TSTP Solution File: SWW295+1 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW295+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n022.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 53.32s 52.38s
% Output : Proof 53.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW295+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : nanocop.sh %s %d
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 18 22:44:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 53.32/52.38
% 53.32/52.38 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 53.32/52.38 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 53.32/52.38 %-----------------------------------------------------
% 53.32/52.38 ncf(matrix, plain, [(51527 ^ _2049170) ^ [] : [51528 ^ _2049170 : [(51544 ^ _2049170) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn), 51539 ^ [], hAPP(c_Nat_OSuc, v_n), 51542 ^ []))], (51546 ^ _2049170) ^ [] : [v_Q(51538 ^ [], 51542 ^ [])], (51529 ^ _2049170) ^ [_2049204, _2049206] : [v_P(_2049206, _2049204), 51532 ^ _2049170 : [(51533 ^ _2049170) ^ [_2049269] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn)), _2049204, v_n, _2049269), -(v_Q(_2049206, _2049269))]]], (51541 ^ _2049170) ^ [] : [-(v_P(51538 ^ [], 51539 ^ []))]], 51547 ^ _2049170 : [(51563 ^ _2049170) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn)), 51558 ^ [], v_n, 51561 ^ []))], (51565 ^ _2049170) ^ [] : [v_Q(51557 ^ [], 51561 ^ [])], (51548 ^ _2049170) ^ [_2049455, _2049457] : [v_P(_2049457, _2049455), 51551 ^ _2049170 : [(51552 ^ _2049170) ^ [_2049520] : [c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn), _2049455, hAPP(c_Nat_OSuc, v_n), _2049520), -(v_Q(_2049457, _2049520))]]], (51560 ^ _2049170) ^ [] : [-(v_P(51557 ^ [], 51558 ^ []))]]], !, (50534 ^ _774244) ^ [_1788022, _1788024, _1788026, _1788028, _1788030] : [-(c_List_OtakeWhile(_1788022, _1788024, hAPP(hAPP(c_List_Omap(_1788026, _1788022), _1788028), _1788030)) = hAPP(hAPP(c_List_Omap(_1788026, _1788022), _1788028), c_List_OtakeWhile(_1788026, hAPP(c_Fun_Ocomp(_1788022, tc_HOL_Obool, _1788026, _1788024), _1788028), _1788030)))], (2 ^ _774244) ^ [_774271] : [-(_774271 = _774271)], (3338 ^ _774244) ^ [_825519, _825521] : [_825521 = _825519, -(c_Nitpick_Onum(_825521) = c_Nitpick_Onum(_825519))], (25349 ^ _774244) ^ [_1216361, _1216363, _1216365, _1216367] : [class_Rings_Odvd(_1216361), _1216363 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216361), _1216365), _1216367), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216361), _1216365), _1216363)))], (45598 ^ _774244) ^ [_1669859, _1669861, _1669863, _1669865] : [hAPP(c_List_Oset(_1669859), _1669861) = c_Map_Odom(_1669859, _1669863, _1669865), -(c_Map_Omap__of(_1669859, _1669863, hAPP(hAPP(c_List_Omap(_1669859, tc_prod(_1669859, _1669863)), hAPP(hAPP(c_COMBS(_1669859, _1669863, tc_prod(_1669859, _1669863)), c_Product__Type_OPair(_1669859, _1669863)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1669863), _1669863, _1669859), c_Option_Othe(_1669863)), _1669865))), _1669861)) = _1669865)], (3538 ^ _774244) ^ [_828743, _828745] : [_828745 = _828743, -(c_Wellfounded_Omeasure(_828745) = c_Wellfounded_Omeasure(_828743))], (35116 ^ _774244) ^ [_1417209, _1417211, _1417213, _1417215, _1417217] : [c_Finite__Set_Ofolding__one__idem(_1417209, _1417211, _1417213), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417209), _1417215)), -(_1417217 = c_Orderings_Obot__class_Obot(tc_fun(_1417209, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1417209, tc_HOL_Obool)), _1417217), _1417215)), -(hAPP(hAPP(_1417211, hAPP(_1417213, _1417217)), hAPP(_1417213, _1417215)) = hAPP(_1417213, _1417215))], (44247 ^ _774244) ^ [_1637957, _1637959, _1637961] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1637957, _1637957), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1637959)), _1637961) = hAPP(hAPP(c_Relation_Orel__comp(_1637957, _1637957, _1637957), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1637957, _1637957), tc_HOL_Obool), _1637959), _1637961)), _1637961))], (30969 ^ _774244) ^ [_1329666, _1329668, _1329670] : [hBOOL(hAPP(hAPP(c_member(_1329666), _1329668), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1329666, tc_HOL_Obool)), _1329670))), hBOOL(hAPP(hAPP(c_member(_1329666), _1329668), _1329670))], (34729 ^ _774244) ^ [_1408621, _1408623, _1408625, _1408627] : [-(hAPP(c_Relation_OField(_1408621), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1408621, _1408621)), hAPP(hAPP(c_Product__Type_OPair(_1408621, _1408621), _1408623), _1408625)), _1408627)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408621, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1408621), _1408623), hAPP(hAPP(c_Set_Oinsert(_1408621), _1408625), c_Orderings_Obot__class_Obot(tc_fun(_1408621, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1408621), _1408627)))], (43829 ^ _774244) ^ [_1626973, _1626975, _1626977, _1626979, _1626981] : [_1626973 = c_Orderings_Obot__class_Obot(tc_fun(_1626975, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626975, tc_fun(_1626977, tc_HOL_Obool)), _1626973), hAPP(hAPP(c_COMBC(_1626975, tc_fun(_1626977, tc_HOL_Obool), tc_fun(_1626977, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1626977, tc_HOL_Obool), tc_fun(tc_fun(_1626977, tc_HOL_Obool), tc_fun(_1626977, tc_HOL_Obool)), _1626975), c_Groups_Ominus__class_Ominus(tc_fun(_1626977, tc_HOL_Obool))), _1626979)), _1626981)) = c_Orderings_Otop__class_Otop(tc_fun(_1626977, tc_HOL_Obool)))], (29018 ^ _774244) ^ [_1290619, _1290621, _1290623, _1290625] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1290619, tc_fun(_1290621, tc_HOL_Obool)), _1290623), _1290625) = c_Orderings_Obot__class_Obot(tc_fun(_1290621, tc_HOL_Obool)), 29021 ^ _774244 : [(29022 ^ _774244) ^ [_1290735] : [hBOOL(hAPP(hAPP(c_member(_1290619), _1290735), _1290623)), -(hAPP(_1290625, _1290735) = c_Orderings_Obot__class_Obot(tc_fun(_1290621, tc_HOL_Obool)))]]], (35165 ^ _774244) ^ [_1418216, _1418218] : [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)), _1418216), _1418218)), 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)), _1418216), 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)), _1418218), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (8764 ^ _774244) ^ [_917326, _917328] : [class_Rings_Ocomm__semiring__1(_917326), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917326), _917328), c_Groups_Oone__class_Oone(_917326)) = _917328)], (41019 ^ _774244) ^ [_1555202, _1555204, _1555206] : [class_Lattices_Odistrib__lattice(_1555202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555202), _1555204)), -(_1555204 = c_Orderings_Obot__class_Obot(tc_fun(_1555202, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1555202), _1555206), c_Big__Operators_Olattice__class_OSup__fin(_1555202, _1555204)) = c_Big__Operators_Olattice__class_OSup__fin(_1555202, hAPP(c_Set_OCollect(_1555202), hAPP(hAPP(c_COMBB(tc_fun(_1555202, tc_HOL_Obool), tc_HOL_Obool, _1555202), c_HOL_OEx(_1555202)), hAPP(hAPP(c_COMBC(_1555202, tc_fun(_1555202, tc_HOL_Obool), tc_fun(_1555202, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555202, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1555202, tc_HOL_Obool), tc_fun(_1555202, tc_HOL_Obool)), _1555202), c_COMBS(_1555202, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555202, tc_HOL_Obool), tc_fun(_1555202, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1555202), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1555202), c_fconj)), hAPP(hAPP(c_COMBC(_1555202, tc_fun(_1555202, _1555202), tc_fun(_1555202, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555202, tc_HOL_Obool), tc_fun(tc_fun(_1555202, _1555202), tc_fun(_1555202, tc_HOL_Obool)), _1555202), c_COMBB(_1555202, tc_HOL_Obool, _1555202)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1555202), _1555206))))), hAPP(hAPP(c_COMBC(_1555202, tc_fun(_1555202, tc_HOL_Obool), tc_HOL_Obool), c_member(_1555202)), _1555204))))))], (15114 ^ _774244) ^ [_1028270, _1028272, _1028274] : [class_Groups_Ogroup__add(_1028270), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1028270), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1028270), _1028272), _1028274)), _1028274) = _1028272)], (41669 ^ _774244) ^ [_1574937, _1574939, _1574941, _1574943] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1574937, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1574939, _1574937), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1574939, _1574937), tc_HOL_Obool)), _1574941), _1574943))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1574937, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1574939, _1574937), _1574941)), hAPP(c_Relation_ORange(_1574939, _1574937), _1574943)))))], (19863 ^ _774244) ^ [_1114239, _1114241, _1114243, _1114245] : [class_Fields_Ofield__inverse__zero(_1114239), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1114239), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114239), _1114241), _1114243)), _1114245) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114239), hAPP(hAPP(c_Power_Opower__class_Opower(_1114239), _1114241), _1114245)), hAPP(hAPP(c_Power_Opower__class_Opower(_1114239), _1114243), _1114245)))], (39166 ^ _774244) ^ [_1507980, _1507982, _1507984, _1507986, _1507988, _1507990, _1507992] : [c_Big__Operators_Ocomm__monoid__big(_1507980, _1507982, _1507984, _1507986, _1507988), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1507982), _1507990))), -(hAPP(hAPP(_1507988, _1507992), _1507990) = _1507986)], (28537 ^ _774244) ^ [_1279258, _1279260] : [class_Groups_Oordered__ab__group__add(_1279258), -(hAPP(c_Set_Oimage(_1279258, _1279258, c_Groups_Ouminus__class_Ouminus(_1279258)), hAPP(c_SetInterval_Oord__class_OatLeast(_1279258), _1279260)) = hAPP(c_SetInterval_Oord__class_OatMost(_1279258), hAPP(c_Groups_Ouminus__class_Ouminus(_1279258), _1279260)))], (20457 ^ _774244) ^ [_1124100, _1124102, _1124104] : [class_Fields_Olinordered__field(_1124100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124100), c_Groups_Ozero__class_Ozero(_1124100)), _1124102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124100), c_Groups_Ozero__class_Ozero(_1124100)), _1124104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124100), c_Groups_Ozero__class_Ozero(_1124100)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124100), _1124102), _1124104))))], (15466 ^ _774244) ^ [_1035090, _1035092] : [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), _1035090), _1035092))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035092), _1035090)))], (38794 ^ _774244) ^ [_1499250, _1499252, _1499254, _1499256, _1499258] : [-(hAPP(c_Set_Ovimage(_1499250, _1499252, _1499254), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1499252, tc_HOL_Obool)), _1499256), _1499258)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1499250, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1499250, _1499252, _1499254), _1499256)), hAPP(c_Set_Ovimage(_1499250, _1499252, _1499254), _1499258)))], (32644 ^ _774244) ^ [_1365854, _1365856, _1365858] : [class_Lattices_Olattice(_1365854), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365854), _1365856)), hBOOL(hAPP(hAPP(c_member(_1365854), _1365858), _1365856)), 32655 ^ _774244 : [(32662 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365854, tc_HOL_Obool)), _1365856), hAPP(hAPP(c_Set_Oinsert(_1365854), _1365858), c_Orderings_Obot__class_Obot(tc_fun(_1365854, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1365854, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1365854, _1365856) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1365854), _1365858), c_Big__Operators_Olattice__class_OSup__fin(_1365854, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365854, tc_HOL_Obool)), _1365856), hAPP(hAPP(c_Set_Oinsert(_1365854), _1365858), c_Orderings_Obot__class_Obot(tc_fun(_1365854, tc_HOL_Obool)))))))], (32656 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365854, tc_HOL_Obool)), _1365856), hAPP(hAPP(c_Set_Oinsert(_1365854), _1365858), c_Orderings_Obot__class_Obot(tc_fun(_1365854, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1365854, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1365854, _1365856) = _1365858)]]], (33076 ^ _774244) ^ [_1373074, _1373076, _1373078] : [class_Orderings_Olinorder(_1373074), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373074), _1373076)), -(hBOOL(hAPP(hAPP(c_member(_1373074), _1373078), _1373076))), -(_1373076 = c_Orderings_Obot__class_Obot(tc_fun(_1373074, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1373074, hAPP(hAPP(c_Set_Oinsert(_1373074), _1373078), _1373076)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1373074), _1373078), c_Big__Operators_Olinorder__class_OMin(_1373074, _1373076)))], (22362 ^ _774244) ^ [_1159724, _1159726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159724), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1159726, _1159724) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1159726), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1159724)))], (15958 ^ _774244) ^ [_1045292, _1045294, _1045296, _1045298, _1045300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045292), _1045294)), 15961 ^ _774244 : [(15968 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045298), 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), _1045294), _1045292)), _1045296)), _1045300))), -(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), _1045292), _1045296)), _1045298)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045294), _1045296)), _1045300))))], (15962 ^ _774244) ^ [] : [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), _1045292), _1045296)), _1045298)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045294), _1045296)), _1045300))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045298), 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), _1045294), _1045292)), _1045296)), _1045300))))]]], (41980 ^ _774244) ^ [_1582634, _1582636, _1582638] : [-(hAPP(c_New__DSequence_Oneg__single(_1582634, _1582636), _1582638) = c_Lazy__Sequence_Ohb__single(_1582634, _1582636))], (48604 ^ _774244) ^ [_1745463, _1745465, _1745467, _1745469, _1745471] : [-(hAPP(c_List_Orotate(_1745463, _1745465), hAPP(hAPP(c_List_Omap(_1745467, _1745463), _1745469), _1745471)) = hAPP(hAPP(c_List_Omap(_1745467, _1745463), _1745469), hAPP(c_List_Orotate(_1745467, _1745465), _1745471)))], (18783 ^ _774244) ^ [_1094500, _1094502] : [class_Int_Onumber__ring(_1094500), class_Rings_Olinordered__idom(_1094500), 18790 ^ _774244 : [(18797 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1094502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094500), c_Groups_Oone__class_Oone(_1094500)), hAPP(c_Int_Onumber__class_Onumber__of(_1094500), _1094502))))], (18791 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094500), c_Groups_Oone__class_Oone(_1094500)), hAPP(c_Int_Onumber__class_Onumber__of(_1094500), _1094502))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1094502)))]]], (4158 ^ _774244) ^ [_838541, _838543, _838545, _838547, _838549, _838551, _838553, _838555] : [-(c_Wellfounded_Olex__prod(_838555, _838551, _838547, _838543) = c_Wellfounded_Olex__prod(_838553, _838549, _838545, _838541)), _838555 = _838553, _838551 = _838549, _838547 = _838545, _838543 = _838541], (1304 ^ _774244) ^ [_793268, _793270] : [-(class_Orderings_Otop(_793268)), _793270 = _793268, class_Orderings_Otop(_793270)], (47706 ^ _774244) ^ [_1722684, _1722686, _1722688] : [_1722688 = c_List_Olist_ONil(_1722686), -(_1722684 = hAPP(hAPP(c_List_Oappend(_1722686), _1722688), _1722684))], (24465 ^ _774244) ^ [_1199838, _1199840, _1199842, _1199844, _1199846, _1199848, _1199850] : [-(hAPP(c_Product__Type_Oapsnd(_1199838, _1199840, _1199842, _1199844), hAPP(c_Product__Type_Oapfst(_1199846, _1199842, _1199838, _1199848), _1199850)) = hAPP(c_Product__Type_Oapfst(_1199846, _1199842, _1199840, _1199848), hAPP(c_Product__Type_Oapsnd(_1199838, _1199840, _1199846, _1199844), _1199850)))], (24991 ^ _774244) ^ [_1210523, _1210525] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210523), _1210525)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210525), _1210523))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210525), _1210523)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210523), _1210525)))], (41500 ^ _774244) ^ [_1571009, _1571011, _1571013] : [c_Wellfounded_Owf(_1571009, _1571011), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1571009, tc_HOL_Obool)), _1571013), hAPP(c_Relation_OImage(_1571009, _1571009, _1571011), _1571013))), -(_1571013 = c_Orderings_Obot__class_Obot(tc_fun(_1571009, tc_HOL_Obool)))], (37049 ^ _774244) ^ [_1461462, _1461464, _1461466] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1461462), _1461464)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461462), _1461466)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461462, tc_HOL_Obool)), _1461464), _1461466) = c_Orderings_Obot__class_Obot(tc_fun(_1461462, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1461462), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461462, tc_HOL_Obool)), _1461464), _1461466)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1461462), _1461464)), hAPP(c_Finite__Set_Ocard(_1461462), _1461466)))], (49161 ^ _774244) ^ [_1757641, _1757643, _1757645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1757641), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757643)), _1757645))), -(c_List_Obutlast(_1757643, hAPP(hAPP(c_List_Otake(_1757643), _1757641), _1757645)) = hAPP(hAPP(c_List_Otake(_1757643), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1757641), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1757645))], (18155 ^ _774244) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (32574 ^ _774244) ^ [_1364649, _1364651, _1364653] : [class_Rings_Osemiring__1(_1364649), hBOOL(hAPP(hAPP(c_member(_1364649), _1364651), c_Nat_Osemiring__1__class_ONats(_1364649))), hBOOL(hAPP(hAPP(c_member(_1364649), _1364653), c_Nat_Osemiring__1__class_ONats(_1364649))), -(hBOOL(hAPP(hAPP(c_member(_1364649), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364649), _1364651), _1364653)), c_Nat_Osemiring__1__class_ONats(_1364649))))], (17269 ^ _774244) ^ [_1069612, _1069614, _1069616, _1069618] : [class_Rings_Olinordered__semidom(_1069612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069612), c_Groups_Oone__class_Oone(_1069612)), _1069614)), 17276 ^ _774244 : [(17283 ^ _774244) ^ [] : [_1069616 = _1069618, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1069612), _1069614), _1069616) = hAPP(hAPP(c_Power_Opower__class_Opower(_1069612), _1069614), _1069618))], (17277 ^ _774244) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1069612), _1069614), _1069616) = hAPP(hAPP(c_Power_Opower__class_Opower(_1069612), _1069614), _1069618), -(_1069616 = _1069618)]]], (41354 ^ _774244) ^ [] : [-(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)))))], (37755 ^ _774244) ^ [_1477475, _1477477, _1477479] : [class_Lattices_Olattice(_1477475), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477475), _1477477)), -(hBOOL(hAPP(hAPP(c_member(_1477475), _1477479), _1477477))), -(_1477477 = c_Orderings_Obot__class_Obot(tc_fun(_1477475, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1477475, hAPP(hAPP(c_Set_Oinsert(_1477475), _1477479), _1477477)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1477475), _1477479), c_Big__Operators_Olattice__class_OInf__fin(_1477475, _1477477)))], (40368 ^ _774244) ^ [_1536772, _1536774, _1536776] : [class_Groups_Oab__semigroup__mult(_1536772), -(_1536774 = c_Orderings_Obot__class_Obot(tc_fun(_1536772, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536772), _1536774)), -(hBOOL(hAPP(hAPP(c_member(_1536772), _1536776), _1536774))), -(hAPP(c_Finite__Set_Ofold1(_1536772, c_Groups_Otimes__class_Otimes(_1536772)), hAPP(hAPP(c_Set_Oinsert(_1536772), _1536776), _1536774)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1536772), _1536776), hAPP(c_Finite__Set_Ofold1(_1536772, c_Groups_Otimes__class_Otimes(_1536772)), _1536774)))], (29913 ^ _774244) ^ [_1307168, _1307170] : [class_Finite__Set_Ofinite(_1307168), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307168), _1307170)))], (29506 ^ _774244) ^ [] : [-(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))))], (12836 ^ _774244) ^ [_987438, _987440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987438), _987440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987438), c_Groups_Oone__class_Oone(tc_Int_Oint))), _987440)))], (50959 ^ _774244) ^ [_1796527, _1796529] : [class_Lattices_Odistrib__lattice(_1796527), -(class_Lattices_Odistrib__lattice(tc_fun(_1796529, _1796527)))], (35570 ^ _774244) ^ [_1428553, _1428555, _1428557] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1428553), hAPP(hAPP(c_Set_Oinsert(_1428553), _1428555), c_Orderings_Obot__class_Obot(tc_fun(_1428553, tc_HOL_Obool)))), _1428557) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1428553, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1428553, _1428553, _1428557), hAPP(hAPP(c_Set_Oinsert(_1428553), _1428555), c_Orderings_Obot__class_Obot(tc_fun(_1428553, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1428553, tc_HOL_Obool), tc_HOL_Obool))))], (10081 ^ _774244) ^ [_940349, _940351, _940353] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940349), _940351)), _940353) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940349), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940351), _940353)))], (44233 ^ _774244) ^ [_1637603, _1637605, _1637607, _1637609] : [-(hAPP(hAPP(c_Nat_Ocompow(_1637603, _1637603), _1637605), hAPP(hAPP(c_Nat_Ocompow(_1637603, _1637603), _1637607), _1637609)) = hAPP(hAPP(c_Nat_Ocompow(_1637603, _1637603), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1637607), _1637605)), _1637609))], (17029 ^ _774244) ^ [_1065430, _1065432] : [17030 ^ _774244 : [(17033 ^ _774244) ^ [] : [_1065430 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17031 ^ _774244) ^ [] : [_1065432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1065430), _1065432) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (41885 ^ _774244) ^ [_1580891, _1580893] : [c_Wellfounded_OwfP(_1580891, _1580893), -(c_Wellfounded_Oacyclic(_1580891, hAPP(c_Set_OCollect(tc_prod(_1580891, _1580891)), hAPP(c_Product__Type_Oprod_Oprod__case(_1580891, _1580891, tc_HOL_Obool), _1580893))))], (34942 ^ _774244) ^ [_1413366, _1413368, _1413370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413366, tc_HOL_Obool)), _1413368), _1413370)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1413366, tc_HOL_Obool)), _1413368), hAPP(c_Set_OPow(_1413366), _1413370))))], (7832 ^ _774244) ^ [_902191, _902193, _902195] : [-(c_Sum__Type_OProjr(_902191, _902193, hAPP(c_Sum__Type_OInr(_902193, _902191), _902195)) = _902195)], (30037 ^ _774244) ^ [_1309281] : [class_Orderings_Olinorder(_1309281), -(c_Finite__Set_Ofun__left__comm__idem(_1309281, _1309281, c_Orderings_Oord__class_Omin(_1309281)))], (26894 ^ _774244) ^ [_1246708, _1246710, _1246712, _1246714, _1246716] : [class_Groups_Ocomm__monoid__add(_1246708), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1246710), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1246712), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246708), _1246714), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1246710, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1246712), _1246716))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1246708), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246708), _1246714), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1246710, _1246712))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246708), _1246714), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1246712), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1246712), _1246716)))))], (40665 ^ _774244) ^ [_1543107, _1543109, _1543111] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1543107, tc_HOL_Obool)), _1543109), _1543111) = hAPP(c_Set_OCollect(_1543107), hAPP(hAPP(c_COMBS(_1543107, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543107), c_fconj), hAPP(hAPP(c_COMBC(_1543107, tc_fun(_1543107, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543107)), _1543109))), hAPP(hAPP(c_COMBC(_1543107, tc_fun(_1543107, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543107)), _1543111))))], (28374 ^ _774244) ^ [_1276134, _1276136, _1276138, _1276140] : [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), _1276134, _1276136)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276138, _1276140))), 28377 ^ _774244 : [(28378 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276134), _1276136)), 28381 ^ _774244 : [(28386 ^ _774244) ^ [] : [28387 ^ _774244 : [(28390 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276134), _1276138))], (28388 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276138), _1276134)))]], 28391 ^ _774244 : [(28394 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276140), _1276136))], (28392 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276136), _1276140)))]]], (28384 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276136), _1276140)))], (28382 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276138), _1276134)))]]], (28396 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276138), _1276140)))]]], (26416 ^ _774244) ^ [_1235907, _1235909, _1235911] : [26417 ^ _774244 : [(26418 ^ _774244) ^ [_1235988, _1235990] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1235907), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235909), _1235990)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1235911), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235909), _1235988))]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1235907, _1235909) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1235911, _1235909))], (24691 ^ _774244) ^ [_1204484, _1204486, _1204488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1204484), c_Nitpick_Oplus__frac(_1204484, _1204486, c_Nitpick_Ouminus__frac(_1204484, _1204488)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1204484, _1204486, _1204488))], (24727 ^ _774244) ^ [_1205819, _1205821] : [-(c_Divides_Odivmod__nat(_1205819, _1205821) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1205819, _1205821)))], (35963 ^ _774244) ^ [_1437030, _1437032, _1437034, _1437036] : [class_Lattices_Osemilattice__inf(_1437030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437030), _1437032), _1437034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437030), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1437030), _1437036), _1437032)), _1437034)))], (42024 ^ _774244) ^ [_1584149, _1584151, _1584153] : [42026 ^ _774244 : [(42029 ^ _774244) ^ [] : [hBOOL(hAPP(_1584151, 42025 ^ [_1584149, _1584151, _1584153]))], (42027 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1584149), 42025 ^ [_1584149, _1584151, _1584153]), _1584153)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1584149, _1584151), _1584153)))], (28232 ^ _774244) ^ [_1273285] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1273285)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1273285))], (18447 ^ _774244) ^ [_1089062, _1089064] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1089062)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089064)) = 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)))), _1089062)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089064)))], (30831 ^ _774244) ^ [_1327202, _1327204, _1327206, _1327208] : [-(hBOOL(hAPP(hAPP(c_member(_1327202), _1327204), _1327206))), -(hBOOL(hAPP(hAPP(c_member(_1327202), _1327204), _1327208))), 30838 ^ _774244 : [(30845 ^ _774244) ^ [] : [_1327206 = _1327208, -(hAPP(hAPP(c_Set_Oinsert(_1327202), _1327204), _1327206) = hAPP(hAPP(c_Set_Oinsert(_1327202), _1327204), _1327208))], (30839 ^ _774244) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_1327202), _1327204), _1327206) = hAPP(hAPP(c_Set_Oinsert(_1327202), _1327204), _1327208), -(_1327206 = _1327208)]]], (28833 ^ _774244) ^ [_1286478, _1286480] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1286478, 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(_1286478, tc_HOL_Obool)), tc_fun(_1286478, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1286478, tc_HOL_Obool)), tc_fun(_1286478, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1286478, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1286480)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1286478, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1286480))], (28098 ^ _774244) ^ [_1270420, _1270422, _1270424] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270420, tc_HOL_Obool)), _1270422), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270420, tc_HOL_Obool)), _1270422), _1270424))))], (51071 ^ _774244) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (25675 ^ _774244) ^ [_1222259, _1222261, _1222263, _1222265, _1222267] : [class_Rings_Ocomm__semiring__1(_1222259), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222259), _1222261), _1222263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1222265), _1222267)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222259), hAPP(hAPP(c_Power_Opower__class_Opower(_1222259), _1222261), _1222265)), hAPP(hAPP(c_Power_Opower__class_Opower(_1222259), _1222263), _1222267))))], (7457 ^ _774244) ^ [_895223, _895225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _895223), hAPP(c_Nat_OSuc, _895225))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _895223), _895225))), -(_895223 = _895225)], (47814 ^ _774244) ^ [_1724947, _1724949, _1724951] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1724947), tc_List_Olist(_1724947))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1724947), tc_List_Olist(_1724947)), _1724949), c_List_Olist_ONil(_1724947))), c_List_Olexord(_1724947, _1724951)))], (45238 ^ _774244) ^ [_1661497, _1661499, _1661501, _1661503, _1661505, _1661507] : [-(hBOOL(hAPP(hAPP(c_member(_1661497), _1661499), c_Map_Odom(_1661497, _1661501, _1661503)))), -(c_Map_Omap__add(_1661497, _1661501, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1661497, tc_Option_Ooption(_1661501)), _1661505), _1661499), hAPP(c_Option_Ooption_OSome(_1661501), _1661507)), _1661503) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1661497, tc_Option_Ooption(_1661501)), c_Map_Omap__add(_1661497, _1661501, _1661505, _1661503)), _1661499), hAPP(c_Option_Ooption_OSome(_1661501), _1661507)))], (38521 ^ _774244) ^ [_1493011, _1493013, _1493015, _1493017, _1493019] : [c_Fun_Oinj__on(_1493011, _1493013, _1493015, hAPP(hAPP(c_Set_Oinsert(_1493011), _1493017), _1493019)), 38524 ^ _774244 : [(38527 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1493013), hAPP(_1493015, _1493017)), hAPP(c_Set_Oimage(_1493011, _1493013, _1493015), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493011, tc_HOL_Obool)), _1493019), hAPP(hAPP(c_Set_Oinsert(_1493011), _1493017), c_Orderings_Obot__class_Obot(tc_fun(_1493011, tc_HOL_Obool)))))))], (38525 ^ _774244) ^ [] : [-(c_Fun_Oinj__on(_1493011, _1493013, _1493015, _1493019))]]], (15176 ^ _774244) ^ [_1029488, _1029490] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029488)), hAPP(c_Nat_OSuc, _1029490)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029488), _1029490))], (51449 ^ _774244) ^ [_1801577] : [hBOOL(hAPP(c_fNot, _1801577)), hBOOL(_1801577)], (28811 ^ _774244) ^ [_1286040, _1286042, _1286044, _1286046, _1286048] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1286040, tc_fun(_1286042, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1286040), _1286044), _1286046)), _1286048) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286042, tc_HOL_Obool)), hAPP(_1286048, _1286044)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1286040, tc_fun(_1286042, tc_HOL_Obool)), _1286046), _1286048)))], (31059 ^ _774244) ^ [_1331319, _1331321, _1331323, _1331325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1331319, tc_HOL_Obool)), _1331321), _1331323)), hBOOL(hAPP(hAPP(c_member(_1331319), _1331325), _1331321)), -(hBOOL(hAPP(hAPP(c_member(_1331319), _1331325), _1331323)))], (48540 ^ _774244) ^ [_1744540, _1744542, _1744544] : [-(hAPP(c_List_Ohd(_1744540), hAPP(hAPP(c_List_Olist_OCons(_1744540), _1744542), _1744544)) = _1744542)], (46681 ^ _774244) ^ [_1699091, _1699093] : [class_Groups_Ocomm__monoid__add(_1699091), hBOOL(hAPP(c_List_Odistinct(_1699091), _1699093)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1699091), _1699093) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1699091, _1699091), c_COMBI(_1699091)), hAPP(c_List_Oset(_1699091), _1699093)))], (51405 ^ _774244) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (46866 ^ _774244) ^ [_1702895, _1702897] : [_1702897 = c_List_Olist_ONil(_1702895), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702895)), _1702897) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32776 ^ _774244) ^ [_1368320, _1368322, _1368324] : [class_Orderings_Olinorder(_1368320), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368320), _1368322)), hBOOL(hAPP(hAPP(c_member(_1368320), _1368324), _1368322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368320), c_Big__Operators_Olinorder__class_OMin(_1368320, _1368322)), _1368324)))], (7149 ^ _774244) ^ [_890367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890367), _890367))], (22144 ^ _774244) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (11403 ^ _774244) ^ [_961928, _961930, _961932] : [class_Rings_Olinordered__idom(_961928), -(c_Groups_Osgn__class_Osgn(_961928, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961928), _961930), _961932)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961928), c_Groups_Osgn__class_Osgn(_961928, _961930)), c_Groups_Osgn__class_Osgn(_961928, _961932)))], (31106 ^ _774244) ^ [_1332292, _1332294, _1332296, _1332298, _1332300, _1332302] : [hBOOL(hAPP(hAPP(c_member(_1332292), _1332294), _1332296)), _1332298 = hAPP(_1332300, _1332294), -(hBOOL(hAPP(hAPP(c_member(_1332302), _1332298), hAPP(c_Set_Oimage(_1332292, _1332302, _1332300), _1332296))))], (18165 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (47718 ^ _774244) ^ [_1722898, _1722900, _1722902] : [_1722902 = c_List_Olist_ONil(_1722900), -(_1722898 = hAPP(hAPP(c_List_Oappend(_1722900), _1722898), _1722902))], (45680 ^ _774244) ^ [_1671974, _1671976, _1671978, _1671980, _1671982, _1671984, _1671986] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1671974), tc_Option_Ooption(_1671976), _1671978, hAPP(c_Option_Omap(_1671974, _1671976), _1671980)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1671978, tc_Option_Ooption(_1671974)), _1671982), _1671984), hAPP(c_Option_Ooption_OSome(_1671974), _1671986))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1671978, tc_Option_Ooption(_1671976)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1671974), tc_Option_Ooption(_1671976), _1671978, hAPP(c_Option_Omap(_1671974, _1671976), _1671980)), _1671982)), _1671984), hAPP(c_Option_Ooption_OSome(_1671976), hAPP(_1671980, _1671986))))], (46930 ^ _774244) ^ [_1703999, _1704001] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1703999), tc_List_Olist(_1703999))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1703999), tc_List_Olist(_1703999)), c_List_Olist_ONil(_1703999)), c_List_Olist_ONil(_1703999))), c_List_Olistrel(_1703999, _1704001))))], (12862 ^ _774244) ^ [_987882, _987884, _987886, _987888, _987890, _987892] : [class_Rings_Olinordered__semiring__1(_987882), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987882), _987884), _987886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987882), _987888), _987886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987882), c_Groups_Ozero__class_Ozero(_987882)), _987890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987882), c_Groups_Ozero__class_Ozero(_987882)), _987892)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987882), _987890), _987892) = c_Groups_Oone__class_Oone(_987882), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987882), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987882), _987890), _987884)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987882), _987892), _987888))), _987886)))], (51117 ^ _774244) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (50268 ^ _774244) ^ [_1780867] : [-(c_List_Oconcat(_1780867, c_List_Olist_ONil(tc_List_Olist(_1780867))) = c_List_Olist_ONil(_1780867))], (43583 ^ _774244) ^ [_1620305, _1620307, _1620309, _1620311, _1620313] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620305, _1620307)), hAPP(hAPP(c_Product__Type_OPair(_1620305, _1620307), _1620309), _1620311)), _1620313)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620307, _1620305)), hAPP(hAPP(c_Product__Type_OPair(_1620307, _1620305), _1620311), _1620309)), hAPP(c_Relation_Oconverse(_1620305, _1620307), _1620313))))], (23221 ^ _774244) ^ [_1175614, _1175616, _1175618, _1175620, _1175622] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1175614, _1175616), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1175618), _1175620))), -(_1175616 = 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), _1175622), _1175614), _1175616), 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), _1175622), _1175618)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175622), _1175620)), _1175616))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175622), _1175620), _1175616)))))], (31185 ^ _774244) ^ [_1334236, _1334238, _1334240, _1334242, _1334244, _1334246] : [-(hBOOL(hAPP(hAPP(c_member(_1334236), _1334238), c_SetInterval_Oord_OatLeastLessThan(_1334236, _1334240, _1334242, _1334244, _1334246)))), hBOOL(hAPP(hAPP(_1334240, _1334244), _1334238)), hBOOL(hAPP(hAPP(_1334242, _1334238), _1334246))], (10127 ^ _774244) ^ [_941225, _941227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _941225), _941227)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _941227), _941225)), -(_941225 = _941227)], (47903 ^ _774244) ^ [_1727722, _1727724, _1727726] : [hAPP(hAPP(c_List_Otake(_1727722), _1727724), _1727726) = c_List_Olist_ONil(_1727722), -(_1727724 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1727726 = c_List_Olist_ONil(_1727722))], (2392 ^ _774244) ^ [_810326, _810328, _810330, _810332, _810334, _810336, _810338, _810340] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_810340, _810336, _810332, _810328) = c_Nat_Osemiring__1__class_Oof__nat__aux(_810338, _810334, _810330, _810326)), _810340 = _810338, _810336 = _810334, _810332 = _810330, _810328 = _810326], (38664 ^ _774244) ^ [_1496441, _1496443, _1496445] : [-(c_Fun_Oinj__on(_1496441, tc_sum(_1496441, _1496443), c_Sum__Type_OInl(_1496441, _1496443), _1496445))], (24515 ^ _774244) ^ [_1200748] : [-(c_Code__Numeral_OSuc__code__numeral(_1200748) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1200748))))], (38930 ^ _774244) ^ [_1502466, _1502468, _1502470, _1502472] : [c_Fun_Oinj__on(_1502466, _1502468, _1502470, c_Orderings_Otop__class_Otop(tc_fun(_1502466, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1502466, _1502468, _1502470), hAPP(c_Set_Oimage(_1502466, _1502468, _1502470), _1502472)) = _1502472)], (32546 ^ _774244) ^ [_1364165, _1364167] : [class_Rings_Oring__1(_1364165), -(hBOOL(hAPP(hAPP(c_member(_1364165), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1364165), _1364167)), c_Int_Oring__1__class_OInts(_1364165))))], (17525 ^ _774244) ^ [_1074466, _1074468] : [-(c_Nitpick_Onat__lcm(_1074466, _1074468) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074466), _1074468)), c_Nitpick_Onat__gcd(_1074466, _1074468)))], (15194 ^ _774244) ^ [_1029825, _1029827] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029825), _1029827))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029825, _1029827) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029825), _1029827), _1029827))], (38918 ^ _774244) ^ [_1502219, _1502221, _1502223, _1502225] : [-(hAPP(c_Set_Oimage(_1502219, _1502221, _1502223), hAPP(c_Set_Ovimage(_1502219, _1502221, _1502223), _1502225)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1502221, tc_HOL_Obool)), _1502225), hAPP(c_Set_Oimage(_1502219, _1502221, _1502223), c_Orderings_Otop__class_Otop(tc_fun(_1502219, tc_HOL_Obool)))))], (22712 ^ _774244) ^ [] : [-(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)))))], (36563 ^ _774244) ^ [_1450434, _1450436, _1450438, _1450440] : [class_Orderings_Oorder(_1450434), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450434, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1450434, _1450436), _1450438)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1450434, _1450438), _1450440)) = c_Orderings_Obot__class_Obot(tc_fun(_1450434, tc_HOL_Obool)))], (31807 ^ _774244) ^ [_1348813, _1348815, _1348817, _1348819] : [-(hBOOL(hAPP(hAPP(c_member(_1348813), _1348815), _1348817))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348813, tc_Nat_Onat), _1348819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1348813, tc_HOL_Obool)), _1348817), hAPP(hAPP(c_Set_Oinsert(_1348813), _1348815), c_Orderings_Obot__class_Obot(tc_fun(_1348813, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348813, tc_Nat_Onat), _1348819), _1348817))], (47010 ^ _774244) ^ [_1705905, _1705907, _1705909, _1705911, _1705913] : [-(hAPP(hAPP(c_List_Ozip(_1705905, _1705907), hAPP(hAPP(c_List_Olist_OCons(_1705905), _1705909), _1705911)), _1705913) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1705905, _1705907)), _1705907, c_List_Olist_ONil(tc_prod(_1705905, _1705907)), hAPP(hAPP(c_COMBC(_1705907, tc_fun(tc_List_Olist(_1705907), tc_List_Olist(tc_prod(_1705905, _1705907))), tc_fun(tc_List_Olist(_1705907), tc_List_Olist(tc_prod(_1705905, _1705907)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1705905, _1705907)), tc_List_Olist(tc_prod(_1705905, _1705907))), tc_fun(tc_fun(tc_List_Olist(_1705907), tc_List_Olist(tc_prod(_1705905, _1705907))), tc_fun(tc_List_Olist(_1705907), tc_List_Olist(tc_prod(_1705905, _1705907)))), _1705907), c_COMBB(tc_List_Olist(tc_prod(_1705905, _1705907)), tc_List_Olist(tc_prod(_1705905, _1705907)), tc_List_Olist(_1705907))), hAPP(hAPP(c_COMBB(tc_prod(_1705905, _1705907), tc_fun(tc_List_Olist(tc_prod(_1705905, _1705907)), tc_List_Olist(tc_prod(_1705905, _1705907))), _1705907), c_List_Olist_OCons(tc_prod(_1705905, _1705907))), hAPP(c_Product__Type_OPair(_1705905, _1705907), _1705909)))), hAPP(c_List_Ozip(_1705905, _1705907), _1705911))), _1705913))], (45670 ^ _774244) ^ [_1671761, _1671763, _1671765, _1671767] : [_1671767 = c_Option_Ooption_ONone(_1671761), -(hAPP(hAPP(c_Option_Omap(_1671761, _1671763), _1671765), _1671767) = c_Option_Ooption_ONone(_1671763))], (44749 ^ _774244) ^ [_1649763] : [class_Complete__Lattice_Ocomplete__lattice(_1649763), -(c_Complete__Lattice_OSup__class_OSup(_1649763, c_Orderings_Obot__class_Obot(tc_fun(_1649763, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1649763))], (41866 ^ _774244) ^ [_1580532, _1580534, _1580536, _1580538, _1580540] : [hBOOL(hAPP(hAPP(_1580532, _1580534), _1580536)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1580538, _1580540, _1580532), _1580534)))], (5650 ^ _774244) ^ [_864292, _864294] : [_864292 = _864294, -(c_Com_Ocom_OBODY(_864292) = c_Com_Ocom_OBODY(_864294))], (33884 ^ _774244) ^ [_1389632, _1389634, _1389636, _1389638, _1389640] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1389632, tc_Option_Ooption(_1389634)), _1389636), _1389638), hAPP(c_Option_Ooption_OSome(_1389634), _1389640)) = hAPP(c_COMBK(tc_Option_Ooption(_1389634), _1389632), c_Option_Ooption_ONone(_1389634))], (24673 ^ _774244) ^ [_1204127, _1204129, _1204131] : [c_Nitpick_Oless__frac(_1204127, _1204129, _1204131), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1204127), c_Nitpick_Oplus__frac(_1204127, _1204129, c_Nitpick_Ouminus__frac(_1204127, _1204131)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28668 ^ _774244) ^ [_1282724, _1282726, _1282728, _1282730, _1282732] : [28670 ^ _774244 : [(28673 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282724, tc_HOL_Obool)), hAPP(_1282730, 28669 ^ [_1282724, _1282726, _1282728, _1282730, _1282732])), _1282732))], (28671 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1282726), 28669 ^ [_1282724, _1282726, _1282728, _1282730, _1282732]), _1282728)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282724, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1282726, tc_fun(_1282724, tc_HOL_Obool)), _1282728), _1282730)), _1282732)))], (7199 ^ _774244) ^ [_890964, _890966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890964), _890966)), _890966 = _890964], (47210 ^ _774244) ^ [_1710908, _1710910] : [class_Groups_Ocomm__monoid__add(_1710908), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1710908), _1710910) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1710908), hAPP(c_List_Onth(_1710908), _1710910)), 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(_1710908)), _1710910))))], (50438 ^ _774244) ^ [_1785346, _1785348, _1785350, _1785352] : [-(c_List_Oconcat(_1785346, hAPP(hAPP(c_List_Omap(_1785348, tc_List_Olist(_1785346)), hAPP(hAPP(c_COMBC(_1785348, tc_List_Olist(_1785346), tc_List_Olist(_1785346)), hAPP(hAPP(c_COMBB(_1785346, tc_fun(tc_List_Olist(_1785346), tc_List_Olist(_1785346)), _1785348), c_List_Olist_OCons(_1785346)), _1785350)), c_List_Olist_ONil(_1785346))), _1785352)) = hAPP(hAPP(c_List_Omap(_1785348, _1785346), _1785350), _1785352))], (26742 ^ _774244) ^ [_1243516, _1243518, _1243520, _1243522] : [class_Groups_Ocomm__monoid__add(_1243516), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1243516), _1243518), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1243520), hAPP(c_Nat_OSuc, _1243522))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1243516), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1243516, tc_Nat_Onat), _1243518), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1243520, _1243522)))], (19801 ^ _774244) ^ [] : [-(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))], (6784 ^ _774244) ^ [_884007, _884009, _884011, _884013] : [class_Rings_Ocomm__semiring__1(_884007), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884007), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884007), _884009), _884011)), _884013) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884007), _884009), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884007), _884011), _884013)))], (19341 ^ _774244) ^ [] : [-(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))))))], (3796 ^ _774244) ^ [_832770, _832772] : [_832772 = _832770, -(c_Rings_Odvd__class_Odvd(_832772) = c_Rings_Odvd__class_Odvd(_832770))], (8810 ^ _774244) ^ [_918166, _918168, _918170, _918172] : [class_Rings_Ocomm__semiring__1(_918166), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918166), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918166), _918168), _918170)), _918172) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918166), _918168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918166), _918170), _918172)))], (47929 ^ _774244) ^ [_1728209, _1728211, _1728213] : [hBOOL(hAPP(c_List_Odistinct(_1728209), _1728211)), -(hBOOL(hAPP(c_List_Odistinct(_1728209), hAPP(hAPP(c_List_Otake(_1728209), _1728213), _1728211))))], (25971 ^ _774244) ^ [_1227952, _1227954, _1227956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227952)), 25974 ^ _774244 : [(25981 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227954), _1227956)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227952), _1227954)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227952), _1227956))))], (25975 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227952), _1227954)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227952), _1227956))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227954), _1227956)))]]], (47319 ^ _774244) ^ [_1713754, _1713756, _1713758, _1713760, _1713762, _1713764] : [-(hAPP(hAPP(c_List_Omap(_1713754, _1713756), _1713758), hAPP(hAPP(c_List_Olist__update(_1713754, _1713760), _1713762), _1713764)) = hAPP(hAPP(c_List_Olist__update(_1713756, hAPP(hAPP(c_List_Omap(_1713754, _1713756), _1713758), _1713760)), _1713762), hAPP(_1713758, _1713764)))], (9420 ^ _774244) ^ [_929053, _929055, _929057] : [class_Rings_Olinordered__semiring__strict(_929053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929053), _929055), c_Groups_Ozero__class_Ozero(_929053))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929053), c_Groups_Ozero__class_Ozero(_929053)), _929057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929053), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929053), _929055), _929057)), c_Groups_Ozero__class_Ozero(_929053))))], (43319 ^ _774244) ^ [_1612707, _1612709, _1612711] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1612707, _1612707), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1612707, _1612707), _1612709)), c_Transitive__Closure_Ortrancl(_1612707, _1612709)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1612707, _1612707), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1612707, _1612707)), hAPP(hAPP(c_Product__Type_OPair(_1612707, _1612707), _1612711), _1612711)), c_Transitive__Closure_Otrancl(_1612707, _1612709)))], (40844 ^ _774244) ^ [_1548832, _1548834, _1548836, _1548838] : [-(c_Fun_Ooverride__on(_1548832, _1548834, _1548836, _1548838, c_Orderings_Obot__class_Obot(tc_fun(_1548832, tc_HOL_Obool))) = _1548836)], (43415 ^ _774244) ^ [_1614815, _1614817, _1614819] : [-(hAPP(c_Relation_ORange(_1614815, _1614817), _1614819) = hAPP(c_Relation_ODomain(_1614817, _1614815), hAPP(c_Relation_Oconverse(_1614815, _1614817), _1614819)))], (36055 ^ _774244) ^ [_1438669, _1438671, _1438673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438669, tc_HOL_Obool)), _1438671), _1438673)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438669, tc_HOL_Obool)), _1438673), _1438671) = _1438671)], (18643 ^ _774244) ^ [_1092373, _1092375] : [c_Int_Oiszero(_1092373, hAPP(c_Int_Onumber__class_Onumber__of(_1092373), c_Int_OBit1(_1092375))), class_Int_Onumber__ring(_1092373), class_Int_Oring__char__0(_1092373)], (33332 ^ _774244) ^ [_1378886, _1378888, _1378890] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1378886, tc_HOL_Obool), tc_fun(_1378886, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1378886, tc_HOL_Obool), tc_fun(_1378886, tc_HOL_Obool)), _1378888), _1378890)), c_Wellfounded_Ofinite__psubset(_1378886)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1378886, tc_HOL_Obool)), _1378888), _1378890)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378886), _1378890))], (29678 ^ _774244) ^ [_1302705, _1302707] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1302705), _1302707)), -(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)))), _1302707, _1302705) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (41636 ^ _774244) ^ [_1574134, _1574136, _1574138] : [_1574138 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1574134, _1574136), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1574134, _1574136), _1574138) = c_Orderings_Obot__class_Obot(tc_fun(_1574136, tc_HOL_Obool)))], (31515 ^ _774244) ^ [_1341205, _1341207, _1341209, _1341211, _1341213, _1341215] : [hBOOL(hAPP(hAPP(c_member(_1341205), _1341207), _1341209)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1341205, tc_fun(_1341211, tc_HOL_Obool)), _1341209), hAPP(hAPP(c_COMBB(tc_fun(_1341211, tc_HOL_Obool), tc_fun(_1341211, tc_HOL_Obool), _1341205), hAPP(c_Set_Oinsert(_1341211), _1341213)), _1341215)) = hAPP(hAPP(c_Set_Oinsert(_1341211), _1341213), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1341205, tc_fun(_1341211, tc_HOL_Obool)), _1341209), _1341215)))], (49043 ^ _774244) ^ [_1755339, _1755341, _1755343] : [_1755339 = c_List_Olist_ONil(_1755341), -(c_List_Olast(_1755341, hAPP(hAPP(c_List_Olist_OCons(_1755341), _1755343), _1755339)) = _1755343)], (39930 ^ _774244) ^ [_1528040, _1528042, _1528044] : [-(hAPP(c_Product__Type_Omap__pair(_1528040, _1528040, _1528042, _1528042, c_COMBI(_1528040), c_COMBI(_1528042)), _1528044) = _1528044)], (49483 ^ _774244) ^ [_1765153, _1765155, _1765157, _1765159] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1765153, tc_Nat_Onat), _1765153), c_Product__Type_Ofst(_1765153, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1765153, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1765153, tc_Nat_Onat)), _1765155), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1765153, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1765153, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1765153, tc_Nat_Onat), _1765157), _1765159))) = hAPP(hAPP(c_List_Omap(tc_prod(_1765153, tc_Nat_Onat), _1765153), c_Product__Type_Ofst(_1765153, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1765153, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1765153, tc_Nat_Onat)), _1765155), c_Product__Type_Osnd(_1765153, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1765153, tc_Nat_Onat), _1765157), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1765159)))))], (458 ^ _774244) ^ [_781273, _781275, _781277, _781279, _781281, _781283] : [-(c_Big__Operators_Osemilattice__big(_781281, _781277, _781273)), c_Big__Operators_Osemilattice__big(_781283, _781279, _781275), _781283 = _781281, _781279 = _781277, _781275 = _781273], (44434 ^ _774244) ^ [_1642556, _1642558, _1642560] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1642556, tc_HOL_Obool)), _1642558), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1642556, tc_HOL_Obool), _1642560)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1642556, tc_HOL_Obool), tc_fun(_1642556, tc_HOL_Obool)), _1642560), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1642556, tc_HOL_Obool)), _1642558)))], (37307 ^ _774244) ^ [_1466600, _1466602, _1466604, _1466606, _1466608, _1466610] : [c_Finite__Set_Ofolding(_1466600, _1466602, _1466604, _1466606), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466600), _1466608)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466600), _1466610)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466600, tc_HOL_Obool)), _1466608), _1466610) = c_Orderings_Obot__class_Obot(tc_fun(_1466600, tc_HOL_Obool)), -(hAPP(_1466606, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1466600, tc_HOL_Obool)), _1466608), _1466610)) = hAPP(c_Fun_Ocomp(_1466602, _1466602, _1466602, hAPP(_1466606, _1466608)), hAPP(_1466606, _1466610)))], (41739 ^ _774244) ^ [_1576890, _1576892, _1576894, _1576896, _1576898] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576890, _1576892)), hAPP(hAPP(c_Product__Type_OPair(_1576890, _1576892), _1576894), _1576896)), _1576898)), -(hBOOL(hAPP(hAPP(c_member(_1576890), _1576894), hAPP(c_Relation_ODomain(_1576890, _1576892), _1576898))))], (33058 ^ _774244) ^ [_1372837, _1372839, _1372841] : [class_Lattices_Olattice(_1372837), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372837), _1372839)), -(hBOOL(hAPP(hAPP(c_member(_1372837), _1372841), _1372839))), -(_1372839 = c_Orderings_Obot__class_Obot(tc_fun(_1372837, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1372837, hAPP(hAPP(c_Set_Oinsert(_1372837), _1372841), _1372839)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1372837), _1372841), c_Big__Operators_Olattice__class_OSup__fin(_1372837, _1372839)))], (50550 ^ _774244) ^ [_1788448, _1788450, _1788452] : [c_List_OtakeWhile(_1788448, _1788450, _1788452) = _1788452, 50553 ^ _774244 : [(50554 ^ _774244) ^ [_1788535] : [hBOOL(hAPP(hAPP(c_member(_1788448), _1788535), hAPP(c_List_Oset(_1788448), _1788452))), -(hBOOL(hAPP(_1788450, _1788535)))]]], (32274 ^ _774244) ^ [_1358608, _1358610, _1358612, _1358614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1358614, _1358610)), hAPP(_1358614, _1358612))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1358608, _1358608)), hAPP(hAPP(c_Product__Type_OPair(_1358608, _1358608), _1358610), _1358612)), hAPP(c_Wellfounded_Omeasure(_1358608), _1358614))))], (9288 ^ _774244) ^ [_926685, _926687] : [class_Groups_Ogroup__add(_926685), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926685), _926687), hAPP(c_Groups_Ouminus__class_Ouminus(_926685), _926687)) = c_Groups_Ozero__class_Ozero(_926685))], (31631 ^ _774244) ^ [_1345077, _1345079, _1345081, _1345083, _1345085] : [hBOOL(hAPP(hAPP(c_member(_1345077), _1345079), _1345081)), -(hAPP(c_Set_Oimage(_1345077, _1345083, hAPP(c_COMBK(_1345083, _1345077), _1345085)), _1345081) = hAPP(hAPP(c_Set_Oinsert(_1345083), _1345085), c_Orderings_Obot__class_Obot(tc_fun(_1345083, tc_HOL_Obool))))], (10137 ^ _774244) ^ [_941374, _941376, _941378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _941374), _941376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _941376), _941378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _941374), _941378)))], (35193 ^ _774244) ^ [_1418978, _1418980, _1418982, _1418984, _1418986, _1418988] : [-(hAPP(hAPP(c_Fun_Ocomp(_1418978, _1418980, _1418982, _1418984), _1418986), _1418988) = hAPP(_1418984, hAPP(_1418986, _1418988)))], (17375 ^ _774244) ^ [_1071690, _1071692, _1071694] : [class_Rings_Olinordered__semidom(_1071690), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071690), c_Groups_Oone__class_Oone(_1071690)), _1071692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071690), c_Groups_Oone__class_Oone(_1071690)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071690), _1071692), hAPP(hAPP(c_Power_Opower__class_Opower(_1071690), _1071692), _1071694)))))], (31407 ^ _774244) ^ [_1338437, _1338439, _1338441] : [class_Orderings_Oord(_1338437), 31410 ^ _774244 : [(31417 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338437), _1338441), _1338439)), -(hBOOL(hAPP(hAPP(c_member(_1338437), _1338439), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338437), _1338441))))], (31411 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1338437), _1338439), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1338437), _1338441))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338437), _1338441), _1338439)))]]], (46497 ^ _774244) ^ [_1693489, _1693491, _1693493] : [-(hBOOL(hAPP(c_List_Odistinct(_1693489), hAPP(hAPP(c_List_Olist_OCons(_1693489), _1693491), _1693493)))), -(hBOOL(hAPP(hAPP(c_member(_1693489), _1693491), hAPP(c_List_Oset(_1693489), _1693493)))), hBOOL(hAPP(c_List_Odistinct(_1693489), _1693493))], (51059 ^ _774244) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (51153 ^ _774244) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (42385 ^ _774244) ^ [_1592499, _1592501, _1592503] : [c_Wellfounded_Owf(_1592499, _1592501), hBOOL(hAPP(hAPP(c_member(tc_prod(_1592499, _1592499)), hAPP(hAPP(c_Product__Type_OPair(_1592499, _1592499), hAPP(_1592503, hAPP(c_Nat_OSuc, 42388 ^ [_1592499, _1592501, _1592503]))), hAPP(_1592503, 42388 ^ [_1592499, _1592501, _1592503]))), _1592501))], (33212 ^ _774244) ^ [_1375846, _1375848] : [class_Lattices_Olattice(_1375846), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375846), _1375848)), -(_1375848 = c_Orderings_Obot__class_Obot(tc_fun(_1375846, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1375846), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1375846), 33225 ^ [_1375846, _1375848]), 33226 ^ [_1375846, _1375848])), hAPP(hAPP(c_Set_Oinsert(_1375846), 33225 ^ [_1375846, _1375848]), hAPP(hAPP(c_Set_Oinsert(_1375846), 33226 ^ [_1375846, _1375848]), c_Orderings_Obot__class_Obot(tc_fun(_1375846, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1375846), c_Big__Operators_Olattice__class_OSup__fin(_1375846, _1375848)), _1375848)))], (208 ^ _774244) ^ [_777256, _777258, _777260, _777262] : [-(c_Nitpick_Orefl_H(_777260, _777256)), c_Nitpick_Orefl_H(_777262, _777258), _777262 = _777260, _777258 = _777256], (36255 ^ _774244) ^ [_1443259, _1443261, _1443263, _1443265] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443259, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443259, tc_HOL_Obool)), _1443261), _1443263)), _1443265) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443259, tc_HOL_Obool)), _1443261), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443259, tc_HOL_Obool)), _1443263), _1443265)))], (45912 ^ _774244) ^ [_1677170, _1677172, _1677174, _1677176] : [-(hBOOL(hAPP(hAPP(c_member(_1677170), _1677172), hAPP(c_List_Oset(_1677170), _1677174)))), hBOOL(hAPP(hAPP(c_member(_1677170), _1677172), hAPP(c_List_Oset(_1677170), c_List_Oremove1(_1677170, _1677176, _1677174))))], (19387 ^ _774244) ^ [_1105179] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1105179)), 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, _1105179, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (40447 ^ _774244) ^ [_1538363, _1538365, _1538367] : [class_Lattices_Oab__semigroup__idem__mult(_1538363), hAPP(_1538365, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1538363), 40452 ^ [_1538363, _1538365, _1538367]), 40453 ^ [_1538363, _1538365, _1538367])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1538363), hAPP(_1538365, 40452 ^ [_1538363, _1538365, _1538367])), hAPP(_1538365, 40453 ^ [_1538363, _1538365, _1538367])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538363), _1538367)), -(_1538367 = c_Orderings_Obot__class_Obot(tc_fun(_1538363, tc_HOL_Obool))), -(hAPP(_1538365, hAPP(c_Finite__Set_Ofold1(_1538363, c_Groups_Otimes__class_Otimes(_1538363)), _1538367)) = hAPP(c_Finite__Set_Ofold1(_1538363, c_Groups_Otimes__class_Otimes(_1538363)), hAPP(c_Set_Oimage(_1538363, _1538363, _1538365), _1538367)))], (35655 ^ _774244) ^ [_1430472, _1430474, _1430476, _1430478, _1430480] : [c_Equiv__Relations_Oequiv(_1430472, _1430474, _1430476), hBOOL(hAPP(hAPP(c_member(tc_prod(_1430472, _1430472)), hAPP(hAPP(c_Product__Type_OPair(_1430472, _1430472), _1430478), _1430480)), _1430476)), -(hAPP(c_Relation_OImage(_1430472, _1430472, _1430476), hAPP(hAPP(c_Set_Oinsert(_1430472), _1430478), c_Orderings_Obot__class_Obot(tc_fun(_1430472, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1430472, _1430472, _1430476), hAPP(hAPP(c_Set_Oinsert(_1430472), _1430480), c_Orderings_Obot__class_Obot(tc_fun(_1430472, tc_HOL_Obool)))))], (46288 ^ _774244) ^ [_1686954, _1686956, _1686958] : [-(hBOOL(hAPP(hAPP(c_member(_1686954), _1686956), hAPP(c_List_Oset(_1686954), _1686958)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686954)), c_List_Oremove1(_1686954, _1686956, _1686958)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686954)), _1686958))], (23953 ^ _774244) ^ [_1189930, _1189932, _1189934] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1189930, _1189932), _1189934))), _1189930 = 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), _1189934)), _1189932)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1189934)), 23960 ^ _774244 : [(23963 ^ _774244) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1189934) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23961 ^ _774244) ^ [] : [-(_1189932 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 23964 ^ _774244 : [(23967 ^ _774244) ^ [] : [23968 ^ _774244 : [(23971 ^ _774244) ^ [] : [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), _1189934))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1189934)), _1189932))], (23969 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1189932)))]], 23976 ^ _774244 : [(23979 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189932), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1189934))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1189934)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23977 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1189932))]]], (23965 ^ _774244) ^ [] : [_1189932 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (38107 ^ _774244) ^ [_1484775, _1484777, _1484779, _1484781, _1484783] : [c_Fun_Oinj__on(_1484775, _1484777, _1484779, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484775, tc_HOL_Obool)), _1484781), _1484783)), 38110 ^ _774244 : [(38117 ^ _774244) ^ [] : [_1484781 = _1484783, -(hAPP(c_Set_Oimage(_1484775, _1484777, _1484779), _1484781) = hAPP(c_Set_Oimage(_1484775, _1484777, _1484779), _1484783))], (38111 ^ _774244) ^ [] : [hAPP(c_Set_Oimage(_1484775, _1484777, _1484779), _1484781) = hAPP(c_Set_Oimage(_1484775, _1484777, _1484779), _1484783), -(_1484781 = _1484783)]]], (35302 ^ _774244) ^ [_1421878, _1421880, _1421882] : [class_Rings_Oring__1(_1421878), -(hAPP(c_Int_Oring__1__class_Oof__int(_1421878), 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), _1421880), _1421882)), 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(_1421878), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1421878), _1421880)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1421878), _1421882)))], (27294 ^ _774244) ^ [_1255144, _1255146, _1255148] : [class_Groups_Oordered__ab__group__add(_1255144), -(hAPP(c_Set_Oimage(_1255144, _1255144, c_Groups_Ouminus__class_Ouminus(_1255144)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1255144, _1255146, _1255148)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255144, hAPP(c_Groups_Ouminus__class_Ouminus(_1255144), _1255148)), hAPP(c_Groups_Ouminus__class_Ouminus(_1255144), _1255146)))], (48847 ^ _774244) ^ [_1750648, _1750650, _1750652, _1750654, _1750656] : [hBOOL(hAPP(hAPP(c_member(_1750648), _1750650), hAPP(c_List_Oset(_1750648), _1750652))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1750654), hAPP(_1750656, _1750650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1750654), c_List_Olist_Olist__size(_1750648, _1750656, _1750652))))], (47028 ^ _774244) ^ [_1706559, _1706561, _1706563, _1706565] : [-(hAPP(hAPP(c_List_Onth(_1706559), hAPP(hAPP(c_List_Olist_OCons(_1706559), _1706561), _1706563)), hAPP(c_Nat_OSuc, _1706565)) = hAPP(hAPP(c_List_Onth(_1706559), _1706563), _1706565))], (24487 ^ _774244) ^ [_1200288, _1200290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1200288)), hAPP(c_Code__Numeral_Onat__of, _1200290))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1200288), _1200290)))], (44506 ^ _774244) ^ [_1644070, _1644072, _1644074] : [class_Complete__Lattice_Ocomplete__lattice(_1644070), hBOOL(hAPP(hAPP(c_member(_1644070), _1644072), _1644074)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1644070), c_Complete__Lattice_OInf__class_OInf(_1644070, _1644074)), _1644072)))], (40025 ^ _774244) ^ [_1530644] : [-(c_Relation_Orefl__on(_1530644, c_Orderings_Obot__class_Obot(tc_fun(_1530644, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530644, _1530644), tc_HOL_Obool))))], (51397 ^ _774244) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (6045 ^ _774244) ^ [_871069] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _871069)], (49394 ^ _774244) ^ [_1762459, _1762461, _1762463, _1762465, _1762467] : [-(hAPP(c_List_Ofilter(_1762459, _1762461), hAPP(hAPP(c_List_Omap(_1762463, _1762459), _1762465), _1762467)) = hAPP(hAPP(c_List_Omap(_1762463, _1762459), _1762465), hAPP(c_List_Ofilter(_1762463, hAPP(c_Fun_Ocomp(_1762459, tc_HOL_Obool, _1762463, _1762461), _1762465)), _1762467)))], (33812 ^ _774244) ^ [_1388270, _1388272, _1388274, _1388276] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388270, _1388272), _1388274), _1388276), hAPP(_1388274, _1388276)) = _1388274)], (48680 ^ _774244) ^ [_1747055, _1747057] : [class_Lattices_Oab__semigroup__idem__mult(_1747055), -(_1747057 = c_List_Olist_ONil(_1747055)), -(hAPP(c_Finite__Set_Ofold1(_1747055, c_Groups_Otimes__class_Otimes(_1747055)), hAPP(c_List_Oset(_1747055), _1747057)) = hAPP(c_List_Ofoldl(_1747055, _1747055, c_Groups_Otimes__class_Otimes(_1747055), hAPP(c_List_Ohd(_1747055), _1747057)), hAPP(c_List_Otl(_1747055), _1747057)))], (47323 ^ _774244) ^ [_1713894, _1713896, _1713898, _1713900] : [-(hAPP(hAPP(c_List_Olist__update(_1713894, hAPP(hAPP(c_List_Olist_OCons(_1713894), _1713896), _1713898)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1713900) = hAPP(hAPP(c_List_Olist_OCons(_1713894), _1713900), _1713898))], (36309 ^ _774244) ^ [_1444414, _1444416, _1444418, _1444420] : [class_Lattices_Osemilattice__inf(_1444414), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444414), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444414), _1444416), _1444418)), _1444420) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444414), _1444416), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444414), _1444418), _1444420)))], (15990 ^ _774244) ^ [_1046083, _1046085] : [_1046083 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046083), _1046085) = _1046085)], (44622 ^ _774244) ^ [_1646937, _1646939, _1646941, _1646943] : [-(hAPP(c_Set_Oimage(_1646937, _1646939, _1646941), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646937, tc_HOL_Obool), _1646943)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1646937, tc_HOL_Obool), tc_fun(_1646939, tc_HOL_Obool)), _1646943), c_Set_Oimage(_1646937, _1646939, _1646941)))], (30406 ^ _774244) ^ [_1316502, _1316504, _1316506] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1316502), _1316504)), -(hAPP(c_Finite__Set_Ocard(_1316502), hAPP(hAPP(c_Set_Oinsert(_1316502), _1316506), _1316504)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1316502), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316502, tc_HOL_Obool)), _1316504), hAPP(hAPP(c_Set_Oinsert(_1316502), _1316506), c_Orderings_Obot__class_Obot(tc_fun(_1316502, tc_HOL_Obool)))))))], (49456 ^ _774244) ^ [_1764547, _1764549, _1764551, _1764553] : [-(c_List_Otranspose(_1764547, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1764549), tc_List_Olist(_1764547)), hAPP(c_List_Omap(_1764549, _1764547), _1764551)), _1764553)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1764549), tc_List_Olist(_1764547)), hAPP(c_List_Omap(_1764549, _1764547), _1764551)), c_List_Otranspose(_1764549, _1764553)))], (10237 ^ _774244) ^ [_942897, _942899, _942901, _942903] : [class_Orderings_Oorder(_942897), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942897), _942899), _942901)), _942899 = _942903, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942897), _942903), _942901)))], (41356 ^ _774244) ^ [_1568105] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1568105)))], (19391 ^ _774244) ^ [_1105260, _1105262] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1105260)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1105262))) = 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), _1105260), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1105262))))], (40876 ^ _774244) ^ [_1549941, _1549943] : [c_Predicate_Oreflp(_1549941, _1549943), -(c_Relation_Orefl__on(_1549941, c_Orderings_Otop__class_Otop(tc_fun(_1549941, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1549941, _1549941)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549941, _1549941, tc_HOL_Obool), _1549943))))], (48104 ^ _774244) ^ [_1732637, _1732639, _1732641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1732637, _1732637), tc_HOL_Obool)), _1732639), _1732641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1732637), tc_List_Olist(_1732637)), tc_HOL_Obool)), c_List_Olistrel1(_1732637, _1732639)), c_List_Olistrel1(_1732637, _1732641))))], (4418 ^ _774244) ^ [_842627, _842629] : [_842629 = _842627, -(c_Fun_Oid(_842629) = c_Fun_Oid(_842627))], (3586 ^ _774244) ^ [_829453, _829455, _829457, _829459, _829461, _829463, _829465, _829467] : [-(c_Recdef_Osame__fst(_829467, _829463, _829459, _829455) = c_Recdef_Osame__fst(_829465, _829461, _829457, _829453)), _829467 = _829465, _829463 = _829461, _829459 = _829457, _829455 = _829453], (35929 ^ _774244) ^ [_1436459, _1436461, _1436463, _1436465] : [class_Lattices_Osemilattice__inf(_1436459), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436459), _1436461), _1436463)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436459), _1436461), _1436465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436459), _1436461), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1436459), _1436463), _1436465))))], (5026 ^ _774244) ^ [_851927, _851929] : [_851929 = _851927, -(c_List_Otranspose__rel(_851929) = c_List_Otranspose__rel(_851927))], (35330 ^ _774244) ^ [_1422624, _1422626] : [-(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), _1422624), _1422626)), 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), _1422624), _1422626))], (17143 ^ _774244) ^ [_1067385, _1067387, _1067389] : [class_Groups_Omonoid__mult(_1067385), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067385), hAPP(hAPP(c_Power_Opower__class_Opower(_1067385), _1067387), _1067389)), _1067387) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067385), _1067387), hAPP(hAPP(c_Power_Opower__class_Opower(_1067385), _1067387), _1067389)))], (2734 ^ _774244) ^ [_815665, _815667, _815669, _815671, _815673, _815675] : [-(c_Nitpick_Otimes__frac(_815675, _815671, _815667) = c_Nitpick_Otimes__frac(_815673, _815669, _815665)), _815675 = _815673, _815671 = _815669, _815667 = _815665], (41136 ^ _774244) ^ [_1561183, _1561185] : [-(hAPP(c_Fun_Oid(_1561183), _1561185) = _1561185)], (6568 ^ _774244) ^ [_880090, _880092] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _880090), hAPP(c_Nat_OSuc, _880092)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _880090), _880092)))], (4292 ^ _774244) ^ [_840652, _840654, _840656, _840658, _840660, _840662, _840664, _840666] : [-(c_Product__Type_Oscomp(_840666, _840662, _840658, _840654) = c_Product__Type_Oscomp(_840664, _840660, _840656, _840652)), _840666 = _840664, _840662 = _840660, _840658 = _840656, _840654 = _840652], (17685 ^ _774244) ^ [_1076981, _1076983, _1076985] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076981))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076981)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076983)), _1076985)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076983)), _1076985))], (14826 ^ _774244) ^ [_1023134, _1023136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023134)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023136)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1023134), hAPP(c_Int_Onat, _1023136)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1023134, _1023136)))], (33830 ^ _774244) ^ [_1388698, _1388700, _1388702, _1388704, _1388706, _1388708] : [_1388698 = _1388700, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388702, _1388704), _1388706), _1388700), _1388708), _1388698) = _1388708)], (36387 ^ _774244) ^ [_1446065, _1446067] : [class_Lattices_Osemilattice__inf(_1446065), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1446065), _1446067), _1446067) = _1446067)], (13112 ^ _774244) ^ [_992020, _992022, _992024, _992026, _992028, _992030] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _992020), _992022)), _992024) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _992026), _992028)), _992030), 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), _992026), _992028)), _992030))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992030), _992026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _992024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _992026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _992026), _992020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _992022), _992028)))], (29592 ^ _774244) ^ [] : [-(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))))], (7756 ^ _774244) ^ [_900829, _900831, _900833, _900835] : [hAPP(c_Sum__Type_OInr(_900829, _900831), _900833) = hAPP(c_Sum__Type_OInl(_900831, _900829), _900835)], (2100 ^ _774244) ^ [_805632, _805634, _805636, _805638, _805640, _805642, _805644, _805646, _805648, _805650] : [-(c_Nitpick_Opair__box_Opair__box__rec(_805650, _805646, _805642, _805638, _805634) = c_Nitpick_Opair__box_Opair__box__rec(_805648, _805644, _805640, _805636, _805632)), _805650 = _805648, _805646 = _805644, _805642 = _805640, _805638 = _805636, _805634 = _805632], (24447 ^ _774244) ^ [_1199340, _1199342, _1199344, _1199346, _1199348, _1199350] : [-(hAPP(c_Product__Type_Oapfst(_1199340, _1199342, _1199344, _1199346), hAPP(hAPP(c_Product__Type_OPair(_1199340, _1199344), _1199348), _1199350)) = hAPP(hAPP(c_Product__Type_OPair(_1199342, _1199344), hAPP(_1199346, _1199348)), _1199350))], (4570 ^ _774244) ^ [_844899, _844901] : [_844901 = _844899, -(c_Orderings_Otop__class_Otop(_844901) = c_Orderings_Otop__class_Otop(_844899))], (43089 ^ _774244) ^ [_1607374, _1607376, _1607378] : [-(c_Transitive__Closure_Ortrancl(_1607374, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1607374, _1607374), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1607374, _1607376)), c_Transitive__Closure_Ortrancl(_1607374, _1607378))) = c_Transitive__Closure_Ortrancl(_1607374, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1607374, _1607374), tc_HOL_Obool)), _1607376), _1607378)))], (17855 ^ _774244) ^ [_1079989] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1079989), c_Int_OMin) = c_Int_Osucc(_1079989))], (21003 ^ _774244) ^ [_1134006, _1134008, _1134010, _1134012] : [class_Fields_Ofield__inverse__zero(_1134006), class_Int_Onumber(_1134006), 21010 ^ _774244 : [(21011 ^ _774244) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134006), _1134008), _1134010) = hAPP(c_Int_Onumber__class_Onumber__of(_1134006), _1134012), 21014 ^ _774244 : [(21021 ^ _774244) ^ [] : [_1134010 = c_Groups_Ozero__class_Ozero(_1134006), -(hAPP(c_Int_Onumber__class_Onumber__of(_1134006), _1134012) = c_Groups_Ozero__class_Ozero(_1134006))], (21015 ^ _774244) ^ [] : [-(_1134010 = c_Groups_Ozero__class_Ozero(_1134006)), -(_1134008 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134006), hAPP(c_Int_Onumber__class_Onumber__of(_1134006), _1134012)), _1134010))]]], (21027 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134006), _1134008), _1134010) = hAPP(c_Int_Onumber__class_Onumber__of(_1134006), _1134012)), 21030 ^ _774244 : [(21033 ^ _774244) ^ [] : [_1134008 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134006), hAPP(c_Int_Onumber__class_Onumber__of(_1134006), _1134012)), _1134010)], (21031 ^ _774244) ^ [] : [_1134010 = c_Groups_Ozero__class_Ozero(_1134006)]], 21034 ^ _774244 : [(21037 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1134006), _1134012) = c_Groups_Ozero__class_Ozero(_1134006)], (21035 ^ _774244) ^ [] : [-(_1134010 = c_Groups_Ozero__class_Ozero(_1134006))]]]]], (49772 ^ _774244) ^ [_1770871, _1770873, _1770875] : [class_Orderings_Olinorder(_1770871), c_List_Olinorder__class_Osorted(_1770871, _1770873), -(c_List_Olinorder__class_Osorted(_1770871, c_List_Olinorder__class_Oinsort__insert__key(_1770871, _1770871, c_COMBI(_1770871), _1770875, _1770873)))], (5010 ^ _774244) ^ [_851693, _851695] : [_851695 = _851693, -(c_Orderings_Oord__class_Omax(_851695) = c_Orderings_Oord__class_Omax(_851693))], (10798 ^ _774244) ^ [_951595, _951597, _951599, _951601] : [class_Orderings_Opreorder(_951595), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951595), _951597), _951599)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951595), _951599), _951601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951595), _951597), _951601)))], (18453 ^ _774244) ^ [_1089230, _1089232] : [c_Int_OBit1(_1089230) = c_Int_OBit1(_1089232), -(_1089230 = _1089232)], (33474 ^ _774244) ^ [_1381875, _1381877, _1381879, _1381881] : [c_Finite__Set_Ofolding__one(_1381875, _1381877, _1381879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381875), _1381881)), -(_1381881 = c_Orderings_Obot__class_Obot(tc_fun(_1381875, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1381875), hAPP(hAPP(_1381877, 33487 ^ [_1381875, _1381877, _1381879, _1381881]), 33488 ^ [_1381875, _1381877, _1381879, _1381881])), hAPP(hAPP(c_Set_Oinsert(_1381875), 33487 ^ [_1381875, _1381877, _1381879, _1381881]), hAPP(hAPP(c_Set_Oinsert(_1381875), 33488 ^ [_1381875, _1381877, _1381879, _1381881]), c_Orderings_Obot__class_Obot(tc_fun(_1381875, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1381875), hAPP(_1381879, _1381881)), _1381881)))], (22288 ^ _774244) ^ [_1158379, _1158381] : [-(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), _1158379)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1158381), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1158379))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (39560 ^ _774244) ^ [_1517389, _1517391, _1517393, _1517395, _1517397, _1517399] : [hBOOL(hAPP(hAPP(c_member(_1517389), _1517391), _1517393)), hBOOL(hAPP(hAPP(c_member(_1517395), _1517397), hAPP(_1517399, _1517391))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517389, _1517395)), hAPP(hAPP(c_Product__Type_OPair(_1517389, _1517395), _1517391), _1517397)), hAPP(hAPP(c_Product__Type_OSigma(_1517389, _1517395), _1517393), _1517399))))], (7952 ^ _774244) ^ [_904281] : [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), _904281))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _904281)))], (29264 ^ _774244) ^ [_1295053, _1295055] : [_1295055 = c_Orderings_Obot__class_Obot(tc_fun(_1295053, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1295053, tc_HOL_Obool)), _1295055), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1295053, tc_HOL_Obool)), _1295055))))], (50378 ^ _774244) ^ [_1783171, _1783173, _1783175] : [-(hAPP(c_List_Orev(_1783171), hAPP(hAPP(c_List_Odrop(_1783171), _1783173), _1783175)) = hAPP(hAPP(c_List_Otake(_1783171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783171)), _1783175)), _1783173)), hAPP(c_List_Orev(_1783171), _1783175)))], (36049 ^ _774244) ^ [_1438548, _1438550, _1438552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438548, tc_HOL_Obool)), _1438550), _1438552)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438548, tc_HOL_Obool)), _1438550), _1438552) = _1438550)], (32244 ^ _774244) ^ [_1357968, _1357970, _1357972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357968)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1357970), _1357972)), 32251 ^ _774244 : [(32252 ^ _774244) ^ [_1358164] : [32254 ^ _774244 : [(32260 ^ _774244) ^ [] : [-(_1358164 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32256 ^ [_1357968, _1357970, _1357972, _1358164]), 32253 ^ [_1357968, _1357970, _1357972, _1358164]))], (32258 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32256 ^ [_1357968, _1357970, _1357972, _1358164]), _1357972)))], (32255 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32253 ^ [_1357968, _1357970, _1357972, _1358164]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1357968))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1358164), _1357970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1358164), _1357968)), _1357970)))]]], (13080 ^ _774244) ^ [_991432, _991434, _991436] : [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), _991432), _991434)), _991436)), 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)), _991436)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _991434), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16857 ^ _774244) ^ [_1062211, _1062213, _1062215] : [class_Int_Onumber__ring(_1062211), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1062211), hAPP(c_Int_Onumber__class_Onumber__of(_1062211), _1062213)), hAPP(c_Int_Onumber__class_Onumber__of(_1062211), _1062215)) = hAPP(c_Int_Onumber__class_Onumber__of(_1062211), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1062213), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1062215))))], (43305 ^ _774244) ^ [_1612433, _1612435, _1612437, _1612439, _1612441] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612433, _1612433)), hAPP(hAPP(c_Product__Type_OPair(_1612433, _1612433), _1612435), _1612437)), c_Transitive__Closure_Ortrancl(_1612433, _1612439))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1612433, _1612433), tc_HOL_Obool)), _1612439), hAPP(hAPP(c_Product__Type_OSigma(_1612433, _1612433), _1612441), hAPP(c_COMBK(tc_fun(_1612433, tc_HOL_Obool), _1612433), _1612441)))), -(_1612435 = _1612437), -(hBOOL(hAPP(hAPP(c_member(_1612433), _1612435), _1612441)))], (49659 ^ _774244) ^ [_1768870, _1768872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1768870), _1768872)), -(c_List_Oupt(_1768872, _1768870) = c_List_Olist_ONil(tc_Nat_Onat))], (41538 ^ _774244) ^ [_1571858, _1571860] : [-(c_FunDef_Oreduction__pair(_1571858, _1571860)), c_Wellfounded_Owf(_1571858, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1571858, _1571858), tc_HOL_Obool), tc_fun(tc_prod(_1571858, _1571858), tc_HOL_Obool)), _1571860)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571858, _1571858), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1571858, _1571858, _1571858), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1571858, _1571858), tc_HOL_Obool), tc_fun(tc_prod(_1571858, _1571858), tc_HOL_Obool)), _1571860)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1571858, _1571858), tc_HOL_Obool), tc_fun(tc_prod(_1571858, _1571858), tc_HOL_Obool)), _1571860))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1571858, _1571858), tc_HOL_Obool), tc_fun(tc_prod(_1571858, _1571858), tc_HOL_Obool)), _1571860)))], (34209 ^ _774244) ^ [_1396360, _1396362, _1396364, _1396366, _1396368] : [class_Groups_Ocomm__monoid__mult(_1396360), class_Rings_Odvd(_1396360), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396362), _1396364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1396362, tc_HOL_Obool)), _1396366), _1396364)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1396360), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396362, _1396360), _1396368), _1396366)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396362, _1396360), _1396368), _1396364))))], (50793 ^ _774244) ^ [_1793230, _1793232, _1793234] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1793230)), c_List_OdropWhile(_1793230, _1793232, _1793234))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1793230)), _1793234))))], (41510 ^ _774244) ^ [_1571186, _1571188, _1571190] : [c_Wellfounded_Owf(_1571186, _1571188), c_Wellfounded_Owf(_1571186, _1571190), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571186, _1571186), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1571186, _1571186, _1571186), _1571188), _1571190)), _1571188)), -(c_Wellfounded_Owf(_1571186, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571186, _1571186), tc_HOL_Obool)), _1571188), _1571190)))], (44779 ^ _774244) ^ [_1650460, _1650462, _1650464] : [class_Complete__Lattice_Ocomplete__lattice(_1650460), -(c_Complete__Lattice_OSup__class_OSup(_1650460, hAPP(hAPP(c_Set_Oinsert(_1650460), _1650462), hAPP(hAPP(c_Set_Oinsert(_1650460), _1650464), c_Orderings_Obot__class_Obot(tc_fun(_1650460, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1650460), _1650462), _1650464))], (25551 ^ _774244) ^ [_1219867, _1219869, _1219871] : [class_Divides_Osemiring__div(_1219867), 25554 ^ _774244 : [(25561 ^ _774244) ^ [] : [c_Divides_Odiv__class_Omod(_1219867, _1219871, _1219869) = c_Groups_Ozero__class_Ozero(_1219867), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1219867), _1219869), _1219871)))], (25555 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1219867), _1219869), _1219871)), -(c_Divides_Odiv__class_Omod(_1219867, _1219871, _1219869) = c_Groups_Ozero__class_Ozero(_1219867))]]], (36475 ^ _774244) ^ [_1448254, _1448256, _1448258] : [class_Lattices_Oboolean__algebra(_1448254), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1448254), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1448254), _1448256), _1448258)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1448254), hAPP(c_Groups_Ouminus__class_Ouminus(_1448254), _1448256)), hAPP(c_Groups_Ouminus__class_Ouminus(_1448254), _1448258)))], (35665 ^ _774244) ^ [_1430733, _1430735, _1430737, _1430739, _1430741, _1430743, _1430745] : [c_Equiv__Relations_Oequiv(_1430733, _1430735, _1430737), hBOOL(hAPP(hAPP(c_member(tc_fun(_1430733, tc_HOL_Obool)), _1430739), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1430733), _1430735), _1430737))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1430733, tc_HOL_Obool)), _1430741), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1430733), _1430735), _1430737))), hBOOL(hAPP(hAPP(c_member(_1430733), _1430743), _1430739)), hBOOL(hAPP(hAPP(c_member(_1430733), _1430745), _1430741)), 35684 ^ _774244 : [(35691 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1430733, _1430733)), hAPP(hAPP(c_Product__Type_OPair(_1430733, _1430733), _1430743), _1430745)), _1430737)), -(_1430739 = _1430741)], (35685 ^ _774244) ^ [] : [_1430739 = _1430741, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1430733, _1430733)), hAPP(hAPP(c_Product__Type_OPair(_1430733, _1430733), _1430743), _1430745)), _1430737)))]]], (42120 ^ _774244) ^ [_1586492, _1586494, _1586496, _1586498, _1586500, _1586502] : [hBOOL(hAPP(hAPP(c_member(_1586492), _1586494), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1586496, _1586498, tc_fun(_1586492, tc_HOL_Obool)), _1586500), _1586502))), 42125 ^ _774244 : [(42128 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1586492), _1586494), hAPP(hAPP(_1586500, 42123 ^ [_1586492, _1586494, _1586496, _1586498, _1586500, _1586502]), 42124 ^ [_1586492, _1586494, _1586496, _1586498, _1586500, _1586502]))))], (42126 ^ _774244) ^ [] : [-(_1586502 = hAPP(hAPP(c_Product__Type_OPair(_1586496, _1586498), 42123 ^ [_1586492, _1586494, _1586496, _1586498, _1586500, _1586502]), 42124 ^ [_1586492, _1586494, _1586496, _1586498, _1586500, _1586502]))]]], (11733 ^ _774244) ^ [_967889, _967891, _967893, _967895] : [class_Rings_Oordered__ring(_967889), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967889), _967891), _967893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967889), _967895), c_Groups_Ozero__class_Ozero(_967889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967889), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967889), _967895), _967893)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967889), _967895), _967891))))], (24725 ^ _774244) ^ [_1205741, _1205743, _1205745] : [-(c_HOL_OThe(tc_prod(_1205741, _1205743), _1205745) = c_HOL_OThe(tc_prod(_1205741, _1205743), hAPP(c_Product__Type_Oprod_Oprod__case(_1205741, _1205743, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1205743, tc_prod(_1205741, _1205743)), tc_fun(_1205743, tc_HOL_Obool), _1205741), hAPP(c_COMBB(tc_prod(_1205741, _1205743), tc_HOL_Obool, _1205743), _1205745)), c_Product__Type_OPair(_1205741, _1205743)))))], (15760 ^ _774244) ^ [_1041205, _1041207, _1041209] : [-(hBOOL(hAPP(_1041205, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041207), _1041209)))), 15763 ^ _774244 : [(15766 ^ _774244) ^ [] : [hBOOL(hAPP(_1041205, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15764 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041207), _1041209)))]], 15768 ^ _774244 : [(15771 ^ _774244) ^ [] : [hBOOL(hAPP(_1041205, 15767 ^ [_1041205, _1041207, _1041209]))], (15769 ^ _774244) ^ [] : [-(_1041207 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041209), 15767 ^ [_1041205, _1041207, _1041209]))]]], (28984 ^ _774244) ^ [_1290031, _1290033, _1290035] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290031, tc_HOL_Obool)), _1290033), _1290035) = c_Orderings_Obot__class_Obot(tc_fun(_1290031, tc_HOL_Obool)), 28987 ^ _774244 : [(28990 ^ _774244) ^ [] : [-(_1290035 = c_Orderings_Obot__class_Obot(tc_fun(_1290031, tc_HOL_Obool)))], (28988 ^ _774244) ^ [] : [-(_1290033 = c_Orderings_Obot__class_Obot(tc_fun(_1290031, tc_HOL_Obool)))]]], (48376 ^ _774244) ^ [_1740383, _1740385, _1740387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740383)), _1740385)), _1740387)), -(hAPP(hAPP(c_List_Odrop(_1740383), _1740387), _1740385) = c_List_Olist_ONil(_1740383))], (23341 ^ _774244) ^ [_1178122, _1178124, _1178126, _1178128, _1178130] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1178122, _1178124, _1178126), _1178128), _1178130) = hAPP(hAPP(_1178128, hAPP(c_Product__Type_Ofst(_1178122, _1178124), _1178130)), hAPP(c_Product__Type_Osnd(_1178122, _1178124), _1178130)))], (40565 ^ _774244) ^ [_1540797] : [-(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)), _1540797)))))], (994 ^ _774244) ^ [_789393, _789395] : [-(class_Rings_Oring__1__no__zero__divisors(_789393)), _789395 = _789393, class_Rings_Oring__1__no__zero__divisors(_789395)], (51355 ^ _774244) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (27800 ^ _774244) ^ [_1264925, _1264927, _1264929, _1264931] : [class_Lattices_Olattice(_1264925), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264925), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264925), _1264927), _1264929)), _1264931) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264925), _1264927), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264925), _1264929), _1264931)))], (34594 ^ _774244) ^ [_1404702, _1404704, _1404706, _1404708] : [c_Wellfounded_Omax__extp(_1404702, hAPP(hAPP(c_COMBC(_1404702, tc_fun(tc_prod(_1404702, _1404702), tc_HOL_Obool), tc_fun(_1404702, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404702, tc_fun(tc_fun(tc_prod(_1404702, _1404702), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1404702, _1404702), tc_HOL_Obool), tc_fun(_1404702, tc_HOL_Obool)), _1404702), c_COMBC(_1404702, tc_fun(tc_prod(_1404702, _1404702), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404702, tc_prod(_1404702, _1404702)), tc_fun(_1404702, tc_fun(tc_fun(tc_prod(_1404702, _1404702), tc_HOL_Obool), tc_HOL_Obool)), _1404702), hAPP(c_COMBB(tc_prod(_1404702, _1404702), tc_fun(tc_fun(tc_prod(_1404702, _1404702), tc_HOL_Obool), tc_HOL_Obool), _1404702), c_member(tc_prod(_1404702, _1404702)))), c_Product__Type_OPair(_1404702, _1404702)))), _1404704), _1404706, _1404708), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1404702, tc_HOL_Obool), tc_fun(_1404702, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1404702, tc_HOL_Obool), tc_fun(_1404702, tc_HOL_Obool)), _1404706), _1404708)), c_Wellfounded_Omax__ext(_1404702, _1404704))))], (29342 ^ _774244) ^ [_1296298, _1296300, _1296302, _1296304, _1296306] : [_1296298 = c_Orderings_Obot__class_Obot(tc_fun(_1296300, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296300, tc_fun(_1296302, tc_HOL_Obool)), _1296298), hAPP(hAPP(c_COMBB(tc_fun(_1296302, tc_HOL_Obool), tc_fun(_1296302, tc_HOL_Obool), _1296300), hAPP(c_Set_Oinsert(_1296302), _1296304)), _1296306)) = c_Orderings_Obot__class_Obot(tc_fun(_1296302, tc_HOL_Obool)))], (42515 ^ _774244) ^ [_1595254, _1595256] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595254, _1595254)), hAPP(hAPP(c_Product__Type_OPair(_1595254, _1595254), 42516 ^ [_1595254, _1595256]), 42516 ^ [_1595254, _1595256])), c_Transitive__Closure_Otrancl(_1595254, _1595256)))), -(c_Wellfounded_Oacyclic(_1595254, _1595256))], (43145 ^ _774244) ^ [_1608715, _1608717, _1608719, _1608721] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608715, _1608715)), hAPP(hAPP(c_Product__Type_OPair(_1608715, _1608715), _1608717), _1608719)), c_Transitive__Closure_Ortrancl(_1608715, _1608721))), -(_1608717 = _1608719), 43152 ^ _774244 : [(43155 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608715, _1608715)), hAPP(hAPP(c_Product__Type_OPair(_1608715, _1608715), _1608717), _1608719)), c_Transitive__Closure_Otrancl(_1608715, _1608721))))], (43153 ^ _774244) ^ [] : [_1608717 = _1608719]]], (41893 ^ _774244) ^ [_1581061, _1581063] : [c_Wellfounded_Owf(_1581061, _1581063), -(c_Wellfounded_Oacyclic(_1581061, _1581063))], (49485 ^ _774244) ^ [_1765296, _1765298] : [-(c_Random_Oselect__weight(_1765296, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1765296), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1765296, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1765296, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1765296)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1765298)) = c_Random_Oselect__weight(_1765296, _1765298))], (19379 ^ _774244) ^ [_1105044, _1105046] : [class_Rings_Olinordered__idom(_1105044), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1105044), hAPP(c_Groups_Oabs__class_Oabs(_1105044), _1105046)), 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(_1105044), _1105046), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (41377 ^ _774244) ^ [_1568479, _1568481, _1568483] : [c_Wellfounded_Owf(_1568479, _1568481), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568479, _1568479), tc_HOL_Obool)), _1568483), _1568481)), -(c_Wellfounded_Owf(_1568479, _1568483))], (28430 ^ _774244) ^ [_1277157, _1277159, _1277161] : [class_Orderings_Olinorder(_1277157), 28433 ^ _774244 : [(28440 ^ _774244) ^ [] : [_1277159 = _1277161, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1277157), _1277159) = hAPP(c_SetInterval_Oord__class_OatLeast(_1277157), _1277161))], (28434 ^ _774244) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1277157), _1277159) = hAPP(c_SetInterval_Oord__class_OatLeast(_1277157), _1277161), -(_1277159 = _1277161)]]], (29390 ^ _774244) ^ [_1297228, _1297230] : [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), _1297228, _1297230), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297228), _1297230))], (9524 ^ _774244) ^ [_930964, _930966, _930968, _930970] : [class_Rings_Olinordered__ring__strict(_930964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930964), c_Groups_Ozero__class_Ozero(_930964)), _930966)), 9531 ^ _774244 : [(9538 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930964), _930968), _930970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930964), _930966), _930968)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930964), _930966), _930970))))], (9532 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930964), _930966), _930968)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930964), _930966), _930970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930964), _930968), _930970)))]]], (14446 ^ _774244) ^ [_1016238, _1016240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1016238), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1016240), _1016238)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016238), _1016240) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5611 ^ _774244) ^ [_863581, _863583, _863585, _863587] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _863581)), _863583, _863585, _863587), -(c_Natural_Oevaln(c_Com_Ocom_OBODY(_863581), _863583, hAPP(c_Nat_OSuc, _863585), _863587))], (38549 ^ _774244) ^ [_1493773, _1493775, _1493777, _1493779, _1493781] : [-(c_Fun_Oinj__on(_1493773, _1493775, _1493777, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1493773, tc_HOL_Obool)), _1493779), _1493781))), c_Fun_Oinj__on(_1493773, _1493775, _1493777, _1493779), c_Fun_Oinj__on(_1493773, _1493775, _1493777, _1493781), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493775, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1493773, _1493775, _1493777), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493773, tc_HOL_Obool)), _1493779), _1493781))), hAPP(c_Set_Oimage(_1493773, _1493775, _1493777), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493773, tc_HOL_Obool)), _1493781), _1493779))) = c_Orderings_Obot__class_Obot(tc_fun(_1493775, tc_HOL_Obool))], (17765 ^ _774244) ^ [_1078325, _1078327] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078325)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078325)), _1078327)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1078325))), _1078327))], (23593 ^ _774244) ^ [_1183318] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1183318), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2890 ^ _774244) ^ [_818339, _818341, _818343, _818345, _818347, _818349, _818351, _818353] : [-(c_New__DSequence_Oneg__decr__bind(_818353, _818349, _818345, _818341) = c_New__DSequence_Oneg__decr__bind(_818351, _818347, _818343, _818339)), _818353 = _818351, _818349 = _818347, _818345 = _818343, _818341 = _818339], (44785 ^ _774244) ^ [_1650601, _1650603, _1650605] : [class_Complete__Lattice_Ocomplete__lattice(_1650601), hBOOL(hAPP(c_Finite__Set_Ofinite(_1650601), _1650603)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1650601), _1650605), c_Complete__Lattice_OSup__class_OSup(_1650601, _1650603)) = hAPP(hAPP(c_Finite__Set_Ofold(_1650601, _1650601, c_Lattices_Osemilattice__sup__class_Osup(_1650601)), _1650605), _1650603))], (50860 ^ _774244) ^ [_1794458, _1794460, _1794462, _1794464, _1794466] : [c_List_OdropWhile(_1794458, _1794460, _1794462) = hAPP(hAPP(c_List_Olist_OCons(_1794458), _1794464), _1794466), 50863 ^ _774244 : [(50866 ^ _774244) ^ [] : [hBOOL(hAPP(_1794460, _1794464))], (50864 ^ _774244) ^ [] : [-(_1794462 = hAPP(hAPP(c_List_Oappend(_1794458), c_List_OtakeWhile(_1794458, _1794460, _1794462)), hAPP(hAPP(c_List_Olist_OCons(_1794458), _1794464), _1794466)))]]], (47818 ^ _774244) ^ [_1725106, _1725108, _1725110, _1725112] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1725106), tc_List_Olist(_1725106))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1725106), tc_List_Olist(_1725106)), _1725108), _1725110)), c_List_Olex(_1725106, _1725112))), 47821 ^ _774244 : [(47824 ^ _774244) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725106)), _1725108) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725106)), _1725110))], (47822 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1725106), tc_List_Olist(_1725106))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1725106), tc_List_Olist(_1725106)), _1725108), _1725110)), c_List_Olexord(_1725106, _1725112))))]]], (38960 ^ _774244) ^ [_1503202, _1503204, _1503206, _1503208, _1503210] : [c_Fun_Oinj__on(_1503202, _1503204, _1503206, c_Orderings_Otop__class_Otop(tc_fun(_1503202, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1503204, tc_HOL_Obool)), _1503208), hAPP(c_Set_Oimage(_1503202, _1503204, _1503206), _1503210))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1503202, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1503202, _1503204, _1503206), _1503208)), _1503210)))], (18123 ^ _774244) ^ [] : [c_Int_OPls = c_Int_OMin], (23443 ^ _774244) ^ [_1180386, _1180388, _1180390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1180386, tc_HOL_Obool)), _1180388), _1180390)), 23446 ^ _774244 : [(23449 ^ _774244) ^ [] : [_1180388 = _1180390], (23447 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1180386, tc_HOL_Obool)), _1180388), _1180390)))]]], (37793 ^ _774244) ^ [_1478182, _1478184, _1478186] : [class_Lattices_Olattice(_1478182), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478182), _1478184)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478182), _1478186)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478182, tc_HOL_Obool)), _1478184), _1478186) = c_Orderings_Obot__class_Obot(tc_fun(_1478182, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1478182), c_Big__Operators_Olattice__class_OInf__fin(_1478182, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478182, tc_HOL_Obool)), _1478184), _1478186))), c_Big__Operators_Olattice__class_OInf__fin(_1478182, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478182, tc_HOL_Obool)), _1478184), _1478186))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1478182), c_Big__Operators_Olattice__class_OInf__fin(_1478182, _1478184)), c_Big__Operators_Olattice__class_OInf__fin(_1478182, _1478186)))], (39120 ^ _774244) ^ [_1506945, _1506947, _1506949, _1506951, _1506953, _1506955, _1506957] : [c_Big__Operators_Ocomm__monoid__big(_1506945, _1506947, _1506949, _1506951, _1506953), 39123 ^ _774244 : [(39130 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506947), _1506955))), -(hAPP(hAPP(_1506953, _1506957), _1506955) = _1506951)], (39124 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506947), _1506955)), -(hAPP(hAPP(_1506953, _1506957), _1506955) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1506945, _1506947, _1506949), _1506957), _1506951), _1506955))]]], (46128 ^ _774244) ^ [_1682733, _1682735] : [hBOOL(hAPP(c_List_Odistinct(_1682733), _1682735)), -(hAPP(c_Finite__Set_Ocard(_1682733), hAPP(c_List_Oset(_1682733), _1682735)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682733)), _1682735))], (7719 ^ _774244) ^ [_900105, _900107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _900105), _900107)), -(_900107 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900105), 7722 ^ [_900105, _900107])))], (13499 ^ _774244) ^ [_998973, _998975, _998977] : [class_Divides_Osemiring__div(_998973), -(c_Divides_Odiv__class_Omod(_998973, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998973), _998975), _998977), _998977) = c_Divides_Odiv__class_Omod(_998973, _998975, _998977))], (49458 ^ _774244) ^ [_1764620] : [-(c_List_Otranspose(_1764620, c_List_Olist_ONil(tc_List_Olist(_1764620))) = c_List_Olist_ONil(tc_List_Olist(_1764620)))], (30529 ^ _774244) ^ [_1319078, _1319080, _1319082, _1319084, _1319086, _1319088, _1319090, _1319092] : [c_Finite__Set_Ofolding__image__simple(_1319078, _1319080, _1319082, _1319084, _1319086, _1319088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319080), _1319090)), -(hAPP(_1319088, hAPP(hAPP(c_Set_Oinsert(_1319080), _1319092), _1319090)) = hAPP(hAPP(_1319082, hAPP(_1319086, _1319092)), hAPP(_1319088, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319080, tc_HOL_Obool)), _1319090), hAPP(hAPP(c_Set_Oinsert(_1319080), _1319092), c_Orderings_Obot__class_Obot(tc_fun(_1319080, tc_HOL_Obool)))))))], (3292 ^ _774244) ^ [_824814, _824816] : [_824816 = _824814, -(c_Int_Oring__1__class_OInts(_824816) = c_Int_Oring__1__class_OInts(_824814))], (5554 ^ _774244) ^ [_859967, _859969, _859971, _859973, _859975, _859977] : [-(c_COMBC(_859977, _859973, _859969) = c_COMBC(_859975, _859971, _859967)), _859977 = _859975, _859973 = _859971, _859969 = _859967], (49968 ^ _774244) ^ [_1774110, _1774112, _1774114, _1774116] : [class_Groups_Ocomm__monoid__add(_1774110), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1774110), _1774112), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1774114, _1774116))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1774110), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1774110), _1774112), c_List_Oupt(_1774114, _1774116))))], (6908 ^ _774244) ^ [_886040, _886042, _886044, _886046, _886048] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_886040, _886042), _886044, _886046, _886048), 6913 ^ _774244 : [(6916 ^ _774244) ^ [] : [hBOOL(hAPP(_886040, _886044))], (6914 ^ _774244) ^ [] : [-(_886048 = _886044)]], 6917 ^ _774244 : [(6923 ^ _774244) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_886040, _886042), 6919 ^ [_886040, _886042, _886044, _886046, _886048], _886046, _886048))], (6921 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_886042, _886044, _886046, 6919 ^ [_886040, _886042, _886044, _886046, _886048]))], (6918 ^ _774244) ^ [] : [-(hBOOL(hAPP(_886040, _886044)))]]], (24699 ^ _774244) ^ [_1204718, _1204720, _1204722, _1204724, _1204726] : [-(hAPP(c_New__DSequence_Oneg__bind(_1204718, _1204720, _1204722, _1204724), _1204726) = c_Lazy__Sequence_Ohb__bind(_1204718, _1204720, hAPP(_1204722, _1204726), hAPP(hAPP(c_COMBC(_1204718, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1204720))), _1204724), _1204726)))], (35845 ^ _774244) ^ [_1434861, _1434863, _1434865, _1434867] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434861, tc_HOL_Obool)), _1434863), _1434865), _1434867)), 35848 ^ _774244 : [(35851 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1434865, _1434867)))], (35849 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1434863, _1434867)))]]], (8056 ^ _774244) ^ [_906207, _906209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _906207)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _906209))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906207), _906209)))], (17301 ^ _774244) ^ [_1070213, _1070215] : [class_Power_Opower(_1070213), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1070213), _1070215), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1070213))], (20147 ^ _774244) ^ [_1119137, _1119139, _1119141, _1119143] : [class_Fields_Olinordered__field(_1119137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119137), _1119139), _1119141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119137), c_Groups_Ozero__class_Ozero(_1119137)), _1119143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119137), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119137), _1119139), _1119143)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119137), _1119141), _1119143))))], (17949 ^ _774244) ^ [_1081300, _1081302] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1081300), _1081302) = c_Groups_Oone__class_Oone(tc_Int_Oint), 17954 ^ _774244 : [(17957 ^ _774244) ^ [] : [-(_1081302 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (17955 ^ _774244) ^ [] : [-(_1081300 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 17958 ^ _774244 : [(17961 ^ _774244) ^ [] : [-(_1081302 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (17959 ^ _774244) ^ [] : [-(_1081300 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (2140 ^ _774244) ^ [_806322, _806324, _806326, _806328, _806330, _806332] : [-(c_Sum__Type_OProjl(_806332, _806328, _806324) = c_Sum__Type_OProjl(_806330, _806326, _806322)), _806332 = _806330, _806328 = _806326, _806324 = _806322], (48350 ^ _774244) ^ [_1739896, _1739898] : [hAPP(c_List_Orotate1(_1739896), _1739898) = c_List_Olist_ONil(_1739896), -(_1739898 = c_List_Olist_ONil(_1739896))], (35328 ^ _774244) ^ [_1422523, _1422525, _1422527, _1422529] : [-(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), _1422523), _1422525)), 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), _1422527), _1422529)), 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), _1422523), _1422527)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1422525), _1422529))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (45637 ^ _774244) ^ [_1671064] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1671064)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671064), tc_HOL_Obool))))], (37325 ^ _774244) ^ [_1466973, _1466975, _1466977, _1466979, _1466981, _1466983] : [c_Equiv__Relations_Ocongruent(_1466973, _1466975, _1466977, _1466979), hBOOL(hAPP(hAPP(c_member(tc_prod(_1466973, _1466973)), hAPP(hAPP(c_Product__Type_OPair(_1466973, _1466973), _1466981), _1466983)), _1466977)), -(hAPP(_1466979, _1466981) = hAPP(_1466979, _1466983))], (506 ^ _774244) ^ [_782087, _782089, _782091, _782093] : [-(c_Predicate_Oreflp(_782091, _782087)), c_Predicate_Oreflp(_782093, _782089), _782093 = _782091, _782089 = _782087], (14121 ^ _774244) ^ [_1010698, _1010700] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1010698)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1010700)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1010698), _1010700)))], (14382 ^ _774244) ^ [_1015084, _1015086, _1015088] : [class_Divides_Osemiring__div(_1015084), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1015084), c_Divides_Odiv__class_Omod(_1015084, _1015086, _1015088)), _1015088) = c_Groups_Ozero__class_Ozero(_1015084))], (23573 ^ _774244) ^ [_1182922, _1182924, _1182926] : [_1182924 = _1182926, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1182922, tc_HOL_Obool)), _1182924) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1182922, tc_HOL_Obool)), _1182926))], (36551 ^ _774244) ^ [_1450015, _1450017, _1450019, _1450021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1450015, tc_HOL_Obool)), _1450021), _1450017)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450015, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450015, tc_HOL_Obool)), _1450017), _1450019)), _1450021) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450015, tc_HOL_Obool)), _1450017), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450015, tc_HOL_Obool)), _1450019), _1450021)))], (38784 ^ _774244) ^ [_1499057, _1499059, _1499061, _1499063, _1499065, _1499067] : [hAPP(_1499057, _1499059) = _1499061, hBOOL(hAPP(hAPP(c_member(_1499063), _1499061), _1499065)), -(hBOOL(hAPP(hAPP(c_member(_1499067), _1499059), hAPP(c_Set_Ovimage(_1499067, _1499063, _1499057), _1499065))))], (6281 ^ _774244) ^ [_875075, _875077, _875079] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OBODY(_875077))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_875075, _875077, _875079))))], (40616 ^ _774244) ^ [_1541870, _1541872] : [-(hBOOL(hAPP(_1541872, 40617 ^ [_1541870, _1541872]))), -(hAPP(c_Set_OCollect(_1541870), _1541872) = c_Orderings_Obot__class_Obot(tc_fun(_1541870, tc_HOL_Obool)))], (41751 ^ _774244) ^ [_1577144, _1577146] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1577144, _1577146), 41752 ^ [_1577144, _1577146])), -(c_Wellfounded_OwfP(_1577144, _1577146))], (22182 ^ _774244) ^ [_1155707, _1155709, _1155711, _1155713] : [-(c_Nat_Onat_Onat__case(_1155707, _1155709, _1155711, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155713)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1155707), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1155713))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1155707, _1155707), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1155707, tc_fun(_1155707, _1155707)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1155707, tc_fun(_1155707, _1155707)), tc_Int_Oint), c_If(_1155707)), c_Nat__Numeral_Oneg)), _1155709)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1155707, tc_Int_Oint), _1155711), c_Int_Onat))))], (12608 ^ _774244) ^ [_983630, _983632, _983634] : [class_Rings_Olinordered__ring__strict(_983630), 12611 ^ _774244 : [(12620 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983630), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983630), _983632), _983632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983630), _983634), _983634))), c_Groups_Ozero__class_Ozero(_983630)))), _983632 = c_Groups_Ozero__class_Ozero(_983630), _983634 = c_Groups_Ozero__class_Ozero(_983630)], (12612 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983630), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983630), _983632), _983632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983630), _983634), _983634))), c_Groups_Ozero__class_Ozero(_983630))), 12615 ^ _774244 : [(12618 ^ _774244) ^ [] : [-(_983634 = c_Groups_Ozero__class_Ozero(_983630))], (12616 ^ _774244) ^ [] : [-(_983632 = c_Groups_Ozero__class_Ozero(_983630))]]]]], (19833 ^ _774244) ^ [_1113598, _1113600, _1113602, _1113604] : [class_Rings_Odivision__ring(_1113598), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113598), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1113598), _1113600), _1113602)), _1113604) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1113598), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113598), _1113600), _1113604)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113598), _1113602), _1113604)))], (16477 ^ _774244) ^ [_1054683, _1054685, _1054687] : [class_Groups_Oordered__ab__group__add__abs(_1054683), 16480 ^ _774244 : [(16489 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054683), hAPP(c_Groups_Oabs__class_Oabs(_1054683), _1054685)), _1054687))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054683), _1054685), _1054687)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054683), hAPP(c_Groups_Ouminus__class_Ouminus(_1054683), _1054685)), _1054687))], (16481 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054683), hAPP(c_Groups_Oabs__class_Oabs(_1054683), _1054685)), _1054687)), 16484 ^ _774244 : [(16487 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054683), hAPP(c_Groups_Ouminus__class_Ouminus(_1054683), _1054685)), _1054687)))], (16485 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054683), _1054685), _1054687)))]]]]], (23267 ^ _774244) ^ [_1176615, _1176617, _1176619] : [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), _1176615), _1176617))), -(hBOOL(hAPP(hAPP(_1176619, _1176615), _1176617))), 23274 ^ _774244 : [(23277 ^ _774244) ^ [] : [-(23273 ^ [_1176615, _1176617, _1176619] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1176619, 23273 ^ [_1176615, _1176617, _1176619]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 23272 ^ [_1176615, _1176617, _1176619], 23273 ^ [_1176615, _1176617, _1176619]))))], (23283 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1176619, 23272 ^ [_1176615, _1176617, _1176619]), 23273 ^ [_1176615, _1176617, _1176619]))], (23275 ^ _774244) ^ [] : [-(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), 23272 ^ [_1176615, _1176617, _1176619]), 23273 ^ [_1176615, _1176617, _1176619]))))]]], (7768 ^ _774244) ^ [_901129, _901131, _901133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _901129), _901131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _901129), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901133), _901131))))], (32180 ^ _774244) ^ [_1356818, _1356820, _1356822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1356818)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1356820), _1356822)), 32187 ^ _774244 : [(32188 ^ _774244) ^ [_1357014] : [32190 ^ _774244 : [(32196 ^ _774244) ^ [] : [-(_1357014 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32192 ^ [_1356818, _1356820, _1356822, _1357014]), 32189 ^ [_1356818, _1356820, _1356822, _1357014]))], (32194 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32192 ^ [_1356818, _1356820, _1356822, _1357014]), _1356822)))], (32191 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32189 ^ [_1356818, _1356820, _1356822, _1357014]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1356818))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1356820), _1357014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1356820), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1357014), _1356818))))]]], (33662 ^ _774244) ^ [_1385220, _1385222, _1385224] : [class_Orderings_Olinorder(_1385220), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385220), _1385222)), -(_1385222 = c_Orderings_Obot__class_Obot(tc_fun(_1385220, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385220), _1385224)), -(_1385224 = c_Orderings_Obot__class_Obot(tc_fun(_1385220, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1385220, c_Orderings_Oord__class_Omax(_1385220), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385220, tc_HOL_Obool)), _1385222), _1385224)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1385220), c_Big__Operators_Olattice_OSup__fin(_1385220, c_Orderings_Oord__class_Omax(_1385220), _1385222)), c_Big__Operators_Olattice_OSup__fin(_1385220, c_Orderings_Oord__class_Omax(_1385220), _1385224)))], (50631 ^ _774244) ^ [_1789950, _1789952, _1789954, _1789956, _1789958] : [-(c_Map_Omap__upds(_1789950, _1789952, _1789954, _1789956, _1789958) = c_Map_Omap__add(_1789950, _1789952, _1789954, c_Map_Omap__of(_1789950, _1789952, hAPP(c_List_Orev(tc_prod(_1789950, _1789952)), hAPP(hAPP(c_List_Ozip(_1789950, _1789952), _1789956), _1789958)))))], (13531 ^ _774244) ^ [_999643, _999645, _999647, _999649] : [class_Divides_Osemiring__div(_999643), -(c_Divides_Odiv__class_Omod(_999643, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999643), _999645), _999647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999643), _999645), _999649)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999643), _999645), c_Divides_Odiv__class_Omod(_999643, _999647, _999649)))], (26732 ^ _774244) ^ [_1243309, _1243311, _1243313, _1243315] : [class_Orderings_Olinorder(_1243309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243309), _1243311), _1243313)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1243309, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243309, _1243311), _1243315)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243309, _1243311), _1243313)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243309, _1243313), _1243315))], (8756 ^ _774244) ^ [_917205, _917207] : [class_Rings_Ocomm__semiring__1(_917205), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917205), c_Groups_Oone__class_Oone(_917205)), _917207) = _917207)], (33760 ^ _774244) ^ [_1387061, _1387063] : [class_Orderings_Olinorder(_1387061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387061), _1387063)), -(_1387063 = c_Orderings_Obot__class_Obot(tc_fun(_1387061, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1387061), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1387061), 33773 ^ [_1387061, _1387063]), 33774 ^ [_1387061, _1387063])), hAPP(hAPP(c_Set_Oinsert(_1387061), 33773 ^ [_1387061, _1387063]), hAPP(hAPP(c_Set_Oinsert(_1387061), 33774 ^ [_1387061, _1387063]), c_Orderings_Obot__class_Obot(tc_fun(_1387061, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1387061), c_Big__Operators_Olattice_OSup__fin(_1387061, c_Orderings_Oord__class_Omax(_1387061), _1387063)), _1387063)))], (45559 ^ _774244) ^ [_1668828, _1668830, _1668832, _1668834, _1668836] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1668828), tc_List_Olist(_1668830), tc_List_Olist(_1668832), hAPP(c_List_Omap(_1668828, _1668830), _1668834)), hAPP(c_List_Omap(_1668832, _1668828), _1668836)) = hAPP(c_List_Omap(_1668832, _1668830), hAPP(c_Fun_Ocomp(_1668828, _1668830, _1668832, _1668834), _1668836)))], (36357 ^ _774244) ^ [_1445522, _1445524, _1445526] : [class_Lattices_Osemilattice__inf(_1445522), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445522), _1445524), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445522), _1445524), _1445526)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445522), _1445524), _1445526))], (48308 ^ _774244) ^ [_1738935, _1738937] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738935)), hAPP(c_List_Orotate1(_1738935), _1738937)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738935)), _1738937))], (4952 ^ _774244) ^ [_850764, _850766, _850768, _850770, _850772, _850774] : [-(c_Product__Type_Oprod_Oprod__case(_850774, _850770, _850766) = c_Product__Type_Oprod_Oprod__case(_850772, _850768, _850764)), _850774 = _850772, _850770 = _850768, _850766 = _850764], (13318 ^ _774244) ^ [_995600, _995602, _995604] : [class_Lattices_Oboolean__algebra(_995600), 13321 ^ _774244 : [(13328 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995600), _995604), _995602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995600), hAPP(c_Groups_Ouminus__class_Ouminus(_995600), _995602)), hAPP(c_Groups_Ouminus__class_Ouminus(_995600), _995604))))], (13322 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995600), hAPP(c_Groups_Ouminus__class_Ouminus(_995600), _995602)), hAPP(c_Groups_Ouminus__class_Ouminus(_995600), _995604))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995600), _995604), _995602)))]]], (22965 ^ _774244) ^ [_1171255, _1171257] : [-(c_Divides_Odivmod__int__rel(_1171255, _1171257) = 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, _1171255))), 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), _1171257)))))), 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)), _1171257))), 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)), _1171257))))), 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)), _1171257)))), 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), _1171257))), 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))))))))], (27155 ^ _774244) ^ [_1252073, _1252075, _1252077, _1252079] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252073), _1252075)), 27158 ^ _774244 : [(27159 ^ _774244) ^ [_1252227] : [27161 ^ _774244 : [(27167 ^ _774244) ^ [] : [-(_1252227 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27163 ^ [_1252073, _1252075, _1252077, _1252079, _1252227]), 27160 ^ [_1252073, _1252075, _1252077, _1252079, _1252227]))], (27165 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27163 ^ [_1252073, _1252075, _1252077, _1252079, _1252227]), _1252077)))], (27162 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27160 ^ [_1252073, _1252075, _1252077, _1252079, _1252227]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1252075))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252073), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1252227), _1252079))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252073), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1252227), _1252075)), _1252079))))]]], (35456 ^ _774244) ^ [_1425720, _1425722, _1425724, _1425726, _1425728, _1425730] : [c_Finite__Set_Ofolding(_1425720, _1425722, _1425724, _1425726), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425720), _1425728)), -(hAPP(_1425726, hAPP(hAPP(c_Set_Oinsert(_1425720), _1425730), _1425728)) = hAPP(c_Fun_Ocomp(_1425722, _1425722, _1425722, hAPP(_1425726, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1425720, tc_HOL_Obool)), _1425728), hAPP(hAPP(c_Set_Oinsert(_1425720), _1425730), c_Orderings_Obot__class_Obot(tc_fun(_1425720, tc_HOL_Obool)))))), hAPP(_1425724, _1425730)))], (15654 ^ _774244) ^ [_1038652, _1038654] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1038652, _1038654) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1038652), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1038652), _1038654)), _1038654)))], (49988 ^ _774244) ^ [_1774568, _1774570, _1774572] : [class_Orderings_Olinorder(_1774568), 49991 ^ _774244 : [(50004 ^ _774244) ^ [] : [-(c_List_Olinorder__class_Osorted(_1774568, hAPP(hAPP(c_List_Olist_OCons(_1774568), _1774570), _1774572))), 50008 ^ _774244 : [(50011 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1774568), _1774570), 50007 ^ [_1774568, _1774570, _1774572]))], (50009 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774568), 50007 ^ [_1774568, _1774570, _1774572]), hAPP(c_List_Oset(_1774568), _1774572))))]], c_List_Olinorder__class_Osorted(_1774568, _1774572)], (49992 ^ _774244) ^ [] : [c_List_Olinorder__class_Osorted(_1774568, hAPP(hAPP(c_List_Olist_OCons(_1774568), _1774570), _1774572)), 49995 ^ _774244 : [(49996 ^ _774244) ^ [_1774736] : [hBOOL(hAPP(hAPP(c_member(_1774568), _1774736), hAPP(c_List_Oset(_1774568), _1774572))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1774568), _1774570), _1774736)))], (50002 ^ _774244) ^ [] : [-(c_List_Olinorder__class_Osorted(_1774568, _1774572))]]]]], (12055 ^ _774244) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34914 ^ _774244) ^ [_1412714, _1412716] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1412714), _1412716)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1412714, tc_HOL_Obool)), hAPP(c_Set_OPow(_1412714), _1412716)) = 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(_1412714), _1412716)))], (30158 ^ _774244) ^ [_1311432, _1311434, _1311436, _1311438, _1311440] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1311432), hAPP(c_Set_Oimage(_1311434, _1311432, _1311436), c_Orderings_Otop__class_Otop(tc_fun(_1311434, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1311438), hAPP(c_Set_Oimage(_1311434, _1311438, hAPP(hAPP(c_COMBB(_1311432, _1311438, _1311434), _1311440), _1311436)), c_Orderings_Otop__class_Otop(tc_fun(_1311434, tc_HOL_Obool))))))], (592 ^ _774244) ^ [_783444, _783446, _783448, _783450, _783452, _783454, _783456, _783458] : [-(c_Equiv__Relations_Ocongruent(_783456, _783452, _783448, _783444)), c_Equiv__Relations_Ocongruent(_783458, _783454, _783450, _783446), _783458 = _783456, _783454 = _783452, _783450 = _783448, _783446 = _783444], (9406 ^ _774244) ^ [_928798, _928800, _928802] : [class_Rings_Olinordered__ring__strict(_928798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928798), _928800), c_Groups_Ozero__class_Ozero(_928798))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928798), _928802), c_Groups_Ozero__class_Ozero(_928798))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928798), c_Groups_Ozero__class_Ozero(_928798)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928798), _928800), _928802))))], (5644 ^ _774244) ^ [_864211, _864213] : [c_Com_Ocom_OBODY(_864211) = c_Com_Ocom_OBODY(_864213), -(_864211 = _864213)], (51407 ^ _774244) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (10059 ^ _774244) ^ [_940014] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940014), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _940014)], (27932 ^ _774244) ^ [_1267505, _1267507, _1267509, _1267511] : [class_Lattices_Osemilattice__sup(_1267505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267505), _1267507), _1267509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267505), _1267507), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267505), _1267511), _1267509))))], (27694 ^ _774244) ^ [_1262513, _1262515, _1262517, _1262519] : [hBOOL(hAPP(_1262513, _1262515)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262517, tc_HOL_Obool)), _1262513), _1262519), _1262515)))], (21966 ^ _774244) ^ [_1151712] : [c_Code__Numeral_OSuc__code__numeral(_1151712) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (41661 ^ _774244) ^ [_1574706, _1574708, _1574710, _1574712] : [41662 ^ _774244 : [(41663 ^ _774244) ^ [_1574781] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574710, _1574706)), hAPP(hAPP(c_Product__Type_OPair(_1574710, _1574706), _1574781), _1574708)), _1574712))]], -(hBOOL(hAPP(hAPP(c_member(_1574706), _1574708), hAPP(c_Relation_ORange(_1574710, _1574706), _1574712))))], (35334 ^ _774244) ^ [_1422735, _1422737, _1422739, _1422741] : [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), _1422735), _1422737)), 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), _1422739), _1422741)), 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), _1422735), _1422741)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1422739), _1422737))))], (38662 ^ _774244) ^ [_1496416] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1496416))], (13066 ^ _774244) ^ [_991199, _991201, _991203] : [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), _991199), _991201)), _991203))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _991203), _991199)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991201)))], (32338 ^ _774244) ^ [_1359936, _1359938, _1359940, _1359942, _1359944] : [class_Groups_Oordered__comm__monoid__add(_1359936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359938), _1359940)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1359938, tc_HOL_Obool)), _1359942), _1359940)), 32352 ^ _774244 : [(32355 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359936), c_Groups_Ozero__class_Ozero(_1359936)), hAPP(_1359944, 32351 ^ [_1359936, _1359938, _1359940, _1359942, _1359944])))], (32353 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359938), 32351 ^ [_1359936, _1359938, _1359940, _1359942, _1359944]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359938, tc_HOL_Obool)), _1359940), _1359942))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359936), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359938, _1359936), _1359944), _1359942)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359938, _1359936), _1359944), _1359940))))], (50364 ^ _774244) ^ [_1783027, _1783029] : [-(_1783027 = c_List_Olist_ONil(_1783029)), -(hAPP(c_List_Ohd(_1783029), hAPP(c_List_Orev(_1783029), _1783027)) = c_List_Olast(_1783029, _1783027))], (7135 ^ _774244) ^ [_890122, _890124] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OAss(_890122, _890124)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41591 ^ _774244) ^ [] : [-(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))))], (39886 ^ _774244) ^ [_1526816, _1526818, _1526820, _1526822, _1526824] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526816, _1526818)), _1526820), hAPP(hAPP(c_Product__Type_OSigma(_1526816, _1526818), _1526822), _1526824))), 39890 ^ _774244 : [(39896 ^ _774244) ^ [] : [-(_1526820 = hAPP(hAPP(c_Product__Type_OPair(_1526816, _1526818), 39889 ^ [_1526816, _1526818, _1526820, _1526822, _1526824]), 39892 ^ [_1526816, _1526818, _1526820, _1526822, _1526824]))], (39894 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526818), 39892 ^ [_1526816, _1526818, _1526820, _1526822, _1526824]), hAPP(_1526824, 39889 ^ [_1526816, _1526818, _1526820, _1526822, _1526824]))))], (39891 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526816), 39889 ^ [_1526816, _1526818, _1526820, _1526822, _1526824]), _1526822)))]]], (14584 ^ _774244) ^ [_1018458, _1018460] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018458), _1018460) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1018460 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14593 ^ _774244 : [(14596 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018458), _1018460)))], (14594 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018458)))]], 14597 ^ _774244 : [(14600 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018460), _1018458)))], (14598 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018458), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (51133 ^ _774244) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (39873 ^ _774244) ^ [_1526479, _1526481, _1526483, _1526485] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526479), _1526481)), 39879 ^ _774244 : [(39882 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526483), hAPP(_1526485, 39878 ^ [_1526479, _1526481, _1526483, _1526485])))], (39880 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526479), 39878 ^ [_1526479, _1526481, _1526483, _1526485]), _1526481)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1526479, _1526483)), hAPP(hAPP(c_Product__Type_OSigma(_1526479, _1526483), _1526481), _1526485)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526479, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1526483, tc_HOL_Obool), tc_Nat_Onat, _1526479), c_Finite__Set_Ocard(_1526483)), _1526485)), _1526481))], (28252 ^ _774244) ^ [_1273647, _1273649, _1273651, _1273653] : [class_Orderings_Olinorder(_1273647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273647), _1273649), _1273651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273647), _1273651), _1273653)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273647, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1273647, _1273649), _1273651)), c_SetInterval_Oord__class_OatLeastAtMost(_1273647, _1273651, _1273653)) = c_SetInterval_Oord__class_OatLeastAtMost(_1273647, _1273649, _1273653))], (10756 ^ _774244) ^ [_950955, _950957, _950959] : [class_Orderings_Oorder(_950955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950955), _950957), _950959)), -(_950959 = _950957), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950955), _950957), _950959)))], (31779 ^ _774244) ^ [_1348068, _1348070, _1348072, _1348074] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1348068, tc_HOL_Obool)), _1348070), hAPP(hAPP(c_Set_Oinsert(_1348068), _1348072), _1348074)))), 31782 ^ _774244 : [(31785 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1348068, tc_HOL_Obool)), _1348070), _1348074))], (31783 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1348068), _1348072), _1348074)))]], 31786 ^ _774244 : [(31789 ^ _774244) ^ [] : [31790 ^ _774244 : [(31793 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1348068, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1348068, tc_HOL_Obool)), _1348070), hAPP(hAPP(c_Set_Oinsert(_1348068), _1348072), c_Orderings_Obot__class_Obot(tc_fun(_1348068, tc_HOL_Obool))))), _1348074))], (31791 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1348068), _1348072), _1348070)))]], 31794 ^ _774244 : [(31797 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1348068, tc_HOL_Obool)), _1348070), _1348074))], (31795 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1348068), _1348072), _1348070))]]], (31787 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1348068), _1348072), _1348074))]]], (28495 ^ _774244) ^ [_1278380, _1278382, _1278384, _1278386] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1278380, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1278382)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1278380, tc_HOL_Obool), tc_Nat_Onat), _1278384), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1278386))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1278380, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1278386, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1278382), _1278386))), _1278384))], (19195 ^ _774244) ^ [_1101816, _1101818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101816), _1101818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1101816)), c_Int_OBit0(_1101818))))], (27510 ^ _774244) ^ [_1259313] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1259313)) = _1259313)], (33172 ^ _774244) ^ [_1374958, _1374960] : [class_Orderings_Olinorder(_1374958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374958), _1374960)), -(_1374960 = c_Orderings_Obot__class_Obot(tc_fun(_1374958, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1374958), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1374958), 33185 ^ [_1374958, _1374960]), 33186 ^ [_1374958, _1374960])), hAPP(hAPP(c_Set_Oinsert(_1374958), 33185 ^ [_1374958, _1374960]), hAPP(hAPP(c_Set_Oinsert(_1374958), 33186 ^ [_1374958, _1374960]), c_Orderings_Obot__class_Obot(tc_fun(_1374958, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1374958), c_Big__Operators_Olinorder__class_OMax(_1374958, _1374960)), _1374960)))], (15572 ^ _774244) ^ [_1037053, _1037055, _1037057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037053), _1037055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037057), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037055), _1037057)), _1037053))))], (36039 ^ _774244) ^ [_1438345, _1438347, _1438349] : [class_Lattices_Olattice(_1438345), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438345), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1438345), _1438347), _1438349)), _1438347)))], (44040 ^ _774244) ^ [_1632925] : [-(c_Relation_Orefl__on(_1632925, c_Orderings_Otop__class_Otop(tc_fun(_1632925, tc_HOL_Obool)), c_Relation_OId(_1632925)))], (50581 ^ _774244) ^ [_1789068, _1789070, _1789072] : [class_Orderings_Olinorder(_1789068), c_List_Olinorder__class_Osorted(_1789068, _1789070), -(c_List_Olinorder__class_Osorted(_1789068, c_List_OtakeWhile(_1789068, _1789072, _1789070)))], (21968 ^ _774244) ^ [_1151746] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1151746)], (34630 ^ _774244) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (51193 ^ _774244) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (30224 ^ _774244) ^ [_1312714, _1312716, _1312718] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312714), _1312716)), 30227 ^ _774244 : [(30247 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1312714, tc_Nat_Onat), _1312718), _1312716) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 30248 ^ _774244 : [(30249 ^ _774244) ^ [_1313195] : [hBOOL(hAPP(hAPP(c_member(_1312714), _1313195), _1312716)), hAPP(_1312718, _1313195) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 30257 ^ _774244 : [(30262 ^ _774244) ^ [] : [hAPP(_1312718, 30256 ^ [_1312714, _1312716, _1312718, _1313195]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30260 ^ _774244) ^ [] : [_1313195 = 30256 ^ [_1312714, _1312716, _1312718, _1313195]], (30258 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1312714), 30256 ^ [_1312714, _1312716, _1312718, _1313195]), _1312716)))]]]]], (30228 ^ _774244) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1312714, tc_Nat_Onat), _1312718), _1312716) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 30232 ^ _774244 : [(30237 ^ _774244) ^ [_1313034] : [hBOOL(hAPP(hAPP(c_member(_1312714), _1313034), _1312716)), -(30231 ^ [_1312714, _1312716, _1312718] = _1313034), -(hAPP(_1312718, _1313034) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30235 ^ _774244) ^ [] : [-(hAPP(_1312718, 30231 ^ [_1312714, _1312716, _1312718]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (30233 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1312714), 30231 ^ [_1312714, _1312716, _1312718]), _1312716)))]]]]], (45982 ^ _774244) ^ [_1678732, _1678734, _1678736, _1678738, _1678740, _1678742, _1678744, _1678746] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1678732, _1678734), _1678736), _1678738), hAPP(hAPP(c_List_Ozip(_1678732, _1678734), _1678740), hAPP(hAPP(c_List_Omap(_1678742, _1678734), _1678744), _1678746))) = hAPP(hAPP(c_List_Omap(tc_prod(_1678732, _1678742), _1678736), hAPP(c_Product__Type_Oprod_Oprod__case(_1678732, _1678742, _1678736), hAPP(hAPP(c_COMBB(tc_fun(_1678742, tc_prod(_1678732, _1678734)), tc_fun(_1678742, _1678736), _1678732), hAPP(c_COMBB(tc_prod(_1678732, _1678734), _1678736, _1678742), _1678738)), hAPP(hAPP(c_COMBC(_1678732, tc_fun(_1678742, _1678734), tc_fun(_1678742, tc_prod(_1678732, _1678734))), hAPP(hAPP(c_COMBB(tc_fun(_1678734, tc_prod(_1678732, _1678734)), tc_fun(tc_fun(_1678742, _1678734), tc_fun(_1678742, tc_prod(_1678732, _1678734))), _1678732), c_COMBB(_1678734, tc_prod(_1678732, _1678734), _1678742)), c_Product__Type_OPair(_1678732, _1678734))), _1678744)))), hAPP(hAPP(c_List_Ozip(_1678732, _1678742), _1678740), _1678746)))], (11975 ^ _774244) ^ [_972229, _972231, _972233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972229), _972231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _972233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972229), _972233)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972231), _972233))))], (2026 ^ _774244) ^ [_804145, _804147, _804149, _804151, _804153, _804155, _804157, _804159, _804161, _804163, _804165, _804167, _804169, _804171, _804173, _804175, _804177, _804179, _804181, _804183] : [-(c_Com_Ocom_Ocom__case(_804183, _804179, _804175, _804171, _804167, _804163, _804159, _804155, _804151, _804147) = c_Com_Ocom_Ocom__case(_804181, _804177, _804173, _804169, _804165, _804161, _804157, _804153, _804149, _804145)), _804183 = _804181, _804179 = _804177, _804175 = _804173, _804171 = _804169, _804167 = _804165, _804163 = _804161, _804159 = _804157, _804155 = _804153, _804151 = _804149, _804147 = _804145], (47383 ^ _774244) ^ [_1715220, _1715222, _1715224] : [class_Orderings_Olinorder(_1715220), hBOOL(hAPP(hAPP(c_member(_1715220), _1715222), hAPP(c_List_Oset(_1715220), _1715224))), -(c_List_Olinorder__class_Oinsort__insert__key(_1715220, _1715220, c_COMBI(_1715220), _1715222, _1715224) = _1715224)], (8548 ^ _774244) ^ [_913773, _913775, _913777] : [class_Rings_Olinordered__semidom(_913773), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913773), c_Groups_Oone__class_Oone(_913773)), _913775)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913773), c_Groups_Oone__class_Oone(_913773)), _913777)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913773), c_Groups_Oone__class_Oone(_913773)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913773), _913775), _913777))))], (24577 ^ _774244) ^ [_1202190] : [-(c_Nitpick_Oone__frac(_1202190) = c_Nitpick_OAbs__Frac(_1202190, 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))))], (34341 ^ _774244) ^ [_1399271, _1399273, _1399275, _1399277, _1399279] : [class_Groups_Ocomm__monoid__mult(_1399271), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399273), _1399275)), hBOOL(hAPP(hAPP(c_member(_1399273), _1399277), _1399275)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399273, _1399271), _1399279), _1399275) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399271), hAPP(_1399279, _1399277)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399273, _1399271), _1399279), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399273, tc_HOL_Obool)), _1399275), hAPP(hAPP(c_Set_Oinsert(_1399273), _1399277), c_Orderings_Obot__class_Obot(tc_fun(_1399273, tc_HOL_Obool)))))))], (38810 ^ _774244) ^ [_1499710, _1499712, _1499714, _1499716, _1499718] : [hBOOL(hAPP(_1499716, hAPP(_1499714, _1499718))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1499710, _1499712, _1499714), _1499716), _1499718)))], (24391 ^ _774244) ^ [_1198366, _1198368] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1198366), hAPP(c_Nat_OSuc, _1198368)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1198368), 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)), _1198368)), _1198366))], (40643 ^ _774244) ^ [_1542335, _1542337, _1542339] : [hBOOL(hAPP(_1542339, _1542337)), -(hBOOL(hAPP(hAPP(c_member(_1542335), _1542337), hAPP(c_Set_OCollect(_1542335), _1542339))))], (27442 ^ _774244) ^ [_1258201, _1258203] : [class_Groups_Oordered__ab__group__add(_1258201), -(hAPP(c_Set_Oimage(_1258201, _1258201, c_Groups_Ouminus__class_Ouminus(_1258201)), hAPP(c_SetInterval_Oord__class_OlessThan(_1258201), _1258203)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1258201), hAPP(c_Groups_Ouminus__class_Ouminus(_1258201), _1258203)))], (48819 ^ _774244) ^ [_1749972, _1749974, _1749976] : [class_Orderings_Olinorder(_1749972), -(c_Big__Operators_Olattice_OSup__fin(_1749972, c_Orderings_Oord__class_Omax(_1749972), hAPP(c_List_Oset(_1749972), hAPP(hAPP(c_List_Olist_OCons(_1749972), _1749974), _1749976))) = hAPP(c_List_Ofoldl(_1749972, _1749972, c_Orderings_Oord__class_Omax(_1749972), _1749974), _1749976))], (45458 ^ _774244) ^ [_1666557, _1666559, _1666561, _1666563, _1666565, _1666567, _1666569] : [c_Fun_Oinj__on(_1666557, _1666559, _1666561, c_Orderings_Otop__class_Otop(tc_fun(_1666557, tc_HOL_Obool))), hAPP(c_Map_Omap__of(_1666557, _1666563, _1666565), _1666567) = hAPP(c_Option_Ooption_OSome(_1666563), _1666569), -(hAPP(c_Map_Omap__of(_1666559, _1666563, hAPP(hAPP(c_List_Omap(tc_prod(_1666557, _1666563), tc_prod(_1666559, _1666563)), hAPP(c_Product__Type_Oprod_Oprod__case(_1666557, _1666563, tc_prod(_1666559, _1666563)), hAPP(hAPP(c_COMBB(_1666559, tc_fun(_1666563, tc_prod(_1666559, _1666563)), _1666557), c_Product__Type_OPair(_1666559, _1666563)), _1666561))), _1666565)), hAPP(_1666561, _1666567)) = hAPP(c_Option_Ooption_OSome(_1666563), _1666569))], (11865 ^ _774244) ^ [_970394] : [class_Rings_Olinordered__semidom(_970394), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970394), c_Groups_Ozero__class_Ozero(_970394)), c_Groups_Oone__class_Oone(_970394))))], (7800 ^ _774244) ^ [_901604, _901606, _901608, _901610] : [hAPP(c_Sum__Type_OInr(_901604, _901606), _901608) = hAPP(c_Sum__Type_OInr(_901604, _901606), _901610), -(_901608 = _901610)], (19277 ^ _774244) ^ [_1103326] : [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), _1103326))), 19280 ^ _774244 : [(19283 ^ _774244) ^ [] : [-(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(_1103326)))))], (19281 ^ _774244) ^ [] : [-(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(_1103326)))))]]], (21511 ^ _774244) ^ [_1143347, _1143349, _1143351, _1143353] : [class_Fields_Olinordered__field__inverse__zero(_1143347), class_Int_Onumber(_1143347), 21518 ^ _774244 : [(21519 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), hAPP(c_Int_Onumber__class_Onumber__of(_1143347), _1143349)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143347), _1143351), _1143353))), 21522 ^ _774244 : [(21529 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), c_Groups_Ozero__class_Ozero(_1143347)), _1143353))), 21532 ^ _774244 : [(21539 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), _1143353), c_Groups_Ozero__class_Ozero(_1143347)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), hAPP(c_Int_Onumber__class_Onumber__of(_1143347), _1143349)), c_Groups_Ozero__class_Ozero(_1143347))))], (21533 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), _1143353), c_Groups_Ozero__class_Ozero(_1143347))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), _1143351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143347), hAPP(c_Int_Onumber__class_Onumber__of(_1143347), _1143349)), _1143353))))]]], (21523 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), c_Groups_Ozero__class_Ozero(_1143347)), _1143353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143347), hAPP(c_Int_Onumber__class_Onumber__of(_1143347), _1143349)), _1143353)), _1143351)))]]], (21545 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), hAPP(c_Int_Onumber__class_Onumber__of(_1143347), _1143349)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143347), _1143351), _1143353)))), 21548 ^ _774244 : [(21551 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143347), hAPP(c_Int_Onumber__class_Onumber__of(_1143347), _1143349)), _1143353)), _1143351))], (21549 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), c_Groups_Ozero__class_Ozero(_1143347)), _1143353)))]], 21552 ^ _774244 : [(21555 ^ _774244) ^ [] : [21556 ^ _774244 : [(21559 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), _1143351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143347), hAPP(c_Int_Onumber__class_Onumber__of(_1143347), _1143349)), _1143353)))], (21557 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), _1143353), c_Groups_Ozero__class_Ozero(_1143347))))]], 21560 ^ _774244 : [(21563 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), hAPP(c_Int_Onumber__class_Onumber__of(_1143347), _1143349)), c_Groups_Ozero__class_Ozero(_1143347)))], (21561 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), _1143353), c_Groups_Ozero__class_Ozero(_1143347)))]]], (21553 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143347), c_Groups_Ozero__class_Ozero(_1143347)), _1143353))]]]]], (42562 ^ _774244) ^ [_1596198, _1596200, _1596202, _1596204] : [class_Lattices_Osemilattice__sup(_1596198), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596198), _1596200)), hBOOL(hAPP(hAPP(c_member(_1596198), _1596202), _1596200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1596198), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1596198), _1596202), _1596204)), hAPP(hAPP(c_Finite__Set_Ofold(_1596198, _1596198, c_Lattices_Osemilattice__sup__class_Osup(_1596198)), _1596204), _1596200))))], (13555 ^ _774244) ^ [_1000199, _1000201, _1000203, _1000205] : [class_Divides_Oring__div(_1000199), c_Divides_Odiv__class_Omod(_1000199, _1000201, _1000203) = c_Divides_Odiv__class_Omod(_1000199, _1000205, _1000203), -(c_Divides_Odiv__class_Omod(_1000199, hAPP(c_Groups_Ouminus__class_Ouminus(_1000199), _1000201), _1000203) = c_Divides_Odiv__class_Omod(_1000199, hAPP(c_Groups_Ouminus__class_Ouminus(_1000199), _1000205), _1000203))], (24905 ^ _774244) ^ [_1209102, _1209104, _1209106] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209102), _1209104)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209104), _1209102))), 24920 ^ _774244 : [(24923 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209106), _1209102))], (24921 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209102), _1209106)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209104), _1209106)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209106), _1209104)))], (47293 ^ _774244) ^ [_1713278, _1713280, _1713282, _1713284] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713278)), hAPP(hAPP(c_List_Olist__update(_1713278, _1713280), _1713282), _1713284)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713278)), _1713280))], (26504 ^ _774244) ^ [_1238343, _1238345, _1238347, _1238349, _1238351] : [class_Groups_Oab__group__add(_1238343), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238345, _1238343), hAPP(hAPP(c_COMBS(_1238345, _1238343, _1238343), hAPP(hAPP(c_COMBB(_1238343, tc_fun(_1238343, _1238343), _1238345), c_Groups_Ominus__class_Ominus(_1238343)), _1238347)), _1238349)), _1238351) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1238343), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238345, _1238343), _1238347), _1238351)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238345, _1238343), _1238349), _1238351)))], (35853 ^ _774244) ^ [_1435006, _1435008, _1435010, _1435012] : [hBOOL(hAPP(_1435006, _1435008)), hBOOL(hAPP(_1435010, _1435008)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435012, tc_HOL_Obool)), _1435006), _1435010), _1435008)))], (11022 ^ _774244) ^ [_955482, _955484, _955486] : [class_Groups_Oordered__ab__group__add(_955482), 11025 ^ _774244 : [(11032 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955482), hAPP(c_Groups_Ouminus__class_Ouminus(_955482), _955486)), _955484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955482), hAPP(c_Groups_Ouminus__class_Ouminus(_955482), _955484)), _955486)))], (11026 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955482), hAPP(c_Groups_Ouminus__class_Ouminus(_955482), _955484)), _955486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955482), hAPP(c_Groups_Ouminus__class_Ouminus(_955482), _955486)), _955484)))]]], (51151 ^ _774244) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (39614 ^ _774244) ^ [_1518891, _1518893, _1518895, _1518897] : [39615 ^ _774244 : [(39618 ^ _774244) ^ [] : [_1518897 = c_Orderings_Obot__class_Obot(tc_fun(_1518893, tc_HOL_Obool))], (39616 ^ _774244) ^ [] : [_1518895 = c_Orderings_Obot__class_Obot(tc_fun(_1518891, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1518891, _1518893), _1518895), hAPP(c_COMBK(tc_fun(_1518893, tc_HOL_Obool), _1518891), _1518897)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518891, _1518893), tc_HOL_Obool)))], (43325 ^ _774244) ^ [_1612893, _1612895, _1612897, _1612899] : [class_Complete__Lattice_Ocomplete__lattice(_1612893), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612895), _1612897)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612895, _1612893), _1612897), _1612899) = hAPP(hAPP(c_Finite__Set_Ofold(_1612895, _1612893, hAPP(hAPP(c_COMBB(_1612893, tc_fun(_1612893, _1612893), _1612895), c_Lattices_Osemilattice__inf__class_Oinf(_1612893)), _1612899)), c_Orderings_Otop__class_Otop(_1612893)), _1612897))], (35006 ^ _774244) ^ [_1414878, _1414880, _1414882, _1414884] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1414878, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414880, tc_fun(tc_fun(_1414878, tc_HOL_Obool), tc_HOL_Obool)), _1414882), hAPP(hAPP(c_COMBB(tc_fun(_1414878, tc_HOL_Obool), tc_fun(tc_fun(_1414878, tc_HOL_Obool), tc_HOL_Obool), _1414880), c_Set_OPow(_1414878)), _1414884))), hAPP(c_Set_OPow(_1414878), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414880, tc_fun(_1414878, tc_HOL_Obool)), _1414882), _1414884)))))], (42175 ^ _774244) ^ [_1587752, _1587754] : [-(c_Hilbert__Choice_OEps(_1587752, hAPP(hAPP(c_COMBC(_1587752, _1587752, tc_HOL_Obool), c_fequal), _1587754)) = _1587754)], (45970 ^ _774244) ^ [_1678338, _1678340, _1678342, _1678344] : [hBOOL(hAPP(c_List_Odistinct(_1678338), _1678340)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1678342, _1678338)), hAPP(hAPP(c_List_Ozip(_1678342, _1678338), _1678344), _1678340))))], (35296 ^ _774244) ^ [_1421701, _1421703, _1421705, _1421707, _1421709] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1421705, _1421701)), hAPP(hAPP(c_Product__Type_OPair(_1421705, _1421701), _1421709), _1421703)), _1421707)), -(hBOOL(hAPP(hAPP(c_member(_1421701), _1421703), hAPP(c_Relation_OImage(_1421705, _1421701, _1421707), hAPP(hAPP(c_Set_Oinsert(_1421705), _1421709), c_Orderings_Obot__class_Obot(tc_fun(_1421705, tc_HOL_Obool)))))))], (38942 ^ _774244) ^ [_1502729, _1502731, _1502733, _1502735] : [-(hBOOL(hAPP(hAPP(c_member(_1502729), _1502731), _1502733))), -(hAPP(c_Set_Ovimage(_1502735, _1502729, hAPP(c_COMBK(_1502729, _1502735), _1502731)), _1502733) = c_Orderings_Obot__class_Obot(tc_fun(_1502735, tc_HOL_Obool)))], (47196 ^ _774244) ^ [_1710567, _1710569] : [-(hAPP(c_List_Oset(_1710567), _1710569) = hAPP(c_Set_OCollect(_1710567), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1710567), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1710567, 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)), _1710567), 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)), _1710567), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1710567, tc_fun(tc_Nat_Onat, _1710567), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1710567, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1710567), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1710567), c_COMBB(_1710567, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1710567), _1710569))))), 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(_1710567)), _1710569))))))], (26492 ^ _774244) ^ [_1237997, _1237999, _1238001, _1238003, _1238005] : [class_Rings_Osemiring__0(_1237997), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237997), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237999, _1237997), _1238001), _1238003)), _1238005) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237999, _1237997), hAPP(hAPP(c_COMBC(_1237999, _1237997, _1237997), hAPP(hAPP(c_COMBB(_1237997, tc_fun(_1237997, _1237997), _1237999), c_Groups_Otimes__class_Otimes(_1237997)), _1238001)), _1238005)), _1238003))], (3298 ^ _774244) ^ [_824899, _824901, _824903, _824905] : [-(c_FunDef_Orp__inv__image(_824905, _824901) = c_FunDef_Orp__inv__image(_824903, _824899)), _824905 = _824903, _824901 = _824899], (30001 ^ _774244) ^ [_1308753] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1308753), c_Orderings_Otop__class_Otop(tc_fun(_1308753, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1308753)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1308753), tc_HOL_Obool)))))], (17435 ^ _774244) ^ [_1072727, _1072729, _1072731, _1072733] : [class_Rings_Olinordered__semidom(_1072727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072727), c_Groups_Oone__class_Oone(_1072727)), _1072729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072727), hAPP(hAPP(c_Power_Opower__class_Opower(_1072727), _1072729), _1072731)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072727), _1072729), _1072733))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1072731), _1072733)))], (7830 ^ _774244) ^ [_902154, _902156, _902158] : [-(c_Sum__Type_OProjl(_902154, _902156, hAPP(c_Sum__Type_OInl(_902154, _902156), _902158)) = _902158)], (48276 ^ _774244) ^ [_1737975, _1737977, _1737979, _1737981] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1737975), tc_List_Olist(_1737975))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1737975), tc_List_Olist(_1737975)), _1737977), _1737979)), c_List_Olistrel1(_1737975, _1737981))), 48281 ^ _774244 : [(48288 ^ _774244) ^ [] : [-(_1737979 = hAPP(hAPP(c_List_Oappend(_1737975), 48283 ^ [_1737975, _1737977, _1737979, _1737981]), hAPP(hAPP(c_List_Olist_OCons(_1737975), 48280 ^ [_1737975, _1737977, _1737979, _1737981]), 48284 ^ [_1737975, _1737977, _1737979, _1737981])))], (48286 ^ _774244) ^ [] : [-(_1737977 = hAPP(hAPP(c_List_Oappend(_1737975), 48283 ^ [_1737975, _1737977, _1737979, _1737981]), hAPP(hAPP(c_List_Olist_OCons(_1737975), 48279 ^ [_1737975, _1737977, _1737979, _1737981]), 48284 ^ [_1737975, _1737977, _1737979, _1737981])))], (48282 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1737975, _1737975)), hAPP(hAPP(c_Product__Type_OPair(_1737975, _1737975), 48279 ^ [_1737975, _1737977, _1737979, _1737981]), 48280 ^ [_1737975, _1737977, _1737979, _1737981])), _1737981)))]]], (44034 ^ _774244) ^ [_1632795] : [-(hAPP(c_Relation_ORange(_1632795, _1632795), c_Relation_OId(_1632795)) = c_Orderings_Otop__class_Otop(tc_fun(_1632795, tc_HOL_Obool)))], (48348 ^ _774244) ^ [_1739805, _1739807, _1739809, _1739811, _1739813] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1739805, _1739807)), _1739809), hAPP(hAPP(c_List_Ozip(_1739805, _1739807), _1739811), _1739813)) = hAPP(hAPP(c_List_Ozip(_1739805, _1739807), hAPP(hAPP(c_List_Odrop(_1739805), _1739809), _1739811)), hAPP(hAPP(c_List_Odrop(_1739807), _1739809), _1739813)))], (24253 ^ _774244) ^ [_1195453, _1195455, _1195457] : [class_Orderings_Olinorder(_1195453), 24256 ^ _774244 : [(24263 ^ _774244) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195453), _1195455), _1195457) = _1195457, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195453), _1195455), _1195457)))], (24257 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195453), _1195455), _1195457)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195453), _1195455), _1195457) = _1195457)]]], (13493 ^ _774244) ^ [_998864, _998866, _998868] : [class_Divides_Osemiring__div(_998864), -(c_Divides_Odiv__class_Omod(_998864, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998864), _998866), _998868), _998866) = c_Divides_Odiv__class_Omod(_998864, _998868, _998866))], (37297 ^ _774244) ^ [_1466307, _1466309, _1466311, _1466313] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466307), _1466309)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466307), _1466311)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466307, tc_Nat_Onat), _1466313), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1466307, tc_HOL_Obool)), _1466309), _1466311)) = 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(_1466307, tc_Nat_Onat), _1466313), _1466309)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466307, tc_Nat_Onat), _1466313), _1466311))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466307, tc_Nat_Onat), _1466313), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466307, tc_HOL_Obool)), _1466309), _1466311))))], (28713 ^ _774244) ^ [_1284016, _1284018] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1284016, tc_HOL_Obool)), _1284018)))], (36617 ^ _774244) ^ [_1451650, _1451652, _1451654] : [class_Lattices_Olattice(_1451650), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451650), _1451652)), hBOOL(hAPP(hAPP(c_member(_1451650), _1451654), _1451652)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1451650), _1451654), c_Big__Operators_Olattice__class_OSup__fin(_1451650, _1451652)) = _1451654)], (7676 ^ _774244) ^ [_899453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _899453), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_899453 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (836 ^ _774244) ^ [_787146, _787148, _787150, _787152, _787154, _787156] : [-(c_Finite__Set_Ofun__left__comm__idem(_787154, _787150, _787146)), c_Finite__Set_Ofun__left__comm__idem(_787156, _787152, _787148), _787156 = _787154, _787152 = _787150, _787148 = _787146], (19325 ^ _774244) ^ [] : [-(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))))], (9670 ^ _774244) ^ [_933571, _933573] : [class_Rings_Olinordered__semidom(_933571), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933571), _933573), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933571), _933573), c_Groups_Oone__class_Oone(_933571)))))], (40427 ^ _774244) ^ [_1537909, _1537911] : [class_Groups_Oab__semigroup__mult(_1537909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537909), _1537911)), -(_1537911 = c_Orderings_Obot__class_Obot(tc_fun(_1537909, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1537909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1537909), 40440 ^ [_1537909, _1537911]), 40441 ^ [_1537909, _1537911])), hAPP(hAPP(c_Set_Oinsert(_1537909), 40440 ^ [_1537909, _1537911]), hAPP(hAPP(c_Set_Oinsert(_1537909), 40441 ^ [_1537909, _1537911]), c_Orderings_Obot__class_Obot(tc_fun(_1537909, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1537909), hAPP(c_Finite__Set_Ofold1(_1537909, c_Groups_Otimes__class_Otimes(_1537909)), _1537911)), _1537911)))], (14912 ^ _774244) ^ [_1024563, _1024565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024563)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1024563), _1024565)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1024565), _1024563) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1024565), _1024563)), _1024563)))], (19179 ^ _774244) ^ [_1101495] : [-(c_Int_Osucc(c_Int_OBit1(_1101495)) = c_Int_OBit0(c_Int_Osucc(_1101495)))], (9722 ^ _774244) ^ [_934417, _934419] : [9723 ^ _774244 : [(9726 ^ _774244) ^ [] : [_934417 = _934419], (9724 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934417), _934419))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _934419), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (5382 ^ _774244) ^ [_857411, _857413] : [_857413 = _857411, -(c_Orderings_Oord__class_Oless(_857413) = c_Orderings_Oord__class_Oless(_857411))], (5238 ^ _774244) ^ [_855265, _855267, _855269, _855271] : [-(c_List_Oremdups(_855271, _855267) = c_List_Oremdups(_855269, _855265)), _855271 = _855269, _855267 = _855265], (42151 ^ _774244) ^ [_1587364, _1587366, _1587368] : [42152 ^ _774244 : [(42153 ^ _774244) ^ [_1587418] : [hBOOL(hAPP(_1587364, _1587418))]], _1587366 = c_Hilbert__Choice_OEps(_1587368, _1587364), -(hBOOL(hAPP(_1587364, _1587366)))], (32114 ^ _774244) ^ [_1355558, _1355560, _1355562, _1355564] : [hBOOL(hAPP(hAPP(_1355562, _1355560), _1355564)), -(hBOOL(hAPP(hAPP(c_member(_1355558), _1355560), c_SetInterval_Oord_OlessThan(_1355558, _1355562, _1355564))))], (23137 ^ _774244) ^ [_1174042, _1174044, _1174046, _1174048, _1174050, _1174052, _1174054] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1174042, _1174044), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1174046), _1174048))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1174050, _1174044), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1174052), _1174054))), -(_1174044 = 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), _1174042), _1174050), _1174044), 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), _1174046), _1174052)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1174048), _1174054)), _1174044))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1174048), _1174054), _1174044)))))], (14193 ^ _774244) ^ [_1012104, _1012106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1012104), _1012106)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1012104), _1012106) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3026 ^ _774244) ^ [_820549, _820551, _820553, _820555] : [-(c_Divides_Odivmod__nat__rel(_820555, _820551) = c_Divides_Odivmod__nat__rel(_820553, _820549)), _820555 = _820553, _820551 = _820549], (17963 ^ _774244) ^ [_1081484, _1081486] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1081484), _1081486) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 17964 ^ _774244 : [(17971 ^ _774244) ^ [] : [_1081484 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1081486 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (17965 ^ _774244) ^ [] : [_1081484 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1081486 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (29202 ^ _774244) ^ [_1294030, _1294032, _1294034] : [class_Orderings_Oorder(_1294030), 29205 ^ _774244 : [(29212 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294030), _1294032), _1294034))), -(c_Orderings_Obot__class_Obot(tc_fun(_1294030, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1294030, _1294032), _1294034))], (29206 ^ _774244) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1294030, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1294030, _1294032), _1294034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294030), _1294032), _1294034))]]], (1554 ^ _774244) ^ [_796393, _796395] : [-(class_Groups_Osemigroup__add(_796393)), _796395 = _796393, class_Groups_Osemigroup__add(_796395)], (39638 ^ _774244) ^ [_1519821, _1519823, _1519825, _1519827] : [-(hAPP(c_Set_Oimage(tc_prod(_1519821, _1519823), tc_prod(_1519823, _1519821), hAPP(c_Product__Type_Oprod_Oprod__case(_1519821, _1519823, tc_prod(_1519823, _1519821)), hAPP(c_COMBC(_1519823, _1519821, tc_prod(_1519823, _1519821)), c_Product__Type_OPair(_1519823, _1519821)))), hAPP(hAPP(c_Product__Type_OSigma(_1519821, _1519823), _1519825), hAPP(c_COMBK(tc_fun(_1519823, tc_HOL_Obool), _1519821), _1519827))) = hAPP(hAPP(c_Product__Type_OSigma(_1519823, _1519821), _1519827), hAPP(c_COMBK(tc_fun(_1519821, tc_HOL_Obool), _1519823), _1519825)))], (15846 ^ _774244) ^ [_1042983, _1042985, _1042987, _1042989, _1042991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042983), _1042985)), -(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), _1042983), _1042987)), _1042989)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042985), _1042987)), _1042991)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042989), 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), _1042985), _1042983)), _1042987)), _1042991)))], (45341 ^ _774244) ^ [_1663537, _1663539, _1663541, _1663543, _1663545] : [-(c_Map_Omap__add(_1663537, _1663539, _1663541, c_Map_Omap__add(_1663537, _1663539, _1663543, _1663545)) = c_Map_Omap__add(_1663537, _1663539, c_Map_Omap__add(_1663537, _1663539, _1663541, _1663543), _1663545))], (36739 ^ _774244) ^ [_1454425, _1454427, _1454429, _1454431] : [class_Orderings_Olinorder(_1454425), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454425, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1454425, _1454427, _1454429)), hAPP(c_SetInterval_Oord__class_OatLeast(_1454425), _1454431)) = c_SetInterval_Oord__class_OatLeastAtMost(_1454425, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1454425), _1454427), _1454431), _1454429))], (13818 ^ _774244) ^ [_1004831, _1004833, _1004835] : [-(hBOOL(hAPP(_1004831, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1004833, _1004835)))), 13821 ^ _774244 : [(13824 ^ _774244) ^ [] : [hBOOL(hAPP(_1004831, _1004833))], (13822 ^ _774244) ^ [] : [-(_1004835 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 13827 ^ _774244 : [(13828 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004835)))], (13834 