAPP(c_Int_Onumber__class_Onumber__of(_1053685), _1053687)), hAPP(c_Int_Onumber__class_Onumber__of(_1053685), _1053689)))], (17879 ^ _775212) ^ [_1078758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1078758))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1078758)))], (29056 ^ _775212) ^ [] : [-(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)))], (52769 ^ _775212) ^ [_1829408, _1829410] : [hBOOL(hAPP(hAPP(c_fimplies, _1829408), _1829410)), hBOOL(_1829408), -(hBOOL(_1829410))]], input).
% 44.90/43.93 ncf('1',plain,[v_fun1(52788 ^ [], 52789 ^ []), 52783 : c_Natural_Oevaln(v_com, 52789 ^ [], hAPP(c_Nat_OSuc, v_n), 52792 ^ []), 52783 : -(v_fun2(52788 ^ [], 52792 ^ []))],start(52779 ^ 0,bind([[_2081214, _2081216, _2081279], [52789 ^ [], 52788 ^ [], 52792 ^ []]]))).
% 44.90/43.93 ncf('1.1',plain,[-(v_fun1(52788 ^ [], 52789 ^ []))],extension(52791 ^ 1)).
% 44.90/43.93 ncf('1.2',plain,[-(c_Natural_Oevaln(v_com, 52789 ^ [], hAPP(c_Nat_OSuc, v_n), 52792 ^ [])), c_Natural_Oevaln(v_com, 52789 ^ [], v_n, 52792 ^ [])],extension(5591 ^ 3,bind([[_863229, _863231, _863233, _863235], [v_com, 52789 ^ [], v_n, 52792 ^ []]]))).
% 44.90/43.93 ncf('1.2.1',plain,[-(c_Natural_Oevaln(v_com, 52789 ^ [], v_n, 52792 ^ []))],extension(52794 ^ 4)).
% 44.90/43.93 ncf('1.3',plain,[v_fun2(52788 ^ [], 52792 ^ [])],extension(52796 ^ 3)).
% 44.90/43.93 %-----------------------------------------------------
% 44.90/43.93 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------