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 13830 ^ [_1004831, _1004833, _1004835]), _1004835)))], (13838 ^ _774244) ^ [] : [hBOOL(hAPP(_1004831, 13830 ^ [_1004831, _1004833, _1004835]))], (13836 ^ _774244) ^ [] : [-(_1004833 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1004835), 13829 ^ [_1004831, _1004833, _1004835])), 13830 ^ [_1004831, _1004833, _1004835]))], (13832 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13830 ^ [_1004831, _1004833, _1004835])))]], 13839 ^ _774244 : [(13840 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1004835), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13846 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 13842 ^ [_1004831, _1004833, _1004835]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13850 ^ _774244) ^ [] : [hBOOL(hAPP(_1004831, 13842 ^ [_1004831, _1004833, _1004835]))], (13848 ^ _774244) ^ [] : [-(_1004833 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1004835), 13841 ^ [_1004831, _1004833, _1004835])), 13842 ^ [_1004831, _1004833, _1004835]))], (13844 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1004835), 13842 ^ [_1004831, _1004833, _1004835])))]]], (39792 ^ _774244) ^ [_1524196, _1524198, _1524200] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1524196), _1524198)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524196, _1524196), tc_HOL_Obool)), _1524200), hAPP(hAPP(c_Product__Type_OSigma(_1524196, _1524196), _1524198), hAPP(c_COMBK(tc_fun(_1524196, tc_HOL_Obool), _1524196), _1524198)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1524196, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1524196), _1524198), _1524200))))], (41764 ^ _774244) ^ [_1577351, _1577353] : [-(hAPP(c_Relation_ODomain(_1577351, _1577351), c_Relation_OId__on(_1577351, _1577353)) = _1577353)], (17065 ^ _774244) ^ [_1065998] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065998) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1065998))], (18803 ^ _774244) ^ [_1094805, _1094807] : [class_Int_Onumber__ring(_1094805), class_Rings_Olinordered__idom(_1094805), 18810 ^ _774244 : [(18817 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094807), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094805), hAPP(c_Int_Onumber__class_Onumber__of(_1094805), _1094807)), c_Groups_Oone__class_Oone(_1094805))))], (18811 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094805), hAPP(c_Int_Onumber__class_Onumber__of(_1094805), _1094807)), c_Groups_Oone__class_Oone(_1094805))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094807), c_Int_OBit1(c_Int_OPls))))]]], (22542 ^ _774244) ^ [_1163272, _1163274] : [_1163272 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1163274, _1163272) = 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), _1163274)))], (46265 ^ _774244) ^ [_1686419, _1686421, _1686423, _1686425, _1686427] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686419)), _1686421) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686423)), _1686425), 46268 ^ _774244 : [(46276 ^ _774244) ^ [] : [46277 ^ _774244 : [(46278 ^ _774244) ^ [_1686707] : [hAPP(c_Map_Omap__of(_1686419, _1686423, hAPP(hAPP(c_List_Ozip(_1686419, _1686423), _1686421), _1686425)), _1686427) = hAPP(c_Option_Ooption_OSome(_1686423), _1686707)]], -(hBOOL(hAPP(hAPP(c_member(_1686419), _1686427), hAPP(c_List_Oset(_1686419), _1686421))))], (46269 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1686419), _1686427), hAPP(c_List_Oset(_1686419), _1686421))), -(hAPP(c_Map_Omap__of(_1686419, _1686423, hAPP(hAPP(c_List_Ozip(_1686419, _1686423), _1686421), _1686425)), _1686427) = hAPP(c_Option_Ooption_OSome(_1686423), 46272 ^ [_1686419, _1686421, _1686423, _1686425, _1686427]))]]], (45200 ^ _774244) ^ [_1660626, _1660628, _1660630, _1660632, _1660634, _1660636, _1660638, _1660640] : [c_Finite__Set_Ofolding__image__simple__idem(_1660626, _1660628, _1660630, _1660632, _1660634, _1660636), hBOOL(hAPP(c_Finite__Set_Ofinite(_1660628), _1660638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660628, tc_HOL_Obool)), _1660640), _1660638)), -(hAPP(hAPP(_1660630, hAPP(_1660636, _1660640)), hAPP(_1660636, _1660638)) = hAPP(_1660636, _1660638))], (41601 ^ _774244) ^ [_1573374, _1573376] : [-(c_List_Olex(_1573374, _1573376) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1573374), tc_List_Olist(_1573374)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1573374, _1573376)))], (14388 ^ _774244) ^ [_1015189, _1015191, _1015193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1015189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015189), _1015191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1015193), _1015191)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1015193), _1015189))))], (48508 ^ _774244) ^ [_1743676, _1743678, _1743680, _1743682, _1743684] : [-(hAPP(hAPP(c_List_Ozip(_1743676, _1743678), _1743680), hAPP(hAPP(c_List_Oappend(_1743678), _1743682), _1743684)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1743676, _1743678)), hAPP(hAPP(c_List_Ozip(_1743676, _1743678), hAPP(hAPP(c_List_Otake(_1743676), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743678)), _1743682)), _1743680)), _1743682)), hAPP(hAPP(c_List_Ozip(_1743676, _1743678), hAPP(hAPP(c_List_Odrop(_1743676), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743678)), _1743682)), _1743680)), _1743684)))], (16675 ^ _774244) ^ [_1058591, _1058593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058591)), -(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), _1058591), _1058593))))], (38431 ^ _774244) ^ [_1491147, _1491149, _1491151, _1491153, _1491155, _1491157, _1491159, _1491161] : [class_Groups_Ocomm__monoid__mult(_1491147), c_Fun_Oinj__on(_1491149, _1491151, _1491153, _1491155), _1491157 = hAPP(c_Set_Oimage(_1491149, _1491151, _1491153), _1491155), _1491159 = hAPP(c_Fun_Ocomp(_1491151, _1491147, _1491149, _1491161), _1491153), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1491151, _1491147), _1491161), _1491157) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1491149, _1491147), _1491159), _1491155))], (51147 ^ _774244) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (42109 ^ _774244) ^ [_1586340, _1586342, _1586344] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1586340), c_Map_Odom(_1586340, _1586342, _1586344))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1586340), c_Orderings_Otop__class_Otop(tc_fun(_1586340, tc_HOL_Obool))))), -(hAPP(_1586344, 42116 ^ [_1586340, _1586342, _1586344]) = c_Option_Ooption_ONone(_1586342))], (2778 ^ _774244) ^ [_816341, _816343, _816345, _816347] : [-(c_Nitpick_OAbs__Frac(_816347, _816343) = c_Nitpick_OAbs__Frac(_816345, _816341)), _816347 = _816345, _816343 = _816341], (20507 ^ _774244) ^ [_1125033, _1125035, _1125037, _1125039, _1125041] : [class_Fields_Olinordered__field(_1125033), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125033), c_Groups_Ozero__class_Ozero(_1125033)), _1125035)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125033), _1125035), _1125037)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125033), c_Groups_Ozero__class_Ozero(_1125033)), _1125039)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125033), _1125039), _1125041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125033), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125033), _1125035), _1125041)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125033), _1125037), _1125039))))], (31539 ^ _774244) ^ [_1342022, _1342024, _1342026, _1342028, _1342030] : [hBOOL(hAPP(hAPP(c_member(_1342022), _1342024), _1342026)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342028, tc_HOL_Obool)), hAPP(_1342030, _1342024)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1342022, tc_fun(_1342028, tc_HOL_Obool)), _1342026), _1342030)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1342022, tc_fun(_1342028, tc_HOL_Obool)), _1342026), _1342030))], (22414 ^ _774244) ^ [_1160538, _1160540] : [-(c_Divides_OposDivAlg(_1160538, _1160540) = hAPP(c_Divides_Oadjust(_1160540), c_Divides_OposDivAlg(_1160538, 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)))), _1160540)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160538), _1160540))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1160540), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11343 ^ _774244) ^ [_960977, _960979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _960977)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _960977), _960979)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _960977)), hAPP(c_Int_Onat, _960979)))], (9468 ^ _774244) ^ [_929944, _929946, _929948] : [class_Rings_Olinordered__semiring__strict(_929944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929944), c_Groups_Ozero__class_Ozero(_929944)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929944), _929946), _929948))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929944), c_Groups_Ozero__class_Ozero(_929944)), _929946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929944), c_Groups_Ozero__class_Ozero(_929944)), _929948)))], (19663 ^ _774244) ^ [_1110231, _1110233, _1110235] : [class_Int_Onumber__ring(_1110231), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1110231), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1110231), _1110233), _1110235)), 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(_1110231), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110231), hAPP(hAPP(c_Power_Opower__class_Opower(_1110231), _1110233), 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(_1110231), _1110235), 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(_1110231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110231), hAPP(c_Int_Onumber__class_Onumber__of(_1110231), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1110233)), _1110235)))], (10728 ^ _774244) ^ [_950609, _950611, _950613] : [class_Orderings_Oorder(_950609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950609), _950611), _950613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950609), _950611), _950613))), -(_950611 = _950613)], (13525 ^ _774244) ^ [_999500, _999502, _999504, _999506] : [class_Divides_Osemiring__div(_999500), -(c_Divides_Odiv__class_Omod(_999500, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999500), _999502), _999504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999500), _999506), _999504)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999500), c_Divides_Odiv__class_Omod(_999500, _999502, _999506)), _999504))], (21950 ^ _774244) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (35235 ^ _774244) ^ [_1420031, _1420033, _1420035, _1420037, _1420039, _1420041, _1420043] : [-(hAPP(c_Fun_Ocomp(_1420031, _1420033, _1420035, _1420037), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1420035, _1420031), _1420039), _1420041), _1420043)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1420035, _1420033), hAPP(c_Fun_Ocomp(_1420031, _1420033, _1420035, _1420037), _1420039)), _1420041), hAPP(_1420037, _1420043)))], (42184 ^ _774244) ^ [_1587904, _1587906] : [42185 ^ _774244 : [(42186 ^ _774244) ^ [_1587950] : [hBOOL(hAPP(_1587904, _1587950))]], -(hBOOL(hAPP(_1587904, c_Hilbert__Choice_OEps(_1587906, _1587904))))], (50458 ^ _774244) ^ [_1785770, _1785772, _1785774] : [class_Orderings_Olinorder(_1785770), c_List_Olinorder__class_Osorted(_1785770, hAPP(c_List_Orev(_1785770), _1785772)), 50465 ^ _774244 : [(50472 ^ _774244) ^ [] : [-(_1785772 = c_List_Olist_ONil(_1785770)), -(c_List_Ofoldr(_1785770, _1785770, c_Orderings_Oord__class_Omax(_1785770), _1785772, _1785774) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1785770), hAPP(hAPP(c_List_Onth(_1785770), _1785772), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1785774))], (50466 ^ _774244) ^ [] : [_1785772 = c_List_Olist_ONil(_1785770), -(c_List_Ofoldr(_1785770, _1785770, c_Orderings_Oord__class_Omax(_1785770), _1785772, _1785774) = _1785774)]]], (41142 ^ _774244) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (14304 ^ _774244) ^ [_1013815] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1013815), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37169 ^ _774244) ^ [_1463759, _1463761, _1463763] : [class_Orderings_Olinorder(_1463759), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463759), _1463761)), -(_1463761 = c_Orderings_Obot__class_Obot(tc_fun(_1463759, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463759), _1463763)), -(_1463763 = c_Orderings_Obot__class_Obot(tc_fun(_1463759, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463759, tc_HOL_Obool)), _1463761), _1463763) = c_Orderings_Obot__class_Obot(tc_fun(_1463759, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1463759, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463759, tc_HOL_Obool)), _1463761), _1463763)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1463759), c_Big__Operators_Olinorder__class_OMax(_1463759, _1463761)), c_Big__Operators_Olinorder__class_OMax(_1463759, _1463763)))], (11903 ^ _774244) ^ [_971031, _971033] : [class_Groups_Olinordered__ab__group__add(_971031), 11906 ^ _774244 : [(11913 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971031), _971033), c_Groups_Ozero__class_Ozero(_971031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971031), _971033), hAPP(c_Groups_Ouminus__class_Ouminus(_971031), _971033))))], (11907 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971031), _971033), hAPP(c_Groups_Ouminus__class_Ouminus(_971031), _971033))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971031), _971033), c_Groups_Ozero__class_Ozero(_971031))))]]], (2382 ^ _774244) ^ [_810177, _810179, _810181, _810183] : [-(c_Quickcheck_Obeyond(_810183, _810179) = c_Quickcheck_Obeyond(_810181, _810177)), _810183 = _810181, _810179 = _810177], (51223 ^ _774244) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (10958 ^ _774244) ^ [_954385, _954387] : [10959 ^ _774244 : [(10962 ^ _774244) ^ [] : [_954387 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10960 ^ _774244) ^ [] : [_954385 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954385), _954387) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8380 ^ _774244) ^ [_910809, _910811, _910813, _910815] : [class_Orderings_Opreorder(_910809), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910809), _910811), _910813)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910809), _910813), _910815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910809), _910811), _910815)))], (35586 ^ _774244) ^ [_1428905, _1428907, _1428909, _1428911, _1428913, _1428915] : [c_Finite__Set_Ofolding__idem(_1428905, _1428907, _1428909, _1428911), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428905), _1428913)), -(hAPP(_1428911, hAPP(hAPP(c_Set_Oinsert(_1428905), _1428915), _1428913)) = hAPP(c_Fun_Ocomp(_1428907, _1428907, _1428907, hAPP(_1428911, _1428913)), hAPP(_1428909, _1428915)))], (13272 ^ _774244) ^ [_994796, _994798, _994800, _994802] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994796), _994798)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994800), _994798)), _994802)) = 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), _994796), _994800)), _994798)), _994802))], (22152 ^ _774244) ^ [_1155062, _1155064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1155062), _1155064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1155062)), hAPP(c_Code__Numeral_Oof__nat, _1155064))))], (46820 ^ _774244) ^ [_1702099, _1702101, _1702103, _1702105] : [hAPP(hAPP(c_List_Omap(_1702099, _1702101), _1702103), _1702105) = c_List_Olist_ONil(_1702101), -(_1702105 = c_List_Olist_ONil(_1702099))], (49252 ^ _774244) ^ [_1759561, _1759563, _1759565, _1759567] : [_1759561 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759563)), _1759565)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1759563, hAPP(hAPP(c_List_Olist__update(_1759563, _1759565), _1759561), _1759567)) = c_List_Obutlast(_1759563, _1759565))], (23381 ^ _774244) ^ [_1179151, _1179153, _1179155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179151, tc_HOL_Obool)), _1179155), _1179153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179151, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1179151, tc_HOL_Obool)), _1179153)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1179151, tc_HOL_Obool)), _1179155))))], (15224 ^ _774244) ^ [_1030298, _1030300, _1030302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030298), _1030300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030302), _1030300)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030302), _1030298))))], (50917 ^ _774244) ^ [_1795856, _1795858, _1795860] : [-(c_Enum_On__lists(_1795856, hAPP(c_Nat_OSuc, _1795858), _1795860) = c_List_Oconcat(tc_List_Olist(_1795856), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1795856), tc_List_Olist(tc_List_Olist(_1795856))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1795856), tc_List_Olist(_1795856), tc_List_Olist(tc_List_Olist(_1795856))), hAPP(hAPP(c_COMBB(tc_fun(_1795856, tc_List_Olist(_1795856)), tc_fun(tc_List_Olist(_1795856), tc_List_Olist(tc_List_Olist(_1795856))), tc_List_Olist(_1795856)), c_List_Omap(_1795856, tc_List_Olist(_1795856))), hAPP(c_COMBC(_1795856, tc_List_Olist(_1795856), tc_List_Olist(_1795856)), c_List_Olist_OCons(_1795856)))), _1795860)), c_Enum_On__lists(_1795856, _1795858, _1795860))))], (6041 ^ _774244) ^ [_870999] : [hAPP(c_Nat_OSuc, _870999) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22312 ^ _774244) ^ [_1158673, _1158675, _1158677] : [class_Int_Onumber__ring(_1158673), 22315 ^ _774244 : [(22322 ^ _774244) ^ [] : [-(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), _1158675)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1158673), hAPP(c_Int_Onumber__class_Onumber__of(_1158673), _1158677)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1158675))) = c_Groups_Oone__class_Oone(_1158673))], (22316 ^ _774244) ^ [] : [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), _1158675))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1158673), hAPP(c_Int_Onumber__class_Onumber__of(_1158673), _1158677)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1158675))) = hAPP(hAPP(c_HOL_OLet(_1158673, _1158673), hAPP(hAPP(c_Power_Opower__class_Opower(_1158673), hAPP(c_Int_Onumber__class_Onumber__of(_1158673), _1158677)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158675))), hAPP(hAPP(c_COMBS(_1158673, _1158673, _1158673), hAPP(hAPP(c_COMBB(_1158673, tc_fun(_1158673, _1158673), _1158673), c_Groups_Otimes__class_Otimes(_1158673)), hAPP(c_Groups_Otimes__class_Otimes(_1158673), hAPP(c_Int_Onumber__class_Onumber__of(_1158673), _1158677)))), c_COMBI(_1158673))))]]], (28980 ^ _774244) ^ [_1289931, _1289933] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289931, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1289931, tc_HOL_Obool))), _1289933) = _1289933)], (49087 ^ _774244) ^ [_1755941, _1755943] : [-(_1755941 = c_List_Olist_ONil(_1755943)), -(c_List_Olast(_1755943, _1755941) = hAPP(hAPP(c_List_Onth(_1755943), _1755941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755943)), _1755941)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (49472 ^ _774244) ^ [_1764915, _1764917] : [49474 ^ _774244 : [(49477 ^ _774244) ^ [] : [49473 ^ [_1764915, _1764917] = c_List_Olist_ONil(_1764915)], (49475 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1764915)), 49473 ^ [_1764915, _1764917]), hAPP(c_List_Oset(tc_List_Olist(_1764915)), _1764917))))]], -(c_List_Otranspose(_1764915, _1764917) = c_List_Olist_ONil(tc_List_Olist(_1764915)))], (5764 ^ _774244) ^ [_866102, _866104, _866106, _866108] : [-(hAPP(c_Nat_Onat_Onat__rec(_866102, _866104, _866106), hAPP(c_Nat_OSuc, _866108)) = hAPP(hAPP(_866106, _866108), hAPP(c_Nat_Onat_Onat__rec(_866102, _866104, _866106), _866108)))], (35324 ^ _774244) ^ [] : [-(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))))))], (34986 ^ _774244) ^ [_1414438, _1414440, _1414442, _1414444, _1414446] : [hAPP(c_Set_Oimage(_1414438, _1414440, _1414442), _1414444) = _1414446, -(hAPP(c_Set_Oimage(tc_fun(_1414438, tc_HOL_Obool), tc_fun(_1414440, tc_HOL_Obool), c_Set_Oimage(_1414438, _1414440, _1414442)), hAPP(c_Set_OPow(_1414438), _1414444)) = hAPP(c_Set_OPow(_1414440), _1414446))], (42248 ^ _774244) ^ [_1589494, _1589496] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1589494), _1589496)), 42254 ^ _774244 : [(42257 ^ _774244) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42255 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589494), 42253 ^ [_1589494, _1589496]), _1589496)))]], -(hAPP(c_Finite__Set_Ocard(_1589494), _1589496) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26704 ^ _774244) ^ [_1242666, _1242668, _1242670, _1242672, _1242674] : [class_Orderings_Olinorder(_1242666), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1242666, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1242666, _1242668), _1242670)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1242666, _1242672), _1242674))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242666), _1242670), _1242668))), 26715 ^ _774244 : [(26718 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242666), _1242670), _1242674)))], (26716 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242666), _1242672), _1242668)))]]], (23055 ^ _774244) ^ [_1172868, _1172870, _1172872] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1172868, _1172868), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1172870), _1172872))), -(_1172868 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1172870 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (14332 ^ _774244) ^ [_1014390, _1014392, _1014394] : [class_Divides_Osemiring__div(_1014390), -(_1014392 = c_Groups_Ozero__class_Ozero(_1014390)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1014390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014390), _1014394), _1014392)), _1014392) = _1014394)], (41164 ^ _774244) ^ [_1561701, _1561703, _1561705, _1561707] : [-(c_Product__Type_Oapsnd(_1561701, _1561703, _1561705, _1561707) = c_Product__Type_Omap__pair(_1561705, _1561705, _1561701, _1561703, c_Fun_Oid(_1561705), _1561707))], (50178 ^ _774244) ^ [_1778985, _1778987] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778985)), c_List_Oconcat(_1778985, _1778987)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1778985), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1778985))), _1778987)))], (16863 ^ _774244) ^ [_1062352, _1062354, _1062356, _1062358] : [class_Int_Onumber__ring(_1062352), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062352), hAPP(c_Int_Onumber__class_Onumber__of(_1062352), _1062354)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1062352), _1062356), hAPP(c_Int_Onumber__class_Onumber__of(_1062352), _1062358))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062352), hAPP(c_Int_Onumber__class_Onumber__of(_1062352), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1062354), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1062358)))), _1062356))], (43753 ^ _774244) ^ [_1625186, _1625188, _1625190, _1625192] : [class_Complete__Lattice_Ocomplete__lattice(_1625186), -(_1625188 = c_Orderings_Obot__class_Obot(tc_fun(_1625190, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625190, _1625186), _1625188), hAPP(c_COMBK(_1625186, _1625190), _1625192)) = _1625192)], (35470 ^ _774244) ^ [_1426026, _1426028, _1426030, _1426032, _1426034, _1426036] : [class_Groups_Ocomm__monoid__add(_1426026), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426028), _1426030)), 35480 ^ _774244 : [(35481 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1426028), 35479 ^ [_1426026, _1426028, _1426030, _1426032, _1426034, _1426036]), _1426030)))], (35486 ^ _774244) ^ [] : [35479 ^ [_1426026, _1426028, _1426030, _1426032, _1426034, _1426036] = 35482 ^ [_1426026, _1426028, _1426030, _1426032, _1426034, _1426036]], (35490 ^ _774244) ^ [] : [hAPP(_1426034, hAPP(_1426032, 35479 ^ [_1426026, _1426028, _1426030, _1426032, _1426034, _1426036])) = c_Groups_Ozero__class_Ozero(_1426026)], (35488 ^ _774244) ^ [] : [-(hAPP(_1426032, 35479 ^ [_1426026, _1426028, _1426030, _1426032, _1426034, _1426036]) = hAPP(_1426032, 35482 ^ [_1426026, _1426028, _1426030, _1426032, _1426034, _1426036]))], (35484 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1426028), 35482 ^ [_1426026, _1426028, _1426030, _1426032, _1426034, _1426036]), _1426030)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426036, _1426026), _1426034), hAPP(c_Set_Oimage(_1426028, _1426036, _1426032), _1426030)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426028, _1426026), hAPP(c_Fun_Ocomp(_1426036, _1426026, _1426028, _1426034), _1426032)), _1426030))], (19201 ^ _774244) ^ [_1101938, _1101940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1101938)), c_Int_OBit0(_1101940))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101938), _1101940)))], (4662 ^ _774244) ^ [_846269, _846271, _846273, _846275, _846277, _846279] : [-(c_List_Opartition(_846279, _846275, _846271) = c_List_Opartition(_846277, _846273, _846269)), _846279 = _846277, _846275 = _846273, _846271 = _846269], (29354 ^ _774244) ^ [_1296563, _1296565] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296563, tc_fun(_1296563, tc_HOL_Obool)), _1296565), hAPP(hAPP(c_COMBC(_1296563, tc_fun(_1296563, tc_HOL_Obool), tc_fun(_1296563, tc_HOL_Obool)), c_Set_Oinsert(_1296563)), c_Orderings_Obot__class_Obot(tc_fun(_1296563, tc_HOL_Obool)))) = _1296565)], (22206 ^ _774244) ^ [_1156312] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156312)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1156312)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156312)), 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)))))], (41428 ^ _774244) ^ [_1569365, _1569367, _1569369] : [c_Wellfounded_Owf(_1569365, _1569367), -(c_Wellfounded_Owf(_1569365, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1569365, _1569365), tc_HOL_Obool)), _1569367), _1569369)))], (13575 ^ _774244) ^ [_1000561, _1000563, _1000565] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1000561), _1000563), _1000565) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1000561), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1000563, _1000565)), _1000565))], (50699 ^ _774244) ^ [_1791234, _1791236] : [_1791236 = c_List_Olist_ONil(_1791234), -(c_List_Olist_ONil(_1791234) = c_List_Oremdups(_1791234, _1791236))], (29470 ^ _774244) ^ [_1298951, _1298953, _1298955, _1298957] : [-(hAPP(c_Set_Oimage(_1298951, _1298953, _1298955), _1298957) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298951, tc_fun(_1298953, tc_HOL_Obool)), _1298957), hAPP(hAPP(c_COMBC(_1298951, tc_fun(_1298953, tc_HOL_Obool), tc_fun(_1298953, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1298953, tc_fun(tc_fun(_1298953, tc_HOL_Obool), tc_fun(_1298953, tc_HOL_Obool)), _1298951), c_Set_Oinsert(_1298953)), _1298955)), c_Orderings_Obot__class_Obot(tc_fun(_1298953, tc_HOL_Obool)))))], (4616 ^ _774244) ^ [_845580, _845582, _845584, _845586] : [-(c_List_Olists(_845586, _845582) = c_List_Olists(_845584, _845580)), _845586 = _845584, _845582 = _845580], (43417 ^ _774244) ^ [_1614860, _1614862, _1614864] : [-(hAPP(c_Relation_ODomain(_1614860, _1614862), hAPP(c_Relation_Oconverse(_1614862, _1614860), _1614864)) = hAPP(c_Relation_ORange(_1614862, _1614860), _1614864))], (44257 ^ _774244) ^ [_1638161, _1638163, _1638165] : [c_Relation_Ototal__on(_1638161, _1638163, _1638165), -(c_Relation_Ototal__on(_1638161, _1638163, hAPP(c_Relation_Oconverse(_1638161, _1638161), _1638165)))], (15308 ^ _774244) ^ [_1031926, _1031928, _1031930] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1031926), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1031928, _1031930)), _1031930) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1031926), _1031928), _1031930))], (43500 ^ _774244) ^ [_1618185, _1618187, _1618189, _1618191] : [-(hAPP(c_Set_OPow(_1618185), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618187, tc_fun(_1618185, tc_HOL_Obool)), _1618189), _1618191)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618187, tc_fun(tc_fun(_1618185, tc_HOL_Obool), tc_HOL_Obool)), _1618189), hAPP(hAPP(c_COMBB(tc_fun(_1618185, tc_HOL_Obool), tc_fun(tc_fun(_1618185, tc_HOL_Obool), tc_HOL_Obool), _1618187), c_Set_OPow(_1618185)), _1618191)))], (34781 ^ _774244) ^ [_1409905, _1409907, _1409909] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1409905, _1409905)), _1409907), c_Relation_OId__on(_1409905, _1409909))), 34785 ^ _774244 : [(34788 ^ _774244) ^ [] : [-(_1409907 = hAPP(hAPP(c_Product__Type_OPair(_1409905, _1409905), 34784 ^ [_1409905, _1409907, _1409909]), 34784 ^ [_1409905, _1409907, _1409909]))], (34786 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409905), 34784 ^ [_1409905, _1409907, _1409909]), _1409909)))]]], (41168 ^ _774244) ^ [_1561787, _1561789] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1561787, _1561789, tc_prod(_1561787, _1561789)), c_Product__Type_OPair(_1561787, _1561789)) = c_Fun_Oid(tc_prod(_1561787, _1561789)))], (6492 ^ _774244) ^ [_878882, _878884, _878886] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878882), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878884), _878886)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878884), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878882), _878886)))], (29628 ^ _774244) ^ [_1301866, _1301868] : [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)))), _1301866, _1301868), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1301866), _1301868)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1301868), _1301866)))], (25725 ^ _774244) ^ [_1223202, _1223204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1223202)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1223202), _1223204)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223204), _1223202))], (2950 ^ _774244) ^ [_819327, _819329] : [_819329 = _819327, -(c_New__DSequence_Opos__empty(_819329) = c_New__DSequence_Opos__empty(_819327))], (49216 ^ _774244) ^ [_1758768, _1758770, _1758772] : [_1758768 = c_List_Olist_ONil(_1758770), -(c_List_Obutlast(_1758770, hAPP(hAPP(c_List_Oappend(_1758770), _1758772), _1758768)) = c_List_Obutlast(_1758770, _1758772))], (40139 ^ _774244) ^ [_1532624, _1532626, _1532628, _1532630] : [c_Relation_Orefl__on(_1532624, _1532626, _1532628), hBOOL(hAPP(hAPP(c_member(_1532624), _1532630), _1532626)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532624, _1532624)), hAPP(hAPP(c_Product__Type_OPair(_1532624, _1532624), _1532630), _1532630)), _1532628)))], (14080 ^ _774244) ^ [_1009867, _1009869, _1009871] : [hBOOL(hAPP(_1009867, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1009869), _1009871))), 14085 ^ _774244 : [(14088 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1009867, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14086 ^ _774244) ^ [] : [-(_1009871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14090 ^ _774244 : [(14095 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1009867, 14089 ^ [_1009867, _1009869, _1009871])))], (14093 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1009869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009871), hAPP(c_Nat_OSuc, 14089 ^ [_1009867, _1009869, _1009871])))))], (14091 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009871), 14089 ^ [_1009867, _1009869, _1009871])), _1009869)))]]], (41982 ^ _774244) ^ [_1582688, _1582690, _1582692] : [c_Relation_Orefl__on(_1582688, _1582690, _1582692), 41985 ^ _774244 : [(41992 ^ _774244) ^ [_1583172] : [hBOOL(hAPP(hAPP(c_member(_1582688), _1583172), _1582690)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582688, _1582688)), hAPP(hAPP(c_Product__Type_OPair(_1582688, _1582688), _1583172), _1583172)), _1582692)))], (41986 ^ _774244) ^ [_1582899] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582688, _1582688)), _1582899), _1582692)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1582688, _1582688, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1582688, tc_fun(_1582688, tc_HOL_Obool), tc_fun(_1582688, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1582688, tc_HOL_Obool), tc_fun(_1582688, tc_HOL_Obool)), _1582688), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1582688)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1582688), c_fconj), hAPP(hAPP(c_COMBC(_1582688, tc_fun(_1582688, tc_HOL_Obool), tc_HOL_Obool), c_member(_1582688)), _1582690)))), hAPP(hAPP(c_COMBC(_1582688, tc_fun(_1582688, tc_HOL_Obool), tc_HOL_Obool), c_member(_1582688)), _1582690))), _1582899)))]]], (16595 ^ _774244) ^ [_1056997, _1056999, _1057001, _1057003] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056997), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056997), _1056999), _1057001)), hAPP(c_Int_Onumber__class_Onumber__of(_1056997), _1057003)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056997), _1056999), hAPP(c_Int_Onumber__class_Onumber__of(_1056997), _1057003))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056997), _1057001), hAPP(c_Int_Onumber__class_Onumber__of(_1056997), _1057003)))), class_Int_Onumber(_1056997), class_Rings_Oring(_1056997)], (50382 ^ _774244) ^ [_1783303, _1783305, _1783307] : [-(hAPP(c_List_Orotate(_1783303, _1783305), hAPP(c_List_Orev(_1783303), _1783307)) = hAPP(c_List_Orev(_1783303), hAPP(c_List_Orotate(_1783303, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783303)), _1783307)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1783305, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783303)), _1783307)))), _1783307)))], (38984 ^ _774244) ^ [_1503703, _1503705, _1503707, _1503709] : [class_Groups_Ocomm__monoid__add(_1503703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503705), _1503707)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503705, _1503703), _1503709), _1503707) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1503703, _1503705, c_Groups_Oplus__class_Oplus(_1503703)), _1503709), c_Groups_Ozero__class_Ozero(_1503703)), _1503707))], (30097 ^ _774244) ^ [_1310252, _1310254] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310252), c_Orderings_Otop__class_Otop(tc_fun(_1310252, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1310252), _1310254) = hAPP(c_Finite__Set_Ocard(_1310252), c_Orderings_Otop__class_Otop(tc_fun(_1310252, tc_HOL_Obool))), -(_1310254 = c_Orderings_Otop__class_Otop(tc_fun(_1310252, tc_HOL_Obool)))], (8408 ^ _774244) ^ [_911275, _911277, _911279] : [class_Orderings_Opreorder(_911275), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911275), _911277), _911279)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911275), _911279), _911277))], (7711 ^ _774244) ^ [_899949, _899951] : [7712 ^ _774244 : [(7715 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _899951))], (7713 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _899949))]], -(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), _899949), _899951))))], (27996 ^ _774244) ^ [_1268676, _1268678, _1268680] : [class_Lattices_Osemilattice__sup(_1268676), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268676), _1268678), _1268680)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268676), _1268680), _1268678) = _1268680)], (37636 ^ _774244) ^ [_1475482, _1475484, _1475486, _1475488] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1475482), _1475484)), c_Equiv__Relations_Oequiv(_1475482, _1475484, _1475486), 37646 ^ _774244 : [(37649 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1475488), hAPP(c_Finite__Set_Ocard(_1475482), 37645 ^ [_1475482, _1475484, _1475486, _1475488])))], (37647 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1475482, tc_HOL_Obool)), 37645 ^ [_1475482, _1475484, _1475486, _1475488]), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1475482), _1475484), _1475486))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1475488), hAPP(c_Finite__Set_Ocard(_1475482), _1475484))))], (29824 ^ _774244) ^ [_1305543] : [class_Finite__Set_Ofinite(_1305543), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305543), c_Orderings_Otop__class_Otop(tc_fun(_1305543, tc_HOL_Obool)))))], (8304 ^ _774244) ^ [_909613, _909615, _909617] : [class_Orderings_Opreorder(_909613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909613), _909615), _909617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909613), _909617), _909615))], (42802 ^ _774244) ^ [_1600587, _1600589, _1600591, _1600593] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600587, _1600587)), hAPP(hAPP(c_Product__Type_OPair(_1600587, _1600587), _1600589), _1600591)), _1600593)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600587, _1600587)), hAPP(hAPP(c_Product__Type_OPair(_1600587, _1600587), _1600589), _1600591)), c_Transitive__Closure_Otrancl(_1600587, _1600593))))], (6810 ^ _774244) ^ [_884576] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _884576)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_884576)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44618 ^ _774244) ^ [_1646786, _1646788, _1646790, _1646792] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1646786, tc_fun(_1646788, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646786, tc_HOL_Obool), _1646790)), _1646792) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1646786, tc_HOL_Obool), tc_fun(_1646788, tc_HOL_Obool)), _1646790), hAPP(hAPP(c_COMBC(tc_fun(_1646786, tc_HOL_Obool), tc_fun(_1646786, tc_fun(_1646788, tc_HOL_Obool)), tc_fun(_1646788, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1646786, tc_fun(_1646788, tc_HOL_Obool))), _1646792)))], (39026 ^ _774244) ^ [_1504682, _1504684, _1504686, _1504688, _1504690, _1504692] : [-(hBOOL(hAPP(hAPP(c_member(_1504682), _1504684), _1504686))), 39029 ^ _774244 : [(39036 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504682), _1504688), _1504686))), -(hAPP(c_Set_Ovimage(_1504690, _1504682, hAPP(hAPP(c_COMBC(_1504690, _1504682, _1504682), hAPP(hAPP(c_COMBC(_1504690, _1504682, tc_fun(_1504682, _1504682)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1504682, tc_fun(_1504682, _1504682)), _1504690), c_If(_1504682)), hAPP(hAPP(c_COMBC(_1504690, tc_fun(_1504690, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504690)), _1504692))), _1504684)), _1504688)), _1504686) = c_Orderings_Obot__class_Obot(tc_fun(_1504690, tc_HOL_Obool)))], (39030 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1504682), _1504688), _1504686)), -(hAPP(c_Set_Ovimage(_1504690, _1504682, hAPP(hAPP(c_COMBC(_1504690, _1504682, _1504682), hAPP(hAPP(c_COMBC(_1504690, _1504682, tc_fun(_1504682, _1504682)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1504682, tc_fun(_1504682, _1504682)), _1504690), c_If(_1504682)), hAPP(hAPP(c_COMBC(_1504690, tc_fun(_1504690, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504690)), _1504692))), _1504684)), _1504688)), _1504686) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1504690, tc_HOL_Obool)), _1504692))]]], (39662 ^ _774244) ^ [_1520576, _1520578] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520576, _1520576), tc_HOL_Obool)), c_Relation_OId__on(_1520576, _1520578)), hAPP(hAPP(c_Product__Type_OSigma(_1520576, _1520576), _1520578), hAPP(c_COMBK(tc_fun(_1520576, tc_HOL_Obool), _1520576), _1520578)))))], (49436 ^ _774244) ^ [_1763531, _1763533, _1763535, _1763537] : [-(c_List_Opartition(_1763531, _1763533, hAPP(hAPP(c_List_Olist_OCons(_1763531), _1763535), _1763537)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1763531), tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1763531), tc_fun(tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531))), tc_fun(tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1763531), tc_fun(tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)))), tc_fun(tc_fun(tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531))), tc_fun(tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)))), tc_List_Olist(_1763531)), c_COMBS(tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531))), tc_fun(tc_List_Olist(_1763531), tc_fun(tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)))), tc_List_Olist(_1763531)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)), tc_fun(tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531))), tc_List_Olist(_1763531)), hAPP(c_If(tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531))), hAPP(_1763533, _1763535)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1763531), tc_fun(tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531))), tc_List_Olist(_1763531)), c_Product__Type_OPair(tc_List_Olist(_1763531), tc_List_Olist(_1763531))), hAPP(c_List_Olist_OCons(_1763531), _1763535))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1763531), tc_fun(tc_List_Olist(_1763531), tc_List_Olist(_1763531)), tc_fun(tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531))), tc_fun(tc_fun(tc_List_Olist(_1763531), tc_List_Olist(_1763531)), tc_fun(tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)))), tc_List_Olist(_1763531)), c_COMBB(tc_List_Olist(_1763531), tc_prod(tc_List_Olist(_1763531), tc_List_Olist(_1763531)), tc_List_Olist(_1763531))), c_Product__Type_OPair(tc_List_Olist(_1763531), tc_List_Olist(_1763531)))), hAPP(c_List_Olist_OCons(_1763531), _1763535)))), c_List_Opartition(_1763531, _1763533, _1763537)))], (12396 ^ _774244) ^ [_979562, _979564, _979566, _979568] : [class_Rings_Olinordered__ring__strict(_979562), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979562), c_Groups_Ozero__class_Ozero(_979562)), _979564)), 12403 ^ _774244 : [(12410 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979562), _979566), _979568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979562), _979564), _979566)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979562), _979564), _979568))))], (12404 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979562), _979564), _979566)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979562), _979564), _979568))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979562), _979566), _979568)))]]], (15806 ^ _774244) ^ [_1042108, _1042110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1042108), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042110), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1042108), _1042110)))], (10153 ^ _774244) ^ [_941579] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _941579), _941579)))], (18127 ^ _774244) ^ [_1083928] : [class_Int_Onumber__ring(_1083928), -(hAPP(c_Int_Onumber__class_Onumber__of(_1083928), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1083928))], (6542 ^ _774244) ^ [_879695, _879697] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _879695), _879697) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 6545 ^ _774244 : [(6548 ^ _774244) ^ [] : [-(_879697 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6546 ^ _774244) ^ [] : [-(_879695 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7762 ^ _774244) ^ [_901006, _901008, _901010, _901012] : [hAPP(c_Sum__Type_OInl(_901006, _901008), _901010) = hAPP(c_Sum__Type_OInr(_901008, _901006), _901012)], (46960 ^ _774244) ^ [_1704582, _1704584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1704582)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1704584))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1704582), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1704584)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1704582)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1704582)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1704584))))], (23121 ^ _774244) ^ [_1173768, _1173770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173768)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173770)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1173768, _1173770) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1173768, _1173770)))], (14163 ^ _774244) ^ [_1011579, _1011581] : [class_Divides_Osemiring__div(_1011579), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1011579), c_Groups_Ozero__class_Ozero(_1011579)), _1011581) = c_Groups_Ozero__class_Ozero(_1011579))], (28026 ^ _774244) ^ [_1269177, _1269179, _1269181, _1269183] : [class_Lattices_Osemilattice__sup(_1269177), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269177), _1269179), _1269181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269177), _1269179), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269177), _1269181), _1269183))))], (5070 ^ _774244) ^ [_852611, _852613, _852615, _852617] : [-(c_Product__Type_Ofst(_852617, _852613) = c_Product__Type_Ofst(_852615, _852611)), _852617 = _852615, _852613 = _852611], (36913 ^ _774244) ^ [_1458527, _1458529] : [class_Orderings_Oorder(_1458527), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458527, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1458527), _1458529)), hAPP(c_SetInterval_Oord__class_OatLeast(_1458527), _1458529)) = hAPP(hAPP(c_Set_Oinsert(_1458527), _1458529), c_Orderings_Obot__class_Obot(tc_fun(_1458527, tc_HOL_Obool))))], (39809 ^ _774244) ^ [_1524681, _1524683, _1524685, _1524687, _1524689, _1524691] : [class_Groups_Ocomm__monoid__mult(_1524681), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524683), _1524685)), 39819 ^ _774244 : [(39822 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1524687), hAPP(_1524689, 39818 ^ [_1524681, _1524683, _1524685, _1524687, _1524689, _1524691])))], (39820 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524683), 39818 ^ [_1524681, _1524683, _1524685, _1524687, _1524689, _1524691]), _1524685)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1524681, _1524683, c_Groups_Otimes__class_Otimes(_1524681)), hAPP(hAPP(c_COMBS(_1524683, tc_fun(_1524687, tc_HOL_Obool), _1524681), hAPP(hAPP(c_COMBC(_1524683, _1524681, tc_fun(tc_fun(_1524687, tc_HOL_Obool), _1524681)), hAPP(hAPP(c_COMBB(tc_fun(_1524687, _1524681), tc_fun(_1524681, tc_fun(tc_fun(_1524687, tc_HOL_Obool), _1524681)), _1524683), c_Finite__Set_Ofold__image(_1524681, _1524687, c_Groups_Otimes__class_Otimes(_1524681))), _1524691)), c_Groups_Oone__class_Oone(_1524681))), _1524689)), c_Groups_Oone__class_Oone(_1524681)), _1524685) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1524681, tc_prod(_1524683, _1524687), c_Groups_Otimes__class_Otimes(_1524681)), hAPP(c_Product__Type_Oprod_Oprod__case(_1524683, _1524687, _1524681), _1524691)), c_Groups_Oone__class_Oone(_1524681)), hAPP(hAPP(c_Product__Type_OSigma(_1524683, _1524687), _1524685), _1524689)))], (7970 ^ _774244) ^ [_904561] : [class_Rings_Osemiring__1(_904561), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904561), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_904561))], (7012 ^ _774244) ^ [_887847, _887849, _887851, _887853] : [-(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887847, _887849), _887851, _887853)), 7013 ^ _774244 : [(7020 ^ _774244) ^ [] : [hBOOL(hAPP(_887847, _887851)), 7023 ^ _774244 : [(7024 ^ _774244) ^ [_888048] : [c_Natural_Oevalc(_887849, _887851, _888048), c_Natural_Oevalc(c_Com_Ocom_OWhile(_887847, _887849), _888048, _887853)]]], (7014 ^ _774244) ^ [] : [_887853 = _887851, -(hBOOL(hAPP(_887847, _887851)))]]], (12782 ^ _774244) ^ [_986564] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986564))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _986564)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13643 ^ _774244) ^ [_1001812, _1001814] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1001812, _1001814) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1001812 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1001814), 13646 ^ [_1001812, _1001814]))], (8966 ^ _774244) ^ [_920876, _920878, _920880] : [class_Groups_Oordered__ab__group__add(_920876), 8969 ^ _774244 : [(8976 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920876), _920880), hAPP(c_Groups_Ouminus__class_Ouminus(_920876), _920878))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920876), _920878), hAPP(c_Groups_Ouminus__class_Ouminus(_920876), _920880))))], (8970 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920876), _920878), hAPP(c_Groups_Ouminus__class_Ouminus(_920876), _920880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920876), _920880), hAPP(c_Groups_Ouminus__class_Ouminus(_920876), _920878))))]]], (26450 ^ _774244) ^ [_1236618, _1236620, _1236622, _1236624] : [class_Rings_Osemiring__1(_1236618), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1236618), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236620, tc_Nat_Onat), _1236622), _1236624)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236620, _1236618), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1236618, _1236620), c_Nat_Osemiring__1__class_Oof__nat(_1236618)), _1236622)), _1236624))], (28793 ^ _774244) ^ [] : [-(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)))], (41166 ^ _774244) ^ [_1561744, _1561746, _1561748, _1561750] : [-(c_Product__Type_Oapfst(_1561744, _1561746, _1561748, _1561750) = c_Product__Type_Omap__pair(_1561744, _1561746, _1561748, _1561748, _1561750, c_Fun_Oid(_1561748)))], (51265 ^ _774244) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (12081 ^ _774244) ^ [_974252, _974254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974252)), _974254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974252), _974254)))], (43678 ^ _774244) ^ [_1622923, _1622925, _1622927, _1622929, _1622931] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622923, tc_fun(_1622925, tc_HOL_Obool)), _1622927), hAPP(hAPP(c_COMBB(tc_fun(_1622925, tc_HOL_Obool), tc_fun(_1622925, tc_HOL_Obool), _1622923), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1622925, tc_HOL_Obool)), _1622929)), _1622931)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1622925, tc_HOL_Obool)), _1622929), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622923, tc_fun(_1622925, tc_HOL_Obool)), _1622927), _1622931)))], (3080 ^ _774244) ^ [_821390, _821392, _821394, _821396, _821398, _821400, _821402, _821404] : [-(c_Product__Type_Ocurry(_821404, _821400, _821396, _821392) = c_Product__Type_Ocurry(_821402, _821398, _821394, _821390)), _821404 = _821402, _821400 = _821398, _821396 = _821394, _821392 = _821390], (7774 ^ _774244) ^ [_901240, _901242, _901244] : [class_Rings_Olinordered__idom(_901240), -(_901242 = _901244), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901240), _901242), _901244))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901240), _901244), _901242)))], (50370 ^ _774244) ^ [_1783074, _1783076] : [-(_1783074 = c_List_Olist_ONil(_1783076)), -(c_List_Olast(_1783076, hAPP(c_List_Orev(_1783076), _1783074)) = hAPP(c_List_Ohd(_1783076), _1783074))], (35596 ^ _774244) ^ [_1429112, _1429114, _1429116, _1429118, _1429120] : [c_Equiv__Relations_Oequiv(_1429112, _1429114, _1429116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429112, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1429112, _1429112, _1429116), hAPP(hAPP(c_Set_Oinsert(_1429112), _1429118), c_Orderings_Obot__class_Obot(tc_fun(_1429112, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1429112, _1429112, _1429116), hAPP(hAPP(c_Set_Oinsert(_1429112), _1429120), c_Orderings_Obot__class_Obot(tc_fun(_1429112, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1429112), _1429118), _1429114)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1429112, _1429112)), hAPP(hAPP(c_Product__Type_OPair(_1429112, _1429112), _1429120), _1429118)), _1429116)))], (21347 ^ _774244) ^ [_1140211, _1140213, _1140215, _1140217] : [class_Fields_Olinordered__field__inverse__zero(_1140211), 21350 ^ _774244 : [(21351 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140211), _1140213), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140211), _1140215), _1140217))), 21354 ^ _774244 : [(21361 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140211), c_Groups_Ozero__class_Ozero(_1140211)), _1140217))), 21364 ^ _774244 : [(21371 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140211), _1140217), c_Groups_Ozero__class_Ozero(_1140211)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140211), _1140213), c_Groups_Ozero__class_Ozero(_1140211))))], (21365 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140211), _1140217), c_Groups_Ozero__class_Ozero(_1140211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140211), _1140215), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140211), _1140213), _1140217))))]]], (21355 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140211), c_Groups_Ozero__class_Ozero(_1140211)), _1140217)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140211), _1140213), _1140217)), _1140215)))]]], (21377 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140211), _1140213), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140211), _1140215), _1140217)))), 21380 ^ _774244 : [(21383 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140211), _1140213), _1140217)), _1140215))], (21381 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140211), c_Groups_Ozero__class_Ozero(_1140211)), _1140217)))]], 21384 ^ _774244 : [(21387 ^ _774244) ^ [] : [21388 ^ _774244 : [(21391 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140211), _1140215), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140211), _1140213), _1140217)))], (21389 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140211), _1140217), c_Groups_Ozero__class_Ozero(_1140211))))]], 21392 ^ _774244 : [(21395 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140211), _1140213), c_Groups_Ozero__class_Ozero(_1140211)))], (21393 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140211), _1140217), c_Groups_Ozero__class_Ozero(_1140211)))]]], (21385 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140211), c_Groups_Ozero__class_Ozero(_1140211)), _1140217))]]]]], (44594 ^ _774244) ^ [_1646082, _1646084, _1646086, _1646088] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1646082, tc_HOL_Obool)), _1646084), _1646086)), hBOOL(hAPP(hAPP(c_member(_1646082), _1646088), _1646084)), -(hBOOL(hAPP(hAPP(c_member(_1646082), _1646088), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646082, tc_HOL_Obool), _1646086))))], (38405 ^ _774244) ^ [_1490644, _1490646, _1490648, _1490650, _1490652, _1490654] : [class_Groups_Ocomm__monoid__add(_1490644), c_Fun_Oinj__on(_1490646, _1490648, _1490650, _1490652), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1490648, _1490644), _1490654), hAPP(c_Set_Oimage(_1490646, _1490648, _1490650), _1490652)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1490646, _1490644), hAPP(c_Fun_Ocomp(_1490648, _1490644, _1490646, _1490654), _1490650)), _1490652))], (50560 ^ _774244) ^ [_1788644, _1788646, _1788648] : [50562 ^ _774244 : [(50565 ^ _774244) ^ [] : [hBOOL(hAPP(_1788646, 50561 ^ [_1788644, _1788646, _1788648]))], (50563 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1788644), 50561 ^ [_1788644, _1788646, _1788648]), hAPP(c_List_Oset(_1788644), _1788648))))]], -(c_List_OtakeWhile(_1788644, _1788646, _1788648) = _1788648)], (43899 ^ _774244) ^ [_1628917, _1628919, _1628921] : [c_Relation_Orefl__on(_1628917, _1628919, _1628921), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1628917, _1628917), tc_HOL_Obool)), _1628921), hAPP(hAPP(c_Relation_Orel__comp(_1628917, _1628917, _1628917), hAPP(c_Relation_Oconverse(_1628917, _1628917), _1628921)), _1628921))))], (41228 ^ _774244) ^ [_1563575, _1563577, _1563579, _1563581, _1563583, _1563585] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1563575, _1563577, _1563579), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563575, _1563577), tc_HOL_Obool)), _1563581), _1563583)), _1563585) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563575, _1563579), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1563575, _1563577, _1563579), _1563581), _1563585)), hAPP(hAPP(c_Relation_Orel__comp(_1563575, _1563577, _1563579), _1563583), _1563585)))], (48726 ^ _774244) ^ [_1748116] : [class_Groups_Omonoid__add(_1748116), -(c_List_Omonoid__add__class_Olistsum(_1748116) = c_List_Ofoldl(_1748116, _1748116, c_Groups_Oplus__class_Oplus(_1748116), c_Groups_Ozero__class_Ozero(_1748116)))], (12277 ^ _774244) ^ [_977443, _977445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _977443)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _977445)), -(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), _977443), _977445))))], (24497 ^ _774244) ^ [_1200465, _1200467] : [class_Orderings_Olinorder(_1200465), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200465), _1200467), _1200467) = _1200467)], (25947 ^ _774244) ^ [_1227536, _1227538, _1227540, _1227542] : [-(c_Product__Type_Ocurry(_1227536, _1227538, _1227540, hAPP(c_Product__Type_Oprod_Oprod__case(_1227536, _1227538, _1227540), _1227542)) = _1227542)], (34 ^ _774244) ^ [_774697, _774699, _774701, _774703, _774705, _774707] : [-(c_Natural_Oevalc(_774705, _774701, _774697)), c_Natural_Oevalc(_774707, _774703, _774699), _774707 = _774705, _774703 = _774701, _774699 = _774697], (47895 ^ _774244) ^ [_1727558, _1727560, _1727562, _1727564] : [-(c_Map_Omap__upds(_1727558, _1727560, _1727562, c_List_Olist_ONil(_1727558), _1727564) = _1727562)], (33594 ^ _774244) ^ [_1384051, _1384053, _1384055] : [class_Orderings_Olinorder(_1384051), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384051), _1384053)), -(_1384055 = c_Orderings_Obot__class_Obot(tc_fun(_1384051, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1384051, tc_HOL_Obool)), _1384055), _1384053)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1384051), c_Big__Operators_Olattice_OSup__fin(_1384051, c_Orderings_Oord__class_Omax(_1384051), _1384055)), c_Big__Operators_Olattice_OSup__fin(_1384051, c_Orderings_Oord__class_Omax(_1384051), _1384053)) = c_Big__Operators_Olattice_OSup__fin(_1384051, c_Orderings_Oord__class_Omax(_1384051), _1384053))], (36575 ^ _774244) ^ [_1450713, _1450715, _1450717, _1450719, _1450721] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1450713, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1450715, _1450713, _1450717), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450715, tc_HOL_Obool)), _1450719), _1450721))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450713, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1450715, _1450713, _1450717), _1450719)), hAPP(c_Relation_OImage(_1450715, _1450713, _1450717), _1450721)))))], (17149 ^ _774244) ^ [_1067526, _1067528] : [class_Groups_Omonoid__mult(_1067526), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1067526), c_Groups_Oone__class_Oone(_1067526)), _1067528) = c_Groups_Oone__class_Oone(_1067526))], (17097 ^ _774244) ^ [_1066535, _1066537] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1066535) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066537), 17100 ^ _774244 : [(17103 ^ _774244) ^ [] : [-(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), _1066537))))], (17101 ^ _774244) ^ [] : [-(_1066535 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066537)))]]], (43577 ^ _774244) ^ [_1620132, _1620134, _1620136, _1620138, _1620140] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620134, _1620132)), hAPP(hAPP(c_Product__Type_OPair(_1620134, _1620132), _1620138), _1620136)), _1620140)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620132, _1620134)), hAPP(hAPP(c_Product__Type_OPair(_1620132, _1620134), _1620136), _1620138)), hAPP(c_Relation_Oconverse(_1620134, _1620132), _1620140))))], (9294 ^ _774244) ^ [_926790, _926792, _926794] : [class_Groups_Ogroup__add(_926790), 9297 ^ _774244 : [(9304 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926790), _926792), _926794) = c_Groups_Ozero__class_Ozero(_926790), -(_926792 = hAPP(c_Groups_Ouminus__class_Ouminus(_926790), _926794))], (9298 ^ _774244) ^ [] : [_926792 = hAPP(c_Groups_Ouminus__class_Ouminus(_926790), _926794), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926790), _926792), _926794) = c_Groups_Ozero__class_Ozero(_926790))]]], (8780 ^ _774244) ^ [_917596, _917598, _917600, _917602] : [class_Rings_Ocomm__semiring__1(_917596), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917596), _917598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917596), _917600), _917602)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917596), _917600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917596), _917598), _917602)))], (47553 ^ _774244) ^ [_1719336, _1719338, _1719340, _1719342, _1719344, _1719346] : [hAPP(hAPP(c_List_Olist_OCons(_1719336), _1719338), _1719340) = _1719342, _1719344 = hAPP(hAPP(c_List_Oappend(_1719336), _1719340), _1719346), -(hAPP(hAPP(c_List_Olist_OCons(_1719336), _1719338), _1719344) = hAPP(hAPP(c_List_Oappend(_1719336), _1719342), _1719346))], (10784 ^ _774244) ^ [_951362, _951364, _951366, _951368] : [class_Orderings_Oorder(_951362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951362), _951364), _951366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951362), _951368), _951364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951362), _951368), _951366)))], (49400 ^ _774244) ^ [_1762685, _1762687, _1762689, _1762691] : [hBOOL(hAPP(hAPP(c_member(_1762685), _1762687), hAPP(c_List_Oset(_1762685), _1762689))), -(hBOOL(hAPP(_1762691, _1762687))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762685)), hAPP(c_List_Ofilter(_1762685, _1762691), _1762689))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762685)), _1762689))))], (1174 ^ _774244) ^ [_791643, _791645] : [-(class_Rings_Oring__1(_791643)), _791645 = _791643, class_Rings_Oring__1(_791645)], (44544 ^ _774244) ^ [_1644776, _1644778, _1644780, _1644782] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1644776, tc_HOL_Obool), hAPP(c_Set_Oimage(_1644778, tc_fun(_1644776, tc_HOL_Obool), _1644780), _1644782)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644778, tc_fun(_1644776, tc_HOL_Obool)), _1644782), _1644780))], (8794 ^ _774244) ^ [_917925, _917927, _917929] : [class_Int_Oring__char__0(_917925), 8797 ^ _774244 : [(8804 ^ _774244) ^ [] : [_917927 = _917929, -(hAPP(c_Int_Oring__1__class_Oof__int(_917925), _917927) = hAPP(c_Int_Oring__1__class_Oof__int(_917925), _917929))], (8798 ^ _774244) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_917925), _917927) = hAPP(c_Int_Oring__1__class_Oof__int(_917925), _917929), -(_917927 = _917929)]]], (2604 ^ _774244) ^ [_813672, _813674, _813676, _813678] : [-(c_Orderings_Oord_Omax(_813678, _813674) = c_Orderings_Oord_Omax(_813676, _813672)), _813678 = _813676, _813674 = _813672], (6958 ^ _774244) ^ [_886909, _886911, _886913, _886915] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_886909, _886911), _886913, _886915, _886913)), 6959 ^ _774244 : [(6962 ^ _774244) ^ [_886996] : [c_Natural_Oevaln(_886911, _886913, _886915, _886996), c_Natural_Oevaln(c_Com_Ocom_OWhile(_886909, _886911), _886996, _886915, _886913)], (6960 ^ _774244) ^ [] : [-(hBOOL(hAPP(_886909, _886913)))]]], (12970 ^ _774244) ^ [_989623, _989625] : [-(hAPP(c_Int_Onat, _989623) = _989625), 12973 ^ _774244 : [(12976 ^ _774244) ^ [] : [_989623 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _989625)], (12974 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989623)))]], 12977 ^ _774244 : [(12980 ^ _774244) ^ [] : [_989625 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12978 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989623))]]], (15050 ^ _774244) ^ [_1027229, _1027231] : [class_Groups_Ogroup__add(_1027229), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1027229), _1027231), _1027231) = c_Groups_Ozero__class_Ozero(_1027229))], (22612 ^ _774244) ^ [_1164515, _1164517, _1164519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1164515, tc_fun(_1164515, tc_HOL_Obool))), _1164517), _1164519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1164515, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1164515, _1164519)), c_Wellfounded_Oaccp(_1164515, _1164517))))], (2594 ^ _774244) ^ [_813523, _813525, _813527, _813529] : [-(c_Code__Numeral_Onat__of__aux(_813529, _813525) = c_Code__Numeral_Onat__of__aux(_813527, _813523)), _813529 = _813527, _813525 = _813523], (24525 ^ _774244) ^ [_1200966, _1200968] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1200966, _1200968) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1200966), hAPP(c_Code__Numeral_Onat__of, _1200968))))], (46599 ^ _774244) ^ [_1696937, _1696939, _1696941, _1696943] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1696937), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1696939), _1696941)))), -(hAPP(c_Random_Opick(_1696939, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1696939)), _1696941), _1696943)), _1696937) = hAPP(c_Random_Opick(_1696939, _1696943), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1696937), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1696939), _1696941))))], (6141 ^ _774244) ^ [_872674, _872676, _872678, _872680, _872682] : [c_Natural_Oevalc(c_Com_Ocom_OCond(_872674, _872676, _872678), _872680, _872682), 6146 ^ _774244 : [(6149 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_872676, _872680, _872682))], (6147 ^ _774244) ^ [] : [-(hBOOL(hAPP(_872674, _872680)))]], 6150 ^ _774244 : [(6153 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_872678, _872680, _872682))], (6151 ^ _774244) ^ [] : [hBOOL(hAPP(_872674, _872680))]]], (10982 ^ _774244) ^ [_954827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954827), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_954827 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28882 ^ _774244) ^ [_1287940, _1287942, _1287944] : [c_Orderings_Obot__class_Obot(tc_fun(_1287940, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_1287940), _1287942), _1287944)], (32482 ^ _774244) ^ [_1363029, _1363031, _1363033] : [class_Rings_Oring__1(_1363029), hBOOL(hAPP(hAPP(c_member(_1363029), _1363031), c_Int_Oring__1__class_OInts(_1363029))), hBOOL(hAPP(hAPP(c_member(_1363029), _1363033), c_Int_Oring__1__class_OInts(_1363029))), -(hBOOL(hAPP(hAPP(c_member(_1363029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363029), _1363031), _1363033)), c_Int_Oring__1__class_OInts(_1363029))))], (18471 ^ _774244) ^ [_1089514, _1089516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1089514), _1089516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1089514)), c_Int_OBit1(_1089516))))], (23339 ^ _774244) ^ [_1178074, _1178076, _1178078] : [-(_1178074 = hAPP(hAPP(c_Product__Type_OPair(_1178076, _1178078), hAPP(c_Product__Type_Ofst(_1178076, _1178078), _1178074)), hAPP(c_Product__Type_Osnd(_1178076, _1178078), _1178074)))], (22282 ^ _774244) ^ [_1158222, _1158224] : [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), _1158222))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1158224), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1158222))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1158224), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158222))), 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), _1158224))), c_COMBI(tc_Int_Oint))))], (8944 ^ _774244) ^ [_920553, _920555] : [class_Groups_Ogroup__add(_920553), 8947 ^ _774244 : [(8954 ^ _774244) ^ [] : [c_Groups_Ozero__class_Ozero(_920553) = _920555, -(c_Groups_Ozero__class_Ozero(_920553) = hAPP(c_Groups_Ouminus__class_Ouminus(_920553), _920555))], (8948 ^ _774244) ^ [] : [c_Groups_Ozero__class_Ozero(_920553) = hAPP(c_Groups_Ouminus__class_Ouminus(_920553), _920555), -(c_Groups_Ozero__class_Ozero(_920553) = _920555)]]], (23027 ^ _774244) ^ [_1172560, _1172562, _1172564] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1172560, _1172560), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1172562), _1172564))), -(_1172560 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1172564 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23561 ^ _774244) ^ [_1182636, _1182638] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1182636)), hAPP(c_Nat_OSuc, _1182638)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1182636))), 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)), _1182638)))))], (23393 ^ _774244) ^ [_1179455, _1179457] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179455, tc_HOL_Obool)), _1179457), _1179457)))], (29941 ^ _774244) ^ [_1307650, _1307652, _1307654, _1307656, _1307658] : [c_Finite__Set_Ofun__left__comm__idem(_1307650, _1307652, _1307654), -(c_Finite__Set_Ofun__left__comm__idem(_1307656, _1307652, hAPP(hAPP(c_COMBB(_1307650, tc_fun(_1307652, _1307652), _1307656), _1307654), _1307658)))], (34893 ^ _774244) ^ [_1412263, _1412265, _1412267, _1412269, _1412271] : [class_Groups_Ocomm__monoid__add(_1412263), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412265), _1412267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412265, tc_HOL_Obool)), _1412269), _1412267)), 34907 ^ _774244 : [(34910 ^ _774244) ^ [] : [hAPP(_1412271, 34906 ^ [_1412263, _1412265, _1412267, _1412269, _1412271]) = c_Groups_Ozero__class_Ozero(_1412263)], (34908 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1412265), 34906 ^ [_1412263, _1412265, _1412267, _1412269, _1412271]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1412265, tc_HOL_Obool)), _1412267), _1412269))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1412265, _1412263), _1412271), _1412267) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1412265, _1412263), _1412271), _1412269))], (46669 ^ _774244) ^ [_1698785, _1698787] : [class_Groups_Oordered__ab__group__add__abs(_1698785), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1698785), hAPP(c_Groups_Oabs__class_Oabs(_1698785), hAPP(c_List_Omonoid__add__class_Olistsum(_1698785), _1698787))), hAPP(c_List_Omonoid__add__class_Olistsum(_1698785), hAPP(hAPP(c_List_Omap(_1698785, _1698785), c_Groups_Oabs__class_Oabs(_1698785)), _1698787)))))], (23621 ^ _774244) ^ [_1183981, _1183983, _1183985, _1183987] : [class_Orderings_Olinorder(_1183981), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183981), _1183983), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183981), _1183985), _1183987)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183981), _1183985), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183981), _1183983), _1183987)))], (12127 ^ _774244) ^ [_975006] : [-(hAPP(c_Nat_OSuc, _975006) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _975006))], (38421 ^ _774244) ^ [_1490987, _1490989, _1490991, _1490993, _1490995, _1490997] : [c_Fun_Oinj__on(_1490987, _1490989, _1490991, _1490993), -(hBOOL(hAPP(hAPP(c_member(_1490989), _1490995), hAPP(c_Set_Oimage(_1490987, _1490989, _1490991), _1490993)))), -(c_Fun_Oinj__on(_1490987, _1490989, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1490987, _1490989), _1490991), _1490997), _1490995), _1490993))], (11006 ^ _774244) ^ [_955199, _955201, _955203] : [class_Groups_Oordered__ab__group__add(_955199), 11009 ^ _774244 : [(11016 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955199), _955203), _955201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955199), hAPP(c_Groups_Ouminus__class_Ouminus(_955199), _955201)), hAPP(c_Groups_Ouminus__class_Ouminus(_955199), _955203))))], (11010 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955199), hAPP(c_Groups_Ouminus__class_Ouminus(_955199), _955201)), hAPP(c_Groups_Ouminus__class_Ouminus(_955199), _955203))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955199), _955203), _955201)))]]], (15534 ^ _774244) ^ [_1036301, _1036303, _1036305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036301), _1036303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036301), _1036305)), 15541 ^ _774244 : [(15548 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036303), _1036305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036303), _1036301)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036305), _1036301))))], (15542 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036303), _1036301)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036305), _1036301))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036303), _1036305)))]]], (39624 ^ _774244) ^ [_1519176, _1519178, _1519180] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1519176, _1519178), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519176, _1519178), _1519180), hAPP(c_COMBK(tc_fun(_1519178, tc_HOL_Obool), _1519176), c_Orderings_Otop__class_Otop(tc_fun(_1519178, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1519176, _1519178), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1519176, tc_HOL_Obool)), _1519180)), hAPP(c_COMBK(tc_fun(_1519178, tc_HOL_Obool), _1519176), c_Orderings_Otop__class_Otop(tc_fun(_1519178, tc_HOL_Obool)))))], (24105 ^ _774244) ^ [_1192838, _1192840, _1192842, _1192844] : [class_Groups_Oordered__ab__group__add(_1192838), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1192838), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1192838), _1192840), _1192842)), _1192844) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1192838), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1192838), _1192840), _1192844)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1192838), _1192842), _1192844)))], (34515 ^ _774244) ^ [_1403077] : [-(_1403077 = 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)), _1403077), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (24443 ^ _774244) ^ [_1199282] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1199282)) = _1199282)], (49428 ^ _774244) ^ [_1763328, _1763330] : [-(c_List_Opartition(_1763328, _1763330, c_List_Olist_ONil(_1763328)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1763328), tc_List_Olist(_1763328)), c_List_Olist_ONil(_1763328)), c_List_Olist_ONil(_1763328)))], (10195 ^ _774244) ^ [_942238, _942240, _942242] : [class_Orderings_Oorder(_942238), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942238), _942240), _942242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942238), _942242), _942240)), -(_942242 = _942240)], (16243 ^ _774244) ^ [_1050399, _1050401, _1050403] : [class_Groups_Oordered__ab__group__add__abs(_1050399), -(hAPP(c_Groups_Oabs__class_Oabs(_1050399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050399), _1050401), _1050403)) = hAPP(c_Groups_Oabs__class_Oabs(_1050399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050399), _1050403), _1050401)))], (27308 ^ _774244) ^ [_1255498, _1255500, _1255502] : [class_Groups_Oordered__ab__group__add(_1255498), -(hAPP(c_Set_Oimage(_1255498, _1255498, c_Groups_Ouminus__class_Ouminus(_1255498)), c_SetInterval_Oord__class_OatLeastAtMost(_1255498, _1255500, _1255502)) = c_SetInterval_Oord__class_OatLeastAtMost(_1255498, hAPP(c_Groups_Ouminus__class_Ouminus(_1255498), _1255502), hAPP(c_Groups_Ouminus__class_Ouminus(_1255498), _1255500)))], (27484 ^ _774244) ^ [_1258919, _1258921] : [c_Nat__Transfer_Onat__set(_1258919), c_Nat__Transfer_Onat__set(_1258921), 27491 ^ _774244 : [(27498 ^ _774244) ^ [] : [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), _1258919)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258919), _1258921)))], (27492 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258919), _1258921)), -(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), _1258919)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258921))))]]], (42280 ^ _774244) ^ [_1590221, _1590223, _1590225, _1590227] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1590221, tc_HOL_Obool), tc_fun(_1590221, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1590221, tc_HOL_Obool), tc_fun(_1590221, tc_HOL_Obool)), _1590223), _1590225)), c_Wellfounded_Omax__ext(_1590221, _1590227)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590221), _1590223)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590221), _1590225)), -(_1590225 = c_Orderings_Obot__class_Obot(tc_fun(_1590221, tc_HOL_Obool))), 42294 ^ _774244 : [(42297 ^ _774244) ^ [_1590626] : [hBOOL(hAPP(hAPP(c_member(_1590221), _1590626), _1590225)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590221, _1590221)), hAPP(hAPP(c_Product__Type_OPair(_1590221, _1590221), 42293 ^ [_1590221, _1590223, _1590225, _1590227]), _1590626)), _1590227))], (42295 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590221), 42293 ^ [_1590221, _1590223, _1590225, _1590227]), _1590223)))]]], (23581 ^ _774244) ^ [_1183095, _1183097, _1183099, _1183101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1183095, tc_HOL_Obool)), _1183097), _1183099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1183095, tc_HOL_Obool)), _1183099), _1183101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1183095, tc_HOL_Obool)), _1183097), _1183101)))], (26786 ^ _774244) ^ [_1244624, _1244626, _1244628, _1244630, _1244632] : [class_Orderings_Oorder(_1244624), 26789 ^ _774244 : [(26810 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1244624, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1244624, _1244626, _1244628)), c_SetInterval_Oord__class_OatLeastAtMost(_1244624, _1244630, _1244632)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244624), _1244630), _1244632)), 26813 ^ _774244 : [(26816 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244624), _1244630), _1244626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244624), _1244628), _1244632)), 26823 ^ _774244 : [(26826 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244624), _1244628), _1244632))], (26824 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244624), _1244630), _1244626))]]], (26814 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244624), _1244626), _1244628)))]]], (26790 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1244624, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1244624, _1244626, _1244628)), c_SetInterval_Oord__class_OatLeastAtMost(_1244624, _1244630, _1244632))), 26793 ^ _774244 : [(26794 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244624), _1244626), _1244628)), 26797 ^ _774244 : [(26802 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244624), _1244630), _1244626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244624), _1244628), _1244632)))], (26800 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244624), _1244628), _1244632)))], (26798 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244624), _1244630), _1244626)))]]], (26808 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244624), _1244630), _1244632)))]]]]], (3166 ^ _774244) ^ [_822785, _822787, _822789, _822791, _822793, _822795, _822797, _822799, _822801, _822803] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_822803, _822799, _822795, _822791, _822787) = c_SetInterval_Oord_OgreaterThanAtMost(_822801, _822797, _822793, _822789, _822785)), _822803 = _822801, _822799 = _822797, _822795 = _822793, _822791 = _822789, _822787 = _822785], (27030 ^ _774244) ^ [_1249458, _1249460, _1249462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249458)), 27033 ^ _774244 : [(27034 ^ _774244) ^ [_1249592] : [27036 ^ _774244 : [(27042 ^ _774244) ^ [] : [-(_1249592 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27038 ^ [_1249458, _1249460, _1249462, _1249592]), 27035 ^ [_1249458, _1249460, _1249462, _1249592]))], (27040 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27038 ^ [_1249458, _1249460, _1249462, _1249592]), _1249460)))], (27037 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27035 ^ [_1249458, _1249460, _1249462, _1249592]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1249458))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249462), _1249592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249462), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1249592), _1249458))))]]], (31321 ^ _774244) ^ [_1336970, _1336972, _1336974] : [class_Orderings_Oord(_1336970), 31324 ^ _774244 : [(31331 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336970), _1336972), _1336974)), -(hBOOL(hAPP(hAPP(c_member(_1336970), _1336972), hAPP(c_SetInterval_Oord__class_OlessThan(_1336970), _1336974))))], (31325 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1336970), _1336972), hAPP(c_SetInterval_Oord__class_OlessThan(_1336970), _1336974))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336970), _1336972), _1336974)))]]], (35889 ^ _774244) ^ [_1435716, _1435718, _1435720, _1435722] : [class_Lattices_Osemilattice__inf(_1435716), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435716), _1435718), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1435716), _1435720), _1435722))), 35896 ^ _774244 : [(35899 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435716), _1435718), _1435722)))], (35897 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435716), _1435718), _1435720)))]]], (17719 ^ _774244) ^ [_1077591, _1077593] : [class_Int_Onumber__ring(_1077591), 17722 ^ _774244 : [(17729 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077593)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1077591), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077593)) = hAPP(c_Int_Onumber__class_Onumber__of(_1077591), _1077593))], (17723 ^ _774244) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077593))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1077591), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077593)) = c_Groups_Ozero__class_Ozero(_1077591))]]], (36071 ^ _774244) ^ [_1439009, _1439011, _1439013, _1439015, _1439017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439009, tc_HOL_Obool)), _1439011), _1439013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439009, tc_HOL_Obool)), _1439015), _1439017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439009, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439009, tc_HOL_Obool)), _1439011), _1439015)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439009, tc_HOL_Obool)), _1439013), _1439017))))], (16793 ^ _774244) ^ [_1061104, _1061106] : [class_Groups_Oordered__ab__group__add__abs(_1061104), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061104), _1061106), c_Groups_Ozero__class_Ozero(_1061104))), -(hAPP(c_Groups_Oabs__class_Oabs(_1061104), _1061106) = hAPP(c_Groups_Ouminus__class_Ouminus(_1061104), _1061106))], (39235 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (40737 ^ _774244) ^ [_1544811, _1544813, _1544815] : [-(hAPP(c_Set_OCollect(_1544811), hAPP(hAPP(c_COMBS(_1544811, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1544811), c_fimplies), _1544813)), _1544815)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1544811, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1544811, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1544811), _1544813))), hAPP(c_Set_OCollect(_1544811), _1544815)))], (23549 ^ _774244) ^ [_1182389, _1182391, _1182393, _1182395, _1182397, _1182399] : [hBOOL(hAPP(_1182389, _1182391)), hBOOL(hAPP(_1182393, _1182395)), 23556 ^ _774244 : [(23559 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1182393, hAPP(c_Product__Type_Osnd(_1182397, _1182399), hAPP(hAPP(c_Product__Type_OPair(_1182397, _1182399), _1182391), _1182395)))))], (23557 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1182389, hAPP(c_Product__Type_Ofst(_1182397, _1182399), hAPP(hAPP(c_Product__Type_OPair(_1182397, _1182399), _1182391), _1182395)))))]]], (3996 ^ _774244) ^ [_835838, _835840, _835842, _835844, _835846, _835848] : [-(c_Smallcheck_Ofull__small_H(_835848, _835844, _835840) = c_Smallcheck_Ofull__small_H(_835846, _835842, _835838)), _835848 = _835846, _835844 = _835842, _835840 = _835838], (17901 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (7363 ^ _774244) ^ [_893795, _893797] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893795), _893797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893797), hAPP(c_Nat_OSuc, _893795))))], (41250 ^ _774244) ^ [_1564376, _1564378, _1564380, _1564382] : [hAPP(hAPP(c_Relation_Orel__comp(_1564376, _1564376, _1564376), _1564378), _1564380) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564376, _1564376), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1564376, _1564376, _1564376), _1564382), _1564380) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564376, _1564376), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1564376, _1564376, _1564376), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564376, _1564376), tc_HOL_Obool)), _1564378), _1564382)), _1564380) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564376, _1564376), tc_HOL_Obool)))], (45281 ^ _774244) ^ [_1662461, _1662463, _1662465, _1662467, _1662469, _1662471] : [hAPP(c_Map_Omap__add(_1662461, _1662463, _1662465, _1662467), _1662469) = hAPP(c_Option_Ooption_OSome(_1662463), _1662471), -(hAPP(_1662467, _1662469) = hAPP(c_Option_Ooption_OSome(_1662463), _1662471)), 45288 ^ _774244 : [(45291 ^ _774244) ^ [] : [-(hAPP(_1662465, _1662469) = hAPP(c_Option_Ooption_OSome(_1662463), _1662471))], (45289 ^ _774244) ^ [] : [-(hAPP(_1662467, _1662469) = c_Option_Ooption_ONone(_1662463))]]], (1754 ^ _774244) ^ [_798893, _798895] : [-(class_Rings_Odvd(_798893)), _798895 = _798893, class_Rings_Odvd(_798895)], (32304 ^ _774244) ^ [_1359228, _1359230, _1359232, _1359234] : [hBOOL(hAPP(hAPP(c_member(_1359228), _1359230), c_SetInterval_Oord_OatLeast(_1359228, _1359232, _1359234))), -(hBOOL(hAPP(hAPP(_1359232, _1359234), _1359230)))], (12502 ^ _774244) ^ [_981593, _981595, _981597, _981599, _981601] : [class_Rings_Olinordered__semiring__strict(_981593), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981593), _981595), _981597)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981593), _981599), _981601)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981593), c_Groups_Ozero__class_Ozero(_981593)), _981595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981593), c_Groups_Ozero__class_Ozero(_981593)), _981599)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981593), _981595), _981599)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981593), _981597), _981601))))], (1364 ^ _774244) ^ [_794018, _794020] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_794018)), _794020 = _794018, class_Groups_Oordered__ab__semigroup__add__imp__le(_794020)], (15566 ^ _774244) ^ [_1036928, _1036930, _1036932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036932), _1036930))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036928), _1036930)), _1036932)))], (6636 ^ _774244) ^ [_881096, _881098, _881100] : [_881098 = _881100, -(hAPP(c_Option_Ooption_OSome(_881096), _881098) = hAPP(c_Option_Ooption_OSome(_881096), _881100))], (6828 ^ _774244) ^ [_884890, _884892] : [c_Option_Ois__none(_884890, _884892), -(_884892 = c_Option_Ooption_ONone(_884890))], (42459 ^ _774244) ^ [_1594012, _1594014, _1594016, _1594018, _1594020] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1594012, _1594014, _1594016), _1594018), _1594020) = c_HOL_OThe(_1594014, c_Finite__Set_Ofold__graph(_1594012, _1594014, _1594016, _1594018, _1594020)))], (32204 ^ _774244) ^ [_1357290, _1357292, _1357294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357290)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1357292), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1357294)), 32214 ^ _774244 : [(32220 ^ _774244) ^ [] : [-(_1357292 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32216 ^ [_1357290, _1357292, _1357294]), 32213 ^ [_1357290, _1357292, _1357294]))], (32218 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32216 ^ [_1357290, _1357292, _1357294]), _1357294)))], (32215 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32213 ^ [_1357290, _1357292, _1357294]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1357290))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1357292), _1357290) = _1357292)], (37454 ^ _774244) ^ [_1471447, _1471449, _1471451] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1471447), _1471449)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471447), _1471451)), 37464 ^ _774244 : [(37467 ^ _774244) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37465 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471447), 37463 ^ [_1471447, _1471449, _1471451]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471447, tc_HOL_Obool)), _1471449), _1471451))))]], -(hAPP(c_Finite__Set_Ocard(_1471447), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1471447, tc_HOL_Obool)), _1471449), _1471451)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1471447), _1471449)), hAPP(c_Finite__Set_Ocard(_1471447), _1471451)))], (49316 ^ _774244) ^ [_1761021, _1761023, _1761025, _1761027] : [-(hBOOL(hAPP(_1761021, _1761023))), -(hAPP(c_List_Ofilter(_1761025, _1761021), hAPP(hAPP(c_List_Olist_OCons(_1761025), _1761023), _1761027)) = hAPP(c_List_Ofilter(_1761025, _1761021), _1761027))], (13519 ^ _774244) ^ [_999365, _999367, _999369, _999371] : [class_Divides_Osemiring__div(_999365), -(c_Divides_Odiv__class_Omod(_999365, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999365), c_Divides_Odiv__class_Omod(_999365, _999367, _999369)), _999371), _999369) = c_Divides_Odiv__class_Omod(_999365, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999365), _999367), _999371), _999369))], (42499 ^ _774244) ^ [_1594888, _1594890, _1594892, _1594894] : [class_Orderings_Olinorder(_1594888), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594888), _1594890)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1594888, _1594888, c_Orderings_Oord__class_Omax(_1594888)), _1594892), hAPP(hAPP(c_Set_Oinsert(_1594888), _1594894), _1594890)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1594888), _1594894), hAPP(hAPP(c_Finite__Set_Ofold(_1594888, _1594888, c_Orderings_Oord__class_Omax(_1594888)), _1594892), _1594890)))], (13156 ^ _774244) ^ [_992874, _992876, _992878, _992880, _992882, _992884] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _992874), _992876)), _992878) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _992880), _992882)), _992884), 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), _992880), _992882)), _992884)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992878), _992874)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _992884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _992880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _992880), _992874)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _992882), _992876)))], (38758 ^ _774244) ^ [_1498421, _1498423, _1498425, _1498427] : [c_Fun_Oinj__on(_1498421, _1498423, _1498425, c_Orderings_Otop__class_Otop(tc_fun(_1498421, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498421, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1498421, _1498423, _1498425), hAPP(hAPP(c_Set_Oinsert(_1498423), _1498427), c_Orderings_Obot__class_Obot(tc_fun(_1498423, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1498421), c_HOL_OThe(_1498421, hAPP(hAPP(c_COMBC(_1498421, _1498423, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1498423, tc_fun(_1498423, tc_HOL_Obool), _1498421), c_fequal), _1498425)), _1498427))), c_Orderings_Obot__class_Obot(tc_fun(_1498421, tc_HOL_Obool))))))], (26862 ^ _774244) ^ [_1246042, _1246044, _1246046, _1246048] : [class_Groups_Ocomm__monoid__add(_1246042), 26865 ^ _774244 : [(26872 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246044), _1246046))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246042), _1246048), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1246046), hAPP(c_Nat_OSuc, _1246044))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1246042), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246042), _1246048), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1246046), _1246044))), hAPP(_1246048, _1246044)))], (26866 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246044), _1246046)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246042), _1246048), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1246046), hAPP(c_Nat_OSuc, _1246044))) = c_Groups_Ozero__class_Ozero(_1246042))]]], (38696 ^ _774244) ^ [_1497075, _1497077, _1497079, _1497081, _1497083, _1497085] : [c_Fun_Oinj__on(_1497075, _1497077, _1497079, _1497081), hAPP(_1497079, _1497083) = _1497085, hBOOL(hAPP(hAPP(c_member(_1497075), _1497083), _1497081)), -(hAPP(c_Fun_Othe__inv__into(_1497075, _1497077, _1497081, _1497079), _1497085) = _1497083)], (29318 ^ _774244) ^ [_1295890, _1295892, _1295894] : [class_Orderings_Oorder(_1295890), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295890), _1295892), _1295894)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1295890, _1295894, _1295892) = c_Orderings_Obot__class_Obot(tc_fun(_1295890, tc_HOL_Obool)))], (11365 ^ _774244) ^ [_961362, _961364] : [class_Rings_Olinordered__idom(_961362), 11368 ^ _774244 : [(11375 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _961364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961362), c_Groups_Ozero__class_Ozero(_961362)), hAPP(c_Int_Oring__1__class_Oof__int(_961362), _961364))))], (11369 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961362), c_Groups_Ozero__class_Ozero(_961362)), hAPP(c_Int_Oring__1__class_Oof__int(_961362), _961364))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _961364)))]]], (30877 ^ _774244) ^ [_1328058, _1328060] : [-(_1328060 = c_Orderings_Obot__class_Obot(tc_fun(_1328058, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1328058), 30880 ^ [_1328058, _1328060]), _1328060)))], (50019 ^ _774244) ^ [_1775132, _1775134, _1775136, _1775138, _1775140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1775132), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1775134), _1775136))), -(hAPP(hAPP(c_List_Onth(_1775138), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1775138), _1775140), c_List_Oupt(_1775136, _1775134))), _1775132) = hAPP(_1775140, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1775136), _1775132)))], (41140 ^ _774244) ^ [_1561250, _1561252] : [-(c_Product__Type_Oapfst(_1561250, _1561250, _1561252, c_Fun_Oid(_1561250)) = c_Fun_Oid(tc_prod(_1561250, _1561252)))], (12824 ^ _774244) ^ [_987222, _987224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987222), c_Groups_Oone__class_Oone(tc_Int_Oint))), _987224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987222), _987224)))], (20209 ^ _774244) ^ [_1120286, _1120288, _1120290, _1120292] : [class_Fields_Ofield__inverse__zero(_1120286), -(_1120288 = c_Groups_Ozero__class_Ozero(_1120286)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120286), _1120290), _1120288)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120286), _1120292), _1120288)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120286), _1120290), _1120292))], (3456 ^ _774244) ^ [_827366, _827368, _827370, _827372, _827374, _827376, _827378, _827380, _827382, _827384] : [-(c_Fun_Ooverride__on(_827384, _827380, _827376, _827372, _827368) = c_Fun_Ooverride__on(_827382, _827378, _827374, _827370, _827366)), _827384 = _827382, _827380 = _827378, _827376 = _827374, _827372 = _827370, _827368 = _827366], (32446 ^ _774244) ^ [_1362392, _1362394] : [class_Int_Onumber__ring(_1362392), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1362394)), -(hBOOL(hAPP(hAPP(c_member(_1362392), hAPP(c_Int_Onumber__class_Onumber__of(_1362392), _1362394)), c_Nat_Osemiring__1__class_ONats(_1362392))))], (46092 ^ _774244) ^ [_1681961] : [class_Orderings_Olinorder(_1681961), -(c_Finite__Set_Ofun__left__comm(_1681961, tc_List_Olist(_1681961), c_List_Olinorder__class_Oinsort__key(_1681961, _1681961, c_COMBI(_1681961))))], (31491 ^ _774244) ^ [_1340683, _1340685, _1340687, _1340689, _1340691] : [c_Finite__Set_Ofolding__one(_1340683, _1340685, _1340687), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340683), _1340689)), hBOOL(hAPP(hAPP(c_member(_1340683), _1340691), _1340689)), 31502 ^ _774244 : [(31509 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340683, tc_HOL_Obool)), _1340689), hAPP(hAPP(c_Set_Oinsert(_1340683), _1340691), c_Orderings_Obot__class_Obot(tc_fun(_1340683, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1340683, tc_HOL_Obool))), -(hAPP(_1340687, _1340689) = hAPP(hAPP(_1340685, _1340691), hAPP(_1340687, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340683, tc_HOL_Obool)), _1340689), hAPP(hAPP(c_Set_Oinsert(_1340683), _1340691), c_Orderings_Obot__class_Obot(tc_fun(_1340683, tc_HOL_Obool)))))))], (31503 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340683, tc_HOL_Obool)), _1340689), hAPP(hAPP(c_Set_Oinsert(_1340683), _1340691), c_Orderings_Obot__class_Obot(tc_fun(_1340683, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1340683, tc_HOL_Obool)), -(hAPP(_1340687, _1340689) = _1340691)]]], (38818 ^ _774244) ^ [_1499882, _1499884] : [-(hAPP(c_Set_Ovimage(_1499882, _1499882, c_COMBI(_1499882)), _1499884) = _1499884)], (35259 ^ _774244) ^ [_1420684, _1420686, _1420688, _1420690, _1420692, _1420694] : [hBOOL(hAPP(hAPP(c_member(_1420684), _1420686), _1420688)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1420684, _1420690)), hAPP(hAPP(c_Product__Type_OPair(_1420684, _1420690), _1420686), _1420692)), _1420694)), -(hBOOL(hAPP(hAPP(c_member(_1420690), _1420692), hAPP(c_Relation_OImage(_1420684, _1420690, _1420694), _1420688))))], (30156 ^ _774244) ^ [_1311404] : [-(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)), _1311404))))], (51069 ^ _774244) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (34426 ^ _774244) ^ [_1401368, _1401370, _1401372, _1401374, _1401376] : [class_Groups_Oordered__ab__group__add(_1401368), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401370), _1401372)), 34436 ^ _774244 : [(34439 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401368), c_Groups_Ozero__class_Ozero(_1401368)), hAPP(_1401374, 34435 ^ [_1401368, _1401370, _1401372, _1401374, _1401376])))], (34437 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401370), 34435 ^ [_1401368, _1401370, _1401372, _1401374, _1401376]), _1401372)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1401370, _1401368), _1401374), _1401372) = c_Groups_Ozero__class_Ozero(_1401368), hBOOL(hAPP(hAPP(c_member(_1401370), _1401376), _1401372)), -(hAPP(_1401374, _1401376) = c_Groups_Ozero__class_Ozero(_1401368))], (51461 ^ _774244) ^ [_1801688, _1801690] : [hBOOL(_1801688), hBOOL(_1801690), -(hBOOL(hAPP(hAPP(c_fconj, _1801688), _1801690)))], (38834 ^ _774244) ^ [_1500296, _1500298, _1500300, _1500302, _1500304] : [hBOOL(hAPP(hAPP(c_member(_1500296), hAPP(_1500298, _1500300)), _1500302)), -(hBOOL(hAPP(hAPP(c_member(_1500304), _1500300), hAPP(c_Set_Ovimage(_1500304, _1500296, _1500298), _1500302))))], (33886 ^ _774244) ^ [_1389692, _1389694, _1389696, _1389698, _1389700, _1389702, _1389704] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1389692, tc_Option_Ooption(_1389694)), _1389696), _1389698), hAPP(c_Option_Ooption_OSome(_1389694), _1389700)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1389692, tc_Option_Ooption(_1389694)), _1389702), _1389698), hAPP(c_Option_Ooption_OSome(_1389694), _1389704)), -(_1389700 = _1389704)], (9332 ^ _774244) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40089 ^ _774244) ^ [_1531751, _1531753] : [class_Orderings_Olinorder(_1531751), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531751), _1531753)), -(c_Big__Operators_Olinorder__class_OMax(_1531751, _1531753) = hAPP(c_Finite__Set_Ofold1(_1531751, c_Orderings_Oord__class_Omax(_1531751)), _1531753))], (3580 ^ _774244) ^ [_829368, _829370] : [_829370 = _829368, -(c_Int_Oint__ge__less__than2(_829370) = c_Int_Oint__ge__less__than2(_829368))], (9322 ^ _774244) ^ [_927256, _927258, _927260] : [class_Groups_Ogroup__add(_927256), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927256), _927258), _927260) = c_Groups_Ozero__class_Ozero(_927256), -(hAPP(c_Groups_Ouminus__class_Ouminus(_927256), _927258) = _927260)], (8120 ^ _774244) ^ [_907196, _907198] : [_907196 = _907198, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _907196) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _907198))], (45882 ^ _774244) ^ [_1676659, _1676661] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1676659), _1676661) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1676659, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1676661), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (43129 ^ _774244) ^ [_1608371, _1608373] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1608371, _1608371, _1608371), _1608373), c_Transitive__Closure_Ortrancl(_1608371, _1608373)) = hAPP(hAPP(c_Relation_Orel__comp(_1608371, _1608371, _1608371), c_Transitive__Closure_Ortrancl(_1608371, _1608373)), _1608373))], (14928 ^ _774244) ^ [_1024881, _1024883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024883)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1024881)), hAPP(c_Int_Onat, _1024883)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1024881, _1024883)))], (30623 ^ _774244) ^ [_1320941, _1320943, _1320945, _1320947] : [hBOOL(hAPP(hAPP(c_member(_1320941), _1320943), _1320945)), -(hBOOL(hAPP(hAPP(c_member(_1320941), _1320943), _1320947))), -(hBOOL(hAPP(hAPP(c_member(_1320941), _1320943), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320941, tc_HOL_Obool)), _1320945), _1320947))))], (17083 ^ _774244) ^ [_1066317, _1066319] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066317)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066319)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1066317), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1066319))))], (19533 ^ _774244) ^ [_1107623, _1107625, _1107627] : [class_Rings_Olinordered__semidom(_1107623), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107623), hAPP(hAPP(c_Power_Opower__class_Opower(_1107623), _1107625), 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(_1107623), _1107627), 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(_1107623), c_Groups_Ozero__class_Ozero(_1107623)), _1107627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107623), _1107625), _1107627)))], (39932 ^ _774244) ^ [_1528081, _1528083, _1528085, _1528087, _1528089, _1528091, _1528093, _1528095, _1528097, _1528099, _1528101] : [-(hAPP(c_Product__Type_Omap__pair(_1528081, _1528083, _1528085, _1528087, _1528089, _1528091), hAPP(c_Product__Type_Omap__pair(_1528093, _1528081, _1528095, _1528085, _1528097, _1528099), _1528101)) = hAPP(c_Product__Type_Omap__pair(_1528093, _1528083, _1528095, _1528087, hAPP(c_Fun_Ocomp(_1528081, _1528083, _1528093, _1528089), _1528097), hAPP(c_Fun_Ocomp(_1528085, _1528087, _1528095, _1528091), _1528099)), _1528101))], (43715 ^ _774244) ^ [_1624395, _1624397, _1624399, _1624401] : [_1624395 = c_Orderings_Obot__class_Obot(tc_fun(_1624397, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1624397, tc_fun(_1624399, tc_HOL_Obool)), _1624395), hAPP(c_COMBK(tc_fun(_1624399, tc_HOL_Obool), _1624397), _1624401)) = c_Orderings_Otop__class_Otop(tc_fun(_1624399, tc_HOL_Obool)))], (3728 ^ _774244) ^ [_831732, _831734, _831736, _831738] : [-(c_New__DSequence_Oneg__single(_831738, _831734) = c_New__DSequence_Oneg__single(_831736, _831732)), _831738 = _831736, _831734 = _831732], (44376 ^ _774244) ^ [_1641343, _1641345, _1641347, _1641349, _1641351] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1641343, _1641343)), hAPP(hAPP(c_Product__Type_OPair(_1641343, _1641343), _1641345), _1641347)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1641343, _1641343), tc_HOL_Obool), _1641349), _1641351))), 44381 ^ _774244 : [(44384 ^ _774244) ^ [] : [-(_1641345 = _1641347)], (44382 ^ _774244) ^ [] : [-(_1641349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 44387 ^ _774244 : [(44392 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641343, _1641343)), hAPP(hAPP(c_Product__Type_OPair(_1641343, _1641343), 44385 ^ [_1641343, _1641345, _1641347, _1641349, _1641351]), _1641347)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1641343, _1641343), tc_HOL_Obool), 44386 ^ [_1641343, _1641345, _1641347, _1641349, _1641351]), _1641351))))], (44390 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641343, _1641343)), hAPP(hAPP(c_Product__Type_OPair(_1641343, _1641343), _1641345), 44385 ^ [_1641343, _1641345, _1641347, _1641349, _1641351])), _1641351)))], (44388 ^ _774244) ^ [] : [-(_1641349 = hAPP(c_Nat_OSuc, 44386 ^ [_1641343, _1641345, _1641347, _1641349, _1641351]))]]], (18719 ^ _774244) ^ [_1093549] : [class_Int_Onumber__ring(_1093549), c_Int_Oiszero(_1093549, hAPP(c_Int_Onumber__class_Onumber__of(_1093549), c_Int_OBit1(c_Int_OPls)))], (21119 ^ _774244) ^ [_1135997, _1135999] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135997), _1135999), hAPP(c_Int_Onumber__class_Onumber__of(_1135997), c_Int_OBit1(c_Int_OPls))) = _1135999), class_Fields_Ofield(_1135997), class_Int_Onumber__ring(_1135997)], (34714 ^ _774244) ^ [_1408382] : [-(c_Wellfounded_Omeasure(_1408382) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1408382), c_Wellfounded_Oless__than))], (9118 ^ _774244) ^ [_923409] : [class_Rings_Ozero__neq__one(_923409), c_Groups_Oone__class_Oone(_923409) = c_Groups_Ozero__class_Ozero(_923409)], (3870 ^ _774244) ^ [_833863, _833865, _833867, _833869] : [-(c_Relation_ODomain(_833869, _833865) = c_Relation_ODomain(_833867, _833863)), _833869 = _833867, _833865 = _833863], (45641 ^ _774244) ^ [_1671135] : [-(hAPP(c_Option_Omap(_1671135, _1671135), c_Fun_Oid(_1671135)) = c_Fun_Oid(tc_Option_Ooption(_1671135)))], (30509 ^ _774244) ^ [_1318596, _1318598, _1318600, _1318602, _1318604] : [c_Finite__Set_Ofolding__one(_1318596, _1318598, _1318600), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318596), _1318602)), 30516 ^ _774244 : [(30523 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318596, tc_HOL_Obool)), _1318602), hAPP(hAPP(c_Set_Oinsert(_1318596), _1318604), c_Orderings_Obot__class_Obot(tc_fun(_1318596, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1318596, tc_HOL_Obool))), -(hAPP(_1318600, hAPP(hAPP(c_Set_Oinsert(_1318596), _1318604), _1318602)) = hAPP(hAPP(_1318598, _1318604), hAPP(_1318600, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318596, tc_HOL_Obool)), _1318602), hAPP(hAPP(c_Set_Oinsert(_1318596), _1318604), c_Orderings_Obot__class_Obot(tc_fun(_1318596, tc_HOL_Obool)))))))], (30517 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318596, tc_HOL_Obool)), _1318602), hAPP(hAPP(c_Set_Oinsert(_1318596), _1318604), c_Orderings_Obot__class_Obot(tc_fun(_1318596, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1318596, tc_HOL_Obool)), -(hAPP(_1318600, hAPP(hAPP(c_Set_Oinsert(_1318596), _1318604), _1318602)) = _1318604)]]], (3126 ^ _774244) ^ [_822095, _822097, _822099, _822101, _822103, _822105, _822107, _822109] : [-(c_SetInterval_Oord_OatLeastAtMost(_822109, _822105, _822101, _822097) = c_SetInterval_Oord_OatLeastAtMost(_822107, _822103, _822099, _822095)), _822109 = _822107, _822105 = _822103, _822101 = _822099, _822097 = _822095], (26249 ^ _774244) ^ [_1232825, _1232827] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232825), _1232827)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232825)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232827))))], (50156 ^ _774244) ^ [_1778300] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1778300)), c_List_Otranspose__rel(_1778300)), c_List_Olist_ONil(tc_List_Olist(_1778300)))), -(c_List_Otranspose(_1778300, c_List_Olist_ONil(tc_List_Olist(_1778300))) = c_List_Olist_ONil(tc_List_Olist(_1778300)))], (19487 ^ _774244) ^ [_1106922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1106922), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1106922 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1106922 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (35881 ^ _774244) ^ [_1435553, _1435555, _1435557] : [35882 ^ _774244 : [(35885 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1435553), _1435557))], (35883 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1435553), _1435555))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1435553), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435553, tc_HOL_Obool)), _1435555), _1435557))))], (28580 ^ _774244) ^ [_1280419, _1280421, _1280423, _1280425, _1280427] : [28582 ^ _774244 : [(28588 ^ _774244) ^ [] : [hBOOL(hAPP(_1280427, 28584 ^ [_1280419, _1280421, _1280423, _1280425, _1280427]))], (28586 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1280419), 28584 ^ [_1280419, _1280421, _1280423, _1280425, _1280427]), hAPP(_1280425, 28581 ^ [_1280419, _1280421, _1280423, _1280425, _1280427]))))], (28583 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1280421), 28581 ^ [_1280419, _1280421, _1280423, _1280425, _1280427]), _1280423)))]], 28589 ^ _774244 : [(28590 ^ _774244) ^ [_1280729] : [hBOOL(hAPP(hAPP(c_member(_1280419), _1280729), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280421, tc_fun(_1280419, tc_HOL_Obool)), _1280423), _1280425))), -(hBOOL(hAPP(_1280427, _1280729)))]]], (12087 ^ _774244) ^ [_974351, _974353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974351), _974353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974351)), _974353)))], (36733 ^ _774244) ^ [_1454282, _1454284, _1454286, _1454288] : [class_Orderings_Olinorder(_1454282), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454282, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1454282), _1454284)), c_SetInterval_Oord__class_OatLeastAtMost(_1454282, _1454286, _1454288)) = c_SetInterval_Oord__class_OatLeastAtMost(_1454282, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1454282), _1454284), _1454286), _1454288))], (16071 ^ _774244) ^ [_1047378, _1047380, _1047382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1047378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1047380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1047382), 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), _1047382), _1047380))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1047378)))))], (7080 ^ _774244) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42439 ^ _774244) ^ [_1593643, _1593645] : [c_Wellfounded_Owf(_1593643, _1593645), -(c_Wellfounded_Owf(_1593643, c_Transitive__Closure_Otrancl(_1593643, _1593645)))], (31923 ^ _774244) ^ [_1351446, _1351448, _1351450] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1351446), _1351448)), hBOOL(hAPP(hAPP(c_member(_1351446), _1351450), _1351448)), -(hAPP(c_Finite__Set_Ocard(_1351446), _1351448) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1351446), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351446, tc_HOL_Obool)), _1351448), hAPP(hAPP(c_Set_Oinsert(_1351446), _1351450), c_Orderings_Obot__class_Obot(tc_fun(_1351446, tc_HOL_Obool)))))))], (27215 ^ _774244) ^ [_1253481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253481)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253481) = 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, _1253481))))], (28805 ^ _774244) ^ [_1285912] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1285912)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1285912), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1285912)))], (26842 ^ _774244) ^ [_1245584, _1245586, _1245588, _1245590] : [class_Groups_Ocomm__monoid__add(_1245584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1245586), _1245588)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245584), _1245590), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1245586), _1245588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245584), hAPP(_1245590, _1245586)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245584), _1245590), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1245586)), _1245588))))], (41845 ^ _774244) ^ [_1579570, _1579572, _1579574] : [-(hAPP(c_Relation_ODomain(_1579570, _1579572), hAPP(c_Set_OCollect(tc_prod(_1579570, _1579572)), hAPP(c_Product__Type_Oprod_Oprod__case(_1579570, _1579572, tc_HOL_Obool), _1579574))) = hAPP(c_Set_OCollect(_1579570), hAPP(hAPP(c_COMBB(tc_fun(_1579572, tc_HOL_Obool), tc_HOL_Obool, _1579570), c_HOL_OEx(_1579572)), _1579574)))], (39382 ^ _774244) ^ [_1512907, _1512909, _1512911, _1512913] : [hBOOL(hAPP(hAPP(c_member(_1512907), _1512909), c_Wellfounded_Oacc(_1512907, _1512911))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512907, _1512907)), hAPP(hAPP(c_Product__Type_OPair(_1512907, _1512907), _1512913), _1512909)), _1512911)), -(hBOOL(hAPP(hAPP(c_member(_1512907), _1512913), c_Wellfounded_Oacc(_1512907, _1512911))))], (11533 ^ _774244) ^ [_964249, _964251] : [class_Rings_Olinordered__ring(_964249), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964249), c_Groups_Ozero__class_Ozero(_964249)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964249), _964251), _964251))))], (50262 ^ _774244) ^ [_1780770, _1780772] : [_1780772 = c_List_Olist_ONil(_1780770), -(c_List_Olist_ONil(_1780770) = hAPP(c_List_Orev(_1780770), _1780772))], (24449 ^ _774244) ^ [_1199429, _1199431, _1199433, _1199435, _1199437, _1199439] : [hAPP(c_Product__Type_Oapfst(_1199429, _1199431, _1199433, _1199435), _1199437) = hAPP(c_Product__Type_Oapfst(_1199429, _1199431, _1199433, _1199439), _1199437), -(hAPP(_1199435, hAPP(c_Product__Type_Ofst(_1199429, _1199433), _1199437)) = hAPP(_1199439, hAPP(c_Product__Type_Ofst(_1199429, _1199433), _1199437)))], (37741 ^ _774244) ^ [_1477289, _1477291] : [class_Lattices_Olattice(_1477289), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477289), _1477291)), -(_1477291 = c_Orderings_Obot__class_Obot(tc_fun(_1477289, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1477289), c_Big__Operators_Olattice__class_OInf__fin(_1477289, _1477291)), c_Big__Operators_Olattice__class_OSup__fin(_1477289, _1477291))))], (19395 ^ _774244) ^ [_1105347, _1105349, _1105351] : [class_Rings_Olinordered__semidom(_1105347), hAPP(hAPP(c_Power_Opower__class_Opower(_1105347), _1105349), 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(_1105347), _1105351), 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(_1105347), c_Groups_Ozero__class_Ozero(_1105347)), _1105349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105347), c_Groups_Ozero__class_Ozero(_1105347)), _1105351)), -(_1105349 = _1105351)], (30667 ^ _774244) ^ [_1321750, _1321752, _1321754, _1321756, _1321758, _1321760, _1321762] : [hBOOL(hAPP(hAPP(c_member(_1321750), _1321752), hAPP(hAPP(_1321754, _1321756), _1321758))), -(hBOOL(hAPP(hAPP(c_member(_1321750), _1321752), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1321760, _1321762, tc_fun(_1321750, tc_HOL_Obool)), _1321754), hAPP(hAPP(c_Product__Type_OPair(_1321760, _1321762), _1321756), _1321758)))))], (33234 ^ _774244) ^ [_1376357, _1376359, _1376361, _1376363, _1376365, _1376367, _1376369] : [c_Nitpick_Ofold__graph_H(_1376357, _1376359, _1376361, _1376363, _1376365, hAPP(hAPP(_1376361, _1376367), _1376369)), 33239 ^ _774244 : [(33242 ^ _774244) ^ [] : [-(hAPP(hAPP(_1376361, _1376367), _1376369) = _1376363)], (33240 ^ _774244) ^ [] : [-(_1376365 = c_Orderings_Obot__class_Obot(tc_fun(_1376357, tc_HOL_Obool)))]], 33245 ^ _774244 : [(33250 ^ _774244) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1376357, _1376359, _1376361, _1376363, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1376357, tc_HOL_Obool)), _1376365), hAPP(hAPP(c_Set_Oinsert(_1376357), 33243 ^ [_1376357, _1376359, _1376361, _1376363, _1376365, _1376367, _1376369]), c_Orderings_Obot__class_Obot(tc_fun(_1376357, tc_HOL_Obool)))), 33244 ^ [_1376357, _1376359, _1376361, _1376363, _1376365, _1376367, _1376369]))], (33248 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1376357), 33243 ^ [_1376357, _1376359, _1376361, _1376363, _1376365, _1376367, _1376369]), _1376365)))], (33246 ^ _774244) ^ [] : [-(hAPP(hAPP(_1376361, _1376367), _1376369) = hAPP(hAPP(_1376361, 33243 ^ [_1376357, _1376359, _1376361, _1376363, _1376365, _1376367, _1376369]), 33244 ^ [_1376357, _1376359, _1376361, _1376363, _1376365, _1376367, _1376369]))]]], (11501 ^ _774244) ^ [_963683, _963685] : [class_Groups_Olinordered__ab__group__add(_963683), 11504 ^ _774244 : [(11511 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963683), _963685), c_Groups_Ozero__class_Ozero(_963683))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963683), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963683), _963685), _963685)), c_Groups_Ozero__class_Ozero(_963683))))], (11505 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963683), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963683), _963685), _963685)), c_Groups_Ozero__class_Ozero(_963683))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963683), _963685), c_Groups_Ozero__class_Ozero(_963683))))]]], (28346 ^ _774244) ^ [_1275492, _1275494, _1275496] : [class_Groups_Ocomm__monoid__add(_1275492), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1275492), _1275494), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1275496))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1275492), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1275492), _1275494), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1275496))), hAPP(_1275494, hAPP(c_Nat_OSuc, _1275496))))], (22764 ^ _774244) ^ [_1167321, _1167323, _1167325, _1167327, _1167329] : [hBOOL(hAPP(hAPP(_1167321, _1167323), _1167325)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1167327, _1167329, tc_HOL_Obool), _1167321), hAPP(hAPP(c_Product__Type_OPair(_1167327, _1167329), _1167323), _1167325))))], (19359 ^ _774244) ^ [_1104693] : [-(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)))), _1104693) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1104693), _1104693))], (50055 ^ _774244) ^ [_1775792, _1775794, _1775796, _1775798] : [class_Orderings_Olinorder(_1775792), c_List_Olinorder__class_Osorted(_1775792, _1775794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1775796), _1775798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1775798), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775792)), _1775794))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1775792), hAPP(hAPP(c_List_Onth(_1775792), _1775794), _1775796)), hAPP(hAPP(c_List_Onth(_1775792), _1775794), _1775798))))], (23919 ^ _774244) ^ [_1189331, _1189333] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1189331)), _1189333) = 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), _1189331)), _1189333))], (21623 ^ _774244) ^ [_1145530, _1145532, _1145534, _1145536] : [class_Fields_Ofield(_1145530), -(_1145532 = c_Groups_Ozero__class_Ozero(_1145530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1145534), _1145536)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1145530), _1145532), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1145536), _1145534)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145530), hAPP(hAPP(c_Power_Opower__class_Opower(_1145530), _1145532), _1145536)), hAPP(hAPP(c_Power_Opower__class_Opower(_1145530), _1145532), _1145534)))], (33372 ^ _774244) ^ [_1379748, _1379750, _1379752, _1379754] : [-(c_Sum__Type_OPlus(_1379748, _1379750, _1379752, _1379754) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(_1379748, _1379750), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1379748, tc_sum(_1379748, _1379750), c_Sum__Type_OInl(_1379748, _1379750)), _1379752)), hAPP(c_Set_Oimage(_1379750, tc_sum(_1379748, _1379750), c_Sum__Type_OInr(_1379750, _1379748)), _1379754)))], (4700 ^ _774244) ^ [_846876, _846878, _846880, _846882] : [-(c_Random_Oselect__weight(_846882, _846878) = c_Random_Oselect__weight(_846880, _846876)), _846882 = _846880, _846878 = _846876], (6754 ^ _774244) ^ [_883154, _883156, _883158, _883160, _883162, _883164] : [c_Com_Ocom_OLocal(_883154, _883156, _883158) = c_Com_Ocom_OCond(_883160, _883162, _883164)], (51113 ^ _774244) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (35314 ^ _774244) ^ [_1422255] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1422255)) = _1422255)], (16421 ^ _774244) ^ [_1053477, _1053479, _1053481, _1053483, _1053485] : [class_Rings_Olinordered__idom(_1053477), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053477), hAPP(c_Groups_Oabs__class_Oabs(_1053477), _1053479)), _1053481)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053477), hAPP(c_Groups_Oabs__class_Oabs(_1053477), _1053483)), _1053485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053477), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053477), hAPP(c_Groups_Oabs__class_Oabs(_1053477), _1053479)), hAPP(c_Groups_Oabs__class_Oabs(_1053477), _1053483))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053477), _1053481), _1053485))))], (47899 ^ _774244) ^ [_1727632, _1727634] : [-(hAPP(hAPP(c_List_Otake(_1727632), _1727634), c_List_Olist_ONil(_1727632)) = c_List_Olist_ONil(_1727632))], (47796 ^ _774244) ^ [_1724551, _1724553, _1724555, _1724557] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724553)), _1724555)))), -(hAPP(hAPP(c_List_Onth(_1724553), hAPP(hAPP(c_List_Oappend(_1724553), _1724555), _1724557)), _1724551) = hAPP(hAPP(c_List_Onth(_1724553), _1724557), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1724551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724553)), _1724555))))], (43091 ^ _774244) ^ [_1607441, _1607443, _1607445] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607441, _1607441), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1607441, _1607441), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1607441, _1607443)), c_Transitive__Closure_Ortrancl(_1607441, _1607445))), c_Transitive__Closure_Ortrancl(_1607441, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1607441, _1607441), tc_HOL_Obool)), _1607443), _1607445)))))], (27886 ^ _774244) ^ [_1266745, _1266747, _1266749] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266745, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266745, tc_HOL_Obool)), _1266747), _1266749)), _1266749) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266745, tc_HOL_Obool)), _1266747), _1266749))], (43865 ^ _774244) ^ [_1627928, _1627930, _1627932, _1627934] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627928, _1627928)), hAPP(hAPP(c_Product__Type_OPair(_1627928, _1627928), _1627930), _1627932)), c_Transitive__Closure_Otrancl(_1627928, hAPP(c_Relation_Oconverse(_1627928, _1627928), _1627934)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1627928, _1627928)), hAPP(hAPP(c_Product__Type_OPair(_1627928, _1627928), _1627930), _1627932)), hAPP(c_Relation_Oconverse(_1627928, _1627928), c_Transitive__Closure_Otrancl(_1627928, _1627934)))))], (45851 ^ _774244) ^ [_1675953, _1675955, _1675957, _1675959, _1675961] : [hBOOL(hAPP(c_List_Odistinct(_1675953), hAPP(hAPP(c_List_Omap(tc_prod(_1675953, _1675955), _1675953), c_Product__Type_Ofst(_1675953, _1675955)), _1675957))), 45854 ^ _774244 : [(45861 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1675953, _1675955)), hAPP(hAPP(c_Product__Type_OPair(_1675953, _1675955), _1675961), _1675959)), hAPP(c_List_Oset(tc_prod(_1675953, _1675955)), _1675957))), -(hAPP(c_Option_Ooption_OSome(_1675955), _1675959) = hAPP(c_Map_Omap__of(_1675953, _1675955, _1675957), _1675961))], (45855 ^ _774244) ^ [] : [hAPP(c_Option_Ooption_OSome(_1675955), _1675959) = hAPP(c_Map_Omap__of(_1675953, _1675955, _1675957), _1675961), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1675953, _1675955)), hAPP(hAPP(c_Product__Type_OPair(_1675953, _1675955), _1675961), _1675959)), hAPP(c_List_Oset(tc_prod(_1675953, _1675955)), _1675957))))]]], (7437 ^ _774244) ^ [_894930, _894932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894930), _894932)), -(hAPP(c_Nat_OSuc, _894930) = _894932), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _894930)), _894932)))], (13746 ^ _774244) ^ [_1003520, _1003522, _1003524] : [class_Lattices_Oboolean__algebra(_1003520), 13749 ^ _774244 : [(13756 ^ _774244) ^ [] : [_1003522 = _1003524, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1003520), _1003522) = hAPP(c_Groups_Ouminus__class_Ouminus(_1003520), _1003524))], (13750 ^ _774244) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1003520), _1003522) = hAPP(c_Groups_Ouminus__class_Ouminus(_1003520), _1003524), -(_1003522 = _1003524)]]], (29218 ^ _774244) ^ [_1294255, _1294257] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1294255, tc_HOL_Obool)), _1294257), c_Orderings_Otop__class_Otop(tc_fun(_1294255, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1294255, tc_HOL_Obool)))], (41758 ^ _774244) ^ [_1577262, _1577264, _1577266] : [c_Wellfounded_OwfP(_1577262, _1577264), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1577262, _1577264), _1577266)))], (22188 ^ _774244) ^ [_1156001, _1156003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1156001)), hAPP(c_Code__Numeral_Oof__nat, _1156003))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1156001), _1156003)))], (45523 ^ _774244) ^ [_1668055, _1668057, _1668059] : [c_Fun_Oinj__on(tc_List_Olist(_1668055), tc_List_Olist(_1668057), hAPP(c_List_Omap(_1668055, _1668057), _1668059), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1668055), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1668055, _1668057, _1668059, c_Orderings_Otop__class_Otop(tc_fun(_1668055, tc_HOL_Obool))))], (39760 ^ _774244) ^ [_1522947, _1522949, _1522951, _1522953] : [_1522947 = c_Orderings_Obot__class_Obot(tc_fun(_1522949, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1522949, _1522951), _1522951, c_Product__Type_Osnd(_1522949, _1522951)), hAPP(hAPP(c_Product__Type_OSigma(_1522949, _1522951), _1522947), hAPP(c_COMBK(tc_fun(_1522951, tc_HOL_Obool), _1522949), _1522953))) = c_Orderings_Obot__class_Obot(tc_fun(_1522951, tc_HOL_Obool)))], (36831 ^ _774244) ^ [_1456493, _1456495, _1456497, _1456499, _1456501] : [class_Groups_Ocomm__monoid__mult(_1456493), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456495), _1456497)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456495), _1456499)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1456493), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456495, _1456493), _1456501), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1456495, tc_HOL_Obool)), _1456497), _1456499))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456495, _1456493), _1456501), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456495, tc_HOL_Obool)), _1456497), _1456499))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1456493), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456495, _1456493), _1456501), _1456497)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456495, _1456493), _1456501), _1456499)))], (22638 ^ _774244) ^ [_1165006, _1165008] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1165006, _1165008), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1165006), _1165008)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1165006, _1165008)))))], (30194 ^ _774244) ^ [_1312145, _1312147, _1312149] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312145), _1312147)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1312145, tc_HOL_Obool)), _1312149), _1312147)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1312145), _1312147)), hAPP(c_Finite__Set_Ocard(_1312145), _1312149))), -(_1312149 = _1312147)], (24697 ^ _774244) ^ [_1204601, _1204603, _1204605, _1204607, _1204609, _1204611, _1204613] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1204601, _1204603, _1204605, _1204607, _1204609, _1204611, _1204613) = c_New__DSequence_Oneg__decr__bind(_1204601, _1204603, hAPP(hAPP(hAPP(_1204605, _1204609), _1204611), _1204613), hAPP(hAPP(c_COMBC(_1204601, 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(_1204603)))), hAPP(hAPP(c_COMBC(_1204601, 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(_1204603))))), hAPP(hAPP(c_COMBC(_1204601, 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(_1204603)))))), _1204607), _1204609)), _1204611)), _1204613)))], (46836 ^ _774244) ^ [_1702373, _1702375, _1702377, _1702379, _1702381] : [class_Orderings_Olinorder(_1702373), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1702375, _1702373, _1702377), _1702379), _1702381) = c_List_Olist_ONil(_1702375)], (23313 ^ _774244) ^ [_1177557, _1177559, _1177561, _1177563] : [-(_1177557 = _1177559), hAPP(c_Product__Type_Ofst(_1177561, _1177563), _1177557) = hAPP(c_Product__Type_Ofst(_1177561, _1177563), _1177559), hAPP(c_Product__Type_Osnd(_1177561, _1177563), _1177557) = hAPP(c_Product__Type_Osnd(_1177561, _1177563), _1177559)], (14959 ^ _774244) ^ [_1025466, _1025468, _1025470] : [class_Fields_Olinordered__field__inverse__zero(_1025466), 14965 ^ _774244 : [(14970 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025466), 14964 ^ [_1025466, _1025468, _1025470]), _1025468)), _1025470))], (14968 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025466), 14964 ^ [_1025466, _1025468, _1025470]), c_Groups_Oone__class_Oone(_1025466))))], (14966 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025466), c_Groups_Ozero__class_Ozero(_1025466)), 14964 ^ [_1025466, _1025468, _1025470])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025466), _1025468), _1025470)))], (17987 ^ _774244) ^ [_1081835] : [-(c_Int_Osucc(_1081835) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1081835), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (50737 ^ _774244) ^ [_1791886, _1791888] : [c_List_Oremdups(_1791886, _1791888) = _1791888, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791886)), c_List_Oremdups(_1791886, _1791888)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791886)), _1791888))], (45904 ^ _774244) ^ [_1677070, _1677072, _1677074] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1677070, tc_HOL_Obool)), hAPP(c_List_Oset(_1677070), c_List_Oremove1(_1677070, _1677072, _1677074))), hAPP(c_List_Oset(_1677070), _1677074))))], (1134 ^ _774244) ^ [_791143, _791145] : [-(class_Int_Oring__char__0(_791143)), _791145 = _791143, class_Int_Oring__char__0(_791145)], (4258 ^ _774244) ^ [_840133, _840135, _840137, _840139, _840141, _840143] : [-(c_List_Oset__Cons(_840143, _840139, _840135) = c_List_Oset__Cons(_840141, _840137, _840133)), _840143 = _840141, _840139 = _840137, _840135 = _840133], (21873 ^ _774244) ^ [_1150388, _1150390] : [_1150388 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1150388, _1150390) = _1150390)], (27410 ^ _774244) ^ [_1257558, _1257560, _1257562] : [class_Orderings_Olinorder(_1257558), 27413 ^ _774244 : [(27420 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257558), _1257562), _1257560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257558, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257558), _1257560)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257558), _1257562))))], (27414 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257558, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257558), _1257560)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257558), _1257562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257558), _1257562), _1257560)))]]], (1534 ^ _774244) ^ [_796143, _796145] : [-(class_Groups_Ocomm__monoid__add(_796143)), _796145 = _796143, class_Groups_Ocomm__monoid__add(_796145)], (25439 ^ _774244) ^ [_1218011, _1218013, _1218015] : [class_Rings_Ocomm__ring__1(_1218011), 25442 ^ _774244 : [(25449 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1218011), _1218013), _1218015)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1218011), hAPP(c_Groups_Ouminus__class_Ouminus(_1218011), _1218013)), _1218015)))], (25443 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1218011), hAPP(c_Groups_Ouminus__class_Ouminus(_1218011), _1218013)), _1218015)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1218011), _1218013), _1218015)))]]], (17635 ^ _774244) ^ [_1076134] : [-(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, _1076134))))))], (28848 ^ _774244) ^ [_1287068, _1287070, _1287072] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1287068), _1287070))), 28851 ^ _774244 : [(28858 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1287072), _1287070))), -(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)), _1287068)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1287072), _1287070)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (28852 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1287072), _1287070)), -(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)), _1287068)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1287072), _1287070)) = 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))))]]], (8018 ^ _774244) ^ [_905410, _905412, _905414, _905416] : [class_Orderings_Oorder(_905410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905410), hAPP(_905412, 8023 ^ [_905410, _905412, _905414, _905416])), hAPP(_905412, hAPP(c_Nat_OSuc, 8023 ^ [_905410, _905412, _905414, _905416])))), 8026 ^ _774244 : [(8033 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905414), _905416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905410), hAPP(_905412, _905414)), hAPP(_905412, _905416))))], (8027 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905410), hAPP(_905412, _905414)), hAPP(_905412, _905416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905414), _905416)))]]], (19147 ^ _774244) ^ [_1101023] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1101023))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1101023)))))], (28182 ^ _774244) ^ [_1272200, _1272202, _1272204, _1272206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272200, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272200, tc_HOL_Obool)), _1272202), _1272204)), _1272206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272200, tc_HOL_Obool)), _1272202), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272200, tc_HOL_Obool)), _1272204), _1272206))))], (30565 ^ _774244) ^ [_1319876, _1319878, _1319880, _1319882] : [30566 ^ _774244 : [(30569 ^ _774244) ^ [] : [_1319878 = _1319882], (30567 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1319876), _1319878), _1319880))]], -(hBOOL(hAPP(hAPP(c_member(_1319876), _1319878), hAPP(hAPP(c_Set_Oinsert(_1319876), _1319882), _1319880))))], (51159 ^ _774244) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (28950 ^ _774244) ^ [_1289351, _1289353] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289351, tc_HOL_Obool)), _1289353), c_Orderings_Obot__class_Obot(tc_fun(_1289351, tc_HOL_Obool))) = _1289353)], (26480 ^ _774244) ^ [_1237457, _1237459, _1237461, _1237463, _1237465] : [class_Groups_Ocomm__monoid__add(_1237457), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237459, _1237457), hAPP(hAPP(c_COMBS(_1237459, _1237457, _1237457), hAPP(hAPP(c_COMBB(_1237457, tc_fun(_1237457, _1237457), _1237459), c_Groups_Oplus__class_Oplus(_1237457)), _1237461)), _1237463)), _1237465) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1237457), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237459, _1237457), _1237461), _1237465)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237459, _1237457), _1237463), _1237465)))], (18893 ^ _774244) ^ [_1096627, _1096629] : [c_Int_OBit0(_1096627) = c_Int_OBit0(_1096629), -(_1096627 = _1096629)], (27546 ^ _774244) ^ [_1259862] : [27548 ^ _774244 : [(27551 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27547 ^ [_1259862]))], (27549 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27547 ^ [_1259862]), _1259862)))]], -(c_Nat__Transfer_Onat__set(_1259862))], (42658 ^ _774244) ^ [_1598016, _1598018, _1598020] : [class_Orderings_Olinorder(_1598016), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598016), _1598018)), -(c_Big__Operators_Olinorder__class_OMax(_1598016, hAPP(hAPP(c_Set_Oinsert(_1598016), _1598020), _1598018)) = hAPP(hAPP(c_Finite__Set_Ofold(_1598016, _1598016, c_Orderings_Oord__class_Omax(_1598016)), _1598020), _1598018))], (16333 ^ _774244) ^ [_1052054, _1052056] : [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), _1052054)), _1052056))), _1052054 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1052056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12306 ^ _774244) ^ [] : [-(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)))], (24085 ^ _774244) ^ [_1192480, _1192482, _1192484, _1192486] : [class_Orderings_Olinorder(_1192480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192480), _1192482), _1192484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192480), _1192482), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1192480), _1192484), _1192486))))], (33408 ^ _774244) ^ [_1380455, _1380457, _1380459, _1380461] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1380455, _1380457)), c_Sum__Type_OPlus(_1380455, _1380457, _1380459, _1380461))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1380457), _1380461)))], (6111 ^ _774244) ^ [_872149, _872151, _872153, _872155, _872157, _872159] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_872149, _872151, _872153), _872155, _872157, _872159), 6116 ^ _774244 : [(6119 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_872151, _872155, _872157, _872159))], (6117 ^ _774244) ^ [] : [-(hBOOL(hAPP(_872149, _872155)))]], 6120 ^ _774244 : [(6123 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_872153, _872155, _872157, _872159))], (6121 ^ _774244) ^ [] : [hBOOL(hAPP(_872149, _872155))]]], (6027 ^ _774244) ^ [_870765, _870767, _870769] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_870765, _870767, _870769)))), hBOOL(hAPP(c_Com_OWT, _870767)), hBOOL(hAPP(c_Com_OWT, _870769))], (42810 ^ _774244) ^ [_1600819, _1600821, _1600823] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600819, _1600819)), _1600821), _1600823)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600819, _1600819)), _1600821), c_Transitive__Closure_Otrancl(_1600819, _1600823))))], (26878 ^ _774244) ^ [_1246372, _1246374, _1246376, _1246378] : [class_Groups_Ocomm__monoid__add(_1246372), 26881 ^ _774244 : [(26888 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1246374)), _1246376))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246372), _1246378), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1246376, hAPP(c_Nat_OSuc, _1246374))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1246372), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246372), _1246378), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1246376, _1246374))), hAPP(_1246378, hAPP(c_Nat_OSuc, _1246374))))], (26882 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1246374)), _1246376)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246372), _1246378), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1246376, hAPP(c_Nat_OSuc, _1246374))) = c_Groups_Ozero__class_Ozero(_1246372))]]], (22911 ^ _774244) ^ [_1170071, _1170073, _1170075, _1170077, _1170079, _1170081] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1170071, _1170073, _1170075), _1170077), hAPP(hAPP(c_Product__Type_OPair(_1170071, _1170073), _1170079), _1170081)) = hAPP(hAPP(_1170077, _1170079), _1170081))], (14404 ^ _774244) ^ [_1015501, _1015503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1015501)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015501), _1015503)), _1015501) = _1015503)], (30318 ^ _774244) ^ [_1314588, _1314590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1314588), _1314590))), 30321 ^ _774244 : [(30324 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1314588), _1314590)))], (30322 ^ _774244) ^ [] : [_1314590 = c_Orderings_Obot__class_Obot(tc_fun(_1314588, tc_HOL_Obool))]]], (45038 ^ _774244) ^ [_1656953, _1656955, _1656957, _1656959] : [class_Orderings_Olinorder(_1656953), hBOOL(hAPP(c_Finite__Set_Ofinite(_1656953), _1656955)), 45048 ^ _774244 : [(45051 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656953), _1656957), 45047 ^ [_1656953, _1656955, _1656957, _1656959]))], (45049 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1656953), 45047 ^ [_1656953, _1656955, _1656957, _1656959]), _1656955)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656953), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1656953), _1656957), _1656959)), hAPP(hAPP(c_Finite__Set_Ofold(_1656953, _1656953, c_Orderings_Oord__class_Omin(_1656953)), _1656959), _1656955))))], (34107 ^ _774244) ^ [_1394364, _1394366, _1394368] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1394364), _1394366)), 34110 ^ _774244 : [(34111 ^ _774244) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1394364, tc_Nat_Onat), _1394368), _1394366) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 34114 ^ _774244 : [(34115 ^ _774244) ^ [_1394526] : [hBOOL(hAPP(hAPP(c_member(_1394364), _1394526), _1394366)), -(hAPP(_1394368, _1394526) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (34121 ^ _774244) ^ [] : [34123 ^ _774244 : [(34126 ^ _774244) ^ [] : [hAPP(_1394368, 34122 ^ [_1394364, _1394366, _1394368]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (34124 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394364), 34122 ^ [_1394364, _1394366, _1394368]), _1394366)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1394364, tc_Nat_Onat), _1394368), _1394366) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (6351 ^ _774244) ^ [_876462] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OBODY(_876462))), -(hAPP(c_Com_Obody, _876462) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 6354 ^ [_876462]))], (41620 ^ _774244) ^ [_1573747, _1573749, _1573751] : [-(hAPP(c_Relation_ORange(_1573747, _1573749), hAPP(c_Set_OCollect(tc_prod(_1573747, _1573749)), hAPP(c_Product__Type_Oprod_Oprod__case(_1573747, _1573749, tc_HOL_Obool), _1573751))) = hAPP(c_Set_OCollect(_1573749), hAPP(hAPP(c_COMBB(tc_fun(_1573747, tc_HOL_Obool), tc_HOL_Obool, _1573749), c_HOL_OEx(_1573747)), hAPP(c_COMBC(_1573747, _1573749, tc_HOL_Obool), _1573751))))], (4626 ^ _774244) ^ [_845729, _845731, _845733, _845735, _845737, _845739] : [-(c_List_Olist_Olist__size(_845739, _845735, _845731) = c_List_Olist_Olist__size(_845737, _845733, _845729)), _845739 = _845737, _845735 = _845733, _845731 = _845729], (3016 ^ _774244) ^ [_820400, _820402, _820404, _820406] : [-(c_Divides_Odivmod__nat(_820406, _820402) = c_Divides_Odivmod__nat(_820404, _820400)), _820406 = _820404, _820402 = _820400], (51187 ^ _774244) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (50993 ^ _774244) ^ [_1796972, _1796974] : [class_Orderings_Oorder(_1796972), -(class_Orderings_Oorder(tc_fun(_1796974, _1796972)))], (49962 ^ _774244) ^ [_1773991, _1773993] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1773991), hAPP(c_List_Onth(_1773991), _1773993)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773991)), _1773993))) = _1773993)], (39592 ^ _774244) ^ [_1518251, _1518253, _1518255, _1518257, _1518259] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518251, _1518253), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1518251, tc_HOL_Obool)), _1518255), _1518257)), _1518259) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1518251, _1518253), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518251, _1518253), _1518255), _1518259)), hAPP(hAPP(c_Product__Type_OSigma(_1518251, _1518253), _1518257), _1518259)))], (10976 ^ _774244) ^ [_954698, _954700, _954702] : [_954700 = _954702, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954698)), _954700) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954698)), _954702))], (32552 ^ _774244) ^ [_1364268, _1364270, _1364272] : [class_Rings_Oring__1(_1364268), hBOOL(hAPP(hAPP(c_member(_1364268), _1364270), c_Int_Oring__1__class_OInts(_1364268))), -(hBOOL(hAPP(hAPP(c_member(_1364268), hAPP(hAPP(c_Power_Opower__class_Opower(_1364268), _1364270), _1364272)), c_Int_Oring__1__class_OInts(_1364268))))], (27778 ^ _774244) ^ [_1264354, _1264356, _1264358, _1264360] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264354, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264354, tc_HOL_Obool)), _1264356), _1264358)), _1264360) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264354, tc_HOL_Obool)), _1264356), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264354, tc_HOL_Obool)), _1264358), _1264360)))], (36119 ^ _774244) ^ [_1439874, _1439876, _1439878, _1439880] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439874, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1439874, tc_fun(_1439874, tc_HOL_Obool), tc_HOL_Obool), c_member(_1439874)), _1439876)), hAPP(hAPP(c_COMBC(_1439874, tc_fun(_1439874, tc_HOL_Obool), tc_HOL_Obool), c_member(_1439874)), _1439878)), _1439880)), -(hBOOL(hAPP(hAPP(c_member(_1439874), _1439880), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439874, tc_HOL_Obool)), _1439876), _1439878))))], (40703 ^ _774244) ^ [_1544029, _1544031, _1544033] : [-(hBOOL(hAPP(_1544029, _1544031))), -(hAPP(c_Set_OCollect(_1544033), hAPP(hAPP(c_COMBS(_1544033, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1544033), c_fconj), hAPP(c_fequal, _1544031))), _1544029)) = c_Orderings_Obot__class_Obot(tc_fun(_1544033, tc_HOL_Obool)))], (45421 ^ _774244) ^ [_1665515, _1665517, _1665519, _1665521] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1665517, _1665515)), _1665519), _1665521) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1665517), hAPP(hAPP(c_COMBC(_1665517, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1665515, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1665517), c_Smallcheck_Osmall__class_Osmall(_1665515)), hAPP(hAPP(c_COMBB(tc_fun(_1665515, tc_prod(_1665517, _1665515)), tc_fun(_1665515, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1665517), hAPP(c_COMBB(tc_prod(_1665517, _1665515), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1665515), _1665519)), c_Product__Type_OPair(_1665517, _1665515)))), _1665521)), _1665521)), class_Smallcheck_Osmall(_1665515), class_Smallcheck_Osmall(_1665517)], (14974 ^ _774244) ^ [_1025815, _1025817, _1025819, _1025821, _1025823] : [class_Groups_Oab__group__add(_1025815), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025815), _1025817), _1025819) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025815), _1025821), _1025823), 14981 ^ _774244 : [(14988 ^ _774244) ^ [] : [_1025821 = _1025823, -(_1025817 = _1025819)], (14982 ^ _774244) ^ [] : [_1025817 = _1025819, -(_1025821 = _1025823)]]], (5432 ^ _774244) ^ [_858134, _858136, _858138, _858140, _858142, _858144] : [-(c_Enum_On__lists(_858144, _858140, _858136) = c_Enum_On__lists(_858142, _858138, _858134)), _858144 = _858142, _858140 = _858138, _858136 = _858134], (38461 ^ _774244) ^ [_1491765, _1491767, _1491769, _1491771, _1491773] : [class_Groups_Ocomm__monoid__add(_1491765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491767), _1491769)), c_Fun_Oinj__on(_1491767, _1491767, _1491771, _1491769), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491767, _1491765), _1491773), hAPP(c_Set_Oimage(_1491767, _1491767, _1491771), _1491769)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491767, _1491765), hAPP(c_Fun_Ocomp(_1491767, _1491765, _1491767, _1491773), _1491771)), _1491769))], (44436 ^ _774244) ^ [_1642623, _1642625, _1642627] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1642623, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1642623, tc_HOL_Obool)), _1642625), _1642627)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1642623, tc_HOL_Obool)), _1642625), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1642623, tc_HOL_Obool), _1642627)))], (29174 ^ _774244) ^ [_1293555, _1293557, _1293559, _1293561] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1293555, tc_HOL_Obool)), _1293557), hAPP(hAPP(c_Set_Oinsert(_1293555), _1293559), _1293561)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1293555, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1293555, tc_HOL_Obool)), _1293557), _1293561)), hAPP(hAPP(c_Set_Oinsert(_1293555), _1293559), c_Orderings_Obot__class_Obot(tc_fun(_1293555, tc_HOL_Obool)))))], (11993 ^ _774244) ^ [_972577, _972579, _972581] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972577), _972579)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972581), _972579)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _972579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972577), _972581))], (43915 ^ _774244) ^ [_1629235, _1629237] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1629235, _1629235)), _1629237)), c_Wellfounded_Oacyclic(_1629235, _1629237), -(c_Wellfounded_Owf(_1629235, hAPP(c_Relation_Oconverse(_1629235, _1629235), _1629237)))], (18993 ^ _774244) ^ [_1098323] : [c_Int_OMin = c_Int_OBit0(_1098323)], (17079 ^ _774244) ^ [_1066231, _1066233] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1066231), _1066233)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1066231)), _1066233))], (49288 ^ _774244) ^ [_1760227, _1760229] : [-(_1760227 = c_List_Olist_ONil(_1760229)), -(hAPP(hAPP(c_List_Oappend(_1760229), c_List_Obutlast(_1760229, _1760227)), hAPP(hAPP(c_List_Olist_OCons(_1760229), c_List_Olast(_1760229, _1760227)), c_List_Olist_ONil(_1760229))) = _1760227)], (45752 ^ _774244) ^ [_1673674, _1673676, _1673678] : [-(hAPP(c_Option_Omap(_1673674, _1673676), _1673678) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1673676), _1673674, c_Option_Ooption_ONone(_1673676), hAPP(hAPP(c_COMBB(_1673676, tc_Option_Ooption(_1673676), _1673674), c_Option_Ooption_OSome(_1673676)), _1673678)))], (49719 ^ _774244) ^ [_1769926, _1769928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1769926), _1769928)), -(c_List_Oupt(_1769926, hAPP(c_Nat_OSuc, _1769928)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1769926, _1769928)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1769928), c_List_Olist_ONil(tc_Nat_Onat))))], (51291 ^ _774244) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (5400 ^ _774244) ^ [_857666, _857668] : [_857668 = _857666, -(c_List_Onth(_857668) = c_List_Onth(_857666))], (33842 ^ _774244) ^ [_1388867, _1388869, _1388871, _1388873, _1388875, _1388877, _1388879] : [-(_1388867 = _1388869), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388871, _1388873), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388871, _1388873), _1388875), _1388867), _1388877)), _1388869), _1388879) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388871, _1388873), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388871, _1388873), _1388875), _1388869), _1388879)), _1388867), _1388877))], (10265 ^ _774244) ^ [_943335, _943337, _943339, _943341] : [class_Orderings_Oorder(_943335), _943337 = _943339, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943335), _943341), _943339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943335), _943341), _943337)))], (26323 ^ _774244) ^ [_1234156, _1234158] : [-(_1234156 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234158), _1234156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1234158)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1234156))))], (33112 ^ _774244) ^ [_1373548, _1373550, _1373552] : [class_Lattices_Olattice(_1373548), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373548), _1373550)), 33119 ^ _774244 : [(33126 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373548, tc_HOL_Obool)), _1373550), hAPP(hAPP(c_Set_Oinsert(_1373548), _1373552), c_Orderings_Obot__class_Obot(tc_fun(_1373548, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1373548, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1373548, hAPP(hAPP(c_Set_Oinsert(_1373548), _1373552), _1373550)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1373548), _1373552), c_Big__Operators_Olattice__class_OSup__fin(_1373548, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373548, tc_HOL_Obool)), _1373550), hAPP(hAPP(c_Set_Oinsert(_1373548), _1373552), c_Orderings_Obot__class_Obot(tc_fun(_1373548, tc_HOL_Obool)))))))], (33120 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373548, tc_HOL_Obool)), _1373550), hAPP(hAPP(c_Set_Oinsert(_1373548), _1373552), c_Orderings_Obot__class_Obot(tc_fun(_1373548, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1373548, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1373548, hAPP(hAPP(c_Set_Oinsert(_1373548), _1373552), _1373550)) = _1373552)]]], (25821 ^ _774244) ^ [_1224899, _1224901, _1224903, _1224905, _1224907, _1224909] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1224899, _1224901, _1224903, _1224905), _1224907), _1224909) = hAPP(_1224905, hAPP(hAPP(c_Product__Type_OPair(_1224899, _1224901), _1224907), _1224909)))], (12524 ^ _774244) ^ [_982016, _982018, _982020, _982022] : [class_Rings_Olinordered__semiring(_982016), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982016), _982018), _982020)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982016), _982022), _982020))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982016), c_Groups_Ozero__class_Ozero(_982016)), _982020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982016), _982018), _982022)))], (18121 ^ _774244) ^ [] : [c_Int_OMin = c_Int_OPls], (2274 ^ _774244) ^ [_808519, _808521, _808523, _808525] : [-(c_SMT_Oz3div(_808525, _808521) = c_SMT_Oz3div(_808523, _808519)), _808525 = _808523, _808521 = _808519], (41393 ^ _774244) ^ [_1568725, _1568727] : [c_Wellfounded_Owf(_1568725, _1568727), -(c_Wellfounded_Owf(tc_fun(_1568725, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1568725, _1568727)))], (16849 ^ _774244) ^ [_1062011, _1062013, _1062015] : [class_Int_Onumber__ring(_1062011), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062011), hAPP(c_Groups_Ouminus__class_Ouminus(_1062011), hAPP(c_Int_Onumber__class_Onumber__of(_1062011), _1062013))), _1062015) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062011), hAPP(c_Int_Onumber__class_Onumber__of(_1062011), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1062013))), _1062015))], (35761 ^ _774244) ^ [_1432795, _1432797, _1432799, _1432801, _1432803] : [c_Equiv__Relations_Oequiv(_1432795, _1432797, _1432799), 35764 ^ _774244 : [(35775 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1432795, _1432795)), hAPP(hAPP(c_Product__Type_OPair(_1432795, _1432795), _1432801), _1432803)), _1432799))), hAPP(c_Relation_OImage(_1432795, _1432795, _1432799), hAPP(hAPP(c_Set_Oinsert(_1432795), _1432801), c_Orderings_Obot__class_Obot(tc_fun(_1432795, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1432795, _1432795, _1432799), hAPP(hAPP(c_Set_Oinsert(_1432795), _1432803), c_Orderings_Obot__class_Obot(tc_fun(_1432795, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1432795), _1432801), _1432797)), hBOOL(hAPP(hAPP(c_member(_1432795), _1432803), _1432797))], (35765 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1432795, _1432795)), hAPP(hAPP(c_Product__Type_OPair(_1432795, _1432795), _1432801), _1432803)), _1432799)), 35768 ^ _774244 : [(35773 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1432795), _1432803), _1432797)))], (35771 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1432795), _1432801), _1432797)))], (35769 ^ _774244) ^ [] : [-(hAPP(c_Relation_OImage(_1432795, _1432795, _1432799), hAPP(hAPP(c_Set_Oinsert(_1432795), _1432801), c_Orderings_Obot__class_Obot(tc_fun(_1432795, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1432795, _1432795, _1432799), hAPP(hAPP(c_Set_Oinsert(_1432795), _1432803), c_Orderings_Obot__class_Obot(tc_fun(_1432795, tc_HOL_Obool)))))]]]]], (41823 ^ _774244) ^ [_1578711, _1578713, _1578715, _1578717] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578711, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1578711, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1578711, _1578713), _1578715)), hAPP(c_Relation_ODomain(_1578711, _1578713), _1578717))), hAPP(c_Relation_ODomain(_1578711, _1578713), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1578711, _1578713), tc_HOL_Obool)), _1578715), _1578717)))))], (45664 ^ _774244) ^ [_1671658, _1671660, _1671662, _1671664] : [hAPP(hAPP(c_Option_Omap(_1671658, _1671660), _1671662), _1671664) = c_Option_Ooption_ONone(_1671660), -(_1671664 = c_Option_Ooption_ONone(_1671658))], (32053 ^ _774244) ^ [_1354341, _1354343, _1354345] : [_1354341 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1354343, _1354343), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1354343, _1354343), tc_HOL_Obool)), _1354341), _1354345)))], (14820 ^ _774244) ^ [_1023027, _1023029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1023027)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023027), _1023029)), _1023027) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5713 ^ _774244) ^ [_865268, _865270, _865272] : [5714 ^ _774244 : [(5715 ^ _774244) ^ [_865312] : [c_Natural_Oevaln(_865268, _865270, _865312, _865272)]], -(c_Natural_Oevalc(_865268, _865270, _865272))], (48100 ^ _774244) ^ [_1732551, _1732553] : [-(c_List_Olistrel1(_1732551, hAPP(c_Relation_Oconverse(_1732551, _1732551), _1732553)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1732551), tc_List_Olist(_1732551)), c_List_Olistrel1(_1732551, _1732553)))], (18729 ^ _774244) ^ [_1093669, _1093671] : [class_Groups_Omonoid__mult(_1093669), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1093669), _1093671), 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(_1093669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093669), _1093671), _1093671)), _1093671))], (16687 ^ _774244) ^ [_1058823, _1058825, _1058827] : [class_Int_Onumber__ring(_1058823), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058823), hAPP(c_Int_Onumber__class_Onumber__of(_1058823), _1058825)), hAPP(c_Int_Onumber__class_Onumber__of(_1058823), _1058827)) = hAPP(c_Int_Onumber__class_Onumber__of(_1058823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1058825), _1058827)))], (24329 ^ _774244) ^ [_1196927, _1196929, _1196931, _1196933] : [class_Orderings_Olinorder(_1196927), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196927), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196927), _1196929), _1196931)), _1196933) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196927), _1196929), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196927), _1196931), _1196933)))], (2154 ^ _774244) ^ [_806543, _806545, _806547, _806549, _806551, _806553] : [-(c_Sum__Type_OProjr(_806553, _806549, _806545) = c_Sum__Type_OProjr(_806551, _806547, _806543)), _806553 = _806551, _806549 = _806547, _806545 = _806543], (6331 ^ _774244) ^ [_876055, _876057, _876059, _876061, _876063] : [c_Com_Ocom_OCall(_876055, _876057, _876059) = c_Com_Ocom_OSemi(_876061, _876063)], (5220 ^ _774244) ^ [_854964, _854966, _854968, _854970, _854972, _854974, _854976, _854978] : [-(c_List_Ofoldl(_854978, _854974, _854970, _854966) = c_List_Ofoldl(_854976, _854972, _854968, _854964)), _854978 = _854976, _854974 = _854972, _854970 = _854968, _854966 = _854964], (9876 ^ _774244) ^ [_937059, _937061] : [class_Rings_Osemiring__1(_937059), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_937059), hAPP(c_Nat_OSuc, _937061)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937059), c_Groups_Oone__class_Oone(_937059)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_937059), _937061)))], (7169 ^ _774244) ^ [_890612, _890614, _890616, _890618] : [c_Com_Ocom_OAss(_890612, _890614) = c_Com_Ocom_OAss(_890616, _890618), 7172 ^ _774244 : [(7175 ^ _774244) ^ [] : [-(_890614 = _890618)], (7173 ^ _774244) ^ [] : [-(_890612 = _890616)]]], (36537 ^ _774244) ^ [_1449622, _1449624, _1449626] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449622, tc_HOL_Obool)), _1449624), _1449626) = c_Orderings_Obot__class_Obot(tc_fun(_1449622, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1449622, tc_HOL_Obool)), _1449624), _1449626) = _1449624)], (46942 ^ _774244) ^ [_1704332, _1704334] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1704332), _1704334))), -(c_List_Oupto(_1704332, _1704334) = c_List_Olist_ONil(tc_Int_Oint))], (24657 ^ _774244) ^ [_1203709, _1203711, _1203713] : [-(c_Nitpick_Oof__frac(_1203711, _1203709, _1203713) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203709), hAPP(c_Int_Oring__1__class_Oof__int(_1203709), hAPP(c_Nitpick_Onum(_1203711), _1203713))), hAPP(c_Int_Oring__1__class_Oof__int(_1203709), hAPP(c_Nitpick_Odenom(_1203711), _1203713)))), class_Rings_Oinverse(_1203709), class_Rings_Oring__1(_1203709)], (29508 ^ _774244) ^ [_1299637, _1299639] : [class_Orderings_Olinorder(_1299637), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299637, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1299637), _1299639)), hAPP(hAPP(c_Set_Oinsert(_1299637), _1299639), c_Orderings_Obot__class_Obot(tc_fun(_1299637, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1299637), _1299639))], (15236 ^ _774244) ^ [_1030544, _1030546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030544), _1030546)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030546), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030546), _1030544)) = _1030544)], (46365 ^ _774244) ^ [_1689891, _1689893, _1689895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1689891, _1689891), tc_HOL_Obool)), _1689893), _1689895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1689891), tc_List_Olist(_1689891)), tc_HOL_Obool)), c_List_Olistrel(_1689891, _1689893)), c_List_Olistrel(_1689891, _1689895))))], (304 ^ _774244) ^ [_778722, _778724, _778726, _778728, _778730, _778732, _778734, _778736, _778738, _778740, _778742, _778744] : [-(c_Equiv__Relations_Ocongruent2(_778742, _778738, _778734, _778730, _778726, _778722)), c_Equiv__Relations_Ocongruent2(_778744, _778740, _778736, _778732, _778728, _778724), _778744 = _778742, _778740 = _778738, _778736 = _778734, _778732 = _778730, _778728 = _778726, _778724 = _778722], (30031 ^ _774244) ^ [_1309202] : [class_Lattices_Osemilattice__sup(_1309202), -(c_Finite__Set_Ofun__left__comm__idem(_1309202, _1309202, c_Lattices_Osemilattice__sup__class_Osup(_1309202)))], (2668 ^ _774244) ^ [_814678, _814680] : [_814680 = _814678, -(c_Nitpick_Oone__frac(_814680) = c_Nitpick_Oone__frac(_814678))], (27591 ^ _774244) ^ [_1260639, _1260641] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1260639), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1260641) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1260639, _1260641))], (3550 ^ _774244) ^ [_828913, _828915, _828917, _828919, _828921, _828923] : [-(c_Wellfounded_Omlex__prod(_828923, _828919, _828915) = c_Wellfounded_Omlex__prod(_828921, _828917, _828913)), _828923 = _828921, _828919 = _828917, _828915 = _828913], (7858 ^ _774244) ^ [_902675, _902677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902675), _902677)), -(_902677 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _902675), 7861 ^ [_902675, _902677])))], (34339 ^ _774244) ^ [_1399227, _1399229] : [-(c_Map_Oran(_1399227, _1399229, hAPP(c_COMBK(tc_Option_Ooption(_1399229), _1399227), c_Option_Ooption_ONone(_1399229))) = c_Orderings_Obot__class_Obot(tc_fun(_1399229, tc_HOL_Obool)))], (34872 ^ _774244) ^ [_1411812, _1411814, _1411816, _1411818, _1411820] : [class_Groups_Ocomm__monoid__add(_1411812), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411814), _1411816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1411814, tc_HOL_Obool)), _1411818), _1411816)), 34886 ^ _774244 : [(34889 ^ _774244) ^ [] : [hAPP(_1411820, 34885 ^ [_1411812, _1411814, _1411816, _1411818, _1411820]) = c_Groups_Ozero__class_Ozero(_1411812)], (34887 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411814), 34885 ^ [_1411812, _1411814, _1411816, _1411818, _1411820]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1411814, tc_HOL_Obool)), _1411816), _1411818))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1411814, _1411812), _1411820), _1411818) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1411814, _1411812), _1411820), _1411816))], (40589 ^ _774244) ^ [_1541374] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1541374, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1541374), hAPP(c_COMBK(tc_HOL_Obool, _1541374), c_fTrue)))], (28942 ^ _774244) ^ [_1289193, _1289195, _1289197, _1289199] : [_1289199 = c_Orderings_Obot__class_Obot(tc_fun(_1289193, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1289193, _1289195, _1289197), _1289199) = c_Orderings_Obot__class_Obot(tc_fun(_1289195, tc_HOL_Obool)))], (19845 ^ _774244) ^ [_1113852, _1113854, _1113856] : [class_Fields_Ofield__inverse__zero(_1113852), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1113852), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113852), _1113854), _1113856)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113852), _1113854), hAPP(c_Groups_Ouminus__class_Ouminus(_1113852), _1113856)))], (43512 ^ _774244) ^ [_1618517, _1618519, _1618521, _1618523] : [43514 ^ _774244 : [(43517 ^ _774244) ^ [] : [hAPP(_1618523, 43513 ^ [_1618517, _1618519, _1618521, _1618523]) = c_Orderings_Otop__class_Otop(tc_fun(_1618519, tc_HOL_Obool))], (43515 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618517), 43513 ^ [_1618517, _1618519, _1618521, _1618523]), _1618521)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618517, tc_fun(_1618519, tc_HOL_Obool)), _1618521), _1618523) = c_Orderings_Otop__class_Otop(tc_fun(_1618519, tc_HOL_Obool)))], (46058 ^ _774244) ^ [_1681233, _1681235, _1681237, _1681239, _1681241] : [class_Orderings_Olinorder(_1681233), -(hAPP(c_List_Oset(_1681235), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681235, _1681233, _1681237), _1681239), _1681241)) = hAPP(hAPP(c_Set_Oinsert(_1681235), _1681239), hAPP(c_List_Oset(_1681235), _1681241)))], (14342 ^ _774244) ^ [_1014518, _1014520, _1014522] : [class_Divides_Osemiring__div(_1014518), -(_1014520 = c_Groups_Ozero__class_Ozero(_1014518)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1014518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014518), _1014520), _1014522)), _1014520) = _1014522)], (6530 ^ _774244) ^ [_879496, _879498] : [class_Groups_Ocomm__monoid__add(_879496), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879496), _879498), c_Groups_Ozero__class_Ozero(_879496)) = _879498)], (12300 ^ _774244) ^ [_977862, _977864] : [12301 ^ _774244 : [(12302 ^ _774244) ^ [_977915] : [_977864 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _977862), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _977915))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _977862), _977864)))], (10630 ^ _774244) ^ [_949179, _949181, _949183] : [class_Orderings_Olinorder(_949179), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949179), _949181), _949183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949179), _949183), _949181)))], (17155 ^ _774244) ^ [_1067625, _1067627, _1067629] : [class_Rings_Osemiring__1(_1067625), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1067625), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1067627), _1067629)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1067625), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1067625), _1067627)), _1067629))], (40653 ^ _774244) ^ [_1542545, _1542547] : [-(hAPP(c_Set_OCollect(_1542545), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1542545), c_fNot), _1542547)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1542545, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1542545), _1542547)))], (10846 ^ _774244) ^ [_952451, _952453, _952455, _952457, _952459] : [class_Groups_Oordered__ab__semigroup__add(_952451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952451), _952453), _952455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952451), _952457), _952459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952451), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952451), _952453), _952457)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952451), _952455), _952459))))], (4402 ^ _774244) ^ [_842393, _842395, _842397, _842399] : [-(c_Nat_Ocompow(_842399, _842395) = c_Nat_Ocompow(_842397, _842393)), _842399 = _842397, _842395 = _842393], (49304 ^ _774244) ^ [_1760680, _1760682, _1760684] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760680)), hAPP(c_List_Ofilter(_1760680, _1760682), _1760684))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760680)), _1760684))))], (6656 ^ _774244) ^ [_881432, _881434, _881436] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_881432), 6659 ^ _774244 : [(6666 ^ _774244) ^ [] : [_881436 = c_Groups_Ozero__class_Ozero(_881432), -(_881434 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881432), _881434), _881436))], (6660 ^ _774244) ^ [] : [_881434 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881432), _881434), _881436), -(_881436 = c_Groups_Ozero__class_Ozero(_881432))]]], (31337 ^ _774244) ^ [_1337262, _1337264, _1337266, _1337268, _1337270] : [hBOOL(hAPP(hAPP(c_member(_1337262), _1337264), c_SetInterval_Oord_OgreaterThanLessThan(_1337262, _1337266, _1337268, _1337270))), 31340 ^ _774244 : [(31343 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1337266, _1337264), _1337270)))], (31341 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1337266, _1337268), _1337264)))]]], (23085 ^ _774244) ^ [_1173240, _1173242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1173240), 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)), _1173242)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1173240, _1173242), c_Divides_OnegDivAlg(_1173240, _1173242))))], (30975 ^ _774244) ^ [_1329790, _1329792, _1329794] : [hBOOL(hAPP(hAPP(c_member(_1329790), _1329792), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1329790, tc_HOL_Obool)), _1329794))), hBOOL(hAPP(hAPP(c_member(_1329790), _1329792), _1329794))], (4208 ^ _774244) ^ [_839310, _839312, _839314, _839316, _839318, _839320, _839322, _839324] : [-(c_Nitpick_Osetsum_H(_839324, _839320, _839316, _839312) = c_Nitpick_Osetsum_H(_839322, _839318, _839314, _839310)), _839324 = _839322, _839320 = _839318, _839316 = _839314, _839312 = _839310], (45389 ^ _774244) ^ [_1664970, _1664972] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1664970, _1664972) = c_Smallcheck_Ofull__small_H(_1664970, hAPP(c_Code__Numeral_Oint__of, _1664972), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1664972))))], (36451 ^ _774244) ^ [_1447752, _1447754, _1447756, _1447758] : [class_Lattices_Olattice(_1447752), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1447752), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1447752), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1447752), _1447754), _1447756)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1447752), _1447754), _1447758))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1447752), _1447754), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1447752), _1447756), _1447758)))))], (12714 ^ _774244) ^ [_985504, _985506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _985504)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _985506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985504), _985506))))], (35227 ^ _774244) ^ [_1419860, _1419862, _1419864, _1419866, _1419868, _1419870] : [-(hAPP(hAPP(c_Fun_Ocomp(_1419860, _1419862, _1419864, hAPP(c_COMBK(_1419862, _1419860), _1419866)), _1419868), _1419870) = _1419866)], (20869 ^ _774244) ^ [_1131773, _1131775, _1131777, _1131779] : [class_Fields_Ofield(_1131773), -(_1131775 = c_Groups_Ozero__class_Ozero(_1131773)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131773), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131773), _1131777), _1131775)), _1131779) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131773), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131773), _1131777), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131773), _1131775), _1131779))), _1131775))], (26073 ^ _774244) ^ [_1229702, _1229704] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229702)), _1229704)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229702), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1229704)))))], (48650 ^ _774244) ^ [_1746394, _1746396, _1746398] : [-(hAPP(c_List_Otl(_1746394), hAPP(hAPP(c_List_Oappend(_1746394), _1746396), _1746398)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1746394), _1746394, hAPP(c_List_Otl(_1746394), _1746398), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1746394), tc_List_Olist(_1746394)), _1746394), hAPP(hAPP(c_COMBC(tc_List_Olist(_1746394), tc_List_Olist(_1746394), tc_List_Olist(_1746394)), c_List_Oappend(_1746394)), _1746398))), _1746396))], (29526 ^ _774244) ^ [_1299964, _1299966] : [class_Orderings_Olinorder(_1299964), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299964, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1299964), _1299966), c_Orderings_Obot__class_Obot(tc_fun(_1299964, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1299964), _1299966)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1299964), _1299966))], (3502 ^ _774244) ^ [_828141, _828143, _828145, _828147, _828149, _828151, _828153, _828155] : [-(c_Product__Type_Oapsnd(_828155, _828151, _828147, _828143) = c_Product__Type_Oapsnd(_828153, _828149, _828145, _828141)), _828155 = _828153, _828151 = _828149, _828147 = _828145, _828143 = _828141], (38686 ^ _774244) ^ [_1496894, _1496896, _1496898, _1496900, _1496902] : [c_Fun_Oinj__on(_1496894, _1496896, _1496898, _1496900), hBOOL(hAPP(hAPP(c_member(_1496894), _1496902), _1496900)), -(hAPP(c_Fun_Othe__inv__into(_1496894, _1496896, _1496900, _1496898), hAPP(_1496898, _1496902)) = _1496902)], (44878 ^ _774244) ^ [_1652552, _1652554, _1652556] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1652552, tc_HOL_Obool)), _1652554)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1652552), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1652552, tc_HOL_Obool), _1652554))), 44888 ^ _774244 : [(44891 ^ _774244) ^ [] : [hAPP(c_Finite__Set_Ocard(_1652552), 44887 ^ [_1652552, _1652554, _1652556]) = _1652556], (44889 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1652552, tc_HOL_Obool)), 44887 ^ [_1652552, _1652554, _1652556]), _1652554)))]], 44895 ^ _774244 : [(44899 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1652552, tc_HOL_Obool)), 44897 ^ [_1652552, _1652554, _1652556]), _1652554)))], (44901 ^ _774244) ^ [] : [44894 ^ [_1652552, _1652554, _1652556] = 44897 ^ [_1652552, _1652554, _1652556]], (44903 ^ _774244) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652552, tc_HOL_Obool)), 44894 ^ [_1652552, _1652554, _1652556]), 44897 ^ [_1652552, _1652554, _1652556]) = c_Orderings_Obot__class_Obot(tc_fun(_1652552, tc_HOL_Obool))], (44896 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1652552, tc_HOL_Obool)), 44894 ^ [_1652552, _1652554, _1652556]), _1652554)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1652556), hAPP(c_Finite__Set_Ocard(tc_fun(_1652552, tc_HOL_Obool)), _1652554)) = hAPP(c_Finite__Set_Ocard(_1652552), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1652552, tc_HOL_Obool), _1652554)))], (28606 ^ _774244) ^ [_1281311, _1281313, _1281315, _1281317, _1281319, _1281321] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281311, tc_fun(_1281313, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281315, tc_fun(_1281311, tc_HOL_Obool)), _1281317), _1281319)), _1281321) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281315, tc_fun(_1281313, tc_HOL_Obool)), _1281317), hAPP(hAPP(c_COMBC(_1281315, tc_fun(_1281311, tc_fun(_1281313, tc_HOL_Obool)), tc_fun(_1281313, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1281311, tc_HOL_Obool), tc_fun(tc_fun(_1281311, tc_fun(_1281313, tc_HOL_Obool)), tc_fun(_1281313, tc_HOL_Obool)), _1281315), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281311, tc_fun(_1281313, tc_HOL_Obool))), _1281319)), _1281321)))], (48654 ^ _774244) ^ [_1746510, _1746512, _1746514] : [-(c_List_Orotate(_1746510, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1746512), _1746514)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1746510), tc_List_Olist(_1746510), tc_List_Olist(_1746510), c_List_Orotate(_1746510, _1746512)), c_List_Orotate(_1746510, _1746514)))], (31213 ^ _774244) ^ [_1334802, _1334804, _1334806, _1334808, _1334810] : [c_Finite__Set_Ofolding__one(_1334802, _1334804, _1334806), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334802), _1334808)), -(hBOOL(hAPP(hAPP(c_member(_1334802), _1334810), _1334808))), -(_1334808 = c_Orderings_Obot__class_Obot(tc_fun(_1334802, tc_HOL_Obool))), -(hAPP(_1334806, hAPP(hAPP(c_Set_Oinsert(_1334802), _1334810), _1334808)) = hAPP(hAPP(_1334804, _1334810), hAPP(_1334806, _1334808)))], (40955 ^ _774244) ^ [_1552645, _1552647, _1552649] : [class_Groups_Olinordered__ab__semigroup__add(_1552645), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552645), _1552647)), -(_1552647 = c_Orderings_Obot__class_Obot(tc_fun(_1552645, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1552645), _1552649), c_Big__Operators_Olinorder__class_OMin(_1552645, _1552647)) = c_Big__Operators_Olinorder__class_OMin(_1552645, hAPP(c_Set_OCollect(_1552645), hAPP(hAPP(c_COMBB(tc_fun(_1552645, tc_HOL_Obool), tc_HOL_Obool, _1552645), c_HOL_OEx(_1552645)), hAPP(hAPP(c_COMBC(_1552645, tc_fun(_1552645, tc_HOL_Obool), tc_fun(_1552645, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552645, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1552645, tc_HOL_Obool), tc_fun(_1552645, tc_HOL_Obool)), _1552645), c_COMBS(_1552645, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552645, tc_HOL_Obool), tc_fun(_1552645, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1552645), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1552645), c_fconj)), hAPP(hAPP(c_COMBC(_1552645, tc_fun(_1552645, _1552645), tc_fun(_1552645, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552645, tc_HOL_Obool), tc_fun(tc_fun(_1552645, _1552645), tc_fun(_1552645, tc_HOL_Obool)), _1552645), c_COMBB(_1552645, tc_HOL_Obool, _1552645)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1552645), _1552649))))), hAPP(hAPP(c_COMBC(_1552645, tc_fun(_1552645, tc_HOL_Obool), tc_HOL_Obool), c_member(_1552645)), _1552647))))))], (13734 ^ _774244) ^ [_1003308, _1003310] : [class_Lattices_Oboolean__algebra(_1003308), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1003308), hAPP(c_Groups_Ouminus__class_Ouminus(_1003308), _1003310)) = _1003310)], (35408 ^ _774244) ^ [_1424737, _1424739, _1424741, _1424743, _1424745, _1424747] : [c_Finite__Set_Ofolding(_1424737, _1424739, _1424741, _1424743), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424737), _1424745)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424737), _1424747)), -(hAPP(c_Fun_Ocomp(_1424739, _1424739, _1424739, hAPP(_1424743, _1424747)), hAPP(_1424743, _1424745)) = hAPP(c_Fun_Ocomp(_1424739, _1424739, _1424739, hAPP(_1424743, _1424745)), hAPP(_1424743, _1424747)))], (39342 ^ _774244) ^ [_1512124, _1512126, _1512128, _1512130] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1512124, _1512126, _1512128, _1512130, c_Orderings_Obot__class_Obot(tc_fun(_1512124, tc_HOL_Obool))), _1512130)))], (15738 ^ _774244) ^ [_1040806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040806)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040806), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1040806)], (49067 ^ _774244) ^ [_1755657, _1755659, _1755661, _1755663] : [-(_1755657 = c_List_Olist_ONil(_1755659)), -(c_List_Olast(_1755661, hAPP(hAPP(c_List_Omap(_1755659, _1755661), _1755663), _1755657)) = hAPP(_1755663, c_List_Olast(_1755659, _1755657)))], (26187 ^ _774244) ^ [_1231598, _1231600, _1231602] : [-(_1231598 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26190 ^ _774244 : [(26197 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231598), _1231600)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231598), _1231602))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231600), _1231602)))], (26191 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231600), _1231602)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231598), _1231600)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231598), _1231602))))]]], (19657 ^ _774244) ^ [_1110136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1110136)), -(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), _1110136), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (32510 ^ _774244) ^ [_1363539, _1363541, _1363543] : [class_Rings_Oring__1(_1363539), hBOOL(hAPP(hAPP(c_member(_1363539), _1363541), c_Int_Oring__1__class_OInts(_1363539))), hBOOL(hAPP(hAPP(c_member(_1363539), _1363543), c_Int_Oring__1__class_OInts(_1363539))), -(hBOOL(hAPP(hAPP(c_member(_1363539), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363539), _1363541), _1363543)), c_Int_Oring__1__class_OInts(_1363539))))], (13254 ^ _774244) ^ [_994541, _994543, _994545] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994541), _994543) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994541), _994545), -(_994541 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_994543 = _994545)], (44297 ^ _774244) ^ [_1639265, _1639267, _1639269] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1639265, _1639265)), _1639267), c_Transitive__Closure_Otrancl(_1639265, _1639269))), 44301 ^ _774244 : [(44304 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639265, _1639265)), _1639267), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1639265, _1639265), tc_HOL_Obool), 44300 ^ [_1639265, _1639267, _1639269]), _1639269))))], (44302 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 44300 ^ [_1639265, _1639267, _1639269])))]]], (44204 ^ _774244) ^ [_1636882, _1636884, _1636886] : [c_Relation_Osingle__valued(_1636882, _1636882, _1636884), -(c_Relation_Osingle__valued(_1636882, _1636882, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1636882, _1636882), tc_HOL_Obool), _1636886), _1636884)))], (15218 ^ _774244) ^ [_1030188, _1030190] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030188), _1030190)), _1030188) = _1030190)], (33640 ^ _774244) ^ [_1384853, _1384855, _1384857] : [class_Orderings_Olinorder(_1384853), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384853), _1384855)), -(_1384855 = c_Orderings_Obot__class_Obot(tc_fun(_1384853, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384853), _1384857)), -(_1384857 = c_Orderings_Obot__class_Obot(tc_fun(_1384853, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1384853, c_Orderings_Oord__class_Omin(_1384853), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1384853, tc_HOL_Obool)), _1384855), _1384857)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1384853), c_Big__Operators_Olattice_OInf__fin(_1384853, c_Orderings_Oord__class_Omin(_1384853), _1384855)), c_Big__Operators_Olattice_OInf__fin(_1384853, c_Orderings_Oord__class_Omin(_1384853), _1384857)))], (41965 ^ _774244) ^ [_1582122, _1582124, _1582126, _1582128, _1582130] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1582122), _1582124), _1582126), _1582128), _1582130) = c_New__DSequence_Oneg__single(_1582122, _1582124))], (28074 ^ _774244) ^ [_1269992, _1269994, _1269996] : [class_Lattices_Osemilattice__sup(_1269992), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269992), _1269994), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269992), _1269996), _1269994))))], (51409 ^ _774244) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (48324 ^ _774244) ^ [_1739328, _1739330, _1739332] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1739328, tc_HOL_Obool)), hAPP(c_List_Oset(_1739328), hAPP(hAPP(c_List_Odrop(_1739328), _1739330), _1739332))), hAPP(c_List_Oset(_1739328), _1739332))))], (26486 ^ _774244) ^ [_1237658, _1237660, _1237662, _1237664, _1237666, _1237668, _1237670] : [class_Rings_Osemiring__0(_1237658), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237658), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237660, _1237658), _1237662), _1237664)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237666, _1237658), _1237668), _1237670)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237660, _1237658), hAPP(hAPP(c_COMBC(_1237660, tc_fun(_1237666, tc_HOL_Obool), _1237658), hAPP(hAPP(c_COMBB(tc_fun(_1237666, _1237658), tc_fun(tc_fun(_1237666, tc_HOL_Obool), _1237658), _1237660), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237666, _1237658)), hAPP(hAPP(c_COMBC(_1237660, tc_fun(_1237666, _1237658), tc_fun(_1237666, _1237658)), hAPP(hAPP(c_COMBB(tc_fun(_1237658, _1237658), tc_fun(tc_fun(_1237666, _1237658), tc_fun(_1237666, _1237658)), _1237660), c_COMBB(_1237658, _1237658, _1237666)), hAPP(hAPP(c_COMBB(_1237658, tc_fun(_1237658, _1237658), _1237660), c_Groups_Otimes__class_Otimes(_1237658)), _1237662))), _1237668))), _1237670)), _1237664))], (19827 ^ _774244) ^ [_1113455, _1113457, _1113459, _1113461] : [class_Rings_Odivision__ring(_1113455), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113455), _1113457), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113455), _1113459), _1113461)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113455), _1113457), _1113459)), _1113461))], (18841 ^ _774244) ^ [_1095490, _1095492] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1095490, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1095492)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1095490, 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)))), _1095492)))], (46992 ^ _774244) ^ [_1705169, _1705171, _1705173, _1705175, _1705177] : [_1705169 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Lazy__Sequence_Oanamorph(_1705171, _1705173, _1705175, _1705169), _1705177) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1705173), _1705171), c_List_Olist_ONil(_1705173)), _1705177))], (25529 ^ _774244) ^ [_1219509, _1219511, _1219513, _1219515] : [class_Rings_Oidom(_1219509), 25532 ^ _774244 : [(25533 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1219509), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219509), _1219511), _1219513)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219509), _1219511), _1219515))), -(_1219511 = c_Groups_Ozero__class_Ozero(_1219509)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1219509), _1219513), _1219515)))], (25543 ^ _774244) ^ [] : [25544 ^ _774244 : [(25547 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1219509), _1219513), _1219515))], (25545 ^ _774244) ^ [] : [_1219511 = c_Groups_Ozero__class_Ozero(_1219509)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1219509), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219509), _1219511), _1219513)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219509), _1219511), _1219515))))]]], (30412 ^ _774244) ^ [_1316679, _1316681] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1316679, _1316681)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1316679, _1316681), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1316681), c_Orderings_Otop__class_Otop(tc_fun(_1316681, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1316679), c_Orderings_Otop__class_Otop(tc_fun(_1316679, tc_HOL_Obool)))))], (46216 ^ _774244) ^ [_1685066, _1685068] : [-(c_List_Olenlex(_1685066, _1685068) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1685066)), tc_List_Olist(_1685066)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1685066), c_Wellfounded_Oless__than, c_List_Olex(_1685066, _1685068))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1685066), tc_List_Olist(_1685066), tc_prod(tc_Nat_Onat, tc_List_Olist(_1685066))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1685066), tc_prod(tc_Nat_Onat, tc_List_Olist(_1685066))), tc_List_Olist(_1685066)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1685066))), c_Nat_Osize__class_Osize(tc_List_Olist(_1685066)))), c_COMBI(tc_List_Olist(_1685066)))))], (30493 ^ _774244) ^ [_1318232, _1318234, _1318236] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1318232), _1318234)), 30496 ^ _774244 : [(30503 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318232), _1318236), _1318234))), -(hAPP(c_Finite__Set_Ocard(_1318232), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318232, tc_HOL_Obool)), _1318234), hAPP(hAPP(c_Set_Oinsert(_1318232), _1318236), c_Orderings_Obot__class_Obot(tc_fun(_1318232, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1318232), _1318234))], (30497 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1318232), _1318236), _1318234)), -(hAPP(c_Finite__Set_Ocard(_1318232), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318232, tc_HOL_Obool)), _1318234), hAPP(hAPP(c_Set_Oinsert(_1318232), _1318236), c_Orderings_Obot__class_Obot(tc_fun(_1318232, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1318232), _1318234)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (9126 ^ _774244) ^ [_923509] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _923509)) = _923509)], (45244 ^ _774244) ^ [_1661600, _1661602, _1661604, _1661606, _1661608, _1661610] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1661600, _1661602)), _1661604), hAPP(hAPP(c_Relation_Orel__comp(_1661600, _1661606, _1661602), _1661608), _1661610))), 45250 ^ _774244 : [(45255 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1661606, _1661602)), hAPP(hAPP(c_Product__Type_OPair(_1661606, _1661602), 45248 ^ [_1661600, _1661602, _1661604, _1661606, _1661608, _1661610]), 45249 ^ [_1661600, _1661602, _1661604, _1661606, _1661608, _1661610])), _1661610)))], (45253 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1661600, _1661606)), hAPP(hAPP(c_Product__Type_OPair(_1661600, _1661606), 45247 ^ [_1661600, _1661602, _1661604, _1661606, _1661608, _1661610]), 45248 ^ [_1661600, _1661602, _1661604, _1661606, _1661608, _1661610])), _1661608)))], (45251 ^ _774244) ^ [] : [-(_1661604 = hAPP(hAPP(c_Product__Type_OPair(_1661600, _1661602), 45247 ^ [_1661600, _1661602, _1661604, _1661606, _1661608, _1661610]), 45249 ^ [_1661600, _1661602, _1661604, _1661606, _1661608, _1661610]))]]], (10083 ^ _774244) ^ [_940400, _940402, _940404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940400), _940402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940400), _940404)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940402), _940404))))], (24221 ^ _774244) ^ [_1194894, _1194896, _1194898, _1194900] : [class_Orderings_Olinorder(_1194894), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194894), _1194896), _1194898)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194894), _1194896), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194894), _1194898), _1194900))))], (45714 ^ _774244) ^ [_1672716, _1672718, _1672720, _1672722] : [c_Fun_Oinj__on(_1672716, _1672718, _1672720, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672716, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1672716), tc_fun(_1672716, tc_HOL_Obool), c_List_Oset(_1672716)), _1672722))), -(c_Fun_Oinj__on(tc_List_Olist(_1672716), tc_List_Olist(_1672718), hAPP(c_List_Omap(_1672716, _1672718), _1672720), _1672722))], (650 ^ _774244) ^ [_784343, _784345, _784347, _784349, _784351, _784353] : [-(c_Finite__Set_Ofolding__one__idem(_784351, _784347, _784343)), c_Finite__Set_Ofolding__one__idem(_784353, _784349, _784345), _784353 = _784351, _784349 = _784347, _784345 = _784343], (20565 ^ _774244) ^ [_1126134, _1126136, _1126138] : [class_Fields_Olinordered__field(_1126134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126134), _1126136), c_Groups_Ozero__class_Ozero(_1126134))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126134), _1126138), c_Groups_Ozero__class_Ozero(_1126134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126134), c_Groups_Ozero__class_Ozero(_1126134)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126134), _1126136), _1126138))))], (28296 ^ _774244) ^ [_1274541, _1274543, _1274545] : [class_Orderings_Olinorder(_1274541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274541), _1274543), _1274545)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274541, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1274541, _1274543, _1274545)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1274541), _1274545)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1274541), _1274543))], (19497 ^ _774244) ^ [] : [-(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))))], (36855 ^ _774244) ^ [_1457111, _1457113, _1457115] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1457111), _1457113)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1457111), _1457115)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1457111), _1457113)), hAPP(c_Finite__Set_Ocard(_1457111), _1457115)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1457111), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1457111, tc_HOL_Obool)), _1457113), _1457115))), hAPP(c_Finite__Set_Ocard(_1457111), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457111, tc_HOL_Obool)), _1457113), _1457115))))], (34992 ^ _774244) ^ [_1414605, _1414607, _1414609] : [hAPP(c_Set_Oimage(_1414607, tc_fun(_1414607, tc_HOL_Obool), _1414605), _1414609) = hAPP(c_Set_OPow(_1414607), _1414609)], (13656 ^ _774244) ^ [_1002028, _1002030] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1002028), _1002030) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1002028, _1002030) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (27780 ^ _774244) ^ [_1264427, _1264429, _1264431, _1264433] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264427, tc_HOL_Obool)), _1264429), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264427, tc_HOL_Obool)), _1264431), _1264433)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264427, tc_HOL_Obool)), _1264431), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264427, tc_HOL_Obool)), _1264429), _1264433)))], (16383 ^ _774244) ^ [_1052850, _1052852] : [class_Groups_Oordered__ab__group__add__abs(_1052850), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052850), hAPP(c_Groups_Oabs__class_Oabs(_1052850), _1052852)), c_Groups_Ozero__class_Ozero(_1052850)))], (45317 ^ _774244) ^ [_1663082, _1663084, _1663086, _1663088, _1663090] : [hAPP(c_Map_Omap__add(_1663082, _1663084, _1663086, _1663088), _1663090) = c_Option_Ooption_ONone(_1663084), 45320 ^ _774244 : [(45323 ^ _774244) ^ [] : [-(hAPP(_1663086, _1663090) = c_Option_Ooption_ONone(_1663084))], (45321 ^ _774244) ^ [] : [-(hAPP(_1663088, _1663090) = c_Option_Ooption_ONone(_1663084))]]], (43905 ^ _774244) ^ [_1629056, _1629058, _1629060] : [hAPP(hAPP(c_Relation_Orel__comp(_1629056, _1629056, _1629056), hAPP(c_Relation_Oconverse(_1629056, _1629056), _1629058)), _1629058) = _1629058, hAPP(c_Relation_ODomain(_1629056, _1629056), _1629058) = _1629060, -(c_Equiv__Relations_Oequiv(_1629056, _1629060, _1629058))], (18489 ^ _774244) ^ [_1089859, _1089861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1089859)), c_Int_OBit1(_1089861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089859), _1089861)))], (12308 ^ _774244) ^ [] : [-(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))], (29736 ^ _774244) ^ [_1303905, _1303907] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1303905), _1303907))))], (48306 ^ _774244) ^ [_1738880, _1738882, _1738884] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738880)), hAPP(hAPP(c_List_Odrop(_1738880), _1738882), _1738884)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738880)), _1738884)), _1738882))], (12105 ^ _774244) ^ [_974662, _974664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974662), _974664)), 12108 ^ _774244 : [(12115 ^ _774244) ^ [] : [_974664 = _974662, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974664), hAPP(c_Nat_OSuc, _974662))))], (12109 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974664), hAPP(c_Nat_OSuc, _974662))), -(_974664 = _974662)]]], (23845 ^ _774244) ^ [_1187957, _1187959, _1187961, _1187963, _1187965] : [class_Orderings_Olinorder(_1187957), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187957), _1187959), _1187961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187957), _1187963), _1187965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187957), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187957), _1187959), _1187963)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187957), _1187961), _1187965))))], (30208 ^ _774244) ^ [_1312390, _1312392, _1312394] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312390), _1312392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1312390, tc_HOL_Obool)), _1312394), _1312392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1312390), _1312394)), hAPP(c_Finite__Set_Ocard(_1312390), _1312392))))], (27620 ^ _774244) ^ [_1261179, _1261181, _1261183, _1261185] : [class_Orderings_Olinorder(_1261179), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261179), _1261181), _1261183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261179), _1261183), _1261185)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261179, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1261179, _1261181, _1261183)), c_SetInterval_Oord__class_OatLeastAtMost(_1261179, _1261183, _1261185)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1261179, _1261181, _1261185))], (32126 ^ _774244) ^ [_1355803, _1355805, _1355807, _1355809] : [hBOOL(hAPP(hAPP(_1355807, _1355809), _1355805)), -(hBOOL(hAPP(hAPP(c_member(_1355803), _1355805), c_SetInterval_Oord_OgreaterThan(_1355803, _1355807, _1355809))))], (222 ^ _774244) ^ [_777449, _777451, _777453, _777455, _777457, _777459, _777461, _777463, _777465, _777467, _777469, _777471] : [-(c_Nitpick_Ofold__graph_H(_777469, _777465, _777461, _777457, _777453, _777449)), c_Nitpick_Ofold__graph_H(_777471, _777467, _777463, _777459, _777455, _777451), _777471 = _777469, _777467 = _777465, _777463 = _777461, _777459 = _777457, _777455 = _777453, _777451 = _777449], (44306 ^ _774244) ^ [_1639463, _1639465, _1639467] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639463, _1639463)), _1639465), c_Transitive__Closure_Otrancl(_1639463, _1639467)))), 44307 ^ _774244 : [(44308 ^ _774244) ^ [_1639542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1639542)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1639463, _1639463)), _1639465), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1639463, _1639463), tc_HOL_Obool), _1639542), _1639467)))]]], (19015 ^ _774244) ^ [_1098685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1098685)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1098685))))], (18983 ^ _774244) ^ [_1098123, _1098125] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1098123)), c_Int_OBit0(_1098125)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1098123), _1098125)))], (41652 ^ _774244) ^ [_1574482, _1574484, _1574486] : [-(hAPP(c_Set_Oimage(tc_prod(_1574482, _1574484), _1574484, c_Product__Type_Osnd(_1574482, _1574484)), _1574486) = hAPP(c_Relation_ORange(_1574482, _1574484), _1574486))], (40661 ^ _774244) ^ [_1542929, _1542931, _1542933] : [-(hAPP(hAPP(c_Set_Oinsert(_1542929), _1542931), _1542933) = hAPP(c_Set_OCollect(_1542929), hAPP(hAPP(c_COMBS(_1542929, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542929), c_fdisj), hAPP(hAPP(c_COMBC(_1542929, _1542929, tc_HOL_Obool), c_fequal), _1542931))), hAPP(hAPP(c_COMBC(_1542929, tc_fun(_1542929, tc_HOL_Obool), tc_HOL_Obool), c_member(_1542929)), _1542933))))], (36199 ^ _774244) ^ [_1441869, _1441871, _1441873, _1441875] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441869, tc_HOL_Obool)), _1441871), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441869, tc_HOL_Obool)), _1441873), _1441875)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441869, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441869, tc_HOL_Obool)), _1441871), _1441873)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441869, tc_HOL_Obool)), _1441871), _1441875)))], (36173 ^ _774244) ^ [_1441149, _1441151, _1441153, _1441155] : [class_Lattices_Odistrib__lattice(_1441149), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441149), _1441151), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441149), _1441153), _1441155)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441149), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441149), _1441151), _1441153)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441149), _1441151), _1441155)))], (26498 ^ _774244) ^ [_1238180, _1238182, _1238184, _1238186, _1238188] : [class_Rings_Osemiring__0(_1238180), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238180), _1238182), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238184, _1238180), _1238186), _1238188)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238184, _1238180), hAPP(hAPP(c_COMBB(_1238180, _1238180, _1238184), hAPP(c_Groups_Otimes__class_Otimes(_1238180), _1238182)), _1238186)), _1238188))], (20253 ^ _774244) ^ [_1120942, _1120944, _1120946, _1120948] : [class_Fields_Ofield__inverse__zero(_1120942), 20256 ^ _774244 : [(20257 ^ _774244) ^ [] : [_1120944 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120942), _1120946), _1120948), 20260 ^ _774244 : [(20267 ^ _774244) ^ [] : [_1120948 = c_Groups_Ozero__class_Ozero(_1120942), -(_1120944 = c_Groups_Ozero__class_Ozero(_1120942))], (20261 ^ _774244) ^ [] : [-(_1120948 = c_Groups_Ozero__class_Ozero(_1120942)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120942), _1120944), _1120948) = _1120946)]]], (20273 ^ _774244) ^ [] : [-(_1120944 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120942), _1120946), _1120948)), 20276 ^ _774244 : [(20279 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120942), _1120944), _1120948) = _1120946], (20277 ^ _774244) ^ [] : [_1120948 = c_Groups_Ozero__class_Ozero(_1120942)]], 20280 ^ _774244 : [(20283 ^ _774244) ^ [] : [_1120944 = c_Groups_Ozero__class_Ozero(_1120942)], (20281 ^ _774244) ^ [] : [-(_1120948 = c_Groups_Ozero__class_Ozero(_1120942))]]]]], (826 ^ _774244) ^ [_787021, _787023] : [-(class_Lattices_Oab__semigroup__idem__mult(_787021)), _787023 = _787021, class_Lattices_Oab__semigroup__idem__mult(_787023)], (40872 ^ _774244) ^ [_1549834] : [-(c_Int_Oint__ge__less__than(_1549834) = 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), _1549834)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (16012 ^ _774244) ^ [_1046373, _1046375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046373)), 16015 ^ _774244 : [(16022 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046375), _1046373))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1046375), _1046373) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046375), _1046373)), _1046373)))], (16016 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046375), _1046373)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1046375), _1046373) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (13449 ^ _774244) ^ [_997898, _997900, _997902, _997904, _997906, _997908] : [class_Divides_Osemiring__div(_997898), c_Divides_Odiv__class_Omod(_997898, _997900, _997902) = c_Divides_Odiv__class_Omod(_997898, _997904, _997902), c_Divides_Odiv__class_Omod(_997898, _997906, _997902) = c_Divides_Odiv__class_Omod(_997898, _997908, _997902), -(c_Divides_Odiv__class_Omod(_997898, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997898), _997900), _997906), _997902) = c_Divides_Odiv__class_Omod(_997898, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997898), _997904), _997908), _997902))], (49019 ^ _774244) ^ [_1755005, _1755007, _1755009] : [_1755005 = c_List_Olist_ONil(_1755007), -(c_List_Olast(_1755007, hAPP(hAPP(c_List_Oappend(_1755007), _1755009), _1755005)) = c_List_Olast(_1755007, _1755009))], (10041 ^ _774244) ^ [_939760, _939762] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _939760), _939762), 10044 ^ _774244 : [(10047 ^ _774244) ^ [] : [-(_939762 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10045 ^ _774244) ^ [] : [-(_939760 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (6203 ^ _774244) ^ [_873706, _873708, _873710, _873712] : [c_Com_Ocom_OCond(_873706, _873708, _873710) = c_Com_Ocom_OBODY(_873712)], (5376 ^ _774244) ^ [_857326, _857328] : [_857328 = _857326, -(c_List_Omonoid__add__class_Olistsum(_857328) = c_List_Omonoid__add__class_Olistsum(_857326))], (28006 ^ _774244) ^ [_1268837, _1268839, _1268841] : [class_Lattices_Osemilattice__sup(_1268837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268837), _1268839), _1268841)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268837), _1268839), _1268841) = _1268841)], (7557 ^ _774244) ^ [_897197, _897199, _897201, _897203, _897205] : [c_Com_Ocom_OLocal(_897197, _897199, _897201) = c_Com_Ocom_OAss(_897203, _897205)], (29432 ^ _774244) ^ [_1298130, _1298132, _1298134, _1298136, _1298138] : [-(_1298130 = c_Orderings_Obot__class_Obot(tc_fun(_1298132, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298132, tc_fun(_1298134, tc_HOL_Obool)), _1298130), hAPP(hAPP(c_COMBC(_1298132, tc_fun(_1298134, tc_HOL_Obool), tc_fun(_1298134, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1298134, tc_HOL_Obool), tc_fun(tc_fun(_1298134, tc_HOL_Obool), tc_fun(_1298134, tc_HOL_Obool)), _1298132), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298134, tc_HOL_Obool))), _1298136)), _1298138)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298134, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298132, tc_fun(_1298134, tc_HOL_Obool)), _1298130), _1298136)), _1298138))], (51347 ^ _774244) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (33928 ^ _774244) ^ [_1390617, _1390619, _1390621, _1390623] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1390617, tc_Option_Ooption(_1390619)), hAPP(c_COMBK(tc_Option_Ooption(_1390619), _1390617), c_Option_Ooption_ONone(_1390619))), _1390621), c_Option_Ooption_ONone(_1390619)), _1390623) = c_Option_Ooption_ONone(_1390619))], (1264 ^ _774244) ^ [_792768, _792770] : [-(class_Lattices_Osemilattice__inf(_792768)), _792770 = _792768, class_Lattices_Osemilattice__inf(_792770)], (41486 ^ _774244) ^ [_1570705, _1570707] : [c_Wellfounded_Owf(_1570705, _1570707), 41490 ^ _774244 : [(41491 ^ _774244) ^ [_1570841] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570705, _1570705)), hAPP(hAPP(c_Product__Type_OPair(_1570705, _1570705), hAPP(_1570841, hAPP(c_Nat_OSuc, 41489 ^ [_1570705, _1570707, _1570841]))), hAPP(_1570841, 41489 ^ [_1570705, _1570707, _1570841]))), _1570707))]]], (25111 ^ _774244) ^ [_1212450, _1212452, _1212454] : [_1212450 = _1212452, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212452), _1212454)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212450), _1212454)))], (31978 ^ _774244) ^ [_1352689, _1352691, _1352693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352689)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1352691), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1352693)), 31985 ^ _774244 : [(31986 ^ _774244) ^ [_1352897] : [31988 ^ _774244 : [(31994 ^ _774244) ^ [] : [-(_1352897 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 31990 ^ [_1352689, _1352691, _1352693, _1352897]), 31987 ^ [_1352689, _1352691, _1352693, _1352897]))], (31992 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31990 ^ [_1352689, _1352691, _1352693, _1352897]), _1352693)))], (31989 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31987 ^ [_1352689, _1352691, _1352693, _1352897]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1352689))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1352897), _1352691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1352897), _1352689)), _1352691)))]]], (26917 ^ _774244) ^ [_1247244, _1247246] : [26925 ^ _774244 : [(26928 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1247246, 26924 ^ [_1247244, _1247246])))], (26926 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26924 ^ [_1247244, _1247246]), _1247244)))]], 26918 ^ _774244 : [(26919 ^ _774244) ^ [_1247313] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1247313), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1247244))), hBOOL(hAPP(_1247246, _1247313))]]], (13537 ^ _774244) ^ [_999786, _999788, _999790, _999792] : [class_Divides_Osemiring__div(_999786), -(c_Divides_Odiv__class_Omod(_999786, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999786), _999788), _999790), _999792) = c_Divides_Odiv__class_Omod(_999786, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999786), c_Divides_Odiv__class_Omod(_999786, _999788, _999792)), c_Divides_Odiv__class_Omod(_999786, _999790, _999792)), _999792))], (5604 ^ _774244) ^ [_863455, _863457] : [hAPP(_863455, 5605 ^ [_863455, _863457]) = hAPP(_863457, 5605 ^ [_863455, _863457]), -(_863455 = _863457)], (3098 ^ _774244) ^ [_821691, _821693] : [_821693 = _821691, -(c_Divides_Odiv__class_Odiv(_821693) = c_Divides_Odiv__class_Odiv(_821691))], (8874 ^ _774244) ^ [_919568, _919570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _919568)), 8877 ^ _774244 : [(8886 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _919568), _919570) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _919568 = c_Groups_Oone__class_Oone(tc_Int_Oint), _919570 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (8878 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _919568), _919570) = c_Groups_Oone__class_Oone(tc_Int_Oint), 8881 ^ _774244 : [(8884 ^ _774244) ^ [] : [-(_919570 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (8882 ^ _774244) ^ [] : [-(_919568 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (19369 ^ _774244) ^ [] : [-(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)))))], (26215 ^ _774244) ^ [_1232137, _1232139, _1232141, _1232143, _1232145] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1232137), _1232139)), 26218 ^ _774244 : [(26225 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1232137), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1232141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232145), _1232139))), _1232143))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1232137), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1232141), _1232143))))], (26219 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1232137), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1232141), _1232143))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1232137), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1232141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232145), _1232139))), _1232143))))]]], (7038 ^ _774244) ^ [_888286, _888288] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_888286, _888288))), -(hBOOL(hAPP(c_Com_OWT, _888288)))], (17105 ^ _774244) ^ [_1066668, _1066670] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1066668) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066670)), _1066668 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066670)), 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), _1066670)))], (25203 ^ _774244) ^ [_1213922, _1213924] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213922), _1213924)), 25208 ^ _774244 : [(25211 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213924), _1213922))], (25209 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213922), _1213924)))]], -(_1213922 = _1213924)], (48672 ^ _774244) ^ [_1746899, _1746901, _1746903] : [-(_1746899 = c_List_Olist_ONil(_1746901)), -(hAPP(hAPP(c_List_Otake(_1746901), hAPP(c_Nat_OSuc, _1746903)), _1746899) = hAPP(hAPP(c_List_Olist_OCons(_1746901), hAPP(c_List_Ohd(_1746901), _1746899)), hAPP(hAPP(c_List_Otake(_1746901), _1746903), hAPP(c_List_Otl(_1746901), _1746899))))], (13411 ^ _774244) ^ [_997267, _997269, _997271, _997273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997269)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _997269), _997271)), -(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), _997271), c_Divides_Odiv__class_Omod(tc_Int_Oint, _997273, _997267))), _997269)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _997271), _997267))))], (43099 ^ _774244) ^ [_1607661, _1607663, _1607665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607661, _1607661), tc_HOL_Obool)), _1607663), _1607665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607661, _1607661), tc_HOL_Obool)), _1607665), c_Transitive__Closure_Ortrancl(_1607661, _1607663))), -(c_Transitive__Closure_Ortrancl(_1607661, _1607665) = c_Transitive__Closure_Ortrancl(_1607661, _1607663))], (29348 ^ _774244) ^ [_1296461, _1296463, _1296465, _1296467, _1296469] : [-(_1296461 = c_Orderings_Obot__class_Obot(tc_fun(_1296463, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296463, tc_fun(_1296465, tc_HOL_Obool)), _1296461), hAPP(hAPP(c_COMBB(tc_fun(_1296465, tc_HOL_Obool), tc_fun(_1296465, tc_HOL_Obool), _1296463), hAPP(c_Set_Oinsert(_1296465), _1296467)), _1296469)) = hAPP(hAPP(c_Set_Oinsert(_1296465), _1296467), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296463, tc_fun(_1296465, tc_HOL_Obool)), _1296461), _1296469)))], (4364 ^ _774244) ^ [_841794, _841796, _841798, _841800] : [-(c_Relation_Oconverse(_841800, _841796) = c_Relation_Oconverse(_841798, _841794)), _841800 = _841798, _841796 = _841794], (44210 ^ _774244) ^ [_1636989, _1636991, _1636993, _1636995] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636989, _1636989)), _1636991), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1636989, _1636989), tc_HOL_Obool), _1636993), _1636995))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636989, _1636989)), _1636991), c_Transitive__Closure_Ortrancl(_1636989, _1636995))))], (12099 ^ _774244) ^ [_974559, _974561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974559), _974561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974559)), _974561)))], (16993 ^ _774244) ^ [_1064822, _1064824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1064822), _1064824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1064822)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1064824))))], (47165 ^ _774244) ^ [_1709949, _1709951, _1709953] : [hBOOL(hAPP(hAPP(c_member(_1709949), _1709951), hAPP(c_List_Oset(_1709949), _1709953))), 47169 ^ _774244 : [(47172 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1709949), _1709953), 47168 ^ [_1709949, _1709951, _1709953]) = _1709951)], (47170 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47168 ^ [_1709949, _1709951, _1709953]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709949)), _1709953))))]]], (32098 ^ _774244) ^ [_1355256, _1355258] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1355256), 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)))), _1355258)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355256), _1355258)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355258), _1355256)))], (1464 ^ _774244) ^ [_795268, _795270] : [-(class_Rings_Olinordered__semiring(_795268)), _795270 = _795268, class_Rings_Olinordered__semiring(_795270)], (20199 ^ _774244) ^ [_1120124, _1120126, _1120128, _1120130] : [class_Fields_Ofield__inverse__zero(_1120124), -(_1120126 = c_Groups_Ozero__class_Ozero(_1120124)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120124), _1120126), _1120128)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120124), _1120126), _1120130)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120124), _1120128), _1120130))], (18501 ^ _774244) ^ [_1090082, _1090084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1090082)), c_Int_OBit1(_1090084))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090082), _1090084)))], (44944 ^ _774244) ^ [_1654019, _1654021, _1654023, _1654025, _1654027] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1654019, _1654019)), hAPP(hAPP(c_Product__Type_OPair(_1654019, _1654019), _1654021), _1654023)), c_Transitive__Closure_Ortrancl(_1654019, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1654019, _1654019), tc_HOL_Obool)), _1654025), _1654027)))), 44950 ^ _774244 : [(44956 ^ _774244) ^ [] : [44952 ^ [_1654019, _1654021, _1654023, _1654025, _1654027] = 44949 ^ [_1654019, _1654021, _1654023, _1654025, _1654027]], (44954 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654019, _1654019)), hAPP(hAPP(c_Product__Type_OPair(_1654019, _1654019), 44952 ^ [_1654019, _1654021, _1654023, _1654025, _1654027]), 44949 ^ [_1654019, _1654021, _1654023, _1654025, _1654027])), _1654027)))], (44951 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654019, _1654019)), hAPP(hAPP(c_Product__Type_OPair(_1654019, _1654019), 44949 ^ [_1654019, _1654021, _1654023, _1654025, _1654027]), _1654023)), c_Transitive__Closure_Ortrancl(_1654019, _1654025))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654019, _1654019)), hAPP(hAPP(c_Product__Type_OPair(_1654019, _1654019), _1654021), _1654023)), c_Transitive__Closure_Ortrancl(_1654019, _1654025))))], (1810 ^ _774244) ^ [_799685, _799687, _799689, _799691] : [-(v_Q(_799689, _799685)), v_Q(_799691, _799687), _799691 = _799689, _799687 = _799685], (27812 ^ _774244) ^ [_1265211, _1265213, _1265215, _1265217] : [class_Lattices_Osemilattice__sup(_1265211), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265211), _1265213), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265211), _1265215), _1265217)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265211), _1265215), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265211), _1265213), _1265217)))], (1494 ^ _774244) ^ [_795643, _795645] : [-(class_Groups_Ocomm__monoid__mult(_795643)), _795645 = _795643, class_Groups_Ocomm__monoid__mult(_795645)], (45892 ^ _774244) ^ [_1676828] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1676828)), -(c_List_Onat__list(_1676828))], (41899 ^ _774244) ^ [_1581138, _1581140, _1581142] : [c_Wellfounded_Oacyclic(_1581138, _1581140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1581138, _1581138), tc_HOL_Obool)), _1581142), _1581140)), -(c_Wellfounded_Oacyclic(_1581138, _1581142))], (30422 ^ _774244) ^ [_1316839, _1316841, _1316843, _1316845, _1316847] : [c_Typedef_Otype__definition(_1316839, _1316841, _1316843, _1316845, _1316847), -(hAPP(c_Set_Oimage(_1316839, _1316841, _1316843), c_Orderings_Otop__class_Otop(tc_fun(_1316839, tc_HOL_Obool))) = _1316847)], (7078 ^ _774244) ^ [] : [-(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))], (4646 ^ _774244) ^ [_846035, _846037] : [_846037 = _846035, -(c_Orderings_Obot__class_Obot(_846037) = c_Orderings_Obot__class_Obot(_846035))], (29572 ^ _774244) ^ [_1300951, _1300953] : [-(c_Set_Othe__elem(_1300951, _1300953) = c_HOL_OThe(_1300951, hAPP(hAPP(c_COMBB(tc_fun(_1300951, tc_HOL_Obool), tc_HOL_Obool, _1300951), hAPP(c_fequal, _1300953)), hAPP(hAPP(c_COMBC(_1300951, tc_fun(_1300951, tc_HOL_Obool), tc_fun(_1300951, tc_HOL_Obool)), c_Set_Oinsert(_1300951)), c_Orderings_Obot__class_Obot(tc_fun(_1300951, tc_HOL_Obool))))))], (39586 ^ _774244) ^ [_1517977, _1517979, _1517981] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1517977, _1517979), c_Orderings_Obot__class_Obot(tc_fun(_1517977, tc_HOL_Obool))), _1517981) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517977, _1517979), tc_HOL_Obool)))], (43441 ^ _774244) ^ [_1615870, _1615872, _1615874, _1615876, _1615878] : [hBOOL(hAPP(hAPP(c_member(_1615870), _1615872), _1615874)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615876, tc_HOL_Obool)), hAPP(_1615878, _1615872)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615870, tc_fun(_1615876, tc_HOL_Obool)), _1615874), _1615878)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615870, tc_fun(_1615876, tc_HOL_Obool)), _1615874), _1615878))], (11240 ^ _774244) ^ [_959127, _959129, _959131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959127), _959129)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959127), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959131), _959129))))], (19385 ^ _774244) ^ [] : [-(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))))], (12636 ^ _774244) ^ [_984169, _984171, _984173] : [class_Rings_Olinordered__idom(_984169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984169), c_Groups_Ozero__class_Ozero(_984169)), _984171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984169), c_Groups_Ozero__class_Ozero(_984169)), _984173)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984169), _984173), c_Groups_Oone__class_Oone(_984169))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984169), _984171), _984173)), _984171)))], (24891 ^ _774244) ^ [_1208872, _1208874] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1208872), _1208874)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1208874), _1208872))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1208874), _1208872)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1208872), _1208874)))], (44245 ^ _774244) ^ [_1637886, _1637888, _1637890] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1637886, _1637886, _1637886), _1637888), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1637886, _1637886), tc_HOL_Obool), _1637890), _1637888)) = hAPP(hAPP(c_Relation_Orel__comp(_1637886, _1637886, _1637886), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1637886, _1637886), tc_HOL_Obool), _1637890), _1637888)), _1637888))], (2254 ^ _774244) ^ [_808221, _808223, _808225, _808227] : [-(c_Int_Onat__aux(_808227, _808223) = c_Int_Onat__aux(_808225, _808221)), _808227 = _808225, _808223 = _808221], (7738 ^ _774244) ^ [_900458, _900460, _900462, _900464, _900466, _900468] : [-(c_Nitpick_Opair__box_Opair__box__case(_900458, _900460, _900462, _900464, c_Nitpick_Opair__box_OPairBox(_900458, _900460, _900466, _900468)) = hAPP(hAPP(_900464, _900466), _900468))], (49341 ^ _774244) ^ [_1761495, _1761497, _1761499, _1761501, _1761503, _1761505] : [class_Orderings_Olinorder(_1761495), -(hBOOL(hAPP(_1761497, _1761499))), -(hAPP(c_List_Ofilter(_1761501, _1761497), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1761501, _1761495, _1761503), _1761499), _1761505)) = hAPP(c_List_Ofilter(_1761501, _1761497), _1761505))], (9848 ^ _774244) ^ [_936569, _936571, _936573] : [class_Rings_Olinordered__ring__strict(_936569), 9851 ^ _774244 : [(9852 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936569), c_Groups_Ozero__class_Ozero(_936569)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936569), _936571), _936571)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936569), _936573), _936573)))), _936571 = c_Groups_Ozero__class_Ozero(_936569), _936573 = c_Groups_Ozero__class_Ozero(_936569)], (9862 ^ _774244) ^ [] : [9863 ^ _774244 : [(9866 ^ _774244) ^ [] : [-(_936573 = c_Groups_Ozero__class_Ozero(_936569))], (9864 ^ _774244) ^ [] : [-(_936571 = c_Groups_Ozero__class_Ozero(_936569))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936569), c_Groups_Ozero__class_Ozero(_936569)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936569), _936571), _936571)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936569), _936573), _936573)))))]]], (21996 ^ _774244) ^ [_1152251, _1152253] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152251), c_Int_OPls))), 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[(30178 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1311769), _1311771)))], (30176 ^ _774244) ^ [] : [_1311771 = c_Orderings_Obot__class_Obot(tc_fun(_1311769, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1311769), _1311771) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12029 ^ _774244) ^ [_973248, _973250] : [-(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), _973248), _973250)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _973248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _973250))], (37549 ^ _774244) ^ [_1473491, _1473493, _1473495, _1473497, _1473499] : [class_Groups_Ocomm__monoid__mult(_1473491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473493), _1473495)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473493), _1473497)), 37563 ^ _774244 : [(37566 ^ 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hAPP(c_Groups_Ouminus__class_Ouminus(_1110836), c_Groups_Oone__class_Oone(_1110836))), 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)))), _1110838))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1110836), c_Groups_Oone__class_Oone(_1110836)))], (47808 ^ _774244) ^ [_1724829, _1724831, _1724833, _1724835, _1724837] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724829), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724831)), _1724833)))), -(hAPP(hAPP(c_List_Olist__update(_1724831, hAPP(hAPP(c_List_Oappend(_1724831), _1724833), _1724835)), _1724829), _1724837) = hAPP(hAPP(c_List_Oappend(_1724831), _1724833), hAPP(hAPP(c_List_Olist__update(_1724831, _1724835), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1724829), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724831)), _1724833))), _1724837)))], (3398 ^ _774244) ^ [_826461, _826463] : [_826463 = _826461, 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[hBOOL(hAPP(hAPP(c_member(tc_prod(_1432247, _1432247)), hAPP(hAPP(c_Product__Type_OPair(_1432247, _1432247), _1432253), _1432255)), _1432251)), -(hAPP(c_Relation_OImage(_1432247, _1432247, _1432251), hAPP(hAPP(c_Set_Oinsert(_1432247), _1432253), c_Orderings_Obot__class_Obot(tc_fun(_1432247, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1432247, _1432247, _1432251), hAPP(hAPP(c_Set_Oinsert(_1432247), _1432255), c_Orderings_Obot__class_Obot(tc_fun(_1432247, tc_HOL_Obool)))))], (35749 ^ _774244) ^ [] : [hAPP(c_Relation_OImage(_1432247, _1432247, _1432251), hAPP(hAPP(c_Set_Oinsert(_1432247), _1432253), c_Orderings_Obot__class_Obot(tc_fun(_1432247, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1432247, _1432247, _1432251), hAPP(hAPP(c_Set_Oinsert(_1432247), _1432255), c_Orderings_Obot__class_Obot(tc_fun(_1432247, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1432247, _1432247)), hAPP(hAPP(c_Product__Type_OPair(_1432247, _1432247), _1432253), _1432255)), _1432251)))]]], (5200 ^ _774244) ^ 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[(19599 ^ _774244) ^ [] : [-(_1108573 = c_Groups_Ozero__class_Ozero(_1108569))], (19597 ^ _774244) ^ [] : [-(_1108571 = c_Groups_Ozero__class_Ozero(_1108569))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108569), c_Groups_Ozero__class_Ozero(_1108569)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108569), hAPP(hAPP(c_Power_Opower__class_Opower(_1108569), _1108571), 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(_1108569), _1108573), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (24671 ^ _774244) ^ [_1203998, _1204000, _1204002, _1204004, _1204006, _1204008, _1204010] : [-(c_New__Random__Sequence_Opos__decr__bind(_1203998, _1204000, _1204002, _1204004, _1204006, _1204008, _1204010) = c_New__DSequence_Opos__decr__bind(_1203998, _1204000, hAPP(hAPP(hAPP(_1204002, _1204006), _1204008), _1204010), hAPP(hAPP(c_COMBC(_1203998, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1204000))), hAPP(hAPP(c_COMBC(_1203998, 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(_1204000)))), hAPP(hAPP(c_COMBC(_1203998, 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(_1204000))))), _1204004), _1204006)), _1204008)), _1204010)))], (14352 ^ _774244) ^ [_1014646, _1014648, _1014650, _1014652] : [class_Divides_Osemiring__div(_1014646), -(_1014648 = c_Groups_Ozero__class_Ozero(_1014646)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1014646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014646), _1014650), _1014648)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014646), _1014652), _1014648)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1014646), _1014650), _1014652))], (27678 ^ _774244) ^ [_1262267, _1262269] : [c_Nat__Transfer_Onat__set(_1262267), c_Nat__Transfer_Onat__set(_1262269), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1262267), _1262269)))], (2122 ^ _774244) ^ [_806021, _806023, _806025, _806027, _806029, _806031, _806033, _806035] : [-(c_Nitpick_Opair__box_OPairBox(_806035, _806031, _806027, _806023) = c_Nitpick_Opair__box_OPairBox(_806033, _806029, _806025, _806021)), _806035 = _806033, _806031 = _806029, _806027 = _806025, _806023 = _806021], (17691 ^ _774244) ^ [_1077119, _1077121, _1077123] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077119)))), 17694 ^ _774244 : [(17701 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077121)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077121)), _1077123)) = 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), _1077119), _1077121))), _1077123))], (17695 ^ _774244) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077121))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077121)), _1077123)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077119)), _1077123))]]], (29476 ^ _774244) ^ [_1299115, _1299117, _1299119] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1299115, _1299117) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1299119), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 29479 ^ _774244 : [(29482 ^ _774244) ^ [] : [-(_1299117 = _1299119)], (29480 ^ _774244) ^ [] : [-(_1299115 = _1299117)]]], (48338 ^ _774244) ^ [_1739608, _1739610] : [hBOOL(hAPP(c_List_Odistinct(_1739608), _1739610)), -(hBOOL(hAPP(c_List_Odistinct(_1739608), hAPP(c_List_Orotate1(_1739608), _1739610))))], (5508 ^ _774244) ^ [_859278, _859280] : [_859280 = _859278, -(tc_Option_Ooption(_859280) = tc_Option_Ooption(_859278))], (33362 ^ _774244) ^ [_1379563, _1379565, _1379567, _1379569] : [-(c_Sum__Type_OPlus(_1379563, _1379565, _1379567, _1379569) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1379563, _1379565), tc_HOL_Obool))), _1379567 = c_Orderings_Obot__class_Obot(tc_fun(_1379563, tc_HOL_Obool)), _1379569 = c_Orderings_Obot__class_Obot(tc_fun(_1379565, tc_HOL_Obool))], (47006 ^ _774244) ^ [_1705630, _1705632, _1705634] : [-(c_List_Olistset(_1705630, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1705630, tc_HOL_Obool)), _1705632), _1705634)) = c_List_Oset__Cons(_1705630, _1705632, c_List_Olistset(_1705630, _1705634)))], (1764 ^ _774244) ^ [_799018, _799020] : [-(hBOOL(_799018)), _799020 = _799018, hBOOL(_799020)], (51337 ^ _774244) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (21089 ^ _774244) ^ [_1135426, _1135428, _1135430] : [class_Fields_Olinordered__field(_1135426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135426), _1135428), _1135430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135426), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135426), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135426), _1135428), _1135430)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135426), c_Groups_Oone__class_Oone(_1135426)), c_Groups_Oone__class_Oone(_1135426)))), _1135430)))], (11397 ^ _774244) ^ [_961841] : [class_Groups_Osgn__if(_961841), -(c_Groups_Osgn__class_Osgn(_961841, c_Groups_Ozero__class_Ozero(_961841)) = c_Groups_Ozero__class_Ozero(_961841))], (22658 ^ _774244) ^ [_1165513, _1165515] : [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), _1165513), _1165515))), 22661 ^ _774244 : [(22670 ^ _774244) ^ [] : [-(c_Divides_OposDivAlg(_1165513, _1165515) = hAPP(c_Divides_Oadjust(_1165515), c_Divides_OposDivAlg(_1165513, 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)))), _1165515)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1165513), _1165515))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1165515), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22662 ^ _774244) ^ [] : [22663 ^ _774244 : [(22666 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1165515), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22664 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1165513), _1165515))]], -(c_Divides_OposDivAlg(_1165513, _1165515) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1165513))]]], (20307 ^ _774244) ^ [_1121764, _1121766, _1121768, _1121770] : [class_Rings_Odivision__ring(_1121764), -(_1121766 = c_Groups_Ozero__class_Ozero(_1121764)), 20314 ^ _774244 : [(20321 ^ _774244) ^ [] : [_1121768 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121764), _1121770), _1121766), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121764), _1121768), _1121766) = _1121770)], (20315 ^ _774244) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121764), _1121768), _1121766) = _1121770, -(_1121768 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121764), _1121770), _1121766))]]], (48690 ^ _774244) ^ [_1747215, _1747217, _1747219, _1747221] : [-(c_List_Olist_Olist__size(_1747215, _1747217, hAPP(hAPP(c_List_Olist_OCons(_1747215), _1747219), _1747221)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1747217, _1747219)), c_List_Olist_Olist__size(_1747215, _1747217, _1747221))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29728 ^ _774244) ^ [_1303647] : [-(c_Finite__Set_Ofun__left__comm__idem(_1303647, tc_fun(_1303647, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1303647, tc_HOL_Obool), tc_fun(tc_fun(_1303647, tc_HOL_Obool), tc_fun(_1303647, tc_HOL_Obool)), _1303647), hAPP(c_COMBC(tc_fun(_1303647, tc_HOL_Obool), tc_fun(_1303647, tc_HOL_Obool), tc_fun(_1303647, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1303647, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1303647, tc_fun(_1303647, tc_HOL_Obool), tc_fun(_1303647, tc_HOL_Obool)), c_Set_Oinsert(_1303647)), c_Orderings_Obot__class_Obot(tc_fun(_1303647, tc_HOL_Obool))))))], (18097 ^ _774244) ^ [_1083569, _1083571, _1083573] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083569), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083569)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083571)), _1083573)) = 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), _1083569), _1083571))), _1083573))], (45805 ^ _774244) ^ [_1674893, _1674895, _1674897, _1674899] : [hBOOL(hAPP(c_List_Odistinct(_1674893), hAPP(hAPP(c_List_Omap(tc_prod(_1674893, _1674895), _1674893), c_Product__Type_Ofst(_1674893, _1674895)), _1674897))), hBOOL(hAPP(c_List_Odistinct(_1674893), hAPP(hAPP(c_List_Omap(tc_prod(_1674893, _1674895), _1674893), c_Product__Type_Ofst(_1674893, _1674895)), _1674899))), 45812 ^ _774244 : [(45819 ^ _774244) ^ [] : [hAPP(c_List_Oset(tc_prod(_1674893, _1674895)), _1674897) = hAPP(c_List_Oset(tc_prod(_1674893, _1674895)), _1674899), -(c_Map_Omap__of(_1674893, _1674895, _1674897) = c_Map_Omap__of(_1674893, _1674895, _1674899))], (45813 ^ _774244) ^ [] : [c_Map_Omap__of(_1674893, _1674895, _1674897) = c_Map_Omap__of(_1674893, _1674895, _1674899), -(hAPP(c_List_Oset(tc_prod(_1674893, _1674895)), _1674897) = hAPP(c_List_Oset(tc_prod(_1674893, _1674895)), _1674899))]]], (13230 ^ _774244) ^ [_994103] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994103), _994103)))], (39362 ^ _774244) ^ [_1512530, _1512532, _1512534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1512530, _1512530), tc_HOL_Obool)), _1512532), _1512534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1512530, tc_HOL_Obool)), c_Wellfounded_Oacc(_1512530, _1512534)), c_Wellfounded_Oacc(_1512530, _1512532))))], (31707 ^ _774244) ^ [_1346655, _1346657, _1346659, _1346661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1346655, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346655, tc_HOL_Obool)), _1346657), hAPP(hAPP(c_Set_Oinsert(_1346655), _1346659), c_Orderings_Obot__class_Obot(tc_fun(_1346655, tc_HOL_Obool))))), _1346661)), hBOOL(hAPP(hAPP(c_member(_1346655), _1346659), _1346657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1346655, tc_HOL_Obool)), _1346657), hAPP(hAPP(c_Set_Oinsert(_1346655), _1346659), _1346661))))], (51431 ^ _774244) ^ [_1801302, _1801304, _1801306, _1801308, _1801310, _1801312] : [-(hAPP(hAPP(hAPP(c_COMBS(_1801302, _1801304, _1801306), _1801308), _1801310), _1801312) = hAPP(hAPP(_1801308, _1801312), hAPP(_1801310, _1801312)))], (46651 ^ _774244) ^ [_1698140, _1698142, _1698144, _1698146, _1698148] : [class_Rings_Osemiring__0(_1698140), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1698140), hAPP(hAPP(c_List_Omap(_1698142, _1698140), hAPP(hAPP(c_COMBB(_1698140, _1698140, _1698142), hAPP(c_Groups_Otimes__class_Otimes(_1698140), _1698144)), _1698146)), _1698148)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1698140), _1698144), hAPP(c_List_Omonoid__add__class_Olistsum(_1698140), hAPP(hAPP(c_List_Omap(_1698142, _1698140), _1698146), _1698148))))], (11224 ^ _774244) ^ [_958813, _958815, _958817, _958819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _958813), _958815)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _958817), _958819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958813), _958817)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958815), _958819))))], (4790 ^ _774244) ^ [_848249, _848251, _848253, _848255, _848257, _848259, _848261, _848263, _848265, _848267] : [-(c_List_Olinorder__class_Oinsort__insert__key(_848267, _848263, _848259, _848255, _848251) = c_List_Olinorder__class_Oinsort__insert__key(_848265, _848261, _848257, _848253, _848249)), _848267 = _848265, _848263 = _848261, _848259 = _848257, _848255 = _848253, _848251 = _848249], (26369 ^ _774244) ^ [_1234876, _1234878] : [class_Orderings_Oorder(_1234876), 26376 ^ _774244 : [(26381 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234876), hAPP(_1234878, 26374 ^ [_1234876, _1234878])), hAPP(_1234878, 26375 ^ [_1234876, _1234878])))], (26379 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 26375 ^ [_1234876, _1234878]), 26374 ^ [_1234876, _1234878]))], (26377 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 26374 ^ [_1234876, _1234878]), 26375 ^ [_1234876, _1234878])))]], -(c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1234876, 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)))), _1234878))], (15494 ^ _774244) ^ [_1035581, _1035583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035581), _1035583)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035581), _1035583) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25393 ^ _774244) ^ [_1217155, _1217157, _1217159] : [class_Rings_Ocomm__semiring__1(_1217155), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1217155), _1217157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217155), _1217159), _1217157))))], (19887 ^ _774244) ^ [_1114690] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1114690)))], (13772 ^ _774244) ^ [_1003954, _1003956, _1003958] : [hBOOL(hAPP(_1003954, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1003956, _1003958))), 13775 ^ _774244 : [(13800 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1003958), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13803 ^ _774244 : [(13804 ^ _774244) ^ [_1004576, _1004578] : [-(hBOOL(hAPP(_1003954, _1004576))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1003958), _1004576)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1004576), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1003956 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003958), _1004578)), _1004576)]]], (13782 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003958)), 13785 ^ _774244 : [(13786 ^ _774244) ^ [_1004284, _1004286] : [-(hBOOL(hAPP(_1003954, _1004284))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1004284), _1003958)), _1003956 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1003958), _1004286)), _1004284)]]], (13776 ^ _774244) ^ [] : [_1003958 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1003954, _1003956)))]]], (45880 ^ _774244) ^ [_1676629, _1676631] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1676629, _1676631))))], (51161 ^ _774244) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (23335 ^ _774244) ^ [_1177980, _1177982, _1177984] : [-(hAPP(c_Product__Type_Ofst(_1177980, _1177982), _1177984) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1177980, _1177982, _1177980), c_COMBK(_1177980, _1177982)), _1177984))], (7385 ^ _774244) ^ [_894073, _894075] : [7386 ^ _774244 : [(7389 ^ _774244) ^ [] : [_894073 = _894075], (7387 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894073), _894075))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894073), hAPP(c_Nat_OSuc, _894075))))], (48913 ^ _774244) ^ [_1752457, _1752459, _1752461] : [c_Equiv__Relations_Oequiv(_1752457, _1752459, _1752461), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1752457), c_List_Olists(_1752457, _1752459), c_List_Olistrel(_1752457, _1752461)))], (19087 ^ _774244) ^ [_1099936, _1099938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099936), _1099938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1099936)), c_Int_OBit0(_1099938))))], (6213 ^ _774244) ^ [_873973, _873975, _873977] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_873973, _873975, _873977)], (39722 ^ _774244) ^ [_1522173, _1522175, _1522177, _1522179, _1522181, _1522183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522173, _1522175), tc_HOL_Obool)), _1522177), hAPP(hAPP(c_Product__Type_OSigma(_1522173, _1522175), _1522179), hAPP(c_COMBK(tc_fun(_1522175, tc_HOL_Obool), _1522173), _1522181)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522175, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1522173, _1522175, _1522177), _1522183)), _1522181)))], (34739 ^ _774244) ^ [_1409010, _1409012, _1409014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1409010, _1409010), tc_HOL_Obool)), _1409012), _1409014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1409010, tc_HOL_Obool)), hAPP(c_Relation_OField(_1409010), _1409012)), hAPP(c_Relation_OField(_1409010), _1409014))))], (48326 ^ _774244) ^ [_1739383, _1739385, _1739387] : [hBOOL(hAPP(c_List_Odistinct(_1739383), _1739385)), -(hBOOL(hAPP(c_List_Odistinct(_1739383), hAPP(hAPP(c_List_Odrop(_1739383), _1739387), _1739385))))], (50886 ^ _774244) ^ [_1795090, _1795092, _1795094, _1795096, _1795098] : [class_Groups_Omonoid__add(_1795090), 50892 ^ _774244 : [(50897 ^ _774244) ^ [] : [hAPP(_1795098, 50891 ^ [_1795090, _1795092, _1795094, _1795096, _1795098]) = c_Groups_Ozero__class_Ozero(_1795090)], (50895 ^ _774244) ^ [] : [hBOOL(hAPP(_1795096, 50891 ^ [_1795090, _1795092, _1795094, _1795096, _1795098]))], (50893 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795092), 50891 ^ [_1795090, _1795092, _1795094, _1795096, _1795098]), hAPP(c_List_Oset(_1795092), _1795094))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1795090), hAPP(hAPP(c_List_Omap(_1795092, _1795090), _1795098), hAPP(c_List_Ofilter(_1795092, _1795096), _1795094))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1795090), hAPP(hAPP(c_List_Omap(_1795092, _1795090), _1795098), _1795094)))], (46489 ^ _774244) ^ [_1693322, _1693324, _1693326] : [hBOOL(hAPP(c_List_Odistinct(_1693322), hAPP(hAPP(c_List_Olist_OCons(_1693322), _1693324), _1693326))), 46492 ^ _774244 : [(46495 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1693322), _1693326)))], (46493 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1693322), _1693324), hAPP(c_List_Oset(_1693322), _1693326)))]]], (7623 ^ _774244) ^ [_898514, _898516, _898518] : [class_Groups_Oordered__comm__monoid__add(_898514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_898514), c_Groups_Ozero__class_Ozero(_898514)), _898516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_898514), c_Groups_Ozero__class_Ozero(_898514)), _898518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_898514), c_Groups_Ozero__class_Ozero(_898514)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898514), _898516), _898518))))], (30467 ^ _774244) ^ [_1317736, _1317738, _1317740, _1317742, _1317744, _1317746, _1317748] : [c_Typedef_Otype__definition(_1317736, _1317738, _1317740, _1317742, _1317744), 30470 ^ _774244 : [(30477 ^ _774244) ^ [] : [_1317746 = _1317748, -(hAPP(_1317740, _1317746) = hAPP(_1317740, _1317748))], (30471 ^ _774244) ^ [] : [hAPP(_1317740, _1317746) = hAPP(_1317740, _1317748), -(_1317746 = _1317748)]]], (17613 ^ _774244) ^ [_1075821] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1075821)), -(hAPP(c_Int_Onat, _1075821) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44050 ^ _774244) ^ [_1633115, _1633117] : [-(c_Transitive__Closure_Ortrancl(_1633115, _1633117) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1633115, _1633115), tc_HOL_Obool)), c_Relation_OId(_1633115)), hAPP(hAPP(c_Relation_Orel__comp(_1633115, _1633115, _1633115), c_Transitive__Closure_Ortrancl(_1633115, _1633117)), _1633117)))], (47927 ^ _774244) ^ [_1728154, _1728156, _1728158, _1728160, _1728162, _1728164] : [-(c_Map_Omap__add(_1728154, _1728156, _1728158, c_Map_Omap__upds(_1728154, _1728156, _1728160, _1728162, _1728164)) = c_Map_Omap__upds(_1728154, _1728156, c_Map_Omap__add(_1728154, _1728156, _1728158, _1728160), _1728162, _1728164))], (41234 ^ _774244) ^ [_1563812, _1563814, _1563816, _1563818] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1563812, _1563814, _1563816), _1563818), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1563814, _1563816), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1563812, _1563816), tc_HOL_Obool)))], (42694 ^ _774244) ^ [_1598850, _1598852, _1598854, _1598856, _1598858] : [c_Finite__Set_Ofolding__one(_1598850, _1598852, _1598854), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598850), _1598856)), -(hBOOL(hAPP(hAPP(c_member(_1598850), _1598858), _1598856))), -(hAPP(_1598854, hAPP(hAPP(c_Set_Oinsert(_1598850), _1598858), _1598856)) = hAPP(hAPP(c_Finite__Set_Ofold(_1598850, _1598850, _1598852), _1598858), _1598856))], (48648 ^ _774244) ^ [_1746351, _1746353] : [-(c_List_Orotate(_1746351, _1746353) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1746351), tc_List_Olist(_1746351)), _1746353), c_List_Orotate1(_1746351)))], (1504 ^ _774244) ^ [_795768, _795770] : [-(class_Groups_Oab__semigroup__add(_795768)), _795770 = _795768, class_Groups_Oab__semigroup__add(_795770)], (17589 ^ _774244) ^ [_1075513] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1075513))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1075513)))], (7068 ^ _774244) ^ [_888982, _888984, _888986, _888988, _888990] : [c_Com_Ocom_OWhile(_888982, _888984) = c_Com_Ocom_OLocal(_888986, _888988, _888990)], (24711 ^ _774244) ^ [_1205125, _1205127, _1205129, _1205131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1205125), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1205127, _1205129, _1205125, _1205131) = 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(_1205127)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1205127)))], (34674 ^ _774244) ^ [_1407564, _1407566, _1407568] : [class_Orderings_Olinorder(_1407564), hAPP(_1407566, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1407564), 34679 ^ [_1407564, _1407566, _1407568]), 34680 ^ [_1407564, _1407566, _1407568])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1407564), hAPP(_1407566, 34679 ^ [_1407564, _1407566, _1407568])), hAPP(_1407566, 34680 ^ [_1407564, _1407566, _1407568])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407564), _1407568)), -(_1407568 = c_Orderings_Obot__class_Obot(tc_fun(_1407564, tc_HOL_Obool))), -(hAPP(_1407566, c_Big__Operators_Olattice_OInf__fin(_1407564, c_Orderings_Oord__class_Omin(_1407564), _1407568)) = c_Big__Operators_Olattice_OInf__fin(_1407564, c_Orderings_Oord__class_Omin(_1407564), hAPP(c_Set_Oimage(_1407564, _1407564, _1407566), _1407568)))], (14636 ^ _774244) ^ [_1019242, _1019244, _1019246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019242)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1019246), _1019242)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019244), _1019246)), _1019242))], (10484 ^ _774244) ^ [_947055, _947057, _947059] : [10485 ^ _774244 : [(10488 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _947057), _947059))], (10486 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _947055)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _947055), _947057)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _947055), _947059))))], (45257 ^ _774244) ^ [_1662005, _1662007, _1662009, _1662011, _1662013, _1662015] : [hAPP(c_Map_Omap__add(_1662005, _1662007, _1662009, _1662011), _1662013) = hAPP(c_Option_Ooption_OSome(_1662007), _1662015), -(hAPP(_1662011, _1662013) = hAPP(c_Option_Ooption_OSome(_1662007), _1662015)), 45264 ^ _774244 : [(45267 ^ _774244) ^ [] : [-(hAPP(_1662009, _1662013) = hAPP(c_Option_Ooption_OSome(_1662007), _1662015))], (45265 ^ _774244) ^ [] : [-(hAPP(_1662011, _1662013) = c_Option_Ooption_ONone(_1662007))]]], (46114 ^ _774244) ^ [_1682458, _1682460, _1682462] : [class_Orderings_Olinorder(_1682458), -(c_List_Oremove1(_1682458, _1682460, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1682458, _1682458, c_COMBI(_1682458)), _1682460), _1682462)) = _1682462)], (9392 ^ _774244) ^ [_928529, _928531, _928533, _928535] : [class_Rings_Olinordered__semiring__strict(_928529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928529), _928531), _928533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928529), c_Groups_Ozero__class_Ozero(_928529)), _928535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928529), _928531), _928535)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928529), _928533), _928535))))], (11935 ^ _774244) ^ [_971588, _971590] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971588), _971590) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11938 ^ _774244 : [(11941 ^ _774244) ^ [] : [-(_971590 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11939 ^ _774244) ^ [] : [-(_971588 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (20791 ^ _774244) ^ [_1130357, _1130359, _1130361, _1130363] : [class_Fields_Olinordered__field(_1130357), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130357), _1130359), _1130361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130357), c_Groups_Ozero__class_Ozero(_1130357)), _1130363)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130357), c_Groups_Ozero__class_Ozero(_1130357)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130357), _1130361), _1130359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130357), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130357), _1130363), _1130361)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130357), _1130363), _1130359))))], (984 ^ _774244) ^ [_789268, _789270] : [-(class_Groups_Olinordered__ab__group__add(_789268)), _789270 = _789268, class_Groups_Olinordered__ab__group__add(_789270)], (12796 ^ _774244) ^ [_986738, _986740] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _986738) = _986740), _986738 = hAPP(c_Int_Onat, _986740), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986740))], (34572 ^ _774244) ^ [] : [-(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)))))], (23515 ^ _774244) ^ [_1181698, _1181700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181698)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181700)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181698), _1181700) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1181698, _1181700)))], (9224 ^ _774244) ^ [_925601, _925603] : [class_Groups_Oordered__ab__group__add(_925601), 9227 ^ _774244 : [(9234 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925601), _925603), c_Groups_Ozero__class_Ozero(_925601))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925601), c_Groups_Ozero__class_Ozero(_925601)), hAPP(c_Groups_Ouminus__class_Ouminus(_925601), _925603))))], (9228 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925601), c_Groups_Ozero__class_Ozero(_925601)), hAPP(c_Groups_Ouminus__class_Ouminus(_925601), _925603))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925601), _925603), c_Groups_Ozero__class_Ozero(_925601))))]]], (26674 ^ _774244) ^ [_1242134] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242134) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1242134))], (41387 ^ _774244) ^ [_1568638, _1568640, _1568642] : [c_Wellfounded_Owf(_1568638, _1568640), -(c_Wellfounded_Owf(_1568638, c_Wellfounded_Omlex__prod(_1568638, _1568642, _1568640)))], (45170 ^ _774244) ^ [_1660027, _1660029, _1660031, _1660033, _1660035, _1660037, _1660039] : [c_Finite__Set_Ofolding__image__simple__idem(_1660027, _1660029, _1660031, _1660033, _1660035, _1660037), -(hAPP(hAPP(_1660031, _1660039), _1660039) = _1660039)], (6560 ^ _774244) ^ [_879949] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _879949), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _879949)], (6444 ^ _774244) ^ [_877979, _877981, _877983, _877985] : [class_Groups_Ocancel__semigroup__add(_877979), 6447 ^ _774244 : [(6454 ^ _774244) ^ [] : [_877983 = _877985, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877979), _877981), _877983) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877979), _877981), _877985))], (6448 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877979), _877981), _877983) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877979), _877981), _877985), -(_877983 = _877985)]]], (18005 ^ _774244) ^ [_1082116, _1082118] : [class_Int_Onumber__ring(_1082116), -(hAPP(c_Int_Onumber__class_Onumber__of(_1082116), c_Int_Osucc(_1082118)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082116), c_Groups_Oone__class_Oone(_1082116)), hAPP(c_Int_Onumber__class_Onumber__of(_1082116), _1082118)))], (8274 ^ _774244) ^ [_909161, _909163, _909165] : [class_Orderings_Opreorder(_909161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909161), _909163), _909165)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909161), _909165), _909163))], (45476 ^ _774244) ^ [_1667048, _1667050, _1667052, _1667054, _1667056, _1667058] : [hAPP(_1667048, _1667050) = c_Option_Ooption_ONone(_1667052), -(c_Map_Omap__comp(_1667052, _1667054, _1667056, _1667058, _1667048, _1667050) = c_Option_Ooption_ONone(_1667054))], (13232 ^ _774244) ^ [_994131, _994133, _994135, _994137] : [class_Orderings_Oord(_994131), 13235 ^ _774244 : [(13244 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_994133, _994131)), _994135), _994137))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_994133, _994131)), _994135), _994137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_994133, _994131)), _994137), _994135)))], (13236 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_994133, _994131)), _994135), _994137)), 13239 ^ _774244 : [(13242 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_994133, _994131)), _994137), _994135))], (13240 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_994133, _994131)), _994135), _994137)))]]]]], (50350 ^ _774244) ^ [_1782647, _1782649, _1782651, _1782653, _1782655] : [-(hAPP(c_List_Ofoldl(_1782647, _1782649, _1782651, _1782653), _1782655) = c_List_Ofoldr(_1782649, _1782647, hAPP(c_COMBC(_1782647, _1782649, _1782647), _1782651), hAPP(c_List_Orev(_1782649), _1782655), _1782653))], (24393 ^ _774244) ^ [_1198414, _1198416] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1198414)), hAPP(c_Nat_OSuc, _1198416)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1198414))), 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, _1198416))), 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)), _1198416)))))], (1104 ^ _774244) ^ [_790768, _790770] : [-(class_Groups_Ogroup__add(_790768)), _790770 = _790768, class_Groups_Ogroup__add(_790770)], (25507 ^ _774244) ^ [_1219151, _1219153, _1219155, _1219157] : [class_Rings_Oidom(_1219151), 25510 ^ _774244 : [(25511 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1219151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219151), _1219153), _1219155)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219151), _1219157), _1219155))), -(_1219155 = c_Groups_Ozero__class_Ozero(_1219151)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1219151), _1219153), _1219157)))], (25521 ^ _774244) ^ [] : [25522 ^ _774244 : [(25525 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1219151), _1219153), _1219157))], (25523 ^ _774244) ^ [] : [_1219155 = c_Groups_Ozero__class_Ozero(_1219151)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1219151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219151), _1219153), _1219155)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219151), _1219157), _1219155))))]]], (29646 ^ _774244) ^ [_1302190, _1302192] : [hAPP(c_Int_ORep__Integ, _1302190) = hAPP(c_Int_ORep__Integ, _1302192), -(_1302190 = _1302192)], (38642 ^ _774244) ^ [_1496033, _1496035, _1496037, _1496039, _1496041, _1496043] : [c_Fun_Oinj__on(_1496033, _1496035, _1496037, _1496039), hBOOL(hAPP(hAPP(c_member(_1496035), _1496041), hAPP(c_Set_Oimage(_1496033, _1496035, _1496037), _1496039))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496033, tc_HOL_Obool)), _1496039), _1496043)), -(hBOOL(hAPP(hAPP(c_member(_1496033), hAPP(c_Fun_Othe__inv__into(_1496033, _1496035, _1496039, _1496037), _1496041)), _1496043)))], (16307 ^ _774244) ^ [_1051592, _1051594] : [class_Int_Onumber__ring(_1051592), -(hAPP(c_Int_Onumber__class_Onumber__of(_1051592), _1051594) = hAPP(c_Int_Oring__1__class_Oof__int(_1051592), _1051594))], (35538 ^ _774244) ^ [_1427818, _1427820, _1427822] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427818, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1427818), _1427820), _1427822), -(_1427820 = c_Orderings_Obot__class_Obot(tc_fun(_1427818, tc_HOL_Obool)))], (45551 ^ _774244) ^ [_1668624, _1668626, _1668628] : [c_Fun_Oinj__on(_1668624, _1668626, _1668628, c_Orderings_Otop__class_Otop(tc_fun(_1668624, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1668624), tc_List_Olist(_1668626), hAPP(c_List_Omap(_1668624, _1668626), _1668628), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1668624), tc_HOL_Obool))))], (1564 ^ _774244) ^ [_796518, _796520] : [-(class_Divides_Osemiring__div(_796518)), _796520 = _796518, class_Divides_Osemiring__div(_796520)], (46012 ^ _774244) ^ [_1679730, _1679732, _1679734, _1679736] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1679730, _1679730)), hAPP(hAPP(c_Product__Type_OPair(_1679730, _1679730), _1679732), _1679734)), hAPP(c_List_Oset(tc_prod(_1679730, _1679730)), hAPP(hAPP(c_List_Ozip(_1679730, _1679730), _1679736), _1679736))))), hBOOL(hAPP(hAPP(c_member(_1679730), _1679732), hAPP(c_List_Oset(_1679730), _1679736))), _1679732 = _1679734], (8394 ^ _774244) ^ [_911042, _911044, _911046, _911048] : [class_Orderings_Oorder(_911042), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911042), _911044), _911046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911042), _911048), _911044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911042), _911048), _911046)))], (17939 ^ _774244) ^ [_1081183, _1081185] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1081183), _1081185) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1081183 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1081183 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (47485 ^ _774244) ^ [_1717783, _1717785, _1717787, _1717789, _1717791] : [hAPP(hAPP(c_List_Olist_OCons(_1717783), _1717785), _1717787) = hAPP(hAPP(c_List_Oappend(_1717783), _1717789), _1717791), 47490 ^ _774244 : [(47493 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1717783), _1717785), _1717787) = _1717791)], (47491 ^ _774244) ^ [] : [-(_1717789 = c_List_Olist_ONil(_1717783))]], 47495 ^ _774244 : [(47498 ^ _774244) ^ [] : [-(_1717787 = hAPP(hAPP(c_List_Oappend(_1717783), 47494 ^ [_1717783, _1717785, _1717787, _1717789, _1717791]), _1717791))], (47496 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1717783), _1717785), 47494 ^ [_1717783, _1717785, _1717787, _1717789, _1717791]) = _1717789)]]], (40591 ^ _774244) ^ [_1541413, _1541415] : [-(hAPP(c_Set_OCollect(_1541413), _1541415) = _1541415)], (46407 ^ _774244) ^ [_1691603, _1691605, _1691607, _1691609, _1691611, _1691613] : [-(c_List_Ofoldr(_1691603, _1691605, _1691607, hAPP(hAPP(c_List_Olist_OCons(_1691603), _1691609), _1691611), _1691613) = hAPP(hAPP(_1691607, _1691609), c_List_Ofoldr(_1691603, _1691605, _1691607, _1691611, _1691613)))], (4282 ^ _774244) ^ [_840503, _840505, _840507, _840509] : [-(c_Random_Oselect(_840509, _840505) = c_Random_Oselect(_840507, _840503)), _840509 = _840507, _840505 = _840503], (17067 ^ _774244) ^ [_1066027, _1066029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1066027)), -(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), _1066027), _1066029))))], (29758 ^ _774244) ^ [_1304245, _1304247, _1304249] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1304245), _1304247)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1304245), hAPP(hAPP(c_Set_Oinsert(_1304245), _1304249), _1304247))))], (33152 ^ _774244) ^ [_1374488, _1374490, _1374492] : [class_Orderings_Olinorder(_1374488), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374488), _1374490)), 33159 ^ _774244 : [(33166 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374488, tc_HOL_Obool)), _1374490), hAPP(hAPP(c_Set_Oinsert(_1374488), _1374492), c_Orderings_Obot__class_Obot(tc_fun(_1374488, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1374488, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1374488, hAPP(hAPP(c_Set_Oinsert(_1374488), _1374492), _1374490)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1374488), _1374492), c_Big__Operators_Olinorder__class_OMax(_1374488, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374488, tc_HOL_Obool)), _1374490), hAPP(hAPP(c_Set_Oinsert(_1374488), _1374492), c_Orderings_Obot__class_Obot(tc_fun(_1374488, tc_HOL_Obool)))))))], (33160 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374488, tc_HOL_Obool)), _1374490), hAPP(hAPP(c_Set_Oinsert(_1374488), _1374492), c_Orderings_Obot__class_Obot(tc_fun(_1374488, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1374488, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1374488, hAPP(hAPP(c_Set_Oinsert(_1374488), _1374492), _1374490)) = _1374492)]]], (47014 ^ _774244) ^ [_1706161, _1706163, _1706165, _1706167] : [-(hAPP(c_List_Olist_Olist__case(_1706161, _1706163, _1706165, _1706167), c_List_Olist_ONil(_1706163)) = _1706165)], (19911 ^ _774244) ^ [_1114999, _1115001] : [c_Nat__Transfer_Ois__nat(_1114999), c_Nat__Transfer_Ois__nat(_1115001), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1114999), _1115001)))], (35697 ^ _774244) ^ [_1431377, _1431379, _1431381, _1431383, _1431385, _1431387, _1431389] : [c_Equiv__Relations_Oequiv(_1431377, _1431379, _1431381), hBOOL(hAPP(hAPP(c_member(tc_fun(_1431377, tc_HOL_Obool)), _1431383), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1431377), _1431379), _1431381))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1431377, tc_HOL_Obool)), _1431385), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1431377), _1431379), _1431381))), hBOOL(hAPP(hAPP(c_member(_1431377), _1431387), _1431383)), hBOOL(hAPP(hAPP(c_member(_1431377), _1431389), _1431385)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1431377, _1431377)), hAPP(hAPP(c_Product__Type_OPair(_1431377, _1431377), _1431387), _1431389)), _1431381)), -(_1431383 = _1431385)], (30182 ^ _774244) ^ [_1311913, _1311915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1311913), _1311915))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1311913), _1311915)))], (7571 ^ _774244) ^ [_897539, _897541, _897543, _897545, _897547, _897549, _897551, _897553, _897555, _897557, _897559] : [-(c_Com_Ocom_Ocom__rec(_897539, _897541, _897543, _897545, _897547, _897549, _897551, _897553, _897555, c_Com_Ocom_OAss(_897557, _897559)) = hAPP(hAPP(_897543, _897557), _897559))], (16261 ^ _774244) ^ [_1050724, _1050726, _1050728, _1050730] : [class_Rings_Ocomm__semiring__1(_1050724), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1050724), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050724), _1050726), _1050728)), _1050730) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050724), hAPP(hAPP(c_Power_Opower__class_Opower(_1050724), _1050726), _1050730)), hAPP(hAPP(c_Power_Opower__class_Opower(_1050724), _1050728), _1050730)))], (25405 ^ _774244) ^ [_1217369, _1217371, _1217373, _1217375] : [class_Divides_Osemiring__div(_1217369), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1217369), _1217371), _1217373)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1217369), _1217371), _1217375)), 25416 ^ _774244 : [(25423 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1217369), _1217373), _1217375)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1217369), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1217369), _1217373), _1217371)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1217369), _1217375), _1217371))))], (25417 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1217369), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1217369), _1217373), _1217371)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1217369), _1217375), _1217371))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1217369), _1217373), _1217375)))]]], (19941 ^ _774244) ^ [_1115488, _1115490, _1115492, _1115494] : [class_Fields_Olinordered__field__inverse__zero(_1115488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115488), _1115490), _1115492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115488), c_Groups_Ozero__class_Ozero(_1115488)), _1115494)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115488), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115488), _1115490), _1115494)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115488), _1115492), _1115494))))], (46848 ^ _774244) ^ [_1702578, _1702580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1702578), _1702580)), -(c_List_Oupto(_1702580, _1702578) = c_List_Olist_ONil(tc_Int_Oint))], (50135 ^ _774244) ^ [_1777631, _1777633, _1777635] : [50136 ^ _774244 : [(50139 ^ _774244) ^ [] : [_1777635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50137 ^ _774244) ^ [] : [-(_1777631 = c_List_Olist_ONil(tc_List_Olist(_1777633)))]], 50143 ^ _774244 : [(50146 ^ _774244) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777633)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1777633)), _1777631), 50142 ^ [_1777631, _1777633, _1777635])) = _1777635], (50144 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50142 ^ [_1777631, _1777633, _1777635]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1777633))), _1777631))))]], -(c_List_Otranspose(_1777633, _1777631) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1777633)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1777633)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1777633), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1777633)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1777633)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1777633), hAPP(hAPP(c_COMBB(tc_List_Olist(_1777633), tc_fun(tc_Nat_Onat, _1777633), tc_Nat_Onat), c_List_Onth(_1777633)), hAPP(c_List_Onth(tc_List_Olist(_1777633)), _1777631))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1777633))), _1777631)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1777635)))], (12924 ^ _774244) ^ [_989000, _989002] : [_989000 = hAPP(c_Int_Onat, _989002), 12927 ^ _774244 : [(12934 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989002))), -(_989000 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12928 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989002)), -(_989002 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _989000))]]], (28058 ^ _774244) ^ [_1269736, _1269738, _1269740] : [class_Lattices_Osemilattice__sup(_1269736), 28061 ^ _774244 : [(28068 ^ _774244) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269736), _1269738), _1269740) = _1269740, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269736), _1269738), _1269740)))], (28062 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269736), _1269738), _1269740)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269736), _1269738), _1269740) = _1269740)]]], (49651 ^ _774244) ^ [_1768737, _1768739] : [49652 ^ _774244 : [(49655 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1768739), _1768737))], (49653 ^ _774244) ^ [] : [_1768739 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1768737, _1768739) = c_List_Olist_ONil(tc_Nat_Onat))], (8998 ^ _774244) ^ [_921442, _921444, _921446] : [class_Groups_Oordered__ab__group__add(_921442), 9001 ^ _774244 : [(9008 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921442), _921446), _921444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921442), hAPP(c_Groups_Ouminus__class_Ouminus(_921442), _921444)), hAPP(c_Groups_Ouminus__class_Ouminus(_921442), _921446))))], (9002 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921442), hAPP(c_Groups_Ouminus__class_Ouminus(_921442), _921444)), hAPP(c_Groups_Ouminus__class_Ouminus(_921442), _921446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921442), _921446), _921444)))]]], (28717 ^ _774244) ^ [_1284115, _1284117, _1284119, _1284121] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284115, tc_HOL_Obool)), _1284117), hAPP(hAPP(c_Set_Oinsert(_1284115), _1284119), _1284121)) = hAPP(hAPP(c_Set_Oinsert(_1284115), _1284119), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284115, tc_HOL_Obool)), _1284117), _1284121)))], (19627 ^ _774244) ^ [_1109598, _1109600] : [class_Rings_Oring__1(_1109598), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1109598), hAPP(c_Groups_Ouminus__class_Ouminus(_1109598), c_Groups_Oone__class_Oone(_1109598))), 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)))), _1109600)) = c_Groups_Oone__class_Oone(_1109598))], (49002 ^ _774244) ^ [_1754581, _1754583, _1754585, _1754587, _1754589] : [class_Groups_Omonoid__add(_1754581), class_Groups_Oordered__ab__semigroup__add(_1754581), 49012 ^ _774244 : [(49015 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1754581), hAPP(_1754587, 49011 ^ [_1754581, _1754583, _1754585, _1754587, _1754589])), hAPP(_1754589, 49011 ^ [_1754581, _1754583, _1754585, _1754587, _1754589])))], (49013 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754583), 49011 ^ [_1754581, _1754583, _1754585, _1754587, _1754589]), hAPP(c_List_Oset(_1754583), _1754585))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1754581), hAPP(c_List_Omonoid__add__class_Olistsum(_1754581), hAPP(hAPP(c_List_Omap(_1754583, _1754581), _1754587), _1754585))), hAPP(c_List_Omonoid__add__class_Olistsum(_1754581), hAPP(hAPP(c_List_Omap(_1754583, _1754581), _1754589), _1754585)))))], (4056 ^ _774244) ^ [_836850, _836852, _836854, _836856, _836858, _836860, _836862, _836864, _836866, _836868] : [-(c_Sum__Type_Osum_Osum__case(_836868, _836864, _836860, _836856, _836852) = c_Sum__Type_Osum_Osum__case(_836866, _836862, _836858, _836854, _836850)), _836868 = _836866, _836864 = _836862, _836860 = _836858, _836856 = _836854, _836852 = _836850], (46645 ^ _774244) ^ [_1697937, _1697939, _1697941, _1697943, _1697945] : [class_Rings_Osemiring__0(_1697937), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1697937), hAPP(hAPP(c_List_Omap(_1697939, _1697937), hAPP(hAPP(c_COMBC(_1697939, _1697937, _1697937), hAPP(hAPP(c_COMBB(_1697937, tc_fun(_1697937, _1697937), _1697939), c_Groups_Otimes__class_Otimes(_1697937)), _1697941)), _1697943)), _1697945)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1697937), hAPP(c_List_Omonoid__add__class_Olistsum(_1697937), hAPP(hAPP(c_List_Omap(_1697939, _1697937), _1697941), _1697945))), _1697943))], (21139 ^ _774244) ^ [_1136299, _1136301] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136299), _1136301), hAPP(c_Int_Onumber__class_Onumber__of(_1136299), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1136299), _1136301)), class_Fields_Ofield__inverse__zero(_1136299), class_Int_Onumber__ring(_1136299)], (12734 ^ _774244) ^ [_985834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _985834)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_985834 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37931 ^ _774244) ^ [_1481364, _1481366] : [c_Equiv__Relations_Oequivp(_1481364, _1481366), 37934 ^ _774244 : [(37941 ^ _774244) ^ [_1481557, _1481559] : [hAPP(_1481366, _1481559) = hAPP(_1481366, _1481557), -(hBOOL(hAPP(hAPP(_1481366, _1481559), _1481557)))], (37935 ^ _774244) ^ [_1481458, _1481460] : [hBOOL(hAPP(hAPP(_1481366, _1481460), _1481458)), -(hAPP(_1481366, _1481460) = hAPP(_1481366, _1481458))]]], (10554 ^ _774244) ^ [_948068, _948070, _948072] : [class_Orderings_Oorder(_948068), 10557 ^ _774244 : [(10566 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948068), _948070), _948072))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948068), _948070), _948072)), -(_948070 = _948072)], (10558 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948068), _948070), _948072)), 10561 ^ _774244 : [(10564 ^ _774244) ^ [] : [_948070 = _948072], (10562 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948068), _948070), _948072)))]]]]], (5488 ^ _774244) ^ [_858980, _858982, _858984, _858986] : [-(tc_fun(_858986, _858982) = tc_fun(_858984, _858980)), _858986 = _858984, _858982 = _858980], (34662 ^ _774244) ^ [_1407184, _1407186, _1407188, _1407190, _1407192, _1407194] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1407184, _1407184)), hAPP(hAPP(c_Product__Type_OPair(_1407184, _1407184), _1407186), _1407188)), hAPP(hAPP(c_Relation_Oinv__image(_1407190, _1407184), _1407192), _1407194))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1407190, _1407190)), hAPP(hAPP(c_Product__Type_OPair(_1407190, _1407190), hAPP(_1407194, _1407186)), hAPP(_1407194, _1407188))), _1407192)))], (8692 ^ _774244) ^ [_916103, _916105, _916107] : [class_Groups_Ogroup__add(_916103), 8695 ^ _774244 : [(8702 ^ _774244) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_916103), _916107) = _916105, -(hAPP(c_Groups_Ouminus__class_Ouminus(_916103), _916105) = _916107)], (8696 ^ _774244) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_916103), _916105) = _916107, -(hAPP(c_Groups_Ouminus__class_Ouminus(_916103), _916107) = _916105)]]], (44229 ^ _774244) ^ [_1637481, _1637483, _1637485, _1637487] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1637481, _1637483), tc_fun(_1637481, _1637483)), _1637485), c_Fun_Ocomp(_1637483, _1637483, _1637481, _1637487)) = c_Fun_Ocomp(_1637483, _1637483, _1637481, hAPP(hAPP(c_Nat_Ocompow(_1637483, _1637483), _1637485), _1637487)))], (49864 ^ _774244) ^ [_1772267] : [-(c_List_Oupt(_1772267, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (24201 ^ _774244) ^ [_1194554, _1194556, _1194558] : [class_Orderings_Olinorder(_1194554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194554), _1194556), _1194558)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194554), _1194556), _1194558) = _1194558)], (43781 ^ _774244) ^ [_1625624, _1625626, _1625628, _1625630, _1625632] : [class_Complete__Lattice_Ocomplete__lattice(_1625624), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1625626, tc_HOL_Obool)), _1625628), _1625630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625624), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625626, _1625624), _1625630), _1625632)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625626, _1625624), _1625628), _1625632))))], (49184 ^ _774244) ^ [_1758211, _1758213, _1758215, _1758217] : [-(hAPP(hAPP(c_List_Omap(_1758211, _1758213), _1758215), c_List_Obutlast(_1758211, _1758217)) = c_List_Obutlast(_1758213, hAPP(hAPP(c_List_Omap(_1758211, _1758213), _1758215), _1758217)))], (41611 ^ _774244) ^ [_1573562, _1573564, _1573566, _1573568] : [41613 ^ _774244 : [(41616 ^ _774244) ^ [] : [c_Wellfounded_Owf(_1573564, hAPP(_1573566, 41612 ^ [_1573562, _1573564, _1573566, _1573568]))], (41614 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1573562, 41612 ^ [_1573562, _1573564, _1573566, _1573568])))]], -(c_Wellfounded_Owf(tc_prod(_1573568, _1573564), c_Recdef_Osame__fst(_1573568, _1573564, _1573562, _1573566)))], (49882 ^ _774244) ^ [_1772517, _1772519] : [class_Orderings_Olinorder(_1772517), c_List_Olinorder__class_Osorted(_1772517, _1772519), -(c_List_Olinorder__class_Osorted(_1772517, hAPP(c_List_Otl(_1772517), _1772519)))], (31279 ^ _774244) ^ [_1336030, _1336032, _1336034, _1336036] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1336030, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1336030), _1336032), _1336034)), _1336036))), hBOOL(hAPP(hAPP(c_member(_1336030), _1336032), _1336036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1336030, tc_HOL_Obool)), _1336034), _1336036))], (51339 ^ _774244) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (48118 ^ _774244) ^ [_1733096, _1733098, _1733100, _1733102, _1733104] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733096), tc_List_Olist(_1733096))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733096), tc_List_Olist(_1733096)), _1733098), _1733100)), c_List_Olistrel1(_1733096, _1733102))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733096), tc_List_Olist(_1733096))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733096), tc_List_Olist(_1733096)), hAPP(hAPP(c_List_Olist_OCons(_1733096), _1733104), _1733098)), hAPP(hAPP(c_List_Olist_OCons(_1733096), _1733104), _1733100))), c_List_Olistrel1(_1733096, _1733102))))], (41316 ^ _774244) ^ [_1567454] : [-(c_Wellfounded_Owf(_1567454, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1567454, _1567454), tc_HOL_Obool))))], (2348 ^ _774244) ^ [_809642, _809644, _809646, _809648] : [-(c_Random_Oinc__shift(_809648, _809644) = c_Random_Oinc__shift(_809646, _809642)), _809648 = _809646, _809644 = _809642], (43478 ^ _774244) ^ [_1617557, _1617559, _1617561, _1617563] : [-(hAPP(c_Relation_Oconverse(_1617557, _1617557), hAPP(hAPP(c_Relation_Oinv__image(_1617559, _1617557), _1617561), _1617563)) = hAPP(hAPP(c_Relation_Oinv__image(_1617559, _1617557), hAPP(c_Relation_Oconverse(_1617559, _1617559), _1617561)), _1617563))], (7301 ^ _774244) ^ [_892811, _892813, _892815, _892817, _892819] : [class_Groups_Oordered__cancel__ab__semigroup__add(_892811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892811), _892813), _892815)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892811), _892817), _892819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892811), _892813), _892817)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892811), _892815), _892819))))], (30693 ^ _774244) ^ [_1322350, _1322352, _1322354, _1322356, _1322358, _1322360, _1322362] : [c_Typedef_Otype__definition(_1322350, _1322352, _1322354, _1322356, _1322358), hBOOL(hAPP(hAPP(c_member(_1322352), _1322360), _1322358)), hBOOL(hAPP(hAPP(c_member(_1322352), _1322362), _1322358)), 30704 ^ _774244 : [(30711 ^ _774244) ^ [] : [_1322360 = _1322362, -(hAPP(_1322356, _1322360) = hAPP(_1322356, _1322362))], (30705 ^ _774244) ^ [] : [hAPP(_1322356, _1322360) = hAPP(_1322356, _1322362), -(_1322360 = _1322362)]]], (6748 ^ _774244) ^ [_882977, _882979, _882981, _882983] : [c_Com_Ocom_OBODY(_882977) = c_Com_Ocom_OLocal(_882979, _882981, _882983)], (36297 ^ _774244) ^ [_1444132, _1444134, _1444136] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444132, tc_HOL_Obool)), _1444134), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444132, tc_HOL_Obool)), _1444134), _1444136)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444132, tc_HOL_Obool)), _1444134), _1444136))], (15668 ^ _774244) ^ [_1038941, _1038943, _1038945, _1038947, _1038949, _1038951] : [class_Rings_Oordered__ring(_1038941), 15671 ^ _774244 : [(15678 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038941), _1038947), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038941), _1038949), _1038943)), _1038945)), _1038951))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038941), _1038943), _1038945)), _1038947)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038941), _1038949), _1038945)), _1038951))))], (15672 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038941), _1038943), _1038945)), _1038947)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038941), _1038949), _1038945)), _1038951))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038941), _1038947), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038941), _1038949), _1038943)), _1038945)), _1038951))))]]], (29302 ^ _774244) ^ [_1295671, _1295673, _1295675] : [class_Orderings_Oorder(_1295671), 29305 ^ _774244 : [(29312 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295671), _1295673), _1295675))), -(c_Orderings_Obot__class_Obot(tc_fun(_1295671, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1295671, _1295673, _1295675))], (29306 ^ _774244) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1295671, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1295671, _1295673, _1295675), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295671), _1295673), _1295675))]]], (27408 ^ _774244) ^ [_1257529] : [-(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)), _1257529)) = _1257529)], (940 ^ _774244) ^ [_788700, _788702, _788704, _788706] : [-(c_List_Olinorder__class_Osorted(_788704, _788700)), c_List_Olinorder__class_Osorted(_788706, _788702), _788706 = _788704, _788702 = _788700], (21151 ^ _774244) ^ [_1136478, _1136480, _1136482, _1136484] : [class_Fields_Olinordered__field__inverse__zero(_1136478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136478), _1136480), _1136482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136478), _1136484), c_Groups_Ozero__class_Ozero(_1136478))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136478), c_Groups_Ozero__class_Ozero(_1136478)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136478), _1136480), _1136482))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136478), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136478), _1136484), _1136480)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136478), _1136484), _1136482))))], (3772 ^ _774244) ^ [_832400, _832402, _832404, _832406, _832408, _832410] : [-(c_Predicate_ORangeP(_832410, _832406, _832402) = c_Predicate_ORangeP(_832408, _832404, _832400)), _832410 = _832408, _832406 = _832404, _832402 = _832400], (47991 ^ _774244) ^ [_1729797, _1729799, _1729801, _1729803] : [_1729797 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1729799), _1729797), hAPP(hAPP(c_List_Olist_OCons(_1729799), _1729801), _1729803)) = c_List_Olist_ONil(_1729799))], (45618 ^ _774244) ^ [_1670407, _1670409, _1670411, _1670413, _1670415] : [45620 ^ _774244 : [(45623 ^ _774244) ^ [] : [hAPP(_1670411, 45619 ^ [_1670407, _1670409, _1670411, _1670413, _1670415]) = hAPP(_1670415, 45619 ^ [_1670407, _1670409, _1670411, _1670413, _1670415])], (45621 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1670407), 45619 ^ [_1670407, _1670409, _1670411, _1670413, _1670415]), hAPP(c_List_Oset(_1670407), _1670413))))]], -(hAPP(hAPP(c_List_Omap(_1670407, _1670409), _1670411), _1670413) = hAPP(hAPP(c_List_Omap(_1670407, _1670409), _1670415), _1670413))], (6742 ^ _774244) ^ [_882864, _882866, _882868] : [hBOOL(hAPP(c_Com_OWT, _882864)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_882866, _882868, _882864))))], (27595 ^ _774244) ^ [_1260716, _1260718, _1260720, _1260722, _1260724] : [class_Groups_Ocomm__monoid__add(_1260716), class_Groups_Ocomm__monoid__mult(_1260716), _1260718 = _1260720, c_Nat__Transfer_Onat__set(_1260720), 27613 ^ _774244 : [(27616 ^ _774244) ^ [] : [hAPP(_1260722, 27612 ^ [_1260716, _1260718, _1260720, _1260722, _1260724]) = hAPP(_1260724, 27612 ^ [_1260716, _1260718, _1260720, _1260722, _1260724])], (27614 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27612 ^ [_1260716, _1260718, _1260720, _1260722, _1260724])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1260716), _1260722), _1260718) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1260716), _1260724), _1260720))], (38563 ^ _774244) ^ [_1494112, _1494114, _1494116, _1494118, _1494120] : [c_Fun_Oinj__on(_1494112, _1494114, _1494116, _1494118), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494114, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1494112, _1494114, _1494116), _1494118)), _1494120)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494114), _1494120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1494112), _1494118)), hAPP(c_Finite__Set_Ocard(_1494114), _1494120))))], (76 ^ _774244) ^ [_775284, _775286] : [-(class_Rings_Odivision__ring(_775284)), _775286 = _775284, class_Rings_Odivision__ring(_775286)], (34020 ^ _774244) ^ [_1392886, _1392888, _1392890, _1392892] : [class_Fields_Olinordered__field(_1392886), -(hAPP(c_Groups_Oabs__class_Oabs(_1392886), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392888, _1392886), _1392890), _1392892)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392888, _1392886), hAPP(hAPP(c_COMBB(_1392886, _1392886, _1392888), c_Groups_Oabs__class_Oabs(_1392886)), _1392890)), _1392892))], (2818 ^ _774244) ^ [_817079, _817081, _817083, _817085, _817087, _817089, _817091, _817093] : [-(c_New__DSequence_Opos__decr__bind(_817093, _817089, _817085, _817081) = c_New__DSequence_Opos__decr__bind(_817091, _817087, _817083, _817079)), _817093 = _817091, _817089 = _817087, _817085 = _817083, _817081 = _817079], (23871 ^ _774244) ^ [_1188451, _1188453, _1188455, _1188457] : [class_Orderings_Olinorder(_1188451), 23874 ^ _774244 : [(23875 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188451), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188451), _1188453), _1188455)), _1188457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188451), _1188453), _1188457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188451), _1188455), _1188457)))], (23885 ^ _774244) ^ [] : [23886 ^ _774244 : [(23889 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188451), _1188455), _1188457))], (23887 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188451), _1188453), _1188457))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188451), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188451), _1188453), _1188455)), _1188457)))]]], (38898 ^ _774244) ^ [_1501775, _1501777, _1501779, _1501781] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1501775), hAPP(c_Set_Ovimage(_1501775, _1501777, _1501779), _1501781))), hAPP(c_Set_Oimage(_1501775, _1501777, _1501779), c_Orderings_Otop__class_Otop(tc_fun(_1501775, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1501777, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1501777), _1501781)))], (6205 ^ _774244) ^ [_873759, _873761, _873763, _873765] : [c_Com_Ocom_OBODY(_873759) = c_Com_Ocom_OCond(_873761, _873763, _873765)], (42161 ^ _774244) ^ [_1587524, _1587526] : [42162 ^ _774244 : [(42163 ^ _774244) ^ [_1587570] : [hBOOL(hAPP(_1587524, _1587570))]], -(hBOOL(hAPP(_1587524, c_Hilbert__Choice_OEps(_1587526, _1587524))))], (35088 ^ _774244) ^ [_1416746, _1416748, _1416750, _1416752, _1416754] : [c_Finite__Set_Ofolding__one__idem(_1416746, _1416748, _1416750), hBOOL(hAPP(c_Finite__Set_Ofinite(_1416746), _1416752)), hBOOL(hAPP(hAPP(c_member(_1416746), _1416754), _1416752)), -(hAPP(hAPP(_1416748, _1416754), hAPP(_1416750, _1416752)) = hAPP(_1416750, _1416752))], (18623 ^ _774244) ^ [_1092041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1092041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1092041))))], (12818 ^ _774244) ^ [_987096, _987098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _987096), _987098)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987096), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987098), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (28148 ^ _774244) ^ [_1271512, _1271514, _1271516] : [class_Orderings_Olinorder(_1271512), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271512), _1271514), _1271516)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271512, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1271512), _1271514)), c_SetInterval_Oord__class_OatLeastAtMost(_1271512, _1271514, _1271516)) = hAPP(c_SetInterval_Oord__class_OatMost(_1271512), _1271516))], (23479 ^ _774244) ^ [_1181018, _1181020, _1181022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1181018, tc_HOL_Obool)), _1181020), _1181022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1181018, tc_HOL_Obool)), _1181020), _1181022)))], (47646 ^ _774244) ^ [_1721499, _1721501, _1721503, _1721505, _1721507] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1721499), tc_List_Olist(_1721499))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1721499), tc_List_Olist(_1721499)), _1721501), _1721503)), c_List_Olexord(_1721499, _1721505))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1721499), tc_List_Olist(_1721499))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1721499), tc_List_Olist(_1721499)), hAPP(hAPP(c_List_Oappend(_1721499), _1721507), _1721501)), hAPP(hAPP(c_List_Oappend(_1721499), _1721507), _1721503))), c_List_Olexord(_1721499, _1721505))))], (19237 ^ _774244) ^ [_1102592, _1102594] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1102592)), _1102594) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1102592), _1102594))), _1102594))], (8100 ^ _774244) ^ [_906874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _906874)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7842 ^ _774244) ^ [_902422, _902424] : [class_Rings_Olinordered__semidom(_902422), 7845 ^ _774244 : [(7852 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _902424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902422), c_Groups_Ozero__class_Ozero(_902422)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_902422), _902424))))], (7846 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902422), c_Groups_Ozero__class_Ozero(_902422)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_902422), _902424))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _902424)))]]], (6706 ^ _774244) ^ [_882288, _882290, _882292, _882294, _882296, _882298] : [c_Com_Ocom_OLocal(_882288, _882290, _882292) = c_Com_Ocom_OLocal(_882294, _882296, _882298), 6709 ^ _774244 : [(6714 ^ _774244) ^ [] : [-(_882292 = _882298)], (6712 ^ _774244) ^ [] : [-(_882290 = _882296)], (6710 ^ _774244) ^ [] : [-(_882288 = _882294)]]], (14251 ^ _774244) ^ [_1012999, _1013001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012999), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14254 ^ _774244 : [(14261 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1013001), _1012999)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14255 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1013001), _1012999)), 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)), _1013001)))]]], (14692 ^ _774244) ^ [_1020352, _1020354, _1020356] : [class_Divides_Osemiring__div(_1020352), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020352), c_Divides_Odiv__class_Omod(_1020352, _1020354, _1020356)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020352), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020352), _1020354), _1020356)), _1020356)) = _1020354)], (22796 ^ _774244) ^ [_1167829, _1167831] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1167829))), 22799 ^ _774244 : [(22806 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1167831))), -(c_Divides_Odivmod__int(_1167829, _1167831) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1167829), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1167831))))], (22800 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1167831)), -(c_Divides_Odivmod__int(_1167829, _1167831) = c_Divides_OnegDivAlg(_1167829, _1167831))]]], (38716 ^ _774244) ^ [_1497447, _1497449, _1497451, _1497453] : [c_Fun_Oinj__on(_1497447, _1497449, _1497451, _1497453), -(c_Fun_Oinj__on(_1497449, _1497447, c_Fun_Othe__inv__into(_1497447, _1497449, _1497453, _1497451), hAPP(c_Set_Oimage(_1497447, _1497449, _1497451), _1497453)))], (44424 ^ _774244) ^ [_1642359, _1642361, _1642363, _1642365] : [hBOOL(hAPP(hAPP(c_member(_1642359), _1642361), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1642359, tc_HOL_Obool), _1642363))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1642359, tc_HOL_Obool)), _1642365), _1642363)), -(hBOOL(hAPP(hAPP(c_member(_1642359), _1642361), _1642365)))], (36061 ^ _774244) ^ [_1438790, _1438792, _1438794, _1438796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438790, tc_HOL_Obool)), _1438792), _1438794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438790, tc_HOL_Obool)), _1438792), _1438796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438790, tc_HOL_Obool)), _1438792), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438790, tc_HOL_Obool)), _1438794), _1438796))))], (5762 ^ _774244) ^ [_866075, _866077] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _866075, _866077, _866075))], (29608 ^ _774244) ^ [_1301481, _1301483] : [-(c_Option_Oset(_1301481, hAPP(c_Option_Ooption_OSome(_1301481), _1301483)) = hAPP(hAPP(c_Set_Oinsert(_1301481), _1301483), c_Orderings_Obot__class_Obot(tc_fun(_1301481, tc_HOL_Obool))))], (48452 ^ _774244) ^ [_1742269, _1742271, _1742273, _1742275, _1742277] : [-(hAPP(hAPP(c_List_Oappend(_1742269), _1742271), _1742273) = hAPP(hAPP(c_List_Oappend(_1742269), _1742275), _1742277)), 48455 ^ _774244 : [(48458 ^ _774244) ^ [] : [_1742271 = hAPP(hAPP(c_List_Otake(_1742269), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742269)), _1742271)), _1742275), _1742273 = hAPP(hAPP(c_List_Oappend(_1742269), hAPP(hAPP(c_List_Odrop(_1742269), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742269)), _1742271)), _1742275)), _1742277)], (48456 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742269)), _1742271)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742269)), _1742275))))]], 48463 ^ _774244 : [(48466 ^ _774244) ^ [] : [hAPP(hAPP(c_List_Otake(_1742269), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742269)), _1742275)), _1742271) = _1742275, hAPP(hAPP(c_List_Oappend(_1742269), hAPP(hAPP(c_List_Odrop(_1742269), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742269)), _1742275)), _1742271)), _1742273) = _1742277], (48464 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742269)), _1742271)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742269)), _1742275)))]]], (6868 ^ _774244) ^ [_885391, _885393, _885395, _885397, _885399] : [hBOOL(hAPP(_885391, _885393)), c_Natural_Oevalc(_885395, _885393, _885397), c_Natural_Oevalc(c_Com_Ocom_OWhile(_885391, _885395), _885397, _885399), -(c_Natural_Oevalc(c_Com_Ocom_OWhile(_885391, _885395), _885393, _885399))], (24311 ^ _774244) ^ [_1196516, _1196518, _1196520] : [class_Orderings_Olinorder(_1196516), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196516), _1196518), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196516), _1196518), _1196520)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196516), _1196518), _1196520))], (4738 ^ _774244) ^ [_847475, _847477] : [_847477 = _847475, -(c_If(_847477) = c_If(_847475))], (22592 ^ _774244) ^ [_1164191, _1164193, _1164195, _1164197] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1164191, _1164193), _1164195)), hBOOL(hAPP(hAPP(_1164193, _1164197), _1164195)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1164191, _1164193), _1164197)))], (49948 ^ _774244) ^ [_1773702, _1773704, _1773706, _1773708, _1773710, _1773712] : [class_Orderings_Olinorder(_1773702), c_List_Olinorder__class_Osorted(_1773702, hAPP(hAPP(c_List_Omap(_1773704, _1773702), _1773706), _1773708)), hBOOL(hAPP(_1773710, _1773712)), -(hAPP(c_List_Ofilter(_1773704, _1773710), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1773704, _1773702, _1773706), _1773712), _1773708)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1773704, _1773702, _1773706), _1773712), hAPP(c_List_Ofilter(_1773704, _1773710), _1773708)))], (1774 ^ _774244) ^ [_799143, _799145, _799147, _799149] : [-(v_P(_799147, _799143)), v_P(_799149, _799145), _799149 = _799147, _799145 = _799143], (5140 ^ _774244) ^ [_853756, _853758, _853760, _853762] : [-(c_List_Ozip(_853762, _853758) = c_List_Ozip(_853760, _853756)), _853762 = _853760, _853758 = _853756], (39237 ^ _774244) ^ [_1509512, _1509514, _1509516, _1509518] : [hBOOL(hAPP(hAPP(c_member(_1509512), _1509514), c_Map_Odom(_1509512, _1509516, _1509518))), hAPP(_1509518, _1509514) = c_Option_Ooption_ONone(_1509516)], (40194 ^ _774244) ^ [_1533630, _1533632, _1533634] : [class_Orderings_Olinorder(_1533630), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533630), _1533632)), hBOOL(hAPP(hAPP(c_member(_1533630), _1533634), _1533632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1533630), hAPP(c_Finite__Set_Ofold1(_1533630, c_Orderings_Oord__class_Omin(_1533630)), _1533632)), _1533634)))], (43355 ^ _774244) ^ [_1613546, _1613548, _1613550, _1613552, _1613554, _1613556] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613546, tc_fun(_1613548, tc_HOL_Obool)), _1613550), _1613552), _1613554)), hBOOL(hAPP(hAPP(c_member(_1613546), _1613556), _1613550)), -(hBOOL(hAPP(hAPP(_1613552, _1613556), _1613554)))], (18091 ^ _774244) ^ [_1083450, _1083452, _1083454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083450), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083450)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083452)), _1083454)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50633 ^ _774244) ^ [_1790012, _1790014] : [-(_1790012 = c_List_Olist_ONil(_1790014)), hBOOL(hAPP(c_List_Odistinct(_1790014), _1790012)), -(c_List_OtakeWhile(_1790014, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1790014), c_fNot), hAPP(hAPP(c_COMBC(_1790014, _1790014, tc_HOL_Obool), c_fequal), c_List_Olast(_1790014, _1790012))), _1790012) = c_List_Obutlast(_1790014, _1790012))], (7161 ^ _774244) ^ [_890453, _890455] : [7162 ^ _774244 : [(7165 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890455), _890453))], (7163 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890453), _890455))]], _890453 = _890455], (3478 ^ _774244) ^ [_827755, _827757, _827759, _827761, _827763, _827765, _827767, _827769] : [-(c_Nitpick_Oprod(_827769, _827765, _827761, _827757) = c_Nitpick_Oprod(_827767, _827763, _827759, _827755)), _827769 = _827767, _827765 = _827763, _827761 = _827759, _827757 = _827755], (38824 ^ _774244) ^ [_1500009, _1500011, _1500013, _1500015, _1500017] : [-(hAPP(c_Set_Ovimage(_1500009, _1500011, _1500013), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1500011, tc_HOL_Obool)), _1500015), _1500017)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1500009, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1500009, _1500011, _1500013), _1500015)), hAPP(c_Set_Ovimage(_1500009, _1500011, _1500013), _1500017)))], (7343 ^ _774244) ^ [_893547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _893547)), _893547 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43008 ^ _774244) ^ [_1605273, _1605275, _1605277, _1605279, _1605281, _1605283] : [c_Finite__Set_Ofun__left__comm(_1605273, _1605275, _1605277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1605273), _1605279)), -(hBOOL(hAPP(hAPP(c_member(_1605273), _1605281), _1605279))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1605273, _1605275, _1605277), _1605283), hAPP(hAPP(c_Set_Oinsert(_1605273), _1605281), _1605279)) = hAPP(hAPP(c_Finite__Set_Ofold(_1605273, _1605275, _1605277), hAPP(hAPP(_1605277, _1605281), _1605283)), _1605279))], (19499 ^ _774244) ^ [_1107038, _1107040] : [class_Rings_Oring__1__no__zero__divisors(_1107038), 19502 ^ _774244 : [(19503 ^ _774244) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1107038), _1107040), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1107038), -(_1107040 = c_Groups_Oone__class_Oone(_1107038)), -(_1107040 = hAPP(c_Groups_Ouminus__class_Ouminus(_1107038), c_Groups_Oone__class_Oone(_1107038)))], (19513 ^ _774244) ^ [] : [19514 ^ _774244 : [(19517 ^ _774244) ^ [] : [_1107040 = hAPP(c_Groups_Ouminus__class_Ouminus(_1107038), c_Groups_Oone__class_Oone(_1107038))], (19515 ^ _774244) ^ [] : [_1107040 = c_Groups_Oone__class_Oone(_1107038)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1107038), _1107040), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1107038))]]], (11517 ^ _774244) ^ [_963966, _963968] : [class_Groups_Olinordered__ab__group__add(_963966), 11520 ^ _774244 : [(11527 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963966), c_Groups_Ozero__class_Ozero(_963966)), _963968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963966), c_Groups_Ozero__class_Ozero(_963966)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963966), _963968), _963968))))], (11521 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963966), c_Groups_Ozero__class_Ozero(_963966)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963966), _963968), _963968))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963966), c_Groups_Ozero__class_Ozero(_963966)), _963968)))]]], (16869 ^ _774244) ^ [_1062527, _1062529, _1062531, _1062533] : [class_Rings_Olinordered__semidom(_1062527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062527), _1062529), _1062531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062527), c_Groups_Ozero__class_Ozero(_1062527)), _1062529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062527), hAPP(hAPP(c_Power_Opower__class_Opower(_1062527), _1062529), _1062533)), hAPP(hAPP(c_Power_Opower__class_Opower(_1062527), _1062531), _1062533))))], (34978 ^ _774244) ^ [_1414252] : [-(hAPP(c_Set_OPow(_1414252), c_Orderings_Otop__class_Otop(tc_fun(_1414252, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1414252, tc_HOL_Obool), tc_HOL_Obool)))], (46355 ^ _774244) ^ [_1689552, _1689554, _1689556, _1689558, _1689560] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1689552), tc_List_Olist(_1689552))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689552), tc_List_Olist(_1689552)), _1689554), _1689556)), c_List_Olistrel(_1689552, c_Transitive__Closure_Ortrancl(_1689552, _1689558)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1689552), tc_List_Olist(_1689552))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689552), tc_List_Olist(_1689552)), _1689556), _1689560)), c_List_Olistrel(_1689552, c_Transitive__Closure_Ortrancl(_1689552, _1689558)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1689552), tc_List_Olist(_1689552))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689552), tc_List_Olist(_1689552)), _1689554), _1689560)), c_List_Olistrel(_1689552, c_Transitive__Closure_Ortrancl(_1689552, _1689558)))))], (24387 ^ _774244) ^ [_1198275, _1198277] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1198275), _1198277)), _1198277) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1198275), _1198277))], (27579 ^ _774244) ^ [_1260467, _1260469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260467)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1260467, _1260469)))], (4744 ^ _774244) ^ [_847560, _847562] : [_847562 = _847560, -(c_Option_Ooption_OSome(_847562) = c_Option_Ooption_OSome(_847560))], (47243 ^ _774244) ^ [_1712058, _1712060, _1712062, _1712064] : [-(hAPP(c_List_Oset(tc_prod(_1712058, _1712060)), hAPP(hAPP(c_List_Ozip(_1712058, _1712060), _1712062), _1712064)) = hAPP(c_Set_OCollect(tc_prod(_1712058, _1712060)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1712058, _1712060)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1712058, _1712060), 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(_1712058, _1712060)), 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(_1712058, _1712060)), 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(_1712058, _1712060), tc_fun(tc_Nat_Onat, tc_prod(_1712058, _1712060)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1712058, _1712060), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1712058, _1712060)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1712058, _1712060)), c_COMBB(tc_prod(_1712058, _1712060), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1712060, tc_prod(_1712058, _1712060)), hAPP(hAPP(c_COMBB(_1712058, tc_fun(_1712060, tc_prod(_1712058, _1712060)), tc_Nat_Onat), c_Product__Type_OPair(_1712058, _1712060)), hAPP(c_List_Onth(_1712058), _1712062))), hAPP(c_List_Onth(_1712060), _1712064)))))), 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(_1712058)), _1712062)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712060)), _1712064)))))))], (20903 ^ _774244) ^ [_1132376, _1132378, _1132380, _1132382] : [class_Fields_Ofield(_1132376), -(_1132378 = c_Groups_Ozero__class_Ozero(_1132376)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132376), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132376), _1132380), _1132378)), _1132382) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132376), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132376), _1132380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132376), _1132378), _1132382))), _1132378))], (34269 ^ _774244) ^ [_1397825, _1397827, _1397829, _1397831, _1397833] : [hBOOL(hAPP(hAPP(c_member(_1397825), _1397827), _1397829)), -(hAPP(c_Map_Orestrict__map(_1397825, _1397831, _1397833, _1397829), _1397827) = hAPP(_1397833, _1397827))], (8366 ^ _774244) ^ [_910590, _910592, _910594, _910596] : [class_Orderings_Oorder(_910590), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910590), _910592), _910594)), _910592 = _910596, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910590), _910596), _910594)))], (24005 ^ _774244) ^ [_1190897, _1190899, _1190901, _1190903] : [class_Orderings_Olinorder(_1190897), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190897), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1190897), _1190899), _1190901)), _1190903) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1190897), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190897), _1190899), _1190903)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190897), _1190901), _1190903)))], (49120 ^ _774244) ^ [_1756742, _1756744, _1756746] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1756742)), _1756744), c_List_Olists(_1756742, _1756746))), -(_1756744 = c_List_Olist_ONil(_1756742)), 49129 ^ _774244 : [(49134 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1756742)), 49128 ^ [_1756742, _1756744, _1756746]), c_List_Olists(_1756742, _1756746))))], (49132 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756742), 49127 ^ [_1756742, _1756744, _1756746]), _1756746)))], (49130 ^ _774244) ^ [] : [-(_1756744 = hAPP(hAPP(c_List_Olist_OCons(_1756742), 49127 ^ [_1756742, _1756744, _1756746]), 49128 ^ [_1756742, _1756744, _1756746]))]]], (27739 ^ _774244) ^ [_1263552, _1263554, _1263556, _1263558] : [27740 ^ _774244 : [(27741 ^ _774244) ^ [_1263662] : [hBOOL(hAPP(hAPP(c_member(_1263552), _1263662), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263552, tc_HOL_Obool)), _1263554), _1263556))), hBOOL(hAPP(_1263558, _1263662))]], 27749 ^ _774244 : [(27752 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1263558, 27748 ^ [_1263552, _1263554, _1263556, _1263558])))], (27750 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1263552), 27748 ^ [_1263552, _1263554, _1263556, _1263558]), _1263554)))]], 27754 ^ _774244 : [(27757 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1263558, 27753 ^ [_1263552, _1263554, _1263556, _1263558])))], (27755 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1263552), 27753 ^ [_1263552, _1263554, _1263556, _1263558]), _1263556)))]]], (9624 ^ _774244) ^ [_932762] : [class_Rings_Olinordered__semidom(_932762), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932762), c_Groups_Oone__class_Oone(_932762)), c_Groups_Ozero__class_Ozero(_932762)))], (50304 ^ _774244) ^ [_1781762, _1781764] : [hBOOL(hAPP(c_List_Odistinct(_1781762), _1781764)), -(hBOOL(hAPP(c_List_Odistinct(_1781762), hAPP(c_List_Orev(_1781762), _1781764))))], (50619 ^ _774244) ^ [_1789629, _1789631, _1789633, _1789635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1789629), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789631)), c_List_OtakeWhile(_1789631, _1789633, _1789635)))), -(hAPP(hAPP(c_List_Onth(_1789631), c_List_OtakeWhile(_1789631, _1789633, _1789635)), _1789629) = hAPP(hAPP(c_List_Onth(_1789631), _1789635), _1789629))], (25191 ^ _774244) ^ [_1213709, _1213711] : [25198 ^ _774244 : [(25201 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213711), _1213709))], (25199 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213709), _1213711)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213709), _1213711)), -(_1213709 = _1213711)], (13138 ^ _774244) ^ [_992519, _992521, _992523, _992525, _992527] : [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), _992519), _992521)), _992523)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _992519), _992525)), _992527))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _992527), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992519), _992527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992519), _992523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _992525), _992521)))], (47080 ^ _774244) ^ [_1707901, _1707903] : [47082 ^ _774244 : [(47086 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47084 ^ [_1707901, _1707903]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707901)), _1707903))))], (47088 ^ _774244) ^ [] : [47081 ^ [_1707901, _1707903] = 47084 ^ [_1707901, _1707903]], (47090 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1707901), _1707903), 47081 ^ [_1707901, _1707903]) = hAPP(hAPP(c_List_Onth(_1707901), _1707903), 47084 ^ [_1707901, _1707903]))], (47083 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47081 ^ [_1707901, _1707903]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707901)), _1707903))))]], -(hBOOL(hAPP(c_List_Odistinct(_1707901), _1707903)))], (37528 ^ _774244) ^ [_1472996, _1472998, _1473000, _1473002, _1473004] : [class_Groups_Ocomm__monoid__mult(_1472996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472998), _1473000)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472998), _1473002)), 37542 ^ _774244 : [(37545 ^ _774244) ^ [] : [hAPP(_1473004, 37541 ^ [_1472996, _1472998, _1473000, _1473002, _1473004]) = c_Groups_Oone__class_Oone(_1472996)], (37543 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1472998), 37541 ^ [_1472996, _1472998, _1473000, _1473002, _1473004]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472998, tc_HOL_Obool)), _1473000), _1473002))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1472998, _1472996), _1473004), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1472998, tc_HOL_Obool)), _1473000), _1473002)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1472996), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1472998, _1472996), _1473004), _1473000)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1472998, _1472996), _1473004), _1473002)))], (18209 ^ _774244) ^ [_1085150] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085150), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085150)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1085150)))], (18911 ^ _774244) ^ [_1096911, _1096913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096911), _1096913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1096911)), c_Int_OBit0(_1096913))))], (6995 ^ _774244) ^ [_887576, _887578, _887580, _887582] : [c_Natural_Oevalc(c_Com_Ocom_OWhile(_887576, _887578), _887580, _887582), 7000 ^ _774244 : [(7003 ^ _774244) ^ [] : [hBOOL(hAPP(_887576, _887580))], (7001 ^ _774244) ^ [] : [-(_887582 = _887580)]], 7004 ^ _774244 : [(7010 ^ _774244) ^ [] : [-(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887576, _887578), 7006 ^ [_887576, _887578, _887580, _887582], _887582))], (7008 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_887578, _887580, 7006 ^ [_887576, _887578, _887580, _887582]))], (7005 ^ _774244) ^ [] : [-(hBOOL(hAPP(_887576, _887580)))]]], (43413 ^ _774244) ^ [_1614772, _1614774] : [-(c_Transitive__Closure_Otrancl(_1614772, hAPP(c_Relation_Oconverse(_1614772, _1614772), _1614774)) = hAPP(c_Relation_Oconverse(_1614772, _1614772), c_Transitive__Closure_Otrancl(_1614772, _1614774)))], (5953 ^ _774244) ^ [_869511, _869513, _869515, _869517, _869519, _869521] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_869511, _869513, _869515), _869517, _869519, _869521), 5958 ^ _774244 : [(5961 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_869513, _869517, _869519, _869521))], (5959 ^ _774244) ^ [] : [-(hBOOL(hAPP(_869511, _869517)))]], 5962 ^ _774244 : [(5965 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_869515, _869517, _869519, _869521))], (5963 ^ _774244) ^ [] : [hBOOL(hAPP(_869511, _869517))]]], (20161 ^ _774244) ^ [_1119406, _1119408, _1119410, _1119412] : [class_Fields_Olinordered__field(_1119406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119406), _1119408), _1119410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119406), _1119412), c_Groups_Ozero__class_Ozero(_1119406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1119406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119406), _1119410), _1119412)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119406), _1119408), _1119412))))], (39976 ^ _774244) ^ [_1529594, _1529596, _1529598] : [-(c_Relation_Orefl__on(_1529594, _1529596, _1529598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529594, _1529594), tc_HOL_Obool)), _1529598), hAPP(hAPP(c_Product__Type_OSigma(_1529594, _1529594), _1529596), hAPP(c_COMBK(tc_fun(_1529594, tc_HOL_Obool), _1529594), _1529596)))), 39982 ^ _774244 : [(39985 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1529594, _1529594)), hAPP(hAPP(c_Product__Type_OPair(_1529594, _1529594), 39981 ^ [_1529594, _1529596, _1529598]), 39981 ^ [_1529594, _1529596, _1529598])), _1529598))], (39983 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1529594), 39981 ^ [_1529594, _1529596, _1529598]), _1529596)))]]], (38666 ^ _774244) ^ [_1496476] : [class_Nat_Osemiring__char__0(_1496476), -(c_Fun_Oinj__on(tc_Nat_Onat, _1496476, c_Nat_Osemiring__1__class_Oof__nat(_1496476), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51209 ^ _774244) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (12654 ^ _774244) ^ [_984492, _984494, _984496] : [class_Rings_Olinordered__idom(_984492), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984492), c_Groups_Ozero__class_Ozero(_984492)), _984494)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984492), c_Groups_Ozero__class_Ozero(_984492)), _984496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984492), _984496), c_Groups_Oone__class_Oone(_984492))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984492), _984496), _984494)), _984494)))], (14602 ^ _774244) ^ [_1018689, _1018691] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018689), _1018691) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14603 ^ _774244 : [(14612 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018689), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018691), _1018689))], (14606 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018689), _1018691))], (14604 ^ _774244) ^ [] : [_1018691 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (24035 ^ _774244) ^ [_1191642, _1191644, _1191646] : [class_Orderings_Olinorder(_1191642), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191642), _1191644), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191642), _1191644), _1191646)) = _1191644)], (19159 ^ _774244) ^ [_1101202, _1101204] : [class_Int_Onumber__ring(_1101202), class_Int_Oring__char__0(_1101202), 19166 ^ _774244 : [(19173 ^ _774244) ^ [] : [c_Int_Oiszero(_1101202, hAPP(c_Int_Onumber__class_Onumber__of(_1101202), _1101204)), -(c_Int_Oiszero(_1101202, hAPP(c_Int_Onumber__class_Onumber__of(_1101202), c_Int_OBit0(_1101204))))], (19167 ^ _774244) ^ [] : [c_Int_Oiszero(_1101202, hAPP(c_Int_Onumber__class_Onumber__of(_1101202), c_Int_OBit0(_1101204))), -(c_Int_Oiszero(_1101202, hAPP(c_Int_Onumber__class_Onumber__of(_1101202), _1101204)))]]], (1324 ^ _774244) ^ [_793518, _793520] : [-(class_Groups_Ouminus(_793518)), _793520 = _793518, class_Groups_Ouminus(_793520)], (12382 ^ _774244) ^ [_979307, _979309, _979311] : [class_Groups_Oordered__comm__monoid__add(_979307), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979307), _979309), c_Groups_Ozero__class_Ozero(_979307))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979307), _979311), c_Groups_Ozero__class_Ozero(_979307))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979307), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979307), _979309), _979311)), c_Groups_Ozero__class_Ozero(_979307))))], (4576 ^ _774244) ^ [_844984, _844986, _844988, _844990] : [-(c_List_Olistrel(_844990, _844986) = c_List_Olistrel(_844988, _844984)), _844990 = _844988, _844986 = _844984], (10037 ^ _774244) ^ [_939679] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939679), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _939679), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _939679), _939679)))))], (34790 ^ _774244) ^ [_1410104, _1410106, _1410108] : [class_Orderings_Olinorder(_1410104), hAPP(_1410106, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1410104), 34795 ^ [_1410104, _1410106, _1410108]), 34796 ^ [_1410104, _1410106, _1410108])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1410104), hAPP(_1410106, 34795 ^ [_1410104, _1410106, _1410108])), hAPP(_1410106, 34796 ^ [_1410104, _1410106, _1410108])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410104), _1410108)), -(_1410108 = c_Orderings_Obot__class_Obot(tc_fun(_1410104, tc_HOL_Obool))), -(hAPP(_1410106, c_Big__Operators_Olinorder__class_OMin(_1410104, _1410108)) = c_Big__Operators_Olinorder__class_OMin(_1410104, hAPP(c_Set_Oimage(_1410104, _1410104, _1410106), _1410108)))], (14155 ^ _774244) ^ [_1011437, _1011439] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1011437), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1011439)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1011437)), _1011439))], (19335 ^ _774244) ^ [_1104287, _1104289] : [class_Rings_Ocomm__semiring__1(_1104287), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104287), _1104289), _1104289) = hAPP(hAPP(c_Power_Opower__class_Opower(_1104287), _1104289), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (42820 ^ _774244) ^ [_1601026, _1601028] : [-(hAPP(c_Relation_ORange(_1601026, _1601026), c_Transitive__Closure_Otrancl(_1601026, _1601028)) = hAPP(c_Relation_ORange(_1601026, _1601026), _1601028))], (15126 ^ _774244) ^ [_1028498, _1028500, _1028502, _1028504, _1028506, _1028508] : [class_Divides_Oring__div(_1028498), c_Divides_Odiv__class_Omod(_1028498, _1028500, _1028502) = c_Divides_Odiv__class_Omod(_1028498, _1028504, _1028502), c_Divides_Odiv__class_Omod(_1028498, _1028506, _1028502) = c_Divides_Odiv__class_Omod(_1028498, _1028508, _1028502), -(c_Divides_Odiv__class_Omod(_1028498, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1028498), _1028500), _1028506), _1028502) = c_Divides_Odiv__class_Omod(_1028498, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1028498), _1028504), _1028508), _1028502))], (48724 ^ _774244) ^ [_1748051, _1748053, _1748055, _1748057, _1748059, _1748061] : [-(hAPP(c_List_Ofoldl(_1748051, _1748053, _1748055, _1748057), hAPP(hAPP(c_List_Oappend(_1748053), _1748059), _1748061)) = hAPP(c_List_Ofoldl(_1748051, _1748053, _1748055, hAPP(c_List_Ofoldl(_1748051, _1748053, _1748055, _1748057), _1748059)), _1748061))], (51081 ^ _774244) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11038 ^ _774244) ^ [_955765, _955767, _955769] : [class_Groups_Oordered__ab__group__add(_955765), 11041 ^ _774244 : [(11048 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955765), _955769), hAPP(c_Groups_Ouminus__class_Ouminus(_955765), _955767))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955765), _955767), hAPP(c_Groups_Ouminus__class_Ouminus(_955765), _955769))))], (11042 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955765), _955767), hAPP(c_Groups_Ouminus__class_Ouminus(_955765), _955769))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955765), _955769), hAPP(c_Groups_Ouminus__class_Ouminus(_955765), _955767))))]]], (39450 ^ _774244) ^ [_1514465, _1514467, _1514469, _1514471] : [-(c_Wellfounded_Omax__extp(_1514465, _1514467, _1514469, _1514471)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514465), _1514469)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514465), _1514471)), -(_1514471 = c_Orderings_Obot__class_Obot(tc_fun(_1514465, tc_HOL_Obool))), 39464 ^ _774244 : [(39467 ^ _774244) ^ [_1514810] : [hBOOL(hAPP(hAPP(c_member(_1514465), _1514810), _1514471)), hBOOL(hAPP(hAPP(_1514467, 39463 ^ [_1514465, _1514467, _1514469, _1514471]), _1514810))], (39465 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514465), 39463 ^ [_1514465, _1514467, _1514469, _1514471]), _1514469)))]]], (8078 ^ _774244) ^ [_906582, _906584, _906586, _906588] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_906582, _906584), _906586, _906588, c_Natural_Oupdate(_906586, _906582, hAPP(_906584, _906586))))], (19265 ^ _774244) ^ [_1103064] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1103064)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1103064)))], (1094 ^ _774244) ^ [_790643, _790645] : [-(class_Rings_Ocomm__ring__1(_790643)), _790645 = _790643, class_Rings_Ocomm__ring__1(_790645)], (39570 ^ _774244) ^ [_1517624, _1517626, _1517628, _1517630, _1517632, _1517634] : [hBOOL(hAPP(hAPP(c_member(_1517624), _1517626), _1517628)), 39573 ^ _774244 : [(39580 ^ _774244) ^ [] : [_1517632 = _1517634, -(hAPP(hAPP(c_Product__Type_OSigma(_1517630, _1517624), _1517632), hAPP(c_COMBK(tc_fun(_1517624, tc_HOL_Obool), _1517630), _1517628)) = hAPP(hAPP(c_Product__Type_OSigma(_1517630, _1517624), _1517634), hAPP(c_COMBK(tc_fun(_1517624, tc_HOL_Obool), _1517630), _1517628)))], (39574 ^ _774244) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1517630, _1517624), _1517632), hAPP(c_COMBK(tc_fun(_1517624, tc_HOL_Obool), _1517630), _1517628)) = hAPP(hAPP(c_Product__Type_OSigma(_1517630, _1517624), _1517634), hAPP(c_COMBK(tc_fun(_1517624, tc_HOL_Obool), _1517630), _1517628)), -(_1517632 = _1517634)]]], (48652 ^ _774244) ^ [_1746480] : [-(c_List_Orotate(_1746480, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1746480)))], (48692 ^ _774244) ^ [_1747275, _1747277, _1747279, _1747281] : [-(hAPP(c_List_Ofoldl(_1747275, _1747277, _1747279, _1747281), c_List_Olist_ONil(_1747277)) = _1747281)], (41853 ^ _774244) ^ [_1580010, _1580012, _1580014, _1580016] : [hBOOL(hAPP(hAPP(c_member(_1580010), _1580016), hAPP(c_Relation_ODomain(_1580010, _1580012), _1580014))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1580010, _1580012, hAPP(hAPP(c_COMBC(_1580010, tc_fun(tc_prod(_1580010, _1580012), tc_HOL_Obool), tc_fun(_1580012, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1580012, tc_fun(tc_fun(tc_prod(_1580010, _1580012), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1580010, _1580012), tc_HOL_Obool), tc_fun(_1580012, tc_HOL_Obool)), _1580010), c_COMBC(_1580012, tc_fun(tc_prod(_1580010, _1580012), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1580012, tc_prod(_1580010, _1580012)), tc_fun(_1580012, tc_fun(tc_fun(tc_prod(_1580010, _1580012), tc_HOL_Obool), tc_HOL_Obool)), _1580010), hAPP(c_COMBB(tc_prod(_1580010, _1580012), tc_fun(tc_fun(tc_prod(_1580010, _1580012), tc_HOL_Obool), tc_HOL_Obool), _1580012), c_member(tc_prod(_1580010, _1580012)))), c_Product__Type_OPair(_1580010, _1580012)))), _1580014)), _1580016)))], (9836 ^ _774244) ^ [_936314, _936316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _936314)), _936316)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _936314), hAPP(c_Int_Onat, _936316))))], (41270 ^ _774244) ^ [_1565008, _1565010, _1565012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565008, _1565008), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1565008, _1565008, _1565008), _1565010), _1565012)), _1565010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1565008, tc_HOL_Obool), tc_fun(_1565008, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1565008, tc_HOL_Obool), tc_fun(_1565008, tc_HOL_Obool), tc_fun(_1565008, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1565008, _1565010)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1565008, tc_HOL_Obool), tc_fun(_1565008, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1565008, _1565012)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1565008, tc_HOL_Obool), tc_fun(_1565008, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1565008, tc_HOL_Obool), tc_fun(_1565008, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1565008, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1565008, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1565008, tc_HOL_Obool), tc_fun(_1565008, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1565008, _1565010))))], (51129 ^ _774244) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (41238 ^ _774244) ^ [_1563971, _1563973, _1563975, _1563977, _1563979, _1563981, _1563983] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1563971, _1563973, _1563975), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1563977, tc_fun(tc_prod(_1563971, _1563973), tc_HOL_Obool)), _1563979), _1563981)), _1563983) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1563977, tc_fun(tc_prod(_1563971, _1563975), tc_HOL_Obool)), _1563979), hAPP(hAPP(c_COMBC(_1563977, tc_fun(tc_prod(_1563973, _1563975), tc_HOL_Obool), tc_fun(tc_prod(_1563971, _1563975), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1563971, _1563973), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1563973, _1563975), tc_HOL_Obool), tc_fun(tc_prod(_1563971, _1563975), tc_HOL_Obool)), _1563977), c_Relation_Orel__comp(_1563971, _1563973, _1563975)), _1563981)), _1563983)))], (50659 ^ _774244) ^ [_1790537, _1790539] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790537)), c_List_Oremdups(_1790537, c_List_Oconcat(_1790537, _1790539))) = hAPP(c_Finite__Set_Ocard(_1790537), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1790537), tc_fun(_1790537, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1790537)), _1790539)), c_List_Oset(_1790537))))], (16389 ^ _774244) ^ [_1052954, _1052956] : [class_Groups_Oordered__ab__group__add__abs(_1052954), 16392 ^ _774244 : [(16399 ^ _774244) ^ [] : [-(_1052956 = c_Groups_Ozero__class_Ozero(_1052954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052954), c_Groups_Ozero__class_Ozero(_1052954)), hAPP(c_Groups_Oabs__class_Oabs(_1052954), _1052956))))], (16393 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052954), c_Groups_Ozero__class_Ozero(_1052954)), hAPP(c_Groups_Oabs__class_Oabs(_1052954), _1052956))), _1052956 = c_Groups_Ozero__class_Ozero(_1052954)]]], (44673 ^ _774244) ^ [_1648007, _1648009] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1648007, tc_HOL_Obool), hAPP(c_Set_OPow(_1648007), _1648009)) = _1648009)], (49186 ^ _774244) ^ [_1758263, _1758265] : [-(_1758263 = c_List_Olist_ONil(_1758265)), hBOOL(hAPP(c_List_Odistinct(_1758265), _1758263)), -(hBOOL(hAPP(c_List_Odistinct(_1758265), c_List_Obutlast(_1758265, _1758263))))], (14996 ^ _774244) ^ [_1026179, _1026181, _1026183] : [class_Rings_Oring__1(_1026179), -(hAPP(c_Int_Oring__1__class_Oof__int(_1026179), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1026181), _1026183)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1026179), hAPP(c_Int_Oring__1__class_Oof__int(_1026179), _1026181)), hAPP(c_Int_Oring__1__class_Oof__int(_1026179), _1026183)))], (11315 ^ _774244) ^ [_960497, _960499] : [11316 ^ _774244 : [(11319 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _960499))], (11317 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _960497))]], 11320 ^ _774244 : [(11327 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _960497), _960499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _960497)), hAPP(c_Int_Onat, _960499))))], (11321 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _960497)), hAPP(c_Int_Onat, _960499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _960497), _960499)))]]], (5790 ^ _774244) ^ [_866579, _866581] : [c_Com_Ocom_OSemi(_866579, _866581) = c_Com_Ocom_OSKIP], (25167 ^ _774244) ^ [_1213311, _1213313] : [-(_1213311 = _1213313), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213311), _1213313)), 25174 ^ _774244 : [(25177 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213313), _1213311))], (25175 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213311), _1213313)))]]], (43853 ^ _774244) ^ [_1627566, _1627568, _1627570, _1627572] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627566, _1627566)), hAPP(hAPP(c_Product__Type_OPair(_1627566, _1627566), _1627568), _1627570)), c_Transitive__Closure_Ortrancl(_1627566, hAPP(c_Relation_Oconverse(_1627566, _1627566), _1627572)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1627566, _1627566)), hAPP(hAPP(c_Product__Type_OPair(_1627566, _1627566), _1627570), _1627568)), c_Transitive__Closure_Ortrancl(_1627566, _1627572))))], (1714 ^ _774244) ^ [_798393, _798395] : [-(class_Power_Opower(_798393)), _798395 = _798393, class_Power_Opower(_798395)], (47475 ^ _774244) ^ [_1717544, _1717546, _1717548, _1717550, _1717552] : [-(hAPP(hAPP(c_List_Oappend(_1717544), _1717546), hAPP(hAPP(c_List_Olist_OCons(_1717544), _1717548), c_List_Olist_ONil(_1717544))) = hAPP(hAPP(c_List_Oappend(_1717544), _1717550), hAPP(hAPP(c_List_Olist_OCons(_1717544), _1717552), c_List_Olist_ONil(_1717544)))), _1717546 = _1717550, _1717548 = _1717552], (24461 ^ _774244) ^ [_1199733, _1199735, _1199737, _1199739, _1199741] : [-(hAPP(c_Product__Type_Ofst(_1199733, _1199735), hAPP(c_Product__Type_Oapfst(_1199737, _1199733, _1199735, _1199739), _1199741)) = hAPP(_1199739, hAPP(c_Product__Type_Ofst(_1199737, _1199735), _1199741)))], (41148 ^ _774244) ^ [_1561379, _1561381, _1561383, _1561385, _1561387, _1561389, _1561391] : [hAPP(c_Fun_Ocomp(_1561379, _1561381, _1561383, _1561385), _1561387) = hAPP(c_Fun_Ocomp(_1561381, _1561381, _1561383, c_Fun_Oid(_1561381)), _1561389), -(hAPP(_1561385, hAPP(_1561387, _1561391)) = hAPP(_1561389, _1561391))], (45003 ^ _774244) ^ [_1656069, _1656071, _1656073, _1656075] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656069, _1656069)), hAPP(hAPP(c_Product__Type_OPair(_1656069, _1656069), _1656071), _1656073)), c_Transitive__Closure_Otrancl(_1656069, _1656075))), 45007 ^ _774244 : [(45010 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1656069, _1656069)), hAPP(hAPP(c_Product__Type_OPair(_1656069, _1656069), 45006 ^ [_1656069, _1656071, _1656073, _1656075]), _1656073)), c_Transitive__Closure_Ortrancl(_1656069, _1656075))))], (45008 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1656069, _1656069)), hAPP(hAPP(c_Product__Type_OPair(_1656069, _1656069), _1656071), 45006 ^ [_1656069, _1656071, _1656073, _1656075])), _1656075)))]]], (1344 ^ _774244) ^ [_793768, _793770] : [-(class_Smallcheck_Osmall(_793768)), _793770 = _793768, class_Smallcheck_Osmall(_793770)], (31465 ^ _774244) ^ [_1339386, _1339388, _1339390, _1339392, _1339394, _1339396] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339386, tc_fun(_1339388, tc_fun(_1339390, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1339386, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1339388, _1339390), tc_HOL_Obool), tc_fun(_1339388, tc_fun(_1339390, tc_HOL_Obool)), _1339386), hAPP(c_COMBC(_1339388, tc_fun(tc_prod(_1339388, _1339390), tc_HOL_Obool), tc_fun(_1339390, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339390, tc_fun(tc_fun(tc_prod(_1339388, _1339390), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1339388, _1339390), tc_HOL_Obool), tc_fun(_1339390, tc_HOL_Obool)), _1339388), c_COMBC(_1339390, tc_fun(tc_prod(_1339388, _1339390), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339390, tc_prod(_1339388, _1339390)), tc_fun(_1339390, tc_fun(tc_fun(tc_prod(_1339388, _1339390), tc_HOL_Obool), tc_HOL_Obool)), _1339388), hAPP(c_COMBB(tc_prod(_1339388, _1339390), tc_fun(tc_fun(tc_prod(_1339388, _1339390), tc_HOL_Obool), tc_HOL_Obool), _1339390), c_member(tc_prod(_1339388, _1339390)))), c_Product__Type_OPair(_1339388, _1339390))))), _1339392)), _1339394), _1339396)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1339388, _1339390)), hAPP(hAPP(c_Product__Type_OPair(_1339388, _1339390), _1339394), _1339396)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339386, tc_fun(tc_prod(_1339388, _1339390), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1339386, tc_HOL_Obool))), _1339392))))], (11271 ^ _774244) ^ [_959733, _959735] : [11272 ^ _774244 : [(11273 ^ _774244) ^ [_959783] : [_959735 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959733), _959783)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959733), _959735)))], (22026 ^ _774244) ^ [_1152711, _1152713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1152711), _1152713)), -(c_Quickcheck_Obeyond(_1152711, _1152713) = _1152713)], (35512 ^ _774244) ^ [_1427271, _1427273, _1427275, _1427277, _1427279, _1427281] : [c_Finite__Set_Ofolding__idem(_1427271, _1427273, _1427275, _1427277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427271), _1427279)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427271, tc_HOL_Obool)), _1427281), _1427279)), -(hAPP(c_Fun_Ocomp(_1427273, _1427273, _1427273, hAPP(_1427277, _1427279)), hAPP(_1427277, _1427281)) = hAPP(_1427277, _1427279))], (38097 ^ _774244) ^ [_1484576, _1484578, _1484580, _1484582, _1484584] : [c_Fun_Oinj__on(_1484576, _1484578, _1484580, c_Orderings_Otop__class_Otop(tc_fun(_1484576, tc_HOL_Obool))), c_Fun_Oinj__on(_1484582, _1484576, _1484584, c_Orderings_Otop__class_Otop(tc_fun(_1484582, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1484582, _1484578, hAPP(c_Fun_Ocomp(_1484576, _1484578, _1484582, _1484580), _1484584), c_Orderings_Otop__class_Otop(tc_fun(_1484582, tc_HOL_Obool))))], (1294 ^ _774244) ^ [_793143, _793145] : [-(class_Lattices_Olattice(_793143)), _793145 = _793143, class_Lattices_Olattice(_793145)], (26608 ^ _774244) ^ [_1241039, _1241041, _1241043, _1241045, _1241047] : [class_Orderings_Olinorder(_1241039), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241039, _1241041), _1241043) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241039, _1241045), _1241047), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241039), _1241041), _1241043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241039), _1241045), _1241047)), -(_1241043 = _1241047)], (6826 ^ _774244) ^ [_884845, _884847] : [c_Option_Ois__none(_884845, hAPP(c_Option_Ooption_OSome(_884845), _884847))], (11959 ^ _774244) ^ [_971945, _971947] : [class_Rings_Olinordered__semidom(_971945), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971945), c_Groups_Ozero__class_Ozero(_971945)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_971945), _971947))))], (31753 ^ _774244) ^ [_1347541, _1347543, _1347545, _1347547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1347541, tc_HOL_Obool)), _1347543), hAPP(hAPP(c_Set_Oinsert(_1347541), _1347545), _1347547))), 31756 ^ _774244 : [(31763 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347541), _1347545), _1347547))), 31766 ^ _774244 : [(31773 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347541), _1347545), _1347543))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1347541, tc_HOL_Obool)), _1347543), _1347547)))], (31767 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1347541), _1347545), _1347543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1347541, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1347541, tc_HOL_Obool)), _1347543), hAPP(hAPP(c_Set_Oinsert(_1347541), _1347545), c_Orderings_Obot__class_Obot(tc_fun(_1347541, tc_HOL_Obool))))), _1347547)))]]], (31757 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1347541), _1347545), _1347547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1347541, tc_HOL_Obool)), _1347543), _1347547)))]]], (5206 ^ _774244) ^ [_854743, _854745, _854747, _854749, _854751, _854753] : [-(c_Finite__Set_Ofold(_854753, _854749, _854745) = c_Finite__Set_Ofold(_854751, _854747, _854743)), _854753 = _854751, _854749 = _854747, _854745 = _854743], (49481 ^ _774244) ^ [_1765110, _1765112] : [-(c_List_Otranspose(_1765110, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1765110)), c_List_Olist_ONil(_1765110)), _1765112)) = c_List_Otranspose(_1765110, _1765112))], (13425 ^ _774244) ^ [_997532, _997534, _997536] : [class_Divides_Osemiring__div(_997532), -(c_Divides_Odiv__class_Omod(_997532, c_Divides_Odiv__class_Omod(_997532, _997534, _997536), _997536) = c_Divides_Odiv__class_Omod(_997532, _997534, _997536))], (13615 ^ _774244) ^ [_1001345, _1001347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001345)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001347)), -(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, _1001345, _1001347))))], (42542 ^ _774244) ^ [_1595774, _1595776, _1595778, _1595780, _1595782] : [class_Complete__Lattice_Ocomplete__lattice(_1595774), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595776), _1595778)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1595774), _1595780), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1595776, _1595774), _1595778), _1595782)) = hAPP(hAPP(c_Finite__Set_Ofold(_1595776, _1595774, hAPP(hAPP(c_COMBB(_1595774, tc_fun(_1595774, _1595774), _1595776), c_Lattices_Osemilattice__sup__class_Osup(_1595774)), _1595782)), _1595780), _1595778))], (31041 ^ _774244) ^ [_1330924, _1330926, _1330928] : [_1330926 = _1330928, -(hBOOL(hAPP(hAPP(c_member(_1330924), _1330926), hAPP(c_fequal, _1330928))))], (19839 ^ _774244) ^ [_1113757, _1113759] : [class_Rings_Odivision__ring(_1113757), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113757), _1113759), c_Groups_Oone__class_Oone(_1113757)) = _1113759)], (34735 ^ _774244) ^ [_1408930] : [-(c_Relation_OId__on(_1408930, c_Orderings_Obot__class_Obot(tc_fun(_1408930, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1408930, _1408930), tc_HOL_Obool)))], (48300 ^ _774244) ^ [_1738749, _1738751, _1738753, _1738755, _1738757] : [hAPP(hAPP(c_List_Odrop(_1738749), _1738751), _1738753) = hAPP(hAPP(c_List_Olist_OCons(_1738749), _1738755), _1738757), -(hAPP(hAPP(c_List_Onth(_1738749), _1738753), _1738751) = _1738755)], (22224 ^ _774244) ^ [_1156693, _1156695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156693)), hAPP(c_Nat_OSuc, _1156695))), -(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(_1156693))), 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)), _1156695)))))], (22893 ^ _774244) ^ [_1169707, _1169709, _1169711] : [hBOOL(hAPP(_1169707, hAPP(hAPP(c_Product__Type_OPair(_1169709, _1169711), 22894 ^ [_1169707, _1169709, _1169711]), 22895 ^ [_1169707, _1169709, _1169711]))), 22898 ^ _774244 : [(22899 ^ _774244) ^ [_1169854] : [-(hBOOL(hAPP(_1169707, _1169854)))]]], (48174 ^ _774244) ^ [_1734971, _1734973, _1734975, _1734977] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1734971), tc_List_Olist(_1734971))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1734971), tc_List_Olist(_1734971)), _1734973), _1734975)), c_List_Olistrel1(_1734971, _1734977))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1734971), tc_List_Olist(_1734971))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1734971), tc_List_Olist(_1734971)), _1734973), _1734975)), c_List_Olistrel(_1734971, c_Transitive__Closure_Ortrancl(_1734971, _1734977)))))], (10313 ^ _774244) ^ [_944073, _944075, _944077, _944079, _944081] : [class_Orderings_Oord(_944073), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944075, _944073)), _944077), _944079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944073), hAPP(_944077, _944081)), hAPP(_944079, _944081))))], (6043 ^ _774244) ^ [_871034] : [hAPP(c_Nat_OSuc, _871034) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28815 ^ _774244) ^ [_1286135, _1286137] : [class_Lattices_Oboolean__algebra(_1286135), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286135), _1286137), hAPP(c_Groups_Ouminus__class_Ouminus(_1286135), _1286137)) = c_Orderings_Otop__class_Otop(_1286135))], (38577 ^ _774244) ^ [_1494387, _1494389, _1494391, _1494393] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1494387), _1494389)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494391), _1494393)), 38584 ^ _774244 : [(38585 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1494387), _1494389)), hAPP(c_Finite__Set_Ocard(_1494391), _1494393)))), 38586 ^ _774244 : [(38587 ^ _774244) ^ [_1494598] : [c_Fun_Oinj__on(_1494387, _1494391, _1494598, _1494389), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494391, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1494387, _1494391, _1494598), _1494389)), _1494393))]]], (38595 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1494387), _1494389)), hAPP(c_Finite__Set_Ocard(_1494391), _1494393))), 38599 ^ _774244 : [(38602 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494391, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1494387, _1494391, 38598 ^ [_1494387, _1494389, _1494391, _1494393]), _1494389)), _1494393)))], (38600 ^ _774244) ^ [] : [-(c_Fun_Oinj__on(_1494387, _1494391, 38598 ^ [_1494387, _1494389, _1494391, _1494393], _1494389))]]]]], (26291 ^ _774244) ^ [_1233618, _1233620] : [class_Orderings_Oorder(_1233618), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1233618, 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)))), _1233620), -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1233618, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233620))], (33306 ^ _774244) ^ [_1378368, _1378370, _1378372, _1378374] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1378368, _1378372)), c_Sum__Type_OPlus(_1378368, _1378372, _1378370, _1378374)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1378368), _1378370)), hAPP(c_Finite__Set_Ocard(_1378372), _1378374))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378368), _1378370)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378372), _1378374))], (27688 ^ _774244) ^ [_1262402, _1262404, _1262406, _1262408] : [hBOOL(hAPP(_1262402, _1262404)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262406, tc_HOL_Obool)), _1262408), _1262402), _1262404)))], (50536 ^ _774244) ^ [_1788087] : [-(c_List_Oreturn__list(_1788087) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1788087))], (44937 ^ _774244) ^ [_1653947, _1653949] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1653947, _1653947)), hAPP(hAPP(c_Product__Type_OPair(_1653947, _1653947), 44938 ^ [_1653947, _1653949]), 44938 ^ [_1653947, _1653949])), c_Transitive__Closure_Otrancl(_1653947, _1653949)))), -(c_Wellfounded_Oacyclic(_1653947, _1653949))], (2478 ^ _774244) ^ [_811681, _811683, _811685, _811687] : [-(c_Nitpick_Onat__gcd(_811687, _811683) = c_Nitpick_Onat__gcd(_811685, _811681)), _811687 = _811685, _811683 = _811681], (47887 ^ _774244) ^ [_1727352, _1727354, _1727356, _1727358, _1727360, _1727362] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727352)), _1727354) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727356)), _1727358), -(c_Map_Omap__upds(_1727352, _1727356, _1727360, hAPP(hAPP(c_List_Oappend(_1727352), _1727354), _1727362), _1727358) = c_Map_Omap__upds(_1727352, _1727356, _1727360, _1727354, _1727358))], (6808 ^ _774244) ^ [_884545, _884547] : [-(c_Option_Ooption_Ooption__size(_884545, _884547, c_Option_Ooption_ONone(_884545)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19107 ^ _774244) ^ [_1100309, _1100311] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1100309)), c_Int_OBit0(_1100311)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1100309), _1100311)))], (17215 ^ _774244) ^ [_1068782, _1068784, _1068786] : [class_Power_Opower(_1068782), class_Rings_Omult__zero(_1068782), class_Rings_Ono__zero__divisors(_1068782), class_Rings_Ozero__neq__one(_1068782), 17230 ^ _774244 : [(17239 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1068782), _1068784), _1068786) = c_Groups_Ozero__class_Ozero(_1068782)), _1068784 = c_Groups_Ozero__class_Ozero(_1068782), -(_1068786 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17231 ^ _774244) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1068782), _1068784), _1068786) = c_Groups_Ozero__class_Ozero(_1068782), 17234 ^ _774244 : [(17237 ^ _774244) ^ [] : [_1068786 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17235 ^ _774244) ^ [] : [-(_1068784 = c_Groups_Ozero__class_Ozero(_1068782))]]]]], (27345 ^ _774244) ^ [_1256197, _1256199, _1256201, _1256203, _1256205, _1256207, _1256209, _1256211] : [class_Groups_Ocomm__monoid__add(_1256197), class_Orderings_Oord(_1256199), _1256201 = _1256203, _1256205 = _1256207, 27363 ^ _774244 : [(27368 ^ _774244) ^ [] : [hAPP(_1256209, 27362 ^ [_1256197, _1256199, _1256201, _1256203, _1256205, _1256207, _1256209, _1256211]) = hAPP(_1256211, 27362 ^ [_1256197, _1256199, _1256201, _1256203, _1256205, _1256207, _1256209, _1256211])], (27366 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256199), 27362 ^ [_1256197, _1256199, _1256201, _1256203, _1256205, _1256207, _1256209, _1256211]), _1256207)))], (27364 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256199), _1256203), 27362 ^ [_1256197, _1256199, _1256201, _1256203, _1256205, _1256207, _1256209, _1256211])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1256199, _1256197), _1256209), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256199, _1256201), _1256205)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1256199, _1256197), _1256211), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256199, _1256203), _1256207)))], (44496 ^ _774244) ^ [_1643837] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1643837, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1643837, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1643837, tc_HOL_Obool)))], (35943 ^ _774244) ^ [_1436708, _1436710, _1436712] : [class_Lattices_Osemilattice__inf(_1436708), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436708), _1436710), _1436712)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1436708), _1436712), _1436710) = _1436710)], (36271 ^ _774244) ^ [_1443635, _1443637, _1443639, _1443641] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443635, tc_HOL_Obool)), _1443637), _1443639), _1443641)), -(hBOOL(hAPP(_1443639, _1443641)))], (45682 ^ _774244) ^ [_1672086, _1672088, _1672090, _1672092, _1672094] : [hAPP(hAPP(c_List_Omap(_1672086, _1672088), _1672090), _1672092) = hAPP(hAPP(c_List_Omap(_1672086, _1672088), _1672090), _1672094), c_Fun_Oinj__on(_1672086, _1672088, _1672090, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1672086, tc_HOL_Obool)), hAPP(c_List_Oset(_1672086), _1672092)), hAPP(c_List_Oset(_1672086), _1672094))), -(_1672092 = _1672094)], (26167 ^ _774244) ^ [_1231307, _1231309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231307)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231307), _1231309)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231309), _1231307))], (47287 ^ _774244) ^ [_1713053, _1713055, _1713057] : [-(hAPP(hAPP(c_List_Olist__update(_1713053, c_List_Olist_ONil(_1713053)), _1713055), _1713057) = c_List_Olist_ONil(_1713053))], (36469 ^ _774244) ^ [_1448135, _1448137, _1448139] : [class_Lattices_Oboolean__algebra(_1448135), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1448135), _1448137), _1448139) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1448135), _1448137), hAPP(c_Groups_Ouminus__class_Ouminus(_1448135), _1448139)))], (3604 ^ _774244) ^ [_829754, _829756, _829758, _829760, _829762, _829764] : [-(c_FunDef_Oin__rel(_829764, _829760, _829756) = c_FunDef_Oin__rel(_829762, _829758, _829754)), _829764 = _829762, _829760 = _829758, _829756 = _829754], (51181 ^ _774244) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (6736 ^ _774244) ^ [_882767, _882769, _882771] : [hBOOL(hAPP(c_Com_OWT, _882771)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_882767, _882769, _882771))))], (2528 ^ _774244) ^ [_812426, _812428, _812430, _812432, _812434, _812436, _812438, _812440, _812442, _812444] : [-(c_Product__Type_Oprod_Oprod__size(_812444, _812440, _812436, _812432, _812428) = c_Product__Type_Oprod_Oprod__size(_812442, _812438, _812434, _812430, _812426)), _812444 = _812442, _812440 = _812438, _812436 = _812434, _812432 = _812430, _812428 = _812426], (18303 ^ _774244) ^ [_1086655, _1086657] : [class_Int_Onumber__ring(_1086655), class_Rings_Olinordered__idom(_1086655), 18310 ^ _774244 : [(18317 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1086657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086655), c_Groups_Ozero__class_Ozero(_1086655)), hAPP(c_Int_Onumber__class_Onumber__of(_1086655), _1086657))))], (18311 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086655), c_Groups_Ozero__class_Ozero(_1086655)), hAPP(c_Int_Onumber__class_Onumber__of(_1086655), _1086657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1086657)))]]], (42222 ^ _774244) ^ [_1588915, _1588917, _1588919] : [42224 ^ _774244 : [(42227 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1588915), 42223 ^ [_1588915, _1588917, _1588919]), c_Wellfounded_Oacc(_1588915, _1588919)))], (42225 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588915, _1588915)), hAPP(hAPP(c_Product__Type_OPair(_1588915, _1588915), 42223 ^ [_1588915, _1588917, _1588919]), _1588917)), _1588919)))]], -(hBOOL(hAPP(hAPP(c_member(_1588915), _1588917), c_Wellfounded_Oacc(_1588915, _1588919))))], (700 ^ _774244) ^ [_785074, _785076, _785078, _785080, _785082, _785084] : [-(c_Relation_Osingle__valued(_785082, _785078, _785074)), c_Relation_Osingle__valued(_785084, _785080, _785076), _785084 = _785082, _785080 = _785078, _785076 = _785074], (48668 ^ _774244) ^ [_1746794, _1746796] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746794)), hAPP(c_List_Otl(_1746794), _1746796)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746794)), _1746796)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (48881 ^ _774244) ^ [_1751746, _1751748, _1751750] : [c_Relation_Orefl__on(_1751746, _1751748, _1751750), -(c_Relation_Orefl__on(tc_List_Olist(_1751746), c_List_Olists(_1751746, _1751748), c_List_Olistrel(_1751746, _1751750)))], (38415 ^ _774244) ^ [_1490857, _1490859, _1490861, _1490863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1490857), hAPP(c_Set_Oimage(_1490859, _1490857, _1490861), _1490863))), hAPP(c_Finite__Set_Ocard(_1490859), _1490863))), c_Fun_Oinj__on(_1490859, _1490857, _1490861, _1490863)], (29464 ^ _774244) ^ [_1298792, _1298794] : [class_Orderings_Oorder(_1298792), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1298792, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1298792), _1298794), c_Orderings_Obot__class_Obot(tc_fun(_1298792, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1298792), _1298794)) = hAPP(hAPP(c_Set_Oinsert(_1298792), _1298794), c_Orderings_Obot__class_Obot(tc_fun(_1298792, tc_HOL_Obool))))], (29270 ^ _774244) ^ [_1295178] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1295178, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1295178, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1295178, tc_HOL_Obool)))], (46605 ^ _774244) ^ [_1697025, _1697027, _1697029] : [hBOOL(hAPP(c_List_Odistinct(_1697025), _1697027)), -(hBOOL(hAPP(c_List_Odistinct(_1697025), c_List_Osublist(_1697025, _1697027, _1697029))))], (7393 ^ _774244) ^ [_894231, _894233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _894231)), hAPP(c_Nat_OSuc, _894233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894231), _894233)))], (47700 ^ _774244) ^ [_1722589, _1722591, _1722593] : [_1722589 = hAPP(hAPP(c_List_Oappend(_1722591), _1722593), _1722589), -(_1722593 = c_List_Olist_ONil(_1722591))], (39265 ^ _774244) ^ [_1510045, _1510047, _1510049] : [c_Map_Odom(_1510045, _1510047, _1510049) = c_Orderings_Obot__class_Obot(tc_fun(_1510045, tc_HOL_Obool)), -(_1510049 = hAPP(c_COMBK(tc_Option_Ooption(_1510047), _1510045), c_Option_Ooption_ONone(_1510047)))], (46954 ^ _774244) ^ [_1704515, _1704517, _1704519] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1704515))), -(c_List_Osublist(_1704517, hAPP(hAPP(c_List_Olist_OCons(_1704517), _1704519), c_List_Olist_ONil(_1704517)), _1704515) = c_List_Olist_ONil(_1704517))], (9334 ^ _774244) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (27095 ^ _774244) ^ [_1250793, _1250795, _1250797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250793)), 27098 ^ _774244 : [(27099 ^ _774244) ^ [_1250927] : [27101 ^ _774244 : [(27107 ^ _774244) ^ [] : [-(_1250927 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27103 ^ [_1250793, _1250795, _1250797, _1250927]), 27100 ^ [_1250793, _1250795, _1250797, _1250927]))], (27105 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27103 ^ [_1250793, _1250795, _1250797, _1250927]), _1250795)))], (27102 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27100 ^ [_1250793, _1250795, _1250797, _1250927]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1250793))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250927), _1250797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1250927), _1250793)), _1250797)))]]], (23591 ^ _774244) ^ [_1183292] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1183292) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38970 ^ _774244) ^ [_1503425, _1503427, _1503429, _1503431, _1503433, _1503435] : [class_Groups_Oab__semigroup__mult(_1503425), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503427), _1503429)), -(hBOOL(hAPP(hAPP(c_member(_1503427), _1503431), _1503429))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1503425, _1503427, c_Groups_Otimes__class_Otimes(_1503425)), _1503433), _1503435), hAPP(hAPP(c_Set_Oinsert(_1503427), _1503431), _1503429)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1503425), hAPP(_1503433, _1503431)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1503425, _1503427, c_Groups_Otimes__class_Otimes(_1503425)), _1503433), _1503435), _1503429)))], (1624 ^ _774244) ^ [_797268, _797270] : [-(class_Groups_Omonoid__mult(_797268)), _797270 = _797268, class_Groups_Omonoid__mult(_797270)], (33094 ^ _774244) ^ [_1373311, _1373313, _1373315] : [class_Orderings_Olinorder(_1373311), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373311), _1373313)), -(hBOOL(hAPP(hAPP(c_member(_1373311), _1373315), _1373313))), -(_1373313 = c_Orderings_Obot__class_Obot(tc_fun(_1373311, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1373311, hAPP(hAPP(c_Set_Oinsert(_1373311), _1373315), _1373313)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373311), _1373315), c_Big__Operators_Olinorder__class_OMax(_1373311, _1373313)))], (43047 ^ _774244) ^ [_1606281, _1606283, _1606285] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606281, _1606281)), hAPP(hAPP(c_Product__Type_OPair(_1606281, _1606281), _1606283), _1606283)), c_Transitive__Closure_Ortrancl(_1606281, _1606285))))], (16755 ^ _774244) ^ [_1060251, _1060253, _1060255] : [class_Rings_Olinordered__idom(_1060251), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060251), c_Groups_Ozero__class_Ozero(_1060251)), _1060253)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060251), hAPP(c_Groups_Oabs__class_Oabs(_1060251), _1060255)), _1060253) = hAPP(c_Groups_Oabs__class_Oabs(_1060251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060251), _1060255), _1060253)))], (20 ^ _774244) ^ [_774504, _774506, _774508, _774510] : [-(c_Option_Ois__none(_774508, _774504)), c_Option_Ois__none(_774510, _774506), _774510 = _774508, _774506 = _774504], (25121 ^ _774244) ^ [_1212603, _1212605] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212603), _1212605)), -(_1212603 = _1212605), 25128 ^ _774244 : [(25131 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212605), _1212603))], (25129 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212603), _1212605)))]]], (18995 ^ _774244) ^ [_1098357] : [c_Int_OBit0(_1098357) = c_Int_OMin], (22424 ^ _774244) ^ [_1160607] : [-(c_Divides_Oadjust(_1160607) = 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)), _1160607))))), 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)), _1160607))))), 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))))))))], (47997 ^ _774244) ^ [_1729908, _1729910, _1729912, _1729914] : [-(_1729908 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1729910), _1729908), hAPP(hAPP(c_List_Olist_OCons(_1729910), _1729912), _1729914)) = hAPP(hAPP(c_List_Olist_OCons(_1729910), _1729912), hAPP(hAPP(c_List_Otake(_1729910), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1729908), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1729914)))], (16713 ^ _774244) ^ [_1059420, _1059422] : [class_Int_Onumber__ring(_1059420), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1059420), hAPP(c_Int_Onumber__class_Onumber__of(_1059420), _1059422)) = hAPP(c_Int_Onumber__class_Onumber__of(_1059420), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1059422)))], (25285 ^ _774244) ^ [_1215255, _1215257, _1215259, _1215261] : [class_Divides_Osemiring__div(_1215255), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215255), _1215257), _1215259)), -(c_Divides_Odiv__class_Omod(_1215255, c_Divides_Odiv__class_Omod(_1215255, _1215261, _1215259), _1215257) = c_Divides_Odiv__class_Omod(_1215255, _1215261, _1215257))], (45153 ^ _774244) ^ [_1659706, _1659708] : [-(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)))), _1659706)) = 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)))), _1659708))), 45155 ^ _774244 : [(45158 ^ _774244) ^ [] : [45159 ^ _774244 : [(45162 ^ _774244) ^ [] : [hBOOL(hAPP(_1659708, 45154 ^ [_1659706, _1659708]))], (45160 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1659706, 45154 ^ [_1659706, _1659708])))]], 45163 ^ _774244 : [(45166 ^ _774244) ^ [] : [hBOOL(hAPP(_1659706, 45154 ^ [_1659706, _1659708]))], (45164 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1659708, 45154 ^ [_1659706, _1659708])))]]], (45156 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 45154 ^ [_1659706, _1659708])))]]], (45122 ^ _774244) ^ [_1658937, _1658939] : [-(c_Wellfounded_Owf(_1658937, _1658939)), 45125 ^ _774244 : [(45128 ^ _774244) ^ [_1659157] : [hBOOL(hAPP(hAPP(c_member(_1658937), _1659157), 45123 ^ [_1658937, _1658939])), 45132 ^ _774244 : [(45135 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1658937), 45131 ^ [_1658937, _1658939, _1659157]), 45123 ^ [_1658937, _1658939])))], (45133 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1658937, _1658937)), hAPP(hAPP(c_Product__Type_OPair(_1658937, _1658937), 45131 ^ [_1658937, _1658939, _1659157]), _1659157)), _1658939)))]]], (45126 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1658937), 45124 ^ [_1658937, _1658939]), 45123 ^ [_1658937, _1658939])))]]], (7151 ^ _774244) ^ [_890404, _890406] : [-(_890404 = _890406), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890404), _890406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890406), _890404)))], (11064 ^ _774244) ^ [_956265, _956267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956265), hAPP(c_Nat_OSuc, _956267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956265), _956267))), -(_956265 = hAPP(c_Nat_OSuc, _956267))], (41825 ^ _774244) ^ [_1578793, _1578795] : [-(hAPP(c_Relation_OField(_1578793), _1578795) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1578793, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1578793, _1578793), _1578795)), hAPP(c_Relation_ORange(_1578793, _1578793), _1578795)))], (30763 ^ _774244) ^ [_1323675, _1323677, _1323679, _1323681] : [hAPP(hAPP(c_COMBC(_1323675, tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_fun(_1323677, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1323677, tc_fun(tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_fun(_1323677, tc_HOL_Obool)), _1323675), c_COMBC(_1323677, tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1323677, tc_prod(_1323675, _1323677)), tc_fun(_1323677, tc_fun(tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_HOL_Obool)), _1323675), hAPP(c_COMBB(tc_prod(_1323675, _1323677), tc_fun(tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_HOL_Obool), _1323677), c_member(tc_prod(_1323675, _1323677)))), c_Product__Type_OPair(_1323675, _1323677)))), _1323679) = hAPP(hAPP(c_COMBC(_1323675, tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_fun(_1323677, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1323677, tc_fun(tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_fun(_1323677, tc_HOL_Obool)), _1323675), c_COMBC(_1323677, tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1323677, tc_prod(_1323675, _1323677)), tc_fun(_1323677, tc_fun(tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_HOL_Obool)), _1323675), hAPP(c_COMBB(tc_prod(_1323675, _1323677), tc_fun(tc_fun(tc_prod(_1323675, _1323677), tc_HOL_Obool), tc_HOL_Obool), _1323677), c_member(tc_prod(_1323675, _1323677)))), c_Product__Type_OPair(_1323675, _1323677)))), _1323681), -(_1323679 = _1323681)], (11054 ^ _774244) ^ [_956048, _956050, _956052] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _956048), _956050)), _956052) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956048), _956052)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956050), _956052)))], (40059 ^ _774244) ^ [_1531280, _1531282] : [class_Lattices_Olattice(_1531280), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531280), _1531282)), -(c_Big__Operators_Olattice__class_OSup__fin(_1531280, _1531282) = hAPP(c_Finite__Set_Ofold1(_1531280, c_Lattices_Osemilattice__sup__class_Osup(_1531280)), _1531282))], (17365 ^ _774244) ^ [_1071479, _1071481, _1071483] : [class_Rings_Olinordered__semidom(_1071479), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071479), c_Groups_Oone__class_Oone(_1071479)), _1071481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071479), hAPP(hAPP(c_Power_Opower__class_Opower(_1071479), _1071481), _1071483)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071479), _1071481), hAPP(hAPP(c_Power_Opower__class_Opower(_1071479), _1071481), _1071483)))))], (41576 ^ _774244) ^ [_1572771, _1572773] : [c_Wellfounded_Owf(_1572771, _1572773), -(c_Wellfounded_Owf(tc_List_Olist(_1572771), c_List_Olenlex(_1572771, _1572773)))], (51125 ^ _774244) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (50250 ^ _774244) ^ [_1780567, _1780569] : [_1780569 = c_List_Olist_ONil(_1780567), -(hAPP(c_List_Orev(_1780567), _1780569) = c_List_Olist_ONil(_1780567))], (39229 ^ _774244) ^ [_1509285, _1509287, _1509289, _1509291] : [39230 ^ _774244 : [(39231 ^ _774244) ^ [_1509374] : [_1509289 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1509285, tc_Option_Ooption(_1509287)), hAPP(c_COMBK(tc_Option_Ooption(_1509287), _1509285), c_Option_Ooption_ONone(_1509287))), _1509291), hAPP(c_Option_Ooption_OSome(_1509287), _1509374))]], -(c_Map_Odom(_1509285, _1509287, _1509289) = hAPP(hAPP(c_Set_Oinsert(_1509285), _1509291), c_Orderings_Obot__class_Obot(tc_fun(_1509285, tc_HOL_Obool))))], (4544 ^ _774244) ^ [_844516, _844518] : [_844518 = _844516, -(c_Lattices_Osemilattice__inf__class_Oinf(_844518) = c_Lattices_Osemilattice__inf__class_Oinf(_844516))], (51393 ^ _774244) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (51341 ^ _774244) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (21885 ^ _774244) ^ [] : [-(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))], (40715 ^ _774244) ^ [_1544306, _1544308] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544306), hAPP(c_Set_OCollect(_1544306), _1544308))), 40718 ^ _774244 : [(40725 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544306), c_Orderings_Otop__class_Otop(tc_fun(_1544306, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544306), hAPP(c_Set_OCollect(_1544306), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1544306), c_fNot), _1544308)))))], (40719 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544306), hAPP(c_Set_OCollect(_1544306), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1544306), c_fNot), _1544308)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544306), c_Orderings_Otop__class_Otop(tc_fun(_1544306, tc_HOL_Obool)))))]]], (26626 ^ _774244) ^ [_1241346, _1241348, _1241350, _1241352, _1241354] : [class_Orderings_Olinorder(_1241346), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241346, _1241348), _1241350) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241346, _1241352), _1241354), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241346), _1241348), _1241350)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241346), _1241352), _1241354)), -(_1241348 = _1241352)], (46513 ^ _774244) ^ [_1693847, _1693849, _1693851, _1693853, _1693855, _1693857] : [-(_1693847 = _1693849), -(hAPP(c_Map_Omap__of(_1693851, _1693853, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1693851, _1693853)), hAPP(hAPP(c_Product__Type_OPair(_1693851, _1693853), _1693847), _1693855)), _1693857)), _1693849) = hAPP(c_Map_Omap__of(_1693851, _1693853, _1693857), _1693849))], (34958 ^ _774244) ^ [_1413809, _1413811, _1413813] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1413809, tc_HOL_Obool)), _1413811), hAPP(c_Set_OPow(_1413809), _1413813))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413809, tc_HOL_Obool)), _1413811), _1413813)))], (3230 ^ _774244) ^ [_823845, _823847, _823849, _823851, _823853, _823855] : [-(c_SetInterval_Oord_OgreaterThan(_823855, _823851, _823847) = c_SetInterval_Oord_OgreaterThan(_823853, _823849, _823845)), _823855 = _823853, _823851 = _823849, _823847 = _823845], (46617 ^ _774244) ^ [_1697264, _1697266, _1697268, _1697270] : [-(hBOOL(hAPP(hAPP(c_member(_1697264), _1697266), hAPP(c_List_Oset(_1697264), _1697268)))), hBOOL(hAPP(hAPP(c_member(_1697264), _1697266), hAPP(c_List_Oset(_1697264), c_List_Osublist(_1697264, _1697268, _1697270))))], (29092 ^ _774244) ^ [_1292163, _1292165] : [class_Lattices_Obounded__lattice__bot(_1292163), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292163), _1292165), c_Orderings_Obot__class_Obot(_1292163)) = _1292165)], (7032 ^ _774244) ^ [_888180, _888182] : [hBOOL(hAPP(c_Com_OWT, _888180)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_888182, _888180))))], (47608 ^ _774244) ^ [_1720705, _1720707, _1720709, _1720711] : [hAPP(hAPP(c_List_Oappend(_1720705), _1720707), _1720709) = hAPP(hAPP(c_List_Oappend(_1720705), _1720707), _1720711), -(_1720709 = _1720711)], (50384 ^ _774244) ^ [_1783376, _1783378, _1783380, _1783382] : [-(c_List_Otranspose(_1783376, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1783376)), hAPP(hAPP(c_List_Olist_OCons(_1783376), _1783378), _1783380)), _1783382)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1783376)), hAPP(hAPP(c_List_Olist_OCons(_1783376), _1783378), c_List_Oconcat(_1783376, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1783376), tc_List_Olist(_1783376)), c_List_Olist_Olist__case(tc_List_Olist(_1783376), _1783376, c_List_Olist_ONil(_1783376), hAPP(hAPP(c_COMBB(tc_List_Olist(_1783376), tc_fun(tc_List_Olist(_1783376), tc_List_Olist(_1783376)), _1783376), c_COMBK(tc_List_Olist(_1783376), tc_List_Olist(_1783376))), hAPP(hAPP(c_COMBC(_1783376, tc_List_Olist(_1783376), tc_List_Olist(_1783376)), c_List_Olist_OCons(_1783376)), c_List_Olist_ONil(_1783376))))), _1783382)))), c_List_Otranspose(_1783376, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1783376)), _1783380), c_List_Oconcat(tc_List_Olist(_1783376), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1783376), tc_List_Olist(tc_List_Olist(_1783376))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1783376)), _1783376, c_List_Olist_ONil(tc_List_Olist(_1783376)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1783376), tc_List_Olist(tc_List_Olist(_1783376))), _1783376), hAPP(hAPP(c_COMBC(tc_List_Olist(_1783376), tc_List_Olist(tc_List_Olist(_1783376)), tc_List_Olist(tc_List_Olist(_1783376))), c_List_Olist_OCons(tc_List_Olist(_1783376))), c_List_Olist_ONil(tc_List_Olist(_1783376)))))), _1783382))))))], (40805 ^ _774244) ^ [_1547605, _1547607, _1547609, _1547611, _1547613] : [-(c_Map_Odom(_1547605, _1547607, c_Fun_Ooverride__on(_1547605, tc_Option_Ooption(_1547607), _1547609, _1547611, _1547613)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1547605, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1547605, tc_HOL_Obool)), c_Map_Odom(_1547605, _1547607, _1547609)), hAPP(c_Set_OCollect(_1547605), hAPP(hAPP(c_COMBC(_1547605, tc_fun(_1547605, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547605)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1547605, tc_HOL_Obool)), _1547613), c_Map_Odom(_1547605, _1547607, _1547611)))))), hAPP(c_Set_OCollect(_1547605), hAPP(hAPP(c_COMBC(_1547605, tc_fun(_1547605, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547605)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1547605, tc_HOL_Obool)), _1547613), c_Map_Odom(_1547605, _1547607, _1547611))))))], (30069 ^ _774244) ^ [_1309687, _1309689, _1309691, _1309693, _1309695] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1309687), _1309689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309691, tc_HOL_Obool)), _1309693), hAPP(c_Set_Oimage(_1309687, _1309691, _1309695), _1309689))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1309691), _1309693)))], (45565 ^ _774244) ^ [_1669035, _1669037, _1669039, _1669041, _1669043, _1669045, _1669047] : [-(c_List_Ofoldr(_1669035, _1669037, _1669039, hAPP(hAPP(c_List_Omap(_1669041, _1669035), _1669043), _1669045), _1669047) = c_List_Ofoldr(_1669041, _1669037, hAPP(c_Fun_Ocomp(_1669035, tc_fun(_1669037, _1669037), _1669041, _1669039), _1669043), _1669045, _1669047))], (22564 ^ _774244) ^ [_1163615, _1163617, _1163619] : [22566 ^ _774244 : [(22569 ^ _774244) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1163615, _1163617), 22565 ^ [_1163615, _1163617, _1163619]))], (22567 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1163617, 22565 ^ [_1163615, _1163617, _1163619]), _1163619)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1163615, _1163617), _1163619)))], (6390 ^ _774244) ^ [_877017, _877019] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_877017, _877019)) = 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), _877017)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _877019))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34976 ^ _774244) ^ [_1414212, _1414214] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1414212, tc_HOL_Obool)), _1414214), hAPP(c_Set_OPow(_1414212), _1414214))))], (32730 ^ _774244) ^ [_1367572, _1367574] : [class_Groups_Olinordered__ab__group__add(_1367572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367572), _1367574)), -(_1367574 = c_Orderings_Obot__class_Obot(tc_fun(_1367572, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1367572), c_Big__Operators_Olinorder__class_OMax(_1367572, _1367574)) = c_Big__Operators_Olinorder__class_OMin(_1367572, hAPP(c_Set_Oimage(_1367572, _1367572, c_Groups_Ouminus__class_Ouminus(_1367572)), _1367574)))], (22346 ^ _774244) ^ [_1159367, _1159369] : [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), _1159367))), 22349 ^ _774244 : [(22356 ^ _774244) ^ [] : [-(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), _1159369)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1159367))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1159369), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1159367)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1159367)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1159369), 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), _1159367)))))], (22350 ^ _774244) ^ [] : [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), _1159369)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1159367)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1159369), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1159367)) = 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), _1159369)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1159367))))]]], (49444 ^ _774244) ^ [_1764229, _1764231, _1764233, _1764235, _1764237, _1764239] : [hAPP(c_Map_Omap__of(_1764229, _1764231, _1764233), _1764235) = hAPP(c_Option_Ooption_OSome(_1764231), _1764237), hBOOL(hAPP(hAPP(_1764239, _1764235), _1764237)), -(hAPP(c_Map_Omap__of(_1764229, _1764231, hAPP(c_List_Ofilter(tc_prod(_1764229, _1764231), hAPP(c_Product__Type_Oprod_Oprod__case(_1764229, _1764231, tc_HOL_Obool), _1764239)), _1764233)), _1764235) = hAPP(c_Option_Ooption_OSome(_1764231), _1764237))], (18673 ^ _774244) ^ [_1092878] : [class_Int_Onumber__ring(_1092878), -(hAPP(c_Int_Onumber__class_Onumber__of(_1092878), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1092878))], (36585 ^ _774244) ^ [_1451057, _1451059, _1451061, _1451063] : [class_Orderings_Oorder(_1451057), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451057, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1451057, _1451059, _1451061)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1451057, _1451061, _1451063)) = c_Orderings_Obot__class_Obot(tc_fun(_1451057, tc_HOL_Obool)))], (16625 ^ _774244) ^ [_1057571, _1057573] : [class_Rings_Ocomm__semiring__1(_1057571), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1057571), _1057573), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1057571))], (46385 ^ _774244) ^ [_1691114, _1691116, _1691118, _1691120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691114)), _1691116)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691114)), _1691118))), _1691116 = hAPP(hAPP(c_List_Olist_OCons(_1691114), _1691120), _1691118)], (26231 ^ _774244) ^ [_1232489, _1232491] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232489), _1232491)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232489)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232491))))], (19099 ^ _774244) ^ [_1100159, _1100161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100159), _1100161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1100159)), c_Int_OBit0(_1100161))))], (43793 ^ _774244) ^ [_1626016, _1626018, _1626020, _1626022, _1626024] : [_1626016 = c_Orderings_Obot__class_Obot(tc_fun(_1626018, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626018, tc_fun(_1626020, tc_HOL_Obool)), _1626016), hAPP(hAPP(c_COMBB(tc_fun(_1626020, tc_HOL_Obool), tc_fun(_1626020, tc_HOL_Obool), _1626018), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1626020, tc_HOL_Obool)), _1626022)), _1626024)) = c_Orderings_Otop__class_Otop(tc_fun(_1626020, tc_HOL_Obool)))], (7082 ^ _774244) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43682 ^ _774244) ^ [_1623122, _1623124, _1623126, _1623128, _1623130] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623122, tc_HOL_Obool)), _1623124), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623126, tc_fun(_1623122, tc_HOL_Obool)), _1623128), _1623130)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623126, tc_fun(_1623122, tc_HOL_Obool)), _1623128), hAPP(hAPP(c_COMBB(tc_fun(_1623122, tc_HOL_Obool), tc_fun(_1623122, tc_HOL_Obool), _1623126), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623122, tc_HOL_Obool)), _1623124)), _1623130)))], (16681 ^ _774244) ^ [_1058688, _1058690, _1058692] : [class_Int_Onumber__ring(_1058688), -(hAPP(c_Int_Onumber__class_Onumber__of(_1058688), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1058690), _1058692)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058688), hAPP(c_Int_Onumber__class_Onumber__of(_1058688), _1058690)), hAPP(c_Int_Onumber__class_Onumber__of(_1058688), _1058692)))], (7834 ^ _774244) ^ [_902228, _902230, _902232, _902234, _902236, _902238] : [-(c_Sum__Type_Osum_Osum__rec(_902228, _902230, _902232, _902234, _902236, hAPP(c_Sum__Type_OInl(_902228, _902232), _902238)) = hAPP(_902234, _902238))], (20927 ^ _774244) ^ [_1132801, _1132803, _1132805, _1132807] : [class_Fields_Ofield__inverse__zero(_1132801), class_Int_Onumber(_1132801), 20934 ^ _774244 : [(20935 ^ _774244) ^ [] : [_1132803 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132801), _1132805), hAPP(c_Int_Onumber__class_Onumber__of(_1132801), _1132807)), 20938 ^ _774244 : [(20945 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1132801), _1132807) = c_Groups_Ozero__class_Ozero(_1132801), -(_1132803 = c_Groups_Ozero__class_Ozero(_1132801))], (20939 ^ _774244) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1132801), _1132807) = c_Groups_Ozero__class_Ozero(_1132801)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132801), _1132803), hAPP(c_Int_Onumber__class_Onumber__of(_1132801), _1132807)) = _1132805)]]], (20951 ^ _774244) ^ [] : [-(_1132803 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132801), _1132805), hAPP(c_Int_Onumber__class_Onumber__of(_1132801), _1132807))), 20954 ^ _774244 : [(20957 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132801), _1132803), hAPP(c_Int_Onumber__class_Onumber__of(_1132801), _1132807)) = _1132805], (20955 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1132801), _1132807) = c_Groups_Ozero__class_Ozero(_1132801)]], 20958 ^ _774244 : [(20961 ^ _774244) ^ [] : [_1132803 = c_Groups_Ozero__class_Ozero(_1132801)], (20959 ^ _774244) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1132801), _1132807) = c_Groups_Ozero__class_Ozero(_1132801))]]]]], (4652 ^ _774244) ^ [_846120, _846122, _846124, _846126] : [-(c_Product__Type_OPair(_846126, _846122) = c_Product__Type_OPair(_846124, _846120)), _846126 = _846124, _846122 = _846120], (10251 ^ _774244) ^ [_943116, _943118, _943120, _943122] : [class_Orderings_Oord(_943116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943116), _943118), _943120)), _943120 = _943122, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943116), _943118), _943122)))], (22236 ^ _774244) ^ [_1156968, _1156970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1156968)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156970))), -(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(_1156970))), 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), _1156968)), c_Int_Onat))))))], (22927 ^ _774244) ^ [_1170552, _1170554] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1170552, _1170554) = 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), _1170552), _1170554)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1170552, _1170554)))], (12904 ^ _774244) ^ [_988670, _988672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _988670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _988672)), 12911 ^ _774244 : [(12918 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _988670), _988672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _988670)), hAPP(c_Int_Onat, _988672))))], (12912 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _988670)), hAPP(c_Int_Onat, _988672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _988670), _988672)))]]], (38475 ^ _774244) ^ [_1492040, _1492042, _1492044, _1492046, _1492048, _1492050] : [c_Fun_Oinj__on(_1492040, _1492042, _1492044, _1492046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492042, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492040, _1492042, _1492044), _1492046)), _1492048)), c_Fun_Oinj__on(_1492042, _1492040, _1492050, _1492048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492040, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492042, _1492040, _1492050), _1492048)), _1492046)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492040), _1492046)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492042), _1492048)), -(hAPP(c_Finite__Set_Ocard(_1492040), _1492046) = hAPP(c_Finite__Set_Ocard(_1492042), _1492048))], (51455 ^ _774244) ^ [_1801653] : [-(hBOOL(_1801653)), -(hBOOL(hAPP(c_fNot, _1801653)))], (46625 ^ _774244) ^ [_1697439, _1697441, _1697443] : [-(c_Random_Oselect__weight(_1697439, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1697439)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1697439), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1697441)), _1697443)) = c_Random_Oselect__weight(_1697439, _1697443))], (24275 ^ _774244) ^ [_1195816, _1195818, _1195820] : [class_Orderings_Olinorder(_1195816), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195816), _1195818), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195816), _1195818), _1195820))))], (13094 ^ _774244) ^ [_991671, _991673, _991675, _991677, _991679] : [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), _991671), _991673)), _991675)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _991671), _991677)), _991679))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _991675), _991671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _991679), _991671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _991673), _991677)))], (30123 ^ _774244) ^ [_1310717, _1310719, _1310721] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310717), _1310719)), 30126 ^ _774244 : [(30127 ^ _774244) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1310717, tc_Nat_Onat), _1310721), _1310719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 30130 ^ _774244 : [(30131 ^ _774244) ^ [_1310879] : [hBOOL(hAPP(hAPP(c_member(_1310717), _1310879), _1310719)), -(hAPP(_1310721, _1310879) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (30137 ^ _774244) ^ [] : [30139 ^ _774244 : [(30142 ^ _774244) ^ [] : [hAPP(_1310721, 30138 ^ [_1310717, _1310719, _1310721]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30140 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1310717), 30138 ^ [_1310717, _1310719, _1310721]), _1310719)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1310717, tc_Nat_Onat), _1310721), _1310719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43925 ^ _774244) ^ [] : [-(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)))], (41961 ^ _774244) ^ [_1582021, _1582023, _1582025] : [-(hAPP(c_New__DSequence_Opos__single(_1582021, _1582023), _1582025) = c_Lazy__Sequence_Osingle(_1582021, _1582023))], (36865 ^ _774244) ^ [_1457368, _1457370, _1457372] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1457368), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457368, tc_HOL_Obool)), _1457370), _1457372))), -(hAPP(c_Finite__Set_Ocard(_1457368), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1457368, tc_HOL_Obool)), _1457370), _1457372)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1457368), _1457370)), hAPP(c_Finite__Set_Ocard(_1457368), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457368, tc_HOL_Obool)), _1457370), _1457372))))], (10398 ^ _774244) ^ [_945486, _945488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _945486)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _945488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945486), _945488)))], (27884 ^ _774244) ^ [_1266661, _1266663, _1266665, _1266667] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266661, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266661, tc_HOL_Obool)), _1266663), _1266665)), _1266667) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266661, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266661, tc_HOL_Obool)), _1266663), _1266667)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266661, tc_HOL_Obool)), _1266665), _1266667)))], (10115 ^ _774244) ^ [_940957, _940959, _940961] : [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, _940957)), _940959)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _940957)), _940961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940959), _940961)))], (5943 ^ _774244) ^ [_869346, _869348, _869350, _869352, _869354, _869356] : [hBOOL(hAPP(_869346, _869348)), c_Natural_Oevaln(_869350, _869348, _869352, _869354), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_869346, _869350, _869356), _869348, _869352, _869354))], (36207 ^ _774244) ^ [_1442278, _1442280, _1442282] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442278, tc_HOL_Obool)), _1442280), _1442282) = c_Orderings_Obot__class_Obot(tc_fun(_1442278, tc_HOL_Obool)), 36210 ^ _774244 : [(36211 ^ _774244) ^ [_1442402] : [hBOOL(hAPP(hAPP(c_member(_1442278), _1442402), _1442280)), 36214 ^ _774244 : [(36215 ^ _774244) ^ [_1442492] : [hBOOL(hAPP(hAPP(c_member(_1442278), _1442492), _1442282)), _1442402 = _1442492]]]]], (18661 ^ _774244) ^ [_1092676, _1092678] : [class_Int_Onumber__ring(_1092676), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092676), hAPP(c_Int_Onumber__class_Onumber__of(_1092676), c_Int_OBit1(c_Int_OPls))), _1092678) = _1092678)], (14169 ^ _774244) ^ [_1011678, _1011680] : [class_Divides_Osemiring__div(_1011678), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1011678), _1011680), c_Groups_Oone__class_Oone(_1011678)) = _1011680)], (7056 ^ _774244) ^ [_888640, _888642, _888644, _888646, _888648] : [c_Com_Ocom_OWhile(_888640, _888642) = c_Com_Ocom_OCond(_888644, _888646, _888648)], (35288 ^ _774244) ^ [_1421415, _1421417, _1421419, _1421421] : [-(hAPP(c_Relation_OImage(_1421415, _1421417, _1421419), _1421421) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1421415, tc_fun(_1421417, tc_HOL_Obool)), _1421421), hAPP(hAPP(c_COMBB(tc_fun(_1421415, tc_HOL_Obool), tc_fun(_1421417, tc_HOL_Obool), _1421415), c_Relation_OImage(_1421415, _1421417, _1421419)), hAPP(hAPP(c_COMBC(_1421415, tc_fun(_1421415, tc_HOL_Obool), tc_fun(_1421415, tc_HOL_Obool)), c_Set_Oinsert(_1421415)), c_Orderings_Obot__class_Obot(tc_fun(_1421415, tc_HOL_Obool))))))], (794 ^ _774244) ^ [_786543, _786545] : [-(c_Nat__Transfer_Onat__set(_786543)), _786545 = _786543, c_Nat__Transfer_Onat__set(_786545)], (37673 ^ _774244) ^ [_1476183, _1476185, _1476187] : [class_Lattices_Olattice(_1476183), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476183), _1476185)), hBOOL(hAPP(hAPP(c_member(_1476183), _1476187), _1476185)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1476183), _1476187), c_Big__Operators_Olattice__class_OInf__fin(_1476183, _1476185)) = c_Big__Operators_Olattice__class_OInf__fin(_1476183, _1476185))], (28146 ^ _774244) ^ [_1271480] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1271480)) = hAPP(c_Nat_OSuc, _1271480))], (37151 ^ _774244) ^ [_1463411, _1463413, _1463415] : [class_Orderings_Olinorder(_1463411), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463411), _1463413)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463411), _1463415)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463411, tc_HOL_Obool)), _1463413), _1463415) = c_Orderings_Obot__class_Obot(tc_fun(_1463411, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1463411), c_Big__Operators_Olinorder__class_OMax(_1463411, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463411, tc_HOL_Obool)), _1463413), _1463415))), c_Big__Operators_Olinorder__class_OMax(_1463411, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463411, tc_HOL_Obool)), _1463413), _1463415))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1463411), c_Big__Operators_Olinorder__class_OMax(_1463411, _1463413)), c_Big__Operators_Olinorder__class_OMax(_1463411, _1463415)))], (23615 ^ _774244) ^ [_1183838, _1183840, _1183842, _1183844] : [class_Orderings_Olinorder(_1183838), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183838), _1183840), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183838), _1183842), _1183844)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183838), _1183842), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183838), _1183840), _1183844)))], (19927 ^ _774244) ^ [_1115219, _1115221, _1115223, _1115225] : [class_Fields_Olinordered__field__inverse__zero(_1115219), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115219), _1115221), _1115223)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115219), _1115225), c_Groups_Ozero__class_Ozero(_1115219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115219), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115219), _1115223), _1115225)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115219), _1115221), _1115225))))], (17347 ^ _774244) ^ [_1071152, _1071154, _1071156, _1071158] : [class_Rings_Olinordered__semidom(_1071152), hAPP(hAPP(c_Power_Opower__class_Opower(_1071152), _1071154), hAPP(c_Nat_OSuc, _1071156)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1071152), _1071158), hAPP(c_Nat_OSuc, _1071156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071152), c_Groups_Ozero__class_Ozero(_1071152)), _1071154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071152), c_Groups_Ozero__class_Ozero(_1071152)), _1071158)), -(_1071154 = _1071158)], (26279 ^ _774244) ^ [_1233396] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1233396) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1233396), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (49707 ^ _774244) ^ [_1769754, _1769756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1769754), _1769756)), -(c_List_Oupt(_1769754, hAPP(c_Nat_OSuc, _1769756)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1769754, _1769756)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1769756), c_List_Olist_ONil(tc_Nat_Onat))))], (22945 ^ _774244) ^ [_1170814, _1170816, _1170818, _1170820, _1170822] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1170814, _1170816), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1170818), _1170820))), -(_1170816 = 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)), _1170822)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1170814, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1170816), _1170822)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1170818), _1170822)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1170816), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1170818, _1170822))), _1170820)))))], (43480 ^ _774244) ^ [_1617616, _1617618] : [-(hAPP(c_Relation_OField(_1617616), hAPP(c_Relation_Oconverse(_1617616, _1617616), _1617618)) = hAPP(c_Relation_OField(_1617616), _1617618))], (45064 ^ _774244) ^ [_1657533, _1657535, _1657537, _1657539] : [class_Lattices_Osemilattice__inf(_1657533), hBOOL(hAPP(c_Finite__Set_Ofinite(_1657533), _1657535)), 45074 ^ _774244 : [(45077 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1657533), _1657537), 45073 ^ [_1657533, _1657535, _1657537, _1657539]))], (45075 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1657533), 45073 ^ [_1657533, _1657535, _1657537, _1657539]), _1657535)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1657533), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1657533), _1657537), _1657539)), hAPP(hAPP(c_Finite__Set_Ofold(_1657533, _1657533, c_Lattices_Osemilattice__inf__class_Oinf(_1657533)), _1657539), _1657535))))], (45470 ^ _774244) ^ [_1666917, _1666919, _1666921] : [c_Fun_Oinj__on(_1666917, _1666919, _1666921, c_Orderings_Otop__class_Otop(tc_fun(_1666917, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1666917), tc_List_Olist(_1666919), hAPP(c_List_Omap(_1666917, _1666919), _1666921), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1666917), tc_HOL_Obool))))], (27700 ^ _774244) ^ [_1262645, _1262647, _1262649, _1262651] : [27702 ^ _774244 : [(27705 ^ _774244) ^ [] : [hBOOL(hAPP(_1262651, 27701 ^ [_1262645, _1262647, _1262649, _1262651]))], (27703 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1262645), 27701 ^ [_1262645, _1262647, _1262649, _1262651]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262645, tc_HOL_Obool)), _1262647), _1262649))))]], 27706 ^ _774244 : [(27713 ^ _774244) ^ [_1262962] : [hBOOL(hAPP(hAPP(c_member(_1262645), _1262962), _1262649)), -(hBOOL(hAPP(_1262651, _1262962)))], (27707 ^ _774244) ^ [_1262865] : [hBOOL(hAPP(hAPP(c_member(_1262645), _1262865), _1262647)), -(hBOOL(hAPP(_1262651, _1262865)))]]], (16547 ^ _774244) ^ [_1055875, _1055877, _1055879, _1055881] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055875), hAPP(c_Int_Onumber__class_Onumber__of(_1055875), _1055877)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055875), _1055879), _1055881)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055875), hAPP(c_Int_Onumber__class_Onumber__of(_1055875), _1055877)), _1055879)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055875), hAPP(c_Int_Onumber__class_Onumber__of(_1055875), _1055877)), _1055881))), class_Int_Onumber(_1055875), class_Rings_Osemiring(_1055875)], (21295 ^ _774244) ^ [_1139258, _1139260, _1139262, _1139264] : [class_Fields_Olinordered__field__inverse__zero(_1139258), 21298 ^ _774244 : [(21299 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139258), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139258), _1139260), _1139262)), _1139264)), 21302 ^ _774244 : [(21309 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139258), c_Groups_Ozero__class_Ozero(_1139258)), _1139262))), 21312 ^ _774244 : [(21319 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139258), _1139262), c_Groups_Ozero__class_Ozero(_1139258)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139258), c_Groups_Ozero__class_Ozero(_1139258)), _1139264)))], (21313 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139258), _1139262), c_Groups_Ozero__class_Ozero(_1139258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139258), _1139264), _1139262)), _1139260)))]]], (21303 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139258), c_Groups_Ozero__class_Ozero(_1139258)), _1139262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139258), _1139260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139258), _1139264), _1139262))))]]], (21325 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139258), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139258), _1139260), _1139262)), _1139264))), 21328 ^ _774244 : [(21331 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139258), _1139260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139258), _1139264), _1139262)))], (21329 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139258), c_Groups_Ozero__class_Ozero(_1139258)), _1139262)))]], 21332 ^ _774244 : [(21335 ^ _774244) ^ [] : [21336 ^ _774244 : [(21339 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139258), _1139264), _1139262)), _1139260))], (21337 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139258), _1139262), c_Groups_Ozero__class_Ozero(_1139258))))]], 21340 ^ _774244 : [(21343 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139258), c_Groups_Ozero__class_Ozero(_1139258)), _1139264))], (21341 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139258), _1139262), c_Groups_Ozero__class_Ozero(_1139258)))]]], (21333 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139258), c_Groups_Ozero__class_Ozero(_1139258)), _1139262))]]]]], (19157 ^ _774244) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (35494 ^ _774244) ^ [_1426763, _1426765, _1426767, _1426769] : [-(c_Random__Sequence_Omap(_1426763, _1426765, _1426767, _1426769) = c_Random__Sequence_Obind(_1426763, _1426765, _1426769, hAPP(c_Fun_Ocomp(_1426765, 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(_1426765)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1426763, c_Random__Sequence_Osingle(_1426765)), _1426767)))], (49152 ^ _774244) ^ [_1757391, _1757393, _1757395, _1757397] : [49154 ^ _774244 : [(49157 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1757395, 49153 ^ [_1757391, _1757393, _1757395, _1757397])), hAPP(_1757397, 49153 ^ [_1757391, _1757393, _1757395, _1757397])))], (49155 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757391), 49153 ^ [_1757391, _1757393, _1757395, _1757397]), hAPP(c_List_Oset(_1757391), _1757393))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1757391, _1757395, _1757393)), c_List_Olist_Olist__size(_1757391, _1757397, _1757393))))], (38800 ^ _774244) ^ [_1499451, _1499453, _1499455] : [-(hAPP(c_Set_Ovimage(_1499451, _1499453, _1499455), c_Orderings_Otop__class_Otop(tc_fun(_1499453, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1499451, tc_HOL_Obool)))], (44281 ^ _774244) ^ [_1638772, _1638774, _1638776, _1638778, _1638780, _1638782] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1638772, _1638772)), hAPP(hAPP(c_Product__Type_OPair(_1638772, _1638772), _1638774), _1638776)), _1638778)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1638772, _1638772)), hAPP(hAPP(c_Product__Type_OPair(_1638772, _1638772), _1638776), _1638780)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638772, _1638772), tc_HOL_Obool), _1638782), _1638778))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638772, _1638772)), hAPP(hAPP(c_Product__Type_OPair(_1638772, _1638772), _1638774), _1638780)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638772, _1638772), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1638782)), _1638778))))], (21922 ^ _774244) ^ [_1151090, _1151092, _1151094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1151090), _1151092)), -(c_Random_Ominus__shift(_1151094, _1151090, _1151092) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1151094), _1151090)), _1151092))], (15108 ^ _774244) ^ [_1028161, _1028163, _1028165] : [class_Groups_Ogroup__add(_1028161), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1028161), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1028161), _1028163), _1028165)), _1028165) = _1028163)], (36685 ^ _774244) ^ [_1453162, _1453164, _1453166, _1453168] : [class_Orderings_Oorder(_1453162), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453162, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1453162, _1453164, _1453166)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1453162, _1453166, _1453168)) = c_Orderings_Obot__class_Obot(tc_fun(_1453162, tc_HOL_Obool)))], (18323 ^ _774244) ^ [_1086960, _1086962] : [class_Int_Onumber__ring(_1086960), class_Rings_Olinordered__idom(_1086960), 18330 ^ _774244 : [(18337 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1086962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086960), c_Groups_Ozero__class_Ozero(_1086960)), hAPP(c_Int_Onumber__class_Onumber__of(_1086960), _1086962))))], (18331 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086960), c_Groups_Ozero__class_Ozero(_1086960)), hAPP(c_Int_Onumber__class_Onumber__of(_1086960), _1086962))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1086962)))]]], (36845 ^ _774244) ^ [_1456854, _1456856, _1456858] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1456854), _1456856)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456854), _1456858)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1456854), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1456854, tc_HOL_Obool)), _1456856), _1456858))), hAPP(c_Finite__Set_Ocard(_1456854), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456854, tc_HOL_Obool)), _1456856), _1456858))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1456854), _1456856)), hAPP(c_Finite__Set_Ocard(_1456854), _1456858)))], (718 ^ _774244) ^ [_785343, _785345, _785347, _785349, _785351, _785353] : [-(c_Relation_Ototal__on(_785351, _785347, _785343)), c_Relation_Ototal__on(_785353, _785349, _785345), _785353 = _785351, _785349 = _785347, _785345 = _785343], (9945 ^ _774244) ^ [_938178] : [_938178 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _938178) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6418 ^ _774244) ^ [_877547, _877549, _877551, _877553] : [class_Groups_Ocancel__semigroup__add(_877547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877547), _877549), _877551) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877547), _877549), _877553), -(_877551 = _877553)], (4848 ^ _774244) ^ [_849178, _849180, _849182, _849184, _849186, _849188] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_849188, _849184, _849180) = c_SetInterval_Oord__class_OgreaterThanAtMost(_849186, _849182, _849178)), _849188 = _849186, _849184 = _849182, _849180 = _849178], (8136 ^ _774244) ^ [_907481, _907483, _907485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _907481), _907483)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907481), _907485)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907483), _907485))))], (13728 ^ _774244) ^ [_1003183, _1003185, _1003187] : [class_Lattices_Oab__semigroup__idem__mult(_1003183), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003183), _1003185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003183), _1003185), _1003187)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003183), _1003185), _1003187))], (43571 ^ _774244) ^ [_1619965, _1619967, _1619969, _1619971, _1619973] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619965, _1619967)), hAPP(hAPP(c_Product__Type_OPair(_1619965, _1619967), _1619969), _1619971)), hAPP(c_Relation_Oconverse(_1619967, _1619965), _1619973))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619967, _1619965)), hAPP(hAPP(c_Product__Type_OPair(_1619967, _1619965), _1619971), _1619969)), _1619973)))], (22995 ^ _774244) ^ [_1172063, _1172065, _1172067] : [-(hAPP(c_Product__Type_Osnd(_1172063, _1172065), _1172067) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1172063, _1172065, _1172065), hAPP(c_COMBK(tc_fun(_1172065, _1172065), _1172063), c_COMBI(_1172065))), _1172067))], (27448 ^ _774244) ^ [_1258324, _1258326] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1258324, _1258326)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1258326), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1258324), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (44046 ^ _774244) ^ [_1633021, _1633023] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1633021, _1633021), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1633021, _1633023)), c_Relation_OId(_1633021)) = c_Transitive__Closure_Ortrancl(_1633021, _1633023))], (24417 ^ _774244) ^ [_1198886, _1198888] : [hAPP(c_Code__Numeral_Onat__of, _1198886) = hAPP(c_Code__Numeral_Onat__of, _1198888), -(_1198886 = _1198888)], (47303 ^ _774244) ^ [_1713464, _1713466, _1713468, _1713470, _1713472] : [class_Orderings_Olinorder(_1713464), hBOOL(hAPP(c_List_Odistinct(_1713466), _1713468)), -(hBOOL(hAPP(c_List_Odistinct(_1713466), c_List_Olinorder__class_Oinsort__insert__key(_1713466, _1713464, _1713470, _1713472, _1713468))))], (46918 ^ _774244) ^ [_1703856, _1703858] : [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(_1703856)), _1703858))), _1703858 = c_List_Olist_ONil(_1703856)], (23679 ^ _774244) ^ [_1185032, _1185034, _1185036, _1185038] : [class_Orderings_Olinorder(_1185032), 23682 ^ _774244 : [(23691 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185032), _1185034), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1185032), _1185036), _1185038)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185032), _1185034), _1185036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185032), _1185034), _1185038))], (23683 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185032), _1185034), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1185032), _1185036), _1185038))), 23686 ^ _774244 : [(23689 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185032), _1185034), _1185038)))], (23687 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185032), _1185034), _1185036)))]]]]], (26726 ^ _774244) ^ [_1243118, _1243120, _1243122, _1243124, _1243126] : [class_Groups_Ocomm__monoid__add(_1243118), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1243118), _1243120), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1243122), _1243124)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1243126), _1243124))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1243118), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1243118, tc_Nat_Onat), _1243120), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1243124))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1243122), _1243126)))], (32080 ^ _774244) ^ [_1354924, _1354926] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1354924), 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)))), _1354926)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354926), _1354924)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354924), _1354926)))], (10333 ^ _774244) ^ [_944403, _944405, _944407] : [class_Orderings_Oorder(_944403), 10336 ^ _774244 : [(10345 ^ _774244) ^ [] : [-(_944405 = _944407), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944403), _944405), _944407)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944403), _944407), _944405))], (10337 ^ _774244) ^ [] : [_944405 = _944407, 10340 ^ _774244 : [(10343 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944403), _944407), _944405)))], (10341 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944403), _944405), _944407)))]]]]], (6221 ^ _774244) ^ [_874153] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OBODY(_874153)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19081 ^ _774244) ^ [_1099835, _1099837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1099835)), c_Int_OBit0(_1099837))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099835), _1099837)))], (16034 ^ _774244) ^ [_1046719, _1046721] : [-(_1046719 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046719), _1046721) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046721), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046719), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1046721)))], (45942 ^ _774244) ^ [_1677742, _1677744, _1677746] : [class_Orderings_Olinorder(_1677742), hBOOL(hAPP(c_Finite__Set_Ofinite(_1677742), _1677744)), -(c_List_Olinorder__class_Osorted__list__of__set(_1677742, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1677742, tc_HOL_Obool)), _1677744), hAPP(hAPP(c_Set_Oinsert(_1677742), _1677746), c_Orderings_Obot__class_Obot(tc_fun(_1677742, tc_HOL_Obool))))) = c_List_Oremove1(_1677742, _1677746, c_List_Olinorder__class_Osorted__list__of__set(_1677742, _1677744)))], (18253 ^ _774244) ^ [_1085825, _1085827] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085825)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085827)))), 18256 ^ _774244 : [(18259 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1085827))], (18257 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085825), _1085827)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085825), _1085827))], (50440 ^ _774244) ^ [_1785433, _1785435, _1785437, _1785439] : [class_Orderings_Olinorder(_1785433), c_List_Olinorder__class_Osorted(_1785433, hAPP(c_List_Orev(_1785433), _1785435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1785437), _1785439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1785439), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1785433)), _1785435))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1785433), hAPP(hAPP(c_List_Onth(_1785433), _1785435), _1785439)), hAPP(hAPP(c_List_Onth(_1785433), _1785435), _1785437))))], (19815 ^ _774244) ^ [_1113119, _1113121, _1113123, _1113125] : [class_Rings_Odivision__ring(_1113119), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113119), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113119), _1113121), _1113123)), _1113125) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113119), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113119), _1113121), _1113125)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113119), _1113123), _1113125)))], (43721 ^ _774244) ^ [_1624532, _1624534, _1624536, _1624538] : [-(_1624532 = c_Orderings_Obot__class_Obot(tc_fun(_1624534, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1624534, tc_fun(_1624536, tc_HOL_Obool)), _1624532), hAPP(c_COMBK(tc_fun(_1624536, tc_HOL_Obool), _1624534), _1624538)) = _1624538)], (12580 ^ _774244) ^ [_983092, _983094, _983096, _983098] : [class_Rings_Olinordered__semiring__strict(_983092), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983092), _983094), _983096)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983092), _983098), _983096))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983092), c_Groups_Ozero__class_Ozero(_983092)), _983096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983092), _983094), _983098)))], (43941 ^ _774244) ^ [_1629879, _1629881, _1629883, _1629885, _1629887] : [class_Complete__Lattice_Ocomplete__lattice(_1629879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629881), _1629883)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1629879), _1629885), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629881, _1629879), _1629883), _1629887)) = hAPP(hAPP(c_Finite__Set_Ofold(_1629881, _1629879, hAPP(hAPP(c_COMBB(_1629879, tc_fun(_1629879, _1629879), _1629881), c_Lattices_Osemilattice__inf__class_Oinf(_1629879)), _1629887)), _1629885), _1629883))], (32373 ^ _774244) ^ [_1360708, _1360710, _1360712, _1360714] : [-(c_Nitpick_Ofold__graph_H(_1360708, _1360710, _1360712, _1360714, c_Orderings_Obot__class_Obot(tc_fun(_1360708, tc_HOL_Obool)), _1360714))], (51045 ^ _774244) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (3938 ^ _774244) ^ [_834941, _834943, _834945, _834947] : [-(c_Transitive__Closure_Otrancl(_834947, _834943) = c_Transitive__Closure_Otrancl(_834945, _834941)), _834947 = _834945, _834943 = _834941], (47190 ^ _774244) ^ [_1710495, _1710497, _1710499, _1710501] : [-(_1710495 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1710497), hAPP(hAPP(c_List_Olist_OCons(_1710497), _1710499), _1710501)), _1710495) = hAPP(hAPP(c_List_Onth(_1710497), _1710501), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1710495), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (27374 ^ _774244) ^ [_1256873, _1256875] : [class_Groups_Oordered__ab__group__add(_1256873), -(hAPP(c_Set_Oimage(_1256873, _1256873, c_Groups_Ouminus__class_Ouminus(_1256873)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1256873), _1256875)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1256873), hAPP(c_Groups_Ouminus__class_Ouminus(_1256873), _1256875)))], (47859 ^ _774244) ^ [_1726456, _1726458, _1726460, _1726462] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1726456), tc_List_Olist(_1726456))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1726456), tc_List_Olist(_1726456)), _1726458), _1726460)), c_List_Olexord(_1726456, _1726462)))), 47860 ^ _774244 : [(47867 ^ _774244) ^ [_1726763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726763), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726456)), _1726458)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726456)), _1726460)))), hAPP(hAPP(c_List_Otake(_1726456), _1726763), _1726458) = hAPP(hAPP(c_List_Otake(_1726456), _1726763), _1726460), hBOOL(hAPP(hAPP(c_member(tc_prod(_1726456, _1726456)), hAPP(hAPP(c_Product__Type_OPair(_1726456, _1726456), hAPP(hAPP(c_List_Onth(_1726456), _1726458), _1726763)), hAPP(hAPP(c_List_Onth(_1726456), _1726460), _1726763))), _1726462))], (47861 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726456)), _1726458)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726456)), _1726460))), hAPP(hAPP(c_List_Otake(_1726456), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726456)), _1726458)), _1726460) = _1726458]]], (49635 ^ _774244) ^ [_1768483, _1768485, _1768487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1768483), _1768485)), _1768487)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1768485), c_List_Oupt(_1768483, _1768487)) = c_List_Oupt(_1768483, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1768483), _1768485)))], (27380 ^ _774244) ^ [_1256996, _1256998] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1256996, _1256998)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1256998), _1256996)))], (3104 ^ _774244) ^ [_821776, _821778] : [_821778 = _821776, -(c_Int_OBit0(_821778) = c_Int_OBit0(_821776))], (22460 ^ _774244) ^ [_1161252, _1161254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1161252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1161254)), -(c_Divides_OposDivAlg(_1161252, _1161254) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1161252), _1161254)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1161252, _1161254)))], (46854 ^ _774244) ^ [_1702671, _1702673, _1702675] : [-(hAPP(hAPP(c_List_Ozip(_1702671, _1702673), _1702675), c_List_Olist_ONil(_1702673)) = c_List_Olist_ONil(tc_prod(_1702671, _1702673)))], (43087 ^ _774244) ^ [_1607340, _1607342] : [-(c_Relation_Orefl__on(_1607340, c_Orderings_Otop__class_Otop(tc_fun(_1607340, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1607340, _1607342)))], (10404 ^ _774244) ^ [_945591, _945593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945591), _945593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _945591)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _945593))))], (44216 ^ _774244) ^ [_1637158, _1637160, _1637162] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637158, _1637158)), _1637160), c_Transitive__Closure_Ortrancl(_1637158, _1637162))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637158, _1637158)), _1637160), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1637158, _1637158), tc_HOL_Obool), 44219 ^ [_1637158, _1637160, _1637162]), _1637162))))], (34555 ^ _774244) ^ [_1403821, _1403823, _1403825] : [34557 ^ _774244 : [(34560 ^ _774244) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1403825, 34556 ^ [_1403821, _1403823, _1403825]))], (34558 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403821), 34556 ^ [_1403821, _1403823, _1403825]), _1403823)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403821, tc_Int_Oint), _1403825), _1403823) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403821, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1403821), c_Int_Onat), _1403825)), _1403823)))], (32804 ^ _774244) ^ [_1368727, _1368729] : [class_Orderings_Olinorder(_1368727), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368727), _1368729)), -(_1368729 = c_Orderings_Obot__class_Obot(tc_fun(_1368727, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1368727), c_Big__Operators_Olinorder__class_OMin(_1368727, _1368729)), _1368729)))], (43823 ^ _774244) ^ [_1626828, _1626830, _1626832, _1626834, _1626836] : [-(_1626828 = c_Orderings_Obot__class_Obot(tc_fun(_1626830, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1626832, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626830, tc_fun(_1626832, tc_HOL_Obool)), _1626828), _1626834)), _1626836) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626830, tc_fun(_1626832, tc_HOL_Obool)), _1626828), hAPP(hAPP(c_COMBC(_1626830, tc_fun(_1626832, tc_HOL_Obool), tc_fun(_1626832, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1626832, tc_HOL_Obool), tc_fun(tc_fun(_1626832, tc_HOL_Obool), tc_fun(_1626832, tc_HOL_Obool)), _1626830), c_Groups_Ominus__class_Ominus(tc_fun(_1626832, tc_HOL_Obool))), _1626834)), _1626836)))], (5827 ^ _774244) ^ [_867326, _867328, _867330, _867332, _867334] : [-(c_Natural_Oevaln(c_Com_Ocom_OSemi(_867326, _867328), _867330, _867332, _867334)), 5828 ^ _774244 : [(5829 ^ _774244) ^ [_867381] : [c_Natural_Oevaln(_867326, _867330, _867332, _867381), c_Natural_Oevaln(_867328, _867381, _867332, _867334)]]], (7084 ^ _774244) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49073 ^ _774244) ^ [_1755713, _1755715] : [-(_1755713 = c_List_Olist_ONil(_1755715)), -(hBOOL(hAPP(hAPP(c_member(_1755715), c_List_Olast(_1755715, _1755713)), hAPP(c_List_Oset(_1755715), _1755713))))], (11621 ^ _774244) ^ [_965793, _965795, _965797] : [class_Rings_Oordered__cancel__semiring(_965793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965793), c_Groups_Ozero__class_Ozero(_965793)), _965795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965793), _965797), c_Groups_Ozero__class_Ozero(_965793))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965793), _965795), _965797)), c_Groups_Ozero__class_Ozero(_965793))))], (16463 ^ _774244) ^ [_1054436, _1054438, _1054440] : [class_Groups_Oordered__ab__group__add__abs(_1054436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054436), _1054438), _1054440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054436), hAPP(c_Groups_Ouminus__class_Ouminus(_1054436), _1054438)), _1054440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054436), hAPP(c_Groups_Oabs__class_Oabs(_1054436), _1054438)), _1054440)))], (34763 ^ _774244) ^ [_1409547, _1409549, _1409551, _1409553] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1409547, _1409547)), hAPP(hAPP(c_Product__Type_OPair(_1409547, _1409547), _1409549), _1409551)), c_Relation_OId__on(_1409547, _1409553))), 34766 ^ _774244 : [(34769 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409547), _1409549), _1409553)))], (34767 ^ _774244) ^ [] : [-(_1409549 = _1409551)]]], (15554 ^ _774244) ^ [_1036654, _1036656, _1036658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036654), _1036656)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036658), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036656), _1036654)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036658), _1036654)), _1036656))], (7734 ^ _774244) ^ [_900377, _900379] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _900377), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900377), _900379)))))], (34521 ^ _774244) ^ [_1403122, _1403124, _1403126, _1403128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1403122), _1403124)), -(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), _1403122), _1403126)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1403124), _1403128))), c_FunDef_Opair__leq)))], (27010 ^ _774244) ^ [_1249050, _1249052, _1249054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249050)), 27013 ^ _774244 : [(27014 ^ _774244) ^ [_1249184] : [27016 ^ _774244 : [(27022 ^ _774244) ^ [] : [-(_1249184 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27018 ^ [_1249050, _1249052, _1249054, _1249184]), 27015 ^ [_1249050, _1249052, _1249054, _1249184]))], (27020 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27018 ^ [_1249050, _1249052, _1249054, _1249184]), _1249052)))], (27017 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27015 ^ [_1249050, _1249052, _1249054, _1249184]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1249050))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249184), _1249054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1249184), _1249050)), _1249054)))]]], (8152 ^ _774244) ^ [_907653, _907655, _907657, _907659] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_907653, _907655), _907657, _907659, c_Natural_Oupdate(_907657, _907653, hAPP(_907655, _907657))))], (9124 ^ _774244) ^ [] : [-(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))], (51359 ^ _774244) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (44608 ^ _774244) ^ [_1646393, _1646395, _1646397] : [-(hAPP(c_Relation_ORange(_1646393, _1646395), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1646393, _1646395), tc_HOL_Obool), _1646397)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1646393, _1646395), tc_HOL_Obool), tc_fun(_1646395, tc_HOL_Obool)), _1646397), c_Relation_ORange(_1646393, _1646395)))], (3802 ^ _774244) ^ [_832855, _832857, _832859, _832861] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_832861, _832857) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_832859, _832855)), _832861 = _832859, _832857 = _832855], (42944 ^ _774244) ^ [_1604046, _1604048, _1604050, _1604052, _1604054, _1604056, _1604058] : [c_Finite__Set_Ofun__left__comm(_1604046, _1604048, _1604050), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1604046, _1604048, _1604050, _1604052, _1604054), _1604056)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1604046, _1604048, _1604050, _1604052, _1604054), _1604058)), -(_1604058 = _1604056)], (39532 ^ _774244) ^ [_1516438, _1516440, _1516442, _1516444, _1516446] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1516438, _1516440, hAPP(hAPP(c_Set_Oinsert(_1516438), _1516442), _1516444)), _1516446))), 39533 ^ _774244 : [(39534 ^ _774244) ^ [_1516542, _1516544] : [hAPP(hAPP(c_Set_Oinsert(_1516438), _1516442), _1516444) = hAPP(hAPP(c_Set_Oinsert(_1516438), _1516544), _1516542), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1516438, _1516438, _1516440, _1516544, _1516542), _1516446)), -(hBOOL(hAPP(hAPP(c_member(_1516438), _1516544), _1516542)))]]], (11487 ^ _774244) ^ [_963428, _963430, _963432] : [class_Groups_Oordered__comm__monoid__add(_963428), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963428), c_Groups_Ozero__class_Ozero(_963428)), _963430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963428), c_Groups_Ozero__class_Ozero(_963428)), _963432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963428), c_Groups_Ozero__class_Ozero(_963428)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963428), _963430), _963432))))], (24841 ^ _774244) ^ [_1208041, _1208043, _1208045] : [class_Rings_Olinordered__idom(_1208041), 24844 ^ _774244 : [(24851 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208041), _1208043), _1208045)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208041), hAPP(c_Groups_Oabs__class_Oabs(_1208041), _1208043)), _1208045)))], (24845 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208041), hAPP(c_Groups_Oabs__class_Oabs(_1208041), _1208043)), _1208045)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208041), _1208043), _1208045)))]]], (42261 ^ _774244) ^ [_1589715, _1589717, _1589719, _1589721] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1589715, tc_HOL_Obool), tc_fun(_1589715, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1589715, tc_HOL_Obool), tc_fun(_1589715, tc_HOL_Obool)), _1589717), _1589719)), c_Wellfounded_Omax__ext(_1589715, _1589721))), 42264 ^ _774244 : [(42267 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1589715), _1589719)))], (42269 ^ _774244) ^ [] : [_1589719 = c_Orderings_Obot__class_Obot(tc_fun(_1589715, tc_HOL_Obool))], (42271 ^ _774244) ^ [_1590009] : [hBOOL(hAPP(hAPP(c_member(_1589715), _1590009), _1589717)), 42275 ^ _774244 : [(42278 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589715, _1589715)), hAPP(hAPP(c_Product__Type_OPair(_1589715, _1589715), _1590009), 42274 ^ [_1589715, _1589717, _1589719, _1589721, _1590009])), _1589721)))], (42276 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589715), 42274 ^ [_1589715, _1589717, _1589719, _1589721, _1590009]), _1589719)))]]], (42265 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1589715), _1589717)))]]], (12688 ^ _774244) ^ [_985083, _985085] : [class_Rings_Olinordered__idom(_985083), 12691 ^ _774244 : [(12698 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985083), _985085), c_Groups_Ozero__class_Ozero(_985083))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985083), c_Groups_Osgn__class_Osgn(_985083, _985085)), c_Groups_Ozero__class_Ozero(_985083))))], (12692 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985083), c_Groups_Osgn__class_Osgn(_985083, _985085)), c_Groups_Ozero__class_Ozero(_985083))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985083), _985085), c_Groups_Ozero__class_Ozero(_985083))))]]], (30396 ^ _774244) ^ [_1316233, _1316235, _1316237, _1316239, _1316241] : [class_Groups_Ocomm__monoid__add(_1316233), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316235), _1316237)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1316235, _1316233), _1316239), hAPP(hAPP(c_Set_Oinsert(_1316235), _1316241), _1316237)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1316233), hAPP(_1316239, _1316241)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1316235, _1316233), _1316239), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316235, tc_HOL_Obool)), _1316237), hAPP(hAPP(c_Set_Oinsert(_1316235), _1316241), c_Orderings_Obot__class_Obot(tc_fun(_1316235, tc_HOL_Obool)))))))], (30981 ^ _774244) ^ [_1329932, _1329934, _1329936] : [hBOOL(hAPP(hAPP(c_member(_1329932), _1329934), _1329936)), -(hBOOL(hAPP(_1329936, _1329934)))], (40109 ^ _774244) ^ [_1532071, _1532073] : [class_Orderings_Olinorder(_1532071), hBOOL(hAPP(c_Finite__Set_Ofinite(_1532071), _1532073)), -(c_Big__Operators_Olattice_OSup__fin(_1532071, c_Orderings_Oord__class_Omax(_1532071), _1532073) = hAPP(c_Finite__Set_Ofold1(_1532071, c_Orderings_Oord__class_Omax(_1532071)), _1532073))], (48756 ^ _774244) ^ [_1748689, _1748691] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1748689), _1748691) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1748689 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 48762 ^ _774244 : [(48765 ^ _774244) ^ [] : [48761 ^ [_1748689, _1748691] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48763 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 48761 ^ [_1748689, _1748691]), hAPP(c_List_Oset(tc_Nat_Onat), _1748691))))]]], (4176 ^ _774244) ^ [_838842, _838844, _838846, _838848] : [-(c_List_Olexn(_838848, _838844) = c_List_Olexn(_838846, _838842)), _838848 = _838846, _838844 = _838842], (40908 ^ _774244) ^ [_1550764, _1550766, _1550768] : [class_Orderings_Olinorder(_1550764), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550764), _1550766)), -(_1550766 = c_Orderings_Obot__class_Obot(tc_fun(_1550764, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1550764), _1550768), c_Big__Operators_Olattice_OSup__fin(_1550764, c_Orderings_Oord__class_Omax(_1550764), _1550766)) = c_Big__Operators_Olattice_OSup__fin(_1550764, c_Orderings_Oord__class_Omax(_1550764), hAPP(c_Set_OCollect(_1550764), hAPP(hAPP(c_COMBB(tc_fun(_1550764, tc_HOL_Obool), tc_HOL_Obool, _1550764), c_HOL_OEx(_1550764)), hAPP(hAPP(c_COMBC(_1550764, tc_fun(_1550764, tc_HOL_Obool), tc_fun(_1550764, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550764, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1550764, tc_HOL_Obool), tc_fun(_1550764, tc_HOL_Obool)), _1550764), c_COMBS(_1550764, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550764, tc_HOL_Obool), tc_fun(_1550764, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1550764), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550764), c_fconj)), hAPP(hAPP(c_COMBC(_1550764, tc_fun(_1550764, _1550764), tc_fun(_1550764, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550764, tc_HOL_Obool), tc_fun(tc_fun(_1550764, _1550764), tc_fun(_1550764, tc_HOL_Obool)), _1550764), c_COMBB(_1550764, tc_HOL_Obool, _1550764)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1550764), _1550768))))), hAPP(hAPP(c_COMBC(_1550764, tc_fun(_1550764, tc_HOL_Obool), tc_HOL_Obool), c_member(_1550764)), _1550766))))))], (18611 ^ _774244) ^ [_1091845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091845), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1091845)), c_Int_OMin)))], (40709 ^ _774244) ^ [_1544104, _1544106] : [-(hAPP(c_Set_OCollect(_1544104), hAPP(hAPP(c_COMBC(_1544104, _1544104, tc_HOL_Obool), c_fequal), _1544106)) = hAPP(hAPP(c_Set_Oinsert(_1544104), _1544106), c_Orderings_Obot__class_Obot(tc_fun(_1544104, tc_HOL_Obool))))], (43482 ^ _774244) ^ [_1617657, _1617659] : [-(hAPP(c_Relation_Oconverse(_1617657, _1617657), c_Relation_OId__on(_1617657, _1617659)) = c_Relation_OId__on(_1617657, _1617659))], (30863 ^ _774244) ^ [_1327781, _1327783, _1327785] : [_1327781 = c_Orderings_Obot__class_Obot(tc_fun(_1327783, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_1327783), _1327785), _1327781))], (36027 ^ _774244) ^ [_1438131, _1438133, _1438135] : [class_Lattices_Olattice(_1438131), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438131), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1438131), _1438133), _1438135)), _1438135)))], (14310 ^ _774244) ^ [_1013917, _1013919, _1013921] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1013917), _1013919)), _1013921) = 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), _1013917), _1013921)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1013919), _1013921))), 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, _1013917, _1013921)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1013919, _1013921))), _1013921)))], (36573 ^ _774244) ^ [_1450664, _1450666] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450664, tc_HOL_Obool)), _1450666), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450664, tc_HOL_Obool)), _1450666)) = c_Orderings_Obot__class_Obot(tc_fun(_1450664, tc_HOL_Obool)))], (6730 ^ _774244) ^ [_882676, _882678, _882680] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_882676, _882678, _882680))), -(hBOOL(hAPP(c_Com_OWT, _882680)))], (8542 ^ _774244) ^ [_913628, _913630, _913632] : [class_Rings_Ocomm__semiring__1(_913628), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913628), _913630), _913632)), _913632) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913628), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913628), _913630), c_Groups_Oone__class_Oone(_913628))), _913632))], (18023 ^ _774244) ^ [_1082399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1082399), 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), _1082399)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6039 ^ _774244) ^ [_870964] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _870964)], (28813 ^ _774244) ^ [] : [-(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)))], (41472 ^ _774244) ^ [_1570243] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1570243)))], (31569 ^ _774244) ^ [_1343658, _1343660, _1343662] : [hBOOL(hAPP(hAPP(c_member(_1343658), _1343660), _1343662)), -(hAPP(hAPP(c_Set_Oinsert(_1343658), _1343660), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1343658, tc_HOL_Obool)), _1343662), hAPP(hAPP(c_Set_Oinsert(_1343658), _1343660), c_Orderings_Obot__class_Obot(tc_fun(_1343658, tc_HOL_Obool))))) = _1343662)], (24635 ^ _774244) ^ [_1203308, _1203310, _1203312, _1203314] : [hBOOL(hAPP(_1203308, _1203310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203312, tc_HOL_Obool)), _1203308), _1203314)), -(hBOOL(hAPP(_1203314, _1203310)))], (10812 ^ _774244) ^ [_951828, _951830, _951832, _951834] : [class_Orderings_Oorder(_951828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951828), _951830), _951832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951828), _951834), _951830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951828), _951834), _951832)))], (25823 ^ _774244) ^ [_1224955, _1224957, _1224959, _1224961] : [class_Rings_Ocomm__ring(_1224955), class_Rings_Odvd(_1224955), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224955), _1224957), _1224959)), 25834 ^ _774244 : [(25841 ^ _774244) ^ [_1225381, _1225383] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224955), _1224957), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224955), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1224955), _1225383), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224955), _1225381), _1224959))), _1224961))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224955), _1224957), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224955), _1225383), _1224961))))], (25835 ^ _774244) ^ [_1225208, _1225210] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224955), _1224957), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224955), _1225210), _1224961))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224955), _1224957), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224955), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1224955), _1225210), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224955), _1225208), _1224959))), _1224961))))]]], (28332 ^ _774244) ^ [_1275227, _1275229, _1275231, _1275233] : [class_Orderings_Olinorder(_1275227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275227), _1275229), _1275231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275227), _1275231), _1275233)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275227, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1275227, _1275229, _1275231)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1275227, _1275231, _1275233)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1275227, _1275229, _1275233))], (51233 ^ _774244) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (12053 ^ _774244) ^ [_973735, _973737] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973735)), _973737) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973737), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973735), _973737)))], (25485 ^ _774244) ^ [_1218796, _1218798, _1218800] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218796), _1218798)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218796), _1218800)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218796), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1218798), _1218800))))], (3272 ^ _774244) ^ [_824508, _824510, _824512, _824514, _824516, _824518] : [-(c_Partial__Function_Oflat__lub(_824518, _824514, _824510) = c_Partial__Function_Oflat__lub(_824516, _824512, _824508)), _824518 = _824516, _824514 = _824512, _824510 = _824508], (32002 ^ _774244) ^ [_1353173, _1353175, _1353177, _1353179, _1353181, _1353183] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353173, tc_fun(_1353175, tc_HOL_Obool))), _1353177), _1353179), _1353181), _1353183)), -(hBOOL(hAPP(hAPP(_1353177, _1353181), _1353183))), -(hBOOL(hAPP(hAPP(_1353179, _1353181), _1353183)))], (3786 ^ _774244) ^ [_832621, _832623, _832625, _832627] : [-(c_Wellfounded_Omax__ext(_832627, _832623) = c_Wellfounded_Omax__ext(_832625, _832621)), _832627 = _832625, _832623 = _832621], (8568 ^ _774244) ^ [_914157, _914159, _914161] : [class_Rings_Oring(_914157), -(hAPP(c_Groups_Ouminus__class_Ouminus(_914157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914157), _914159), _914161)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914157), hAPP(c_Groups_Ouminus__class_Ouminus(_914157), _914159)), _914161))], (36643 ^ _774244) ^ [_1452189, _1452191, _1452193, _1452195] : [class_Orderings_Oorder(_1452189), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452189, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1452189, _1452191), _1452193)), c_SetInterval_Oord__class_OatLeastAtMost(_1452189, _1452193, _1452195)) = c_Orderings_Obot__class_Obot(tc_fun(_1452189, tc_HOL_Obool)))], (39918 ^ _774244) ^ [_1527630, _1527632, _1527634, _1527636, _1527638, _1527640, _1527642, _1527644, _1527646] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1527630, _1527632)), hAPP(hAPP(c_Product__Type_OPair(_1527630, _1527632), _1527634), _1527636)), _1527638)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1527640, _1527642)), hAPP(hAPP(c_Product__Type_OPair(_1527640, _1527642), hAPP(_1527644, _1527634)), hAPP(_1527646, _1527636))), hAPP(c_Set_Oimage(tc_prod(_1527630, _1527632), tc_prod(_1527640, _1527642), c_Product__Type_Omap__pair(_1527630, _1527640, _1527632, _1527642, _1527644, _1527646)), _1527638))))], (9884 ^ _774244) ^ [_937198, _937200] : [-(c_Int_Onat__aux(_937198, _937200) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _937198)), _937200))], (50971 ^ _774244) ^ [_1796685, _1796687] : [class_Orderings_Opreorder(_1796685), -(class_Orderings_Opreorder(tc_fun(_1796687, _1796685)))], (21129 ^ _774244) ^ [_1136148, _1136150] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136148), _1136150), hAPP(c_Int_Onumber__class_Onumber__of(_1136148), c_Int_OBit1(c_Int_OPls))) = _1136150), class_Fields_Ofield(_1136148), class_Int_Onumber__ring(_1136148)], (5746 ^ _774244) ^ [_865832, _865834, _865836, _865838, _865840, _865842, _865844, _865846, _865848, _865850] : [-(c_Com_Ocom_Ocom__case(_865832, _865834, _865836, _865838, _865840, _865842, _865844, _865846, _865848, c_Com_Ocom_OBODY(_865850)) = hAPP(_865846, _865850))], (47573 ^ _774244) ^ [_1719819, _1719821, _1719823] : [-(hAPP(c_List_Oset(_1719819), hAPP(hAPP(c_List_Oappend(_1719819), _1719821), _1719823)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1719819, tc_HOL_Obool)), hAPP(c_List_Oset(_1719819), _1719821)), hAPP(c_List_Oset(_1719819), _1719823)))], (28719 ^ _774244) ^ [_1284182, _1284184] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284182, tc_HOL_Obool)), _1284184), c_Orderings_Otop__class_Otop(tc_fun(_1284182, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1284182, tc_HOL_Obool)))], (8642 ^ _774244) ^ [_915360, _915362] : [class_Groups_Ocomm__monoid__mult(_915360), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915360), c_Groups_Oone__class_Oone(_915360)), _915362) = _915362)], (3206 ^ _774244) ^ [_823475, _823477, _823479, _823481] : [-(c_Option_Oset(_823481, _823477) = c_Option_Oset(_823479, _823475)), _823481 = _823479, _823477 = _823475], (24591 ^ _774244) ^ [_1202556, _1202558, _1202560, _1202562, _1202564] : [_1202556 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1202558, _1202560, _1202562, _1202564), _1202556) = c_Lazy__Sequence_Oempty(_1202560))], (49248 ^ _774244) ^ [_1759449, _1759451] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759449)), c_List_Obutlast(_1759449, _1759451)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759449)), _1759451)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (51139 ^ _774244) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (37881 ^ _774244) ^ [_1480497, _1480499] : [class_Groups_Oordered__ab__group__add(_1480497), -(c_Fun_Oinj__on(_1480497, _1480497, c_Groups_Ouminus__class_Ouminus(_1480497), _1480499))], (49553 ^ _774244) ^ [_1766971, _1766973] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1766971, _1766973)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1766973), _1766971))], (50194 ^ _774244) ^ [_1779381, _1779383, _1779385] : [hAPP(c_List_Orev(_1779381), _1779383) = hAPP(hAPP(c_List_Olist_OCons(_1779381), _1779385), c_List_Olist_ONil(_1779381)), -(_1779383 = hAPP(hAPP(c_List_Olist_OCons(_1779381), _1779385), c_List_Olist_ONil(_1779381)))], (23543 ^ _774244) ^ [_1182226, _1182228, _1182230, _1182232, _1182234] : [hBOOL(hAPP(hAPP(_1182226, _1182228), _1182230)), -(hBOOL(hAPP(hAPP(_1182226, hAPP(c_Product__Type_Osnd(_1182232, _1182234), hAPP(hAPP(c_Product__Type_OPair(_1182232, _1182234), _1182230), _1182228))), hAPP(c_Product__Type_Ofst(_1182232, _1182234), hAPP(hAPP(c_Product__Type_OPair(_1182232, _1182234), _1182230), _1182228)))))], (8664 ^ _774244) ^ [_915672, _915674] : [class_Groups_Omonoid__mult(_915672), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915672), _915674), c_Groups_Oone__class_Oone(_915672)) = _915674)], (7205 ^ _774244) ^ [_891052, _891054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891052), _891054)), _891052 = _891054], (23567 ^ _774244) ^ [_1182815, _1182817, _1182819] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1182815, tc_HOL_Obool)), _1182817) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1182815, tc_HOL_Obool)), _1182819), -(_1182817 = _1182819)], (43484 ^ _774244) ^ [_1617694, _1617696, _1617698, _1617700, _1617702, _1617704] : [class_Complete__Lattice_Ocomplete__lattice(_1617694), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1617696, tc_fun(_1617698, _1617694)), _1617700), _1617702), _1617704) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1617696, _1617694), _1617700), hAPP(hAPP(c_COMBC(_1617696, _1617698, _1617694), _1617702), _1617704)))], (51089 ^ _774244) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (25245 ^ _774244) ^ [_1214592, _1214594, _1214596, _1214598] : [class_Rings_Ocomm__semiring__1(_1214592), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214592), _1214594), _1214596)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214592), _1214596), _1214598)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214592), _1214594), _1214598)))], (46948 ^ _774244) ^ [_1704390, _1704392, _1704394] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1704390)), -(c_List_Osublist(_1704392, hAPP(hAPP(c_List_Olist_OCons(_1704392), _1704394), c_List_Olist_ONil(_1704392)), _1704390) = hAPP(hAPP(c_List_Olist_OCons(_1704392), _1704394), c_List_Olist_ONil(_1704392)))], (41692 ^ _774244) ^ [_1575995, _1575997, _1575999, _1576001, _1576003] : [hBOOL(hAPP(hAPP(_1575995, _1575997), _1575999)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1576001, _1576003, _1575995), _1575999)))], (34590 ^ _774244) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (42678 ^ _774244) ^ [_1598392, _1598394, _1598396] : [class_Orderings_Olinorder(_1598392), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598392), _1598394)), -(c_Big__Operators_Olattice_OSup__fin(_1598392, c_Orderings_Oord__class_Omax(_1598392), hAPP(hAPP(c_Set_Oinsert(_1598392), _1598396), _1598394)) = hAPP(hAPP(c_Finite__Set_Ofold(_1598392, _1598392, c_Orderings_Oord__class_Omax(_1598392)), _1598396), _1598394))], (19345 ^ _774244) ^ [_1104444] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1104444), 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, _1104444)))], (48322 ^ _774244) ^ [_1739288, _1739290] : [-(hAPP(c_List_Oset(_1739288), hAPP(c_List_Orotate1(_1739288), _1739290)) = hAPP(c_List_Oset(_1739288), _1739290))], (26600 ^ _774244) ^ [_1240878, _1240880] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1240878), hAPP(c_Nat_OSuc, _1240880)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1240878, _1240880))], (23787 ^ _774244) ^ [_1186958, _1186960, _1186962, _1186964] : [class_Orderings_Olinorder(_1186958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186958), _1186960), _1186962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186958), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186958), _1186964), _1186960)), _1186962)))], (41456 ^ _774244) ^ [_1569911, _1569913, _1569915, _1569917] : [c_Wellfounded_Owf(_1569911, _1569913), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569911, _1569911)), hAPP(hAPP(c_Product__Type_OPair(_1569911, _1569911), _1569915), _1569917)), _1569913)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569911, _1569911)), hAPP(hAPP(c_Product__Type_OPair(_1569911, _1569911), _1569917), _1569915)), _1569913))], (35532 ^ _774244) ^ [_1427677, _1427679, _1427681] : [_1427679 = c_Orderings_Obot__class_Obot(tc_fun(_1427677, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1427677), _1427679), _1427681) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427677, tc_HOL_Obool), tc_HOL_Obool)))], (5678 ^ _774244) ^ [_864729, _864731, _864733] : [c_Natural_Oevalc(c_Com_Ocom_OBODY(_864729), _864731, _864733), -(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _864729)), _864731, _864733))], (49495 ^ _774244) ^ [_1765665, _1765667] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1765665))), c_List_Otranspose(_1765665, _1765667)) = c_List_Ofoldr(tc_List_Olist(_1765665), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1765665)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1765665))), _1765667, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46224 ^ _774244) ^ [_1685495, _1685497, _1685499] : [_1685495 = _1685497, 46227 ^ _774244 : [(46230 ^ _774244) ^ [_1685651] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1685499, _1685499)), _1685651), hAPP(c_List_Oset(tc_prod(_1685499, _1685499)), hAPP(hAPP(c_List_Ozip(_1685499, _1685499), _1685495), _1685497)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1685499, _1685499, tc_HOL_Obool), c_fequal), _1685651)))], (46228 ^ _774244) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685499)), _1685495) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685499)), _1685497))]]], (30461 ^ _774244) ^ [_1317633, _1317635, _1317637, _1317639, _1317641, _1317643] : [c_Typedef_Otype__definition(_1317633, _1317635, _1317637, _1317639, _1317641), -(hAPP(_1317639, hAPP(_1317637, _1317643)) = _1317643)], (28759 ^ _774244) ^ [_1284993, _1284995, _1284997, _1284999] : [28760 ^ _774244 : [(28763 ^ _774244) ^ [] : [hBOOL(hAPP(_1284997, _1284999))], (28761 ^ _774244) ^ [] : [_1284995 = _1284999]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1284993), _1284995), _1284997), _1284999)))], (48614 ^ _774244) ^ [_1745688, _1745690, _1745692] : [hBOOL(hAPP(c_List_Odistinct(_1745688), hAPP(c_List_Orotate(_1745688, _1745690), _1745692))), -(hBOOL(hAPP(c_List_Odistinct(_1745688), _1745692)))], (32034 ^ _774244) ^ [_1353870, _1353872, _1353874, _1353876, _1353878, _1353880, _1353882] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353870, tc_fun(_1353872, tc_fun(_1353874, tc_HOL_Obool))), _1353876), _1353878), _1353880), _1353882)), 32038 ^ _774244 : [(32041 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1353878, 32037 ^ [_1353870, _1353872, _1353874, _1353876, _1353878, _1353880, _1353882]), _1353880), _1353882)))], (32039 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1353870), 32037 ^ [_1353870, _1353872, _1353874, _1353876, _1353878, _1353880, _1353882]), _1353876)))]]], (10708 ^ _774244) ^ [_950353, _950355, _950357] : [class_Orderings_Olinorder(_950353), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950353), _950355), _950357)), 10715 ^ _774244 : [(10722 ^ _774244) ^ [] : [_950355 = _950357, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950353), _950355), _950357))], (10716 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950353), _950355), _950357))), -(_950355 = _950357)]]], (31075 ^ _774244) ^ [_1331624, _1331626] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1331624)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1331626))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1331624), _1331626)))], (9951 ^ _774244) ^ [_938254] : [-(_938254 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9954 ^ _774244 : [(9961 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _938254))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _938254) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9955 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _938254)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _938254) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (24455 ^ _774244) ^ [_1199578, _1199580, _1199582, _1199584, _1199586, _1199588] : [hAPP(_1199584, hAPP(c_Product__Type_Ofst(_1199578, _1199582), _1199586)) = hAPP(_1199588, hAPP(c_Product__Type_Ofst(_1199578, _1199582), _1199586)), -(hAPP(c_Product__Type_Oapfst(_1199578, _1199580, _1199582, _1199584), _1199586) = hAPP(c_Product__Type_Oapfst(_1199578, _1199580, _1199582, _1199588), _1199586))], (35544 ^ _774244) ^ [_1427935, _1427937, _1427939] : [_1427937 = c_Orderings_Obot__class_Obot(tc_fun(_1427935, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427935, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1427935), _1427937), _1427939))], (51077 ^ _774244) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (14470 ^ _774244) ^ [_1016644, _1016646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1016644), 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)), _1016646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016644), _1016646)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29776 ^ _774244) ^ [_1304584, _1304586] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1304584), c_Orderings_Otop__class_Otop(tc_fun(_1304584, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304586), c_Orderings_Otop__class_Otop(tc_fun(_1304586, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1304584, _1304586)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1304584, _1304586), tc_HOL_Obool)))))], (32568 ^ _774244) ^ [_1364554] : [class_Rings_Osemiring__1(_1364554), -(hBOOL(hAPP(hAPP(c_member(_1364554), c_Groups_Ozero__class_Ozero(_1364554)), c_Nat_Osemiring__1__class_ONats(_1364554))))], (10674 ^ _774244) ^ [_949818, _949820, _949822] : [class_Orderings_Oorder(_949818), -(_949820 = _949822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949818), _949822), _949820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949818), _949822), _949820)))], (19327 ^ _774244) ^ [] : [-(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))))], (39506 ^ _774244) ^ [_1515728, _1515730, _1515732] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1515728, _1515730, c_Orderings_Obot__class_Obot(tc_fun(_1515728, tc_HOL_Obool))), _1515732))], (45545 ^ _774244) ^ [_1668497, _1668499, _1668501] : [c_Fun_Oinj__on(tc_List_Olist(_1668497), tc_List_Olist(_1668499), hAPP(c_List_Omap(_1668497, _1668499), _1668501), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1668497), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1668497, _1668499, _1668501, c_Orderings_Otop__class_Otop(tc_fun(_1668497, tc_HOL_Obool))))], (6388 ^ _774244) ^ [_876985, _876987] : [c_Option_Ooption_ONone(_876985) = hAPP(c_Option_Ooption_OSome(_876985), _876987)], (13706 ^ _774244) ^ [_1002844, _1002846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002844), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002846), _1002844)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1002844, _1002846) = _1002844)], (43859 ^ _774244) ^ [_1627747, _1627749, _1627751, _1627753] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627747, _1627747)), hAPP(hAPP(c_Product__Type_OPair(_1627747, _1627747), _1627749), _1627751)), c_Transitive__Closure_Ortrancl(_1627747, _1627753))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1627747, _1627747)), hAPP(hAPP(c_Product__Type_OPair(_1627747, _1627747), _1627751), _1627749)), c_Transitive__Closure_Ortrancl(_1627747, hAPP(c_Relation_Oconverse(_1627747, _1627747), _1627753)))))], (35320 ^ _774244) ^ [] : [-(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))], (10836 ^ _774244) ^ [_952256, _952258, _952260, _952262] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_952256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952256), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952256), _952258), _952260)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952256), _952262), _952260))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952256), _952258), _952262)))], (14117 ^ _774244) ^ [_1010569, _1010571, _1010573] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1010569), _1010571)), _1010573) = 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), _1010569), _1010573)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1010571), _1010573))), 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, _1010569, _1010573)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1010571, _1010573))), _1010573)))], (50921 ^ _774244) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (45726 ^ _774244) ^ [_1673046, _1673048, _1673050, _1673052, _1673054] : [hAPP(c_Map_Omap__of(_1673046, _1673048, _1673050), _1673052) = hAPP(c_Option_Ooption_OSome(_1673048), _1673054), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1673046, _1673048)), hAPP(hAPP(c_Product__Type_OPair(_1673046, _1673048), _1673052), _1673054)), hAPP(c_List_Oset(tc_prod(_1673046, _1673048)), _1673050))))], (47577 ^ _774244) ^ [_1719965, _1719967, _1719969, _1719971, _1719973] : [hAPP(hAPP(c_List_Oappend(_1719965), _1719967), _1719969) = hAPP(hAPP(c_List_Oappend(_1719965), _1719971), _1719973), 47583 ^ _774244 : [(47586 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1719965), 47580 ^ [_1719965, _1719967, _1719969, _1719971, _1719973]), _1719969) = _1719973)], (47584 ^ _774244) ^ [] : [-(_1719967 = hAPP(hAPP(c_List_Oappend(_1719965), _1719971), 47580 ^ [_1719965, _1719967, _1719969, _1719971, _1719973]))]], 47587 ^ _774244 : [(47590 ^ _774244) ^ [] : [-(_1719969 = hAPP(hAPP(c_List_Oappend(_1719965), 47580 ^ [_1719965, _1719967, _1719969, _1719971, _1719973]), _1719973))], (47588 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1719965), _1719967), 47580 ^ [_1719965, _1719967, _1719969, _1719971, _1719973]) = _1719971)]]], (43375 ^ _774244) ^ [_1613944, _1613946, _1613948, _1613950, _1613952, _1613954, _1613956, _1613958] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613944, tc_fun(_1613946, tc_fun(_1613948, tc_HOL_Obool))), _1613950), _1613952), _1613954), _1613956)), hBOOL(hAPP(hAPP(c_member(_1613944), _1613958), _1613950)), -(hBOOL(hAPP(hAPP(hAPP(_1613952, _1613958), _1613954), _1613956)))], (18441 ^ _774244) ^ [_1088935, _1088937] : [class_Int_Onumber__ring(_1088935), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088935), hAPP(c_Int_Onumber__class_Onumber__of(_1088935), _1088937)), c_Groups_Oone__class_Oone(_1088935)) = hAPP(c_Int_Onumber__class_Onumber__of(_1088935), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088937), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (51505 ^ _774244) ^ [_1802269, _1802271] : [-(hBOOL(_1802269)), -(hBOOL(hAPP(hAPP(c_fimplies, _1802269), _1802271)))], (28352 ^ _774244) ^ [_1275651, _1275653, _1275655] : [class_Orderings_Olinorder(_1275651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275651), _1275653), _1275655)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275651, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1275651, _1275653, _1275655)), hAPP(c_SetInterval_Oord__class_OatLeast(_1275651), _1275655)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1275651), _1275653))], (48112 ^ _774244) ^ [_1732841, _1732843, _1732845, _1732847, _1732849] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1732841), tc_List_Olist(_1732841))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1732841), tc_List_Olist(_1732841)), _1732843), _1732845)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1732841), c_List_Olistrel1(_1732841, _1732847)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1732841), tc_List_Olist(_1732841))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1732841), tc_List_Olist(_1732841)), hAPP(hAPP(c_List_Olist_OCons(_1732841), _1732849), _1732843)), hAPP(hAPP(c_List_Olist_OCons(_1732841), _1732849), _1732845))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1732841), c_List_Olistrel1(_1732841, _1732847)))))], (4606 ^ _774244) ^ [_845431, _845433, _845435, _845437] : [-(c_List_Olexord(_845437, _845433) = c_List_Olexord(_845435, _845431)), _845437 = _845435, _845433 = _845431], (46990 ^ _774244) ^ [_1705110, _1705112, _1705114] : [-(hAPP(c_Map_Omap__of(_1705110, _1705112, c_List_Olist_ONil(tc_prod(_1705110, _1705112))), _1705114) = c_Option_Ooption_ONone(_1705112))], (12011 ^ _774244) ^ [_972927, _972929, _972931] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972927), _972929)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972927), _972931)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _972927)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972929), _972931))], (24609 ^ _774244) ^ [_1202846, _1202848, _1202850, _1202852, _1202854] : [-(_1202846 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1202848, _1202850, _1202852, _1202854), _1202846) = c_Lazy__Sequence_Ohb__bind(_1202848, _1202850, hAPP(_1202852, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1202846), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1202848, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1202850))), _1202854), _1202846)))], (49222 ^ _774244) ^ [_1758873, _1758875, _1758877] : [-(_1758873 = c_List_Olist_ONil(_1758875)), -(c_List_Obutlast(_1758875, hAPP(hAPP(c_List_Oappend(_1758875), _1758877), _1758873)) = hAPP(hAPP(c_List_Oappend(_1758875), _1758877), c_List_Obutlast(_1758875, _1758873)))], (33562 ^ _774244) ^ [_1383499, _1383501, _1383503] : [class_Orderings_Olinorder(_1383499), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383499), _1383501)), -(_1383501 = c_Orderings_Obot__class_Obot(tc_fun(_1383499, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1383499, c_Orderings_Oord__class_Omax(_1383499), hAPP(hAPP(c_Set_Oinsert(_1383499), _1383503), _1383501)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1383499), _1383503), c_Big__Operators_Olattice_OSup__fin(_1383499, c_Orderings_Oord__class_Omax(_1383499), _1383501)))], (45639 ^ _774244) ^ [_1671100] : [-(hAPP(c_Option_Omap(_1671100, _1671100), c_COMBI(_1671100)) = c_Fun_Oid(tc_Option_Ooption(_1671100)))], (34624 ^ _774244) ^ [_1405877, _1405879, _1405881, _1405883] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1405877), _1405883) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1405881), _1405879), -(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), _1405877), _1405879)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1405881), _1405883))), c_Int_Ointrel)))], (40551 ^ _774244) ^ [_1540479, _1540481, _1540483] : [hBOOL(hAPP(_1540479, _1540481)), -(hBOOL(hAPP(hAPP(c_member(_1540483), _1540481), hAPP(c_Set_OCollect(_1540483), _1540479))))], (2314 ^ _774244) ^ [_809123, _809125, _809127, _809129] : [-(c_Nat__Transfer_Otsub(_809129, _809125) = c_Nat__Transfer_Otsub(_809127, _809123)), _809129 = _809127, _809125 = _809123], (27982 ^ _774244) ^ [_1268427, _1268429, _1268431, _1268433] : [class_Lattices_Osemilattice__sup(_1268427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268427), _1268429), _1268431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268427), _1268433), _1268431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268427), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268427), _1268429), _1268433)), _1268431)))], (6600 ^ _774244) ^ [_880573, _880575] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _880573), _880575) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6605 ^ _774244 : [(6608 ^ _774244) ^ [] : [-(_880575 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6606 ^ _774244) ^ [] : [-(_880573 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6609 ^ _774244 : [(6612 ^ _774244) ^ [] : [-(_880575 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6610 ^ _774244) ^ [] : [-(_880573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7936 ^ _774244) ^ [_903947, _903949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _903947)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _903949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _903947), _903949)))], (49296 ^ _774244) ^ [_1760458, _1760460, _1760462, _1760464, _1760466] : [c_List_Opartition(_1760458, _1760460, _1760462) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1760458), tc_List_Olist(_1760458)), _1760464), _1760466), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1760458, tc_HOL_Obool)), hAPP(c_List_Oset(_1760458), _1760464)), hAPP(c_List_Oset(_1760458), _1760466)) = hAPP(c_List_Oset(_1760458), _1760462))], (41833 ^ _774244) ^ [_1578946, _1578948] : [c_Wellfounded_OwfP(_1578946, hAPP(hAPP(c_COMBC(_1578946, tc_fun(tc_prod(_1578946, _1578946), tc_HOL_Obool), tc_fun(_1578946, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578946, tc_fun(tc_fun(tc_prod(_1578946, _1578946), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1578946, _1578946), tc_HOL_Obool), tc_fun(_1578946, tc_HOL_Obool)), _1578946), c_COMBC(_1578946, tc_fun(tc_prod(_1578946, _1578946), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578946, tc_prod(_1578946, _1578946)), tc_fun(_1578946, tc_fun(tc_fun(tc_prod(_1578946, _1578946), tc_HOL_Obool), tc_HOL_Obool)), _1578946), hAPP(c_COMBB(tc_prod(_1578946, _1578946), tc_fun(tc_fun(tc_prod(_1578946, _1578946), tc_HOL_Obool), tc_HOL_Obool), _1578946), c_member(tc_prod(_1578946, _1578946)))), c_Product__Type_OPair(_1578946, _1578946)))), _1578948)), -(c_Wellfounded_Owf(_1578946, _1578948))], (19989 ^ _774244) ^ [_1116347, _1116349, _1116351] : [class_Fields_Olinordered__field__inverse__zero(_1116347), 19992 ^ _774244 : [(20007 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116347), c_Groups_Ozero__class_Ozero(_1116347)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116347), _1116349), _1116351)))), 20008 ^ _774244 : [(20015 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116347), _1116349), c_Groups_Ozero__class_Ozero(_1116347))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116347), _1116351), c_Groups_Ozero__class_Ozero(_1116347)))], (20009 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116347), c_Groups_Ozero__class_Ozero(_1116347)), _1116349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116347), c_Groups_Ozero__class_Ozero(_1116347)), _1116351))]]], (19993 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116347), c_Groups_Ozero__class_Ozero(_1116347)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116347), _1116349), _1116351))), 19998 ^ _774244 : [(20001 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116347), c_Groups_Ozero__class_Ozero(_1116347)), _1116351)))], (19999 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116347), c_Groups_Ozero__class_Ozero(_1116347)), _1116349)))]], 20002 ^ _774244 : [(20005 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116347), _1116351), c_Groups_Ozero__class_Ozero(_1116347))))], (20003 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116347), _1116349), c_Groups_Ozero__class_Ozero(_1116347))))]]]]], (42774 ^ _774244) ^ [_1600153, _1600155, _1600157] : [class_Orderings_Olinorder(_1600153), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600153), _1600155)), -(hBOOL(hAPP(hAPP(c_member(_1600153), _1600157), _1600155))), -(c_Big__Operators_Olinorder__class_OMax(_1600153, hAPP(hAPP(c_Set_Oinsert(_1600153), _1600157), _1600155)) = hAPP(hAPP(c_Finite__Set_Ofold(_1600153, _1600153, c_Orderings_Oord__class_Omax(_1600153)), _1600157), _1600155))], (28200 ^ _774244) ^ [_1272671, _1272673] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1272671), _1272673) = 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)), _1272671)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1272673))))], (39500 ^ _774244) ^ [_1515609, _1515611, _1515613, _1515615] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1515609, _1515611, _1515613), _1515615)), _1515613 = c_Orderings_Obot__class_Obot(tc_fun(_1515609, tc_HOL_Obool))], (35376 ^ _774244) ^ [_1423923, _1423925, _1423927, _1423929, _1423931, _1423933, _1423935, _1423937, _1423939, _1423941, _1423943] : [c_Finite__Set_Ofolding(_1423923, _1423925, _1423927, _1423929), -(hAPP(c_Fun_Ocomp(_1423931, _1423933, _1423935, _1423937), hAPP(c_Fun_Ocomp(_1423939, _1423931, _1423935, _1423941), _1423943)) = hAPP(c_Fun_Ocomp(_1423939, _1423933, _1423935, hAPP(c_Fun_Ocomp(_1423931, _1423933, _1423939, _1423937), _1423941)), _1423943))], (48656 ^ _774244) ^ [_1746566, _1746568, _1746570] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1746566, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746568)), _1746570)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1746568, _1746566), _1746570) = _1746570)], (18847 ^ _774244) ^ [_1095640, _1095642] : [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), _1095640))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1095642)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1095640))) = 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), _1095642), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1095640)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38279 ^ _774244) ^ [_1487984, _1487986, _1487988] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1487984), _1487986)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1487984, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1487984, _1487984, _1487988), _1487986)), _1487986)), c_Fun_Oinj__on(_1487984, _1487984, _1487988, _1487986), -(hAPP(c_Set_Oimage(_1487984, _1487984, _1487988), _1487986) = _1487986)], (34952 ^ _774244) ^ [_1413634, _1413636] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1413634, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1413634, tc_HOL_Obool))), hAPP(c_Set_OPow(_1413634), _1413636))))], (39666 ^ _774244) ^ [_1520723, _1520725, _1520727, _1520729, _1520731, _1520733] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1520723, _1520725)), hAPP(hAPP(c_Product__Type_OPair(_1520723, _1520725), _1520727), _1520729)), hAPP(hAPP(c_Product__Type_OSigma(_1520723, _1520725), _1520731), _1520733))), 39669 ^ _774244 : [(39672 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1520725), _1520729), hAPP(_1520733, _1520727))))], (39670 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1520723), _1520727), _1520731)))]]], (18111 ^ _774244) ^ [_1083725] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1083725), c_Int_OPls) = _1083725)], (16002 ^ _774244) ^ [_1046225, _1046227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046227), _1046225))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1046227), _1046225) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046227), _1046225)), _1046225)))], (17547 ^ _774244) ^ [_1074817, _1074819] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074817))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1074817)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1074819)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4838 ^ _774244) ^ [_849029, _849031, _849033, _849035] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_849035, _849031) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_849033, _849029)), _849035 = _849033, _849031 = _849029], (27263 ^ _774244) ^ [_1254429, _1254431] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254429) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254431), -(_1254429 = _1254431)], (19851 ^ _774244) ^ [_1113981, _1113983, _1113985] : [class_Fields_Ofield__inverse__zero(_1113981), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113981), hAPP(c_Groups_Ouminus__class_Ouminus(_1113981), _1113983)), hAPP(c_Groups_Ouminus__class_Ouminus(_1113981), _1113985)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113981), _1113983), _1113985))], (51277 ^ _774244) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (7133 ^ _774244) ^ [_890092, _890094] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(_890092, _890094)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48041 ^ _774244) ^ [_1730837, _1730839, _1730841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730837), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730839)), _1730841))), -(hAPP(hAPP(c_List_Otake(_1730839), hAPP(c_Nat_OSuc, _1730837)), _1730841) = hAPP(hAPP(c_List_Oappend(_1730839), hAPP(hAPP(c_List_Otake(_1730839), _1730837), _1730841)), hAPP(hAPP(c_List_Olist_OCons(_1730839), hAPP(hAPP(c_List_Onth(_1730839), _1730841), _1730837)), c_List_Olist_ONil(_1730839))))], (7567 ^ _774244) ^ [_897471, _897473] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OAss(_897471, _897473)], (15906 ^ _774244) ^ [_1044537, _1044539] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044537, _1044539) = 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), _1044537), _1044539) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33948 ^ _774244) ^ [_1391126, _1391128, _1391130, _1391132, _1391134, _1391136] : [class_Groups_Ocomm__monoid__mult(_1391126), hBOOL(hAPP(c_Finite__Set_Ofinite(_1391128), _1391130)), 33955 ^ _774244 : [(33962 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391128), _1391132), _1391130))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391128, _1391126), hAPP(hAPP(c_COMBC(_1391128, _1391126, _1391126), hAPP(hAPP(c_COMBS(_1391128, _1391126, tc_fun(_1391126, _1391126)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1391126, tc_fun(_1391126, _1391126)), _1391128), c_If(_1391126)), hAPP(hAPP(c_COMBC(_1391128, _1391128, tc_HOL_Obool), c_fequal), _1391132))), _1391134)), _1391136)), _1391130) = hAPP(hAPP(c_Power_Opower__class_Opower(_1391126), _1391136), hAPP(c_Finite__Set_Ocard(_1391128), _1391130)))], (33956 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1391128), _1391132), _1391130)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391128, _1391126), hAPP(hAPP(c_COMBC(_1391128, _1391126, _1391126), hAPP(hAPP(c_COMBS(_1391128, _1391126, tc_fun(_1391126, _1391126)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1391126, tc_fun(_1391126, _1391126)), _1391128), c_If(_1391126)), hAPP(hAPP(c_COMBC(_1391128, _1391128, tc_HOL_Obool), c_fequal), _1391132))), _1391134)), _1391136)), _1391130) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391126), hAPP(_1391134, _1391132)), hAPP(hAPP(c_Power_Opower__class_Opower(_1391126), _1391136), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1391128), _1391130)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (19701 ^ _774244) ^ [_1111078, _1111080] : [class_Int_Onumber__ring(_1111078), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1111078), hAPP(c_Int_Onumber__class_Onumber__of(_1111078), 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)))), _1111080))) = hAPP(c_Int_Onumber__class_Onumber__of(_1111078), c_Int_OMin))], (13038 ^ _774244) ^ [_990741, _990743, _990745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990741)), _990741 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _990743), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _990741), _990745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _990745), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (45596 ^ _774244) ^ [_1669720, _1669722, _1669724, _1669726, _1669728] : [-(c_Map_Omap__of(_1669720, _1669722, hAPP(hAPP(c_List_Omap(tc_prod(_1669720, _1669724), tc_prod(_1669720, _1669722)), hAPP(c_Product__Type_Oprod_Oprod__case(_1669720, _1669724, tc_prod(_1669720, _1669722)), hAPP(hAPP(c_COMBC(_1669720, tc_fun(_1669724, _1669722), tc_fun(_1669724, tc_prod(_1669720, _1669722))), hAPP(hAPP(c_COMBB(tc_fun(_1669722, tc_prod(_1669720, _1669722)), tc_fun(tc_fun(_1669724, _1669722), tc_fun(_1669724, tc_prod(_1669720, _1669722))), _1669720), c_COMBB(_1669722, tc_prod(_1669720, _1669722), _1669724)), c_Product__Type_OPair(_1669720, _1669722))), _1669726))), _1669728)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1669724), tc_Option_Ooption(_1669722), _1669720, hAPP(c_Option_Omap(_1669724, _1669722), _1669726)), c_Map_Omap__of(_1669720, _1669724, _1669728)))], (40511 ^ _774244) ^ [_1539664] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1539664), c_Int_OInteg)), -(_1539664 = hAPP(c_Int_ORep__Integ, 40514 ^ [_1539664]))], (41766 ^ _774244) ^ [_1577385, _1577387, _1577389] : [c_Wellfounded_OwfP(_1577385, _1577387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1577385, tc_fun(_1577385, tc_HOL_Obool))), _1577389), _1577387)), -(c_Wellfounded_OwfP(_1577385, _1577389))], (34057 ^ _774244) ^ [_1393568, _1393570, _1393572, _1393574] : [class_Rings_Ocomm__semiring__1(_1393568), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393570), _1393572)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1393570, _1393568), _1393574), _1393572) = c_Groups_Ozero__class_Ozero(_1393568)), 34066 ^ _774244 : [(34067 ^ _774244) ^ [_1393749] : [hBOOL(hAPP(hAPP(c_member(_1393570), _1393749), _1393572)), hAPP(_1393574, _1393749) = c_Groups_Ozero__class_Ozero(_1393568)]]], (43540 ^ _774244) ^ [_1619227, _1619229, _1619231, _1619233] : [-(hAPP(c_Relation_Oconverse(_1619227, _1619229), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1619227, _1619229), tc_HOL_Obool)), _1619231), _1619233)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1619229, _1619227), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1619227, _1619229), _1619231)), hAPP(c_Relation_Oconverse(_1619227, _1619229), _1619233)))], (12057 ^ _774244) ^ [_973814, _973816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973814), _973816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973814)), _973816)))], (15606 ^ _774244) ^ [_1037713, _1037715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037713), _1037715)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037715), _1037713)), _1037713) = _1037715)], (45567 ^ _774244) ^ [_1669102, _1669104, _1669106, _1669108, _1669110] : [-(c_Map_Omap__comp(_1669102, _1669104, _1669106, hAPP(c_COMBK(tc_Option_Ooption(_1669104), _1669102), c_Option_Ooption_ONone(_1669104)), _1669108, _1669110) = c_Option_Ooption_ONone(_1669104))], (22052 ^ _774244) ^ [_1153053] : [-(c_Divides_Odivmod__nat(_1153053, 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)), _1153053))], (26756 ^ _774244) ^ [_1243920, _1243922, _1243924, _1243926, _1243928] : [class_Groups_Ocomm__monoid__add(_1243920), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1243922), _1243924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1243924), _1243926)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1243920), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1243920), _1243928), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1243922), _1243924))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1243920), _1243928), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1243924), _1243926))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1243920), _1243928), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1243922), _1243926)))], (3414 ^ _774244) ^ [_826695, _826697, _826699, _826701] : [-(c_Sum__Type_OInl(_826701, _826697) = c_Sum__Type_OInl(_826699, _826695)), _826701 = _826699, _826697 = _826695], (36251 ^ _774244) ^ [_1443118, _1443120, _1443122, _1443124, _1443126] : [-(c_Map_Orestrict__map(_1443118, _1443120, c_Map_Orestrict__map(_1443118, _1443120, _1443122, _1443124), _1443126) = c_Map_Orestrict__map(_1443118, _1443120, _1443122, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443118, tc_HOL_Obool)), _1443124), _1443126)))], (49920 ^ _774244) ^ [_1773184, _1773186, _1773188, _1773190, _1773192] : [class_Orderings_Olinorder(_1773184), c_List_Olinorder__class_Osorted(_1773184, hAPP(hAPP(c_List_Omap(_1773186, _1773184), _1773188), _1773190)), -(c_List_Olinorder__class_Osorted(_1773184, hAPP(hAPP(c_List_Omap(_1773186, _1773184), _1773188), c_List_Olinorder__class_Oinsort__insert__key(_1773186, _1773184, _1773188, _1773192, _1773190))))], (5899 ^ _774244) ^ [_868645, _868647, _868649, _868651, _868653] : [c_Natural_Oevalc(c_Com_Ocom_OCond(_868645, _868647, _868649), _868651, _868653), 5904 ^ _774244 : [(5907 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_868647, _868651, _868653))], (5905 ^ _774244) ^ [] : [-(hBOOL(hAPP(_868645, _868651)))]], 5908 ^ _774244 : [(5911 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_868649, _868651, _868653))], (5909 ^ _774244) ^ [] : [hBOOL(hAPP(_868645, _868651))]]], (16453 ^ _774244) ^ [_1054257, _1054259, _1054261] : [class_Groups_Oordered__ab__group__add__abs(_1054257), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054257), hAPP(c_Groups_Oabs__class_Oabs(_1054257), _1054259)), _1054261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054257), hAPP(c_Groups_Ouminus__class_Ouminus(_1054257), _1054259)), _1054261)))], (48825 ^ _774244) ^ [_1750107, _1750109, _1750111, _1750113] : [class_Complete__Lattice_Ocomplete__lattice(_1750107), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1750109, _1750107), hAPP(c_List_Oset(_1750109), _1750111)), _1750113) = hAPP(c_List_Ofoldl(_1750107, _1750109, hAPP(c_COMBC(_1750109, _1750107, _1750107), hAPP(hAPP(c_COMBB(_1750107, tc_fun(_1750107, _1750107), _1750109), c_Lattices_Osemilattice__sup__class_Osup(_1750107)), _1750113)), c_Orderings_Obot__class_Obot(_1750107)), _1750111))], (29520 ^ _774244) ^ [_1299912, _1299914] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1299912), _1299914))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1299912), hAPP(c_Nat_OSuc, _1299914)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (23817 ^ _774244) ^ [_1187459, _1187461, _1187463, _1187465] : [class_Orderings_Olinorder(_1187459), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187459), _1187461), _1187463)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187459), _1187461), _1187465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187459), _1187461), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187459), _1187463), _1187465))))], (18713 ^ _774244) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (44994 ^ _774244) ^ [_1655757, _1655759, _1655761, _1655763, _1655765] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1655757, _1655757)), hAPP(hAPP(c_Product__Type_OPair(_1655757, _1655757), _1655759), _1655761)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1655757, _1655757), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1655763)), _1655765))), 44998 ^ _774244 : [(45001 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655757, _1655757)), hAPP(hAPP(c_Product__Type_OPair(_1655757, _1655757), 44997 ^ [_1655757, _1655759, _1655761, _1655763, _1655765]), _1655761)), _1655765)))], (44999 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655757, _1655757)), hAPP(hAPP(c_Product__Type_OPair(_1655757, _1655757), _1655759), 44997 ^ [_1655757, _1655759, _1655761, _1655763, _1655765])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1655757, _1655757), tc_HOL_Obool), _1655763), _1655765))))]]], (51211 ^ _774244) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (25577 ^ _774244) ^ [_1220274, _1220276, _1220278, _1220280] : [class_Divides_Osemiring__div(_1220274), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220274), _1220276), _1220278)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220274), _1220276), _1220280)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1220274), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220274), _1220278), _1220280)), _1220276) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220274), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1220274), _1220278), _1220276)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1220274), _1220280), _1220276)))], (9162 ^ _774244) ^ [_924268, _924270, _924272, _924274, _924276] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_924268), 9165 ^ _774244 : [(9166 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924268), _924270), _924274)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924268), _924272), _924276)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924268), _924270), _924276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924268), _924272), _924274)), -(_924270 = _924272), -(_924274 = _924276)], (9176 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924268), _924270), _924274)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924268), _924272), _924276)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924268), _924270), _924276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924268), _924272), _924274))), 9179 ^ _774244 : [(9182 ^ _774244) ^ [] : [_924274 = _924276], (9180 ^ _774244) ^ [] : [_924270 = _924272]]]]], (30386 ^ _774244) ^ [_1315980, _1315982, _1315984, _1315986] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1315980), _1315982)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315980, tc_HOL_Obool)), _1315982), _1315984)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1315980, tc_Nat_Onat), _1315986), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1315980, tc_HOL_Obool)), _1315984), _1315982)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1315980, tc_Nat_Onat), _1315986), _1315984)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1315980, tc_Nat_Onat), _1315986), _1315982)))], (32365 ^ _774244) ^ [_1360561, _1360563, _1360565] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1360561, tc_HOL_Obool)), _1360563), hAPP(hAPP(c_Set_Oinsert(_1360561), _1360565), c_Orderings_Obot__class_Obot(tc_fun(_1360561, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1360561, _1360565, _1360563) = c_HOL_OThe(_1360561, hAPP(hAPP(c_COMBC(_1360561, tc_fun(_1360561, tc_HOL_Obool), tc_HOL_Obool), c_member(_1360561)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360561, tc_HOL_Obool)), _1360563), hAPP(hAPP(c_Set_Oinsert(_1360561), _1360565), c_Orderings_Obot__class_Obot(tc_fun(_1360561, tc_HOL_Obool)))))))], (50725 ^ _774244) ^ [_1791667, _1791669] : [hBOOL(hAPP(c_List_Odistinct(_1791667), _1791669)), -(c_List_Oremdups(_1791667, _1791669) = _1791669)], (26770 ^ _774244) ^ [_1244243, _1244245, _1244247, _1244249, _1244251] : [class_Groups_Oab__group__add(_1244243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1244245), _1244247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1244247), _1244249)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1244243), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1244243), _1244251), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244245), _1244249))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1244243), _1244251), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244245), _1244247))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1244243), _1244251), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244247), _1244249)))], (19189 ^ _774244) ^ [_1101715, _1101717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1101715)), c_Int_OBit0(_1101717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101715), _1101717)))], (29037 ^ _774244) ^ [_1291093, _1291095, _1291097, _1291099] : [_1291093 = c_Orderings_Obot__class_Obot(tc_fun(_1291095, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291095, tc_fun(_1291097, tc_HOL_Obool)), _1291093), hAPP(c_COMBK(tc_fun(_1291097, tc_HOL_Obool), _1291095), _1291099)) = c_Orderings_Obot__class_Obot(tc_fun(_1291097, tc_HOL_Obool)))], (24551 ^ _774244) ^ [_1201603, _1201605, _1201607, _1201609, _1201611, _1201613, _1201615] : [_1201603 = _1201605, -(hAPP(c_Sum__Type_Osum_Osum__case(_1201607, _1201609, _1201611, _1201613, _1201615), _1201603) = hAPP(c_Sum__Type_Osum_Osum__case(_1201607, _1201609, _1201611, _1201613, _1201615), _1201605))], (24023 ^ _774244) ^ [_1191374, _1191376, _1191378, _1191380] : [class_Orderings_Olinorder(_1191374), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191374), _1191376), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191374), _1191378), _1191380)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191374), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191374), _1191376), _1191378)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191374), _1191376), _1191380)))], (35229 ^ _774244) ^ [_1419910, _1419912, _1419914, _1419916, _1419918, _1419920, _1419922] : [hAPP(c_Fun_Ocomp(_1419910, _1419912, _1419914, _1419916), _1419918) = _1419920, -(hAPP(_1419916, hAPP(_1419918, _1419922)) = hAPP(_1419920, _1419922))], (42467 ^ _774244) ^ [_1594201, _1594203, _1594205, _1594207] : [class_Lattices_Osemilattice__sup(_1594201), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594201), _1594203)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1594201, _1594201, c_Lattices_Osemilattice__sup__class_Osup(_1594201)), _1594205), hAPP(hAPP(c_Set_Oinsert(_1594201), _1594207), _1594203)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1594201), _1594207), hAPP(hAPP(c_Finite__Set_Ofold(_1594201, _1594201, c_Lattices_Osemilattice__sup__class_Osup(_1594201)), _1594205), _1594203)))], (24545 ^ _774244) ^ [_1201351, _1201353, _1201355, _1201357, _1201359, _1201361, _1201363] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1201351, _1201353, _1201355, _1201357), _1201359), _1201361), _1201363) = hAPP(hAPP(_1201361, hAPP(c_Product__Type_Ofst(_1201353, _1201355), hAPP(_1201359, _1201363))), hAPP(c_Product__Type_Osnd(_1201353, _1201355), hAPP(_1201359, _1201363))))], (18989 ^ _774244) ^ [_1098238, _1098240] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1098238)), c_Int_OBit0(_1098240)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1098238), _1098240)))], (15518 ^ _774244) ^ [_1035991, _1035993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035991), _1035993)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1035993)), _1035991) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035993), _1035991)))], (44612 ^ _774244) ^ [_1646546, _1646548, _1646550] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646546, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646546, tc_HOL_Obool), _1646548)), _1646550) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1646546, tc_HOL_Obool), tc_fun(_1646546, tc_HOL_Obool)), _1646548), hAPP(hAPP(c_COMBC(tc_fun(_1646546, tc_HOL_Obool), tc_fun(_1646546, tc_HOL_Obool), tc_fun(_1646546, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646546, tc_HOL_Obool))), _1646550)))], (5394 ^ _774244) ^ [_857581, _857583] : [_857583 = _857581, -(c_Orderings_Oord__class_Oless__eq(_857583) = c_Orderings_Oord__class_Oless__eq(_857581))], (44773 ^ _774244) ^ [_1650177, _1650179, _1650181] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1650177, tc_HOL_Obool)), _1650179), _1650181) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1650177, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1650177, tc_HOL_Obool)), _1650179), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1650177, tc_HOL_Obool)), _1650181), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1650177, tc_HOL_Obool), tc_HOL_Obool))))))], (17625 ^ _774244) ^ [_1075944, _1075946, _1075948, _1075950] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1075944, _1075946, _1075948), _1075950), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1075946)], (51111 ^ _774244) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (17759 ^ _774244) ^ [_1078214, _1078216] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078214))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078214)), _1078216)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1078216))], (38994 ^ _774244) ^ [_1503898, _1503900, _1503902, _1503904] : [class_Groups_Ocomm__monoid__add(_1503898), 38997 ^ _774244 : [(39004 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1503900), _1503902))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503900, _1503898), _1503904), _1503902) = c_Groups_Ozero__class_Ozero(_1503898))], (38998 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503900), _1503902)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503900, _1503898), _1503904), _1503902) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1503898, _1503900, c_Groups_Oplus__class_Oplus(_1503898)), _1503904), c_Groups_Ozero__class_Ozero(_1503898)), _1503902))]]], (46022 ^ _774244) ^ [_1679965, _1679967, _1679969, _1679971, _1679973, _1679975, _1679977, _1679979] : [-(hAPP(hAPP(c_List_Ozip(_1679965, _1679967), hAPP(hAPP(c_List_Omap(_1679969, _1679965), _1679971), _1679973)), hAPP(hAPP(c_List_Omap(_1679975, _1679967), _1679977), _1679979)) = hAPP(hAPP(c_List_Omap(tc_prod(_1679969, _1679975), tc_prod(_1679965, _1679967)), hAPP(c_Product__Type_Oprod_Oprod__case(_1679969, _1679975, tc_prod(_1679965, _1679967)), hAPP(hAPP(c_COMBC(_1679969, tc_fun(_1679975, _1679967), tc_fun(_1679975, tc_prod(_1679965, _1679967))), hAPP(hAPP(c_COMBB(tc_fun(_1679967, tc_prod(_1679965, _1679967)), tc_fun(tc_fun(_1679975, _1679967), tc_fun(_1679975, tc_prod(_1679965, _1679967))), _1679969), c_COMBB(_1679967, tc_prod(_1679965, _1679967), _1679975)), hAPP(hAPP(c_COMBB(_1679965, tc_fun(_1679967, tc_prod(_1679965, _1679967)), _1679969), c_Product__Type_OPair(_1679965, _1679967)), _1679971))), _1679977))), hAPP(hAPP(c_List_Ozip(_1679969, _1679975), _1679973), _1679979)))], (44356 ^ _774244) ^ [_1640873] : [-(c_Nat_Ofunpow(_1640873) = c_Nat_Ocompow(_1640873, _1640873))], (47289 ^ _774244) ^ [_1713093, _1713095, _1713097, _1713099, _1713101, _1713103, _1713105] : [-(hAPP(hAPP(c_List_Ozip(_1713093, _1713095), hAPP(hAPP(c_List_Olist__update(_1713093, _1713097), _1713099), _1713101)), hAPP(hAPP(c_List_Olist__update(_1713095, _1713103), _1713099), _1713105)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1713093, _1713095), hAPP(hAPP(c_List_Ozip(_1713093, _1713095), _1713097), _1713103)), _1713099), hAPP(hAPP(c_Product__Type_OPair(_1713093, _1713095), _1713101), _1713105)))], (48646 ^ _774244) ^ [_1746304, _1746306, _1746308] : [-(hAPP(c_List_Orotate(_1746304, hAPP(c_Nat_OSuc, _1746306)), _1746308) = hAPP(c_List_Orotate1(_1746304), hAPP(c_List_Orotate(_1746304, _1746306), _1746308)))], (38920 ^ _774244) ^ [_1502285, _1502287, _1502289, _1502291] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1502285), _1502287)), c_Fun_Oinj__on(_1502289, _1502285, _1502291, c_Orderings_Otop__class_Otop(tc_fun(_1502289, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1502289), hAPP(c_Set_Ovimage(_1502289, _1502285, _1502291), _1502287))))], (40685 ^ _774244) ^ [_1543603, _1543605, _1543607] : [hBOOL(hAPP(_1543603, _1543605)), -(hAPP(c_Set_OCollect(_1543607), hAPP(hAPP(c_COMBS(_1543607, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543607), c_fconj), hAPP(hAPP(c_COMBC(_1543607, _1543607, tc_HOL_Obool), c_fequal), _1543605))), _1543603)) = hAPP(hAPP(c_Set_Oinsert(_1543607), _1543605), c_Orderings_Obot__class_Obot(tc_fun(_1543607, tc_HOL_Obool))))], (9678 ^ _774244) ^ [_933727, _933729] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _933727)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _933729), 9681 ^ _774244 : [(9684 ^ _774244) ^ [] : [-(_933729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9682 ^ _774244) ^ [] : [-(_933727 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (47516 ^ _774244) ^ [_1718447, _1718449, _1718451, _1718453, _1718455] : [hAPP(hAPP(c_List_Oappend(_1718447), _1718449), _1718451) = hAPP(hAPP(c_List_Olist_OCons(_1718447), _1718453), _1718455), 47521 ^ _774244 : [(47524 ^ _774244) ^ [] : [-(_1718451 = hAPP(hAPP(c_List_Olist_OCons(_1718447), _1718453), _1718455))], (47522 ^ _774244) ^ [] : [-(_1718449 = c_List_Olist_ONil(_1718447))]], 47526 ^ _774244 : [(47529 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1718447), 47525 ^ [_1718447, _1718449, _1718451, _1718453, _1718455]), _1718451) = _1718455)], (47527 ^ _774244) ^ [] : [-(_1718449 = hAPP(hAPP(c_List_Olist_OCons(_1718447), _1718453), 47525 ^ [_1718447, _1718449, _1718451, _1718453, _1718455]))]]], (46781 ^ _774244) ^ [_1701390] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1701390) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 46784 ^ _774244 : [(46785 ^ _774244) ^ [_1701465] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1701465), hAPP(c_List_Oset(tc_Nat_Onat), _1701390))), -(_1701465 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (39514 ^ _774244) ^ [_1515902, _1515904, _1515906, _1515908] : [_1515906 = _1515908, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1515902, _1515904, hAPP(hAPP(c_Set_Oinsert(_1515902), _1515906), c_Orderings_Obot__class_Obot(tc_fun(_1515902, tc_HOL_Obool)))), _1515908)))], (23251 ^ _774244) ^ [_1176309, _1176311, _1176313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1176309, tc_HOL_Obool)), _1176311), _1176313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1176309, tc_HOL_Obool)), _1176313), _1176311)), -(_1176311 = _1176313)], (47726 ^ _774244) ^ [_1723052, _1723054, _1723056] : [c_List_Olist_ONil(_1723052) = hAPP(hAPP(c_List_Oappend(_1723052), _1723054), _1723056), 47729 ^ _774244 : [(47732 ^ _774244) ^ [] : [-(_1723056 = c_List_Olist_ONil(_1723052))], (47730 ^ _774244) ^ [] : [-(_1723054 = c_List_Olist_ONil(_1723052))]]], (24017 ^ _774244) ^ [_1191215, _1191217, _1191219, _1191221] : [class_Orderings_Olinorder(_1191215), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191215), _1191217), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191215), _1191219), _1191221)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191215), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191215), _1191217), _1191219)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191215), _1191217), _1191221)))], (50573 ^ _774244) ^ [_1788932, _1788934, _1788936] : [hBOOL(hAPP(c_List_Odistinct(_1788932), _1788934)), -(hBOOL(hAPP(c_List_Odistinct(_1788932), c_List_OtakeWhile(_1788932, _1788936, _1788934))))], (18567 ^ _774244) ^ [_1091116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1091116)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091116), c_Int_OPls)))], (51389 ^ _774244) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (6945 ^ _774244) ^ [_886695, _886697, _886699, _886701] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_886695, _886697), _886699, _886701, _886699), hBOOL(hAPP(_886695, _886699)), 6953 ^ _774244 : [(6956 ^ _774244) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_886695, _886697), 6952 ^ [_886695, _886697, _886699, _886701], _886701, _886699))], (6954 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_886697, _886699, _886701, 6952 ^ [_886695, _886697, _886699, _886701]))]]], (29576 ^ _774244) ^ [_1301054, _1301056] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1301054), _1301056)), -(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)))), _1301056, _1301054) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (45643 ^ _774244) ^ [_1671194, _1671196, _1671198, _1671200, _1671202] : [hAPP(hAPP(c_Option_Omap(_1671194, _1671196), _1671198), _1671200) = hAPP(c_Option_Ooption_OSome(_1671196), _1671202), 45647 ^ _774244 : [(45650 ^ _774244) ^ [] : [-(hAPP(_1671198, 45646 ^ [_1671194, _1671196, _1671198, _1671200, _1671202]) = _1671202)], (45648 ^ _774244) ^ [] : [-(_1671200 = hAPP(c_Option_Ooption_OSome(_1671194), 45646 ^ [_1671194, _1671196, _1671198, _1671200, _1671202]))]]], (43345 ^ _774244) ^ [_1613325, _1613327, _1613329, _1613331, _1613333, _1613335] : [hBOOL(hAPP(hAPP(c_member(_1613325), _1613327), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613329, tc_fun(_1613325, tc_HOL_Obool)), _1613331), _1613333))), -(hBOOL(hAPP(hAPP(c_member(_1613325), _1613327), hAPP(_1613333, _1613335)))), hBOOL(hAPP(hAPP(c_member(_1613329), _1613335), _1613331))], (21169 ^ _774244) ^ [_1136837, _1136839, _1136841, _1136843] : [class_Fields_Olinordered__field(_1136837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136837), _1136839), _1136841)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136837), c_Groups_Ozero__class_Ozero(_1136837)), _1136843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136837), c_Groups_Ozero__class_Ozero(_1136837)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136837), _1136841), _1136839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136837), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136837), _1136843), _1136841)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136837), _1136843), _1136839))))], (44767 ^ _774244) ^ [_1650084] : [class_Complete__Lattice_Ocomplete__lattice(_1650084), -(c_Complete__Lattice_OSup__class_OSup(_1650084, c_Orderings_Otop__class_Otop(tc_fun(_1650084, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1650084))], (47989 ^ _774244) ^ [_1729693, _1729695, _1729697, _1729699] : [-(hAPP(hAPP(c_List_Otake(_1729693), _1729695), hAPP(hAPP(c_List_Olist_OCons(_1729693), _1729697), _1729699)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1729693), c_List_Olist_ONil(_1729693), hAPP(hAPP(c_COMBB(tc_List_Olist(_1729693), tc_List_Olist(_1729693), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1729693), _1729697)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1729693), tc_List_Olist(_1729693)), c_List_Otake(_1729693)), _1729699)), _1729695))], (41711 ^ _774244) ^ [_1576354, _1576356, _1576358] : [c_Wellfounded_Owf(_1576354, _1576356), c_Wellfounded_Owf(_1576354, _1576358), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1576354, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1576354, _1576354), _1576356)), hAPP(c_Relation_ORange(_1576354, _1576354), _1576358)) = c_Orderings_Obot__class_Obot(tc_fun(_1576354, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1576354, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1576354, _1576354), tc_HOL_Obool)), _1576356), _1576358)))], (4412 ^ _774244) ^ [_842542, _842544] : [_842544 = _842542, -(c_List_Orotate1(_842544) = c_List_Orotate1(_842542))], (15222 ^ _774244) ^ [_1030262, _1030264] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030262), _1030264)), _1030262)))], (45347 ^ _774244) ^ [_1663747, _1663749, _1663751, _1663753] : [c_Fun_Oinj__on(_1663747, tc_Option_Ooption(_1663749), c_Map_Omap__add(_1663747, _1663749, _1663751, _1663753), c_Map_Odom(_1663747, _1663749, _1663753)), -(c_Fun_Oinj__on(_1663747, tc_Option_Ooption(_1663749), _1663753, c_Map_Odom(_1663747, _1663749, _1663753)))], (46322 ^ _774244) ^ [_1687856, _1687858, _1687860, _1687862] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1687856), tc_List_Olist(_1687856))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1687856), tc_List_Olist(_1687856)), _1687858), _1687860)), c_List_Olistrel(_1687856, _1687862))), 46325 ^ _774244 : [(46328 ^ _774244) ^ [_1688192] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1687856, _1687856)), _1688192), hAPP(c_List_Oset(tc_prod(_1687856, _1687856)), hAPP(hAPP(c_List_Ozip(_1687856, _1687856), _1687858), _1687860)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1687856, _1687856, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1687856, tc_fun(tc_prod(_1687856, _1687856), tc_HOL_Obool), tc_fun(_1687856, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1687856, tc_fun(tc_fun(tc_prod(_1687856, _1687856), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1687856, _1687856), tc_HOL_Obool), tc_fun(_1687856, tc_HOL_Obool)), _1687856), c_COMBC(_1687856, tc_fun(tc_prod(_1687856, _1687856), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1687856, tc_prod(_1687856, _1687856)), tc_fun(_1687856, tc_fun(tc_fun(tc_prod(_1687856, _1687856), tc_HOL_Obool), tc_HOL_Obool)), _1687856), hAPP(c_COMBB(tc_prod(_1687856, _1687856), tc_fun(tc_fun(tc_prod(_1687856, _1687856), tc_HOL_Obool), tc_HOL_Obool), _1687856), c_member(tc_prod(_1687856, _1687856)))), c_Product__Type_OPair(_1687856, _1687856)))), _1687862)), _1688192)))], (46326 ^ _774244) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687856)), _1687858) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687856)), _1687860))]]], (30903 ^ _774244) ^ [_1328422, _1328424, _1328426, _1328428] : [hBOOL(hAPP(hAPP(c_member(_1328422), _1328424), _1328426)), -(hBOOL(hAPP(hAPP(c_member(_1328422), _1328424), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328422, tc_HOL_Obool)), _1328426), _1328428))))], (43137 ^ _774244) ^ [_1608544, _1608546] : [-(c_Transitive__Closure_Otrancl(_1608544, _1608546) = hAPP(hAPP(c_Relation_Orel__comp(_1608544, _1608544, _1608544), c_Transitive__Closure_Ortrancl(_1608544, _1608546)), _1608546))], (43115 ^ _774244) ^ [_1608013, _1608015, _1608017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1608013, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1608013, _1608013, _1608015), _1608017)), _1608017)), -(hAPP(c_Relation_OImage(_1608013, _1608013, c_Transitive__Closure_Ortrancl(_1608013, _1608015)), _1608017) = _1608017)], (42457 ^ _774244) ^ [_1593968, _1593970, _1593972, _1593974] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1593968, _1593970, _1593972), _1593974), c_Orderings_Obot__class_Obot(tc_fun(_1593968, tc_HOL_Obool))) = _1593974)], (7369 ^ _774244) ^ [_893840, _893842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893842), hAPP(c_Nat_OSuc, _893840))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893840), _893842))], (46120 ^ _774244) ^ [_1682567, _1682569] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1682567), hAPP(c_List_Oset(_1682567), _1682569))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682567)), _1682569))))], (48732 ^ _774244) ^ [_1748211, _1748213] : [class_Groups_Omonoid__add(_1748211), -(hAPP(c_List_Ofoldl(_1748211, _1748211, c_Groups_Oplus__class_Oplus(_1748211), c_Groups_Ozero__class_Ozero(_1748211)), _1748213) = c_List_Ofoldr(_1748211, _1748211, c_Groups_Oplus__class_Oplus(_1748211), _1748213, c_Groups_Ozero__class_Ozero(_1748211)))], (32268 ^ _774244) ^ [_1358461, _1358463, _1358465, _1358467] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1358461, _1358461)), hAPP(hAPP(c_Product__Type_OPair(_1358461, _1358461), _1358463), _1358465)), hAPP(c_Wellfounded_Omeasure(_1358461), _1358467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1358467, _1358463)), hAPP(_1358467, _1358465))))], (48013 ^ _774244) ^ [_1730223, _1730225, _1730227, _1730229, _1730231, _1730233, _1730235] : [-(hBOOL(hAPP(hAPP(c_member(_1730223), _1730225), hAPP(c_List_Oset(_1730223), _1730227)))), -(c_Map_Omap__upds(_1730223, _1730229, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1730223, tc_Option_Ooption(_1730229)), _1730231), _1730225), hAPP(c_Option_Ooption_OSome(_1730229), _1730233)), _1730227, _1730235) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1730223, tc_Option_Ooption(_1730229)), c_Map_Omap__upds(_1730223, _1730229, _1730231, _1730227, _1730235)), _1730225), hAPP(c_Option_Ooption_OSome(_1730229), _1730233)))], (12806 ^ _774244) ^ [_986885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986885)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _986885)) = _986885)], (47255 ^ _774244) ^ [_1712455, _1712457, _1712459, _1712461] : [hBOOL(hAPP(c_List_Odistinct(_1712455), _1712457)), -(hBOOL(hAPP(hAPP(c_member(_1712455), _1712459), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1712455, tc_HOL_Obool)), hAPP(c_List_Oset(_1712455), _1712457)), hAPP(hAPP(c_Set_Oinsert(_1712455), hAPP(hAPP(c_List_Onth(_1712455), _1712457), _1712461)), c_Orderings_Obot__class_Obot(tc_fun(_1712455, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1712455), hAPP(hAPP(c_List_Olist__update(_1712455, _1712457), _1712461), _1712459))))], (29600 ^ _774244) ^ [_1301380, _1301382] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301380), _1301382))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1301382, _1301380) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1301382), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1301382), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1301380)))], (32692 ^ _774244) ^ [_1366866, _1366868, _1366870] : [class_Orderings_Olinorder(_1366866), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366866), _1366868)), hBOOL(hAPP(hAPP(c_member(_1366866), _1366870), _1366868)), 32703 ^ _774244 : [(32710 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366866, tc_HOL_Obool)), _1366868), hAPP(hAPP(c_Set_Oinsert(_1366866), _1366870), c_Orderings_Obot__class_Obot(tc_fun(_1366866, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1366866, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1366866, _1366868) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1366866), _1366870), c_Big__Operators_Olinorder__class_OMin(_1366866, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366866, tc_HOL_Obool)), _1366868), hAPP(hAPP(c_Set_Oinsert(_1366866), _1366870), c_Orderings_Obot__class_Obot(tc_fun(_1366866, tc_HOL_Obool)))))))], (32704 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366866, tc_HOL_Obool)), _1366868), hAPP(hAPP(c_Set_Oinsert(_1366866), _1366870), c_Orderings_Obot__class_Obot(tc_fun(_1366866, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1366866, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1366866, _1366868) = _1366870)]]], (18145 ^ _774244) ^ [_1084203, _1084205] : [class_Int_Onumber__ring(_1084203), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1084203), hAPP(c_Int_Onumber__class_Onumber__of(_1084203), c_Int_OPls)), _1084205) = _1084205)], (29104 ^ _774244) ^ [_1292353, _1292355, _1292357] : [class_Groups_Ocomm__monoid__add(_1292353), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1292355, _1292353), _1292357), c_Orderings_Obot__class_Obot(tc_fun(_1292355, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1292353))], (8264 ^ _774244) ^ [_909001, _909003, _909005] : [class_Orderings_Opreorder(_909001), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909001), _909003), _909005)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909001), _909005), _909003))], (4918 ^ _774244) ^ [_850245, _850247, _850249, _850251] : [-(c_List_Oupt(_850251, _850247) = c_List_Oupt(_850249, _850245)), _850251 = _850249, _850247 = _850245], (22913 ^ _774244) ^ [_1170129, _1170131, _1170133, _1170135, _1170137, _1170139] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1170129, _1170131, _1170133), _1170135), hAPP(hAPP(c_Product__Type_OPair(_1170129, _1170131), _1170137), _1170139)) = hAPP(hAPP(_1170135, _1170137), _1170139))], (43365 ^ _774244) ^ [_1613743, _1613745, _1613747, _1613749, _1613751, _1613753] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613743, tc_fun(_1613745, tc_HOL_Obool)), _1613747), _1613749), _1613751)), -(hBOOL(hAPP(hAPP(_1613749, _1613753), _1613751))), hBOOL(hAPP(hAPP(c_member(_1613743), _1613753), _1613747))], (41426 ^ _774244) ^ [_1569337] : [-(c_Wellfounded_Owf(tc_fun(_1569337, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1569337)))], (24819 ^ _774244) ^ [_1207662, _1207664] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1207662), _1207664)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1207662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1207664), _1207662))))], (29812 ^ _774244) ^ [_1305322, _1305324] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1305322, _1305324)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1305322, _1305324), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305322), c_Orderings_Otop__class_Otop(tc_fun(_1305322, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305324), c_Orderings_Otop__class_Otop(tc_fun(_1305324, tc_HOL_Obool))))], (15652 ^ _774244) ^ [_1038620] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1038620)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1038620)], (17121 ^ _774244) ^ [_1066950, _1066952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1066950)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1066950), _1066952)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1066950)), _1066952))], (18117 ^ _774244) ^ [_1083806] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1083806), c_Int_OPls) = _1083806)], (15628 ^ _774244) ^ [_1038083, _1038085, _1038087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1038083), _1038085)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038087), _1038085)), _1038083) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038087), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1038085), _1038083)))], (13579 ^ _774244) ^ [_1000663, _1000665] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1000663, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1000665)) = 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), _1000663), _1000665)))], (37903 ^ _774244) ^ [_1480902, _1480904, _1480906, _1480908, _1480910] : [c_Fun_Oinj__on(_1480902, _1480904, _1480906, c_Orderings_Otop__class_Otop(tc_fun(_1480902, tc_HOL_Obool))), hAPP(_1480906, _1480908) = hAPP(_1480906, _1480910), -(_1480908 = _1480910)], (25179 ^ _774244) ^ [_1213517, _1213519] : [25186 ^ _774244 : [(25189 ^ _774244) ^ [] : [_1213517 = _1213519], (25187 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213517), _1213519)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213517), _1213519)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213519), _1213517)))], (32090 ^ _774244) ^ [_1355111, _1355113] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1355111), 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)))), _1355113))), 32093 ^ _774244 : [(32096 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355113), _1355111))], (32094 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355111), _1355113)))]]], (45886 ^ _774244) ^ [_1676755] : [c_List_Onat__list(_1676755), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1676755)))], (23645 ^ _774244) ^ [_1184483, _1184485, _1184487] : [class_Orderings_Olinorder(_1184483), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184483), _1184485), _1184487) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184483), _1184487), _1184485))], (48572 ^ _774244) ^ [_1744913, _1744915] : [-(_1744913 = c_List_Olist_ONil(_1744915)), -(hAPP(c_List_Orotate1(_1744915), _1744913) = hAPP(hAPP(c_List_Oappend(_1744915), hAPP(c_List_Otl(_1744915), _1744913)), hAPP(hAPP(c_List_Olist_OCons(_1744915), hAPP(c_List_Ohd(_1744915), _1744913)), c_List_Olist_ONil(_1744915))))], (29694 ^ _774244) ^ [_1302980, _1302982] : [29695 ^ _774244 : [(29698 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1302982), _1302980))], (29696 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1302980), _1302982)))]], -(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)))), _1302980, _1302982) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (28102 ^ _774244) ^ [_1270534, _1270536, _1270538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270534, tc_HOL_Obool)), _1270536), _1270538)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270534, tc_HOL_Obool)), _1270536), _1270538) = _1270538)], (34229 ^ _774244) ^ [_1396759, _1396761, _1396763, _1396765, _1396767] : [class_Groups_Ocomm__monoid__mult(_1396759), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396761), _1396763)), 34236 ^ _774244 : [(34243 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1396761), _1396765), _1396763))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396761, _1396759), hAPP(hAPP(c_COMBC(_1396761, _1396759, _1396759), hAPP(hAPP(c_COMBS(_1396761, _1396759, tc_fun(_1396759, _1396759)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1396759, tc_fun(_1396759, _1396759)), _1396761), c_If(_1396759)), hAPP(hAPP(c_COMBC(_1396761, _1396761, tc_HOL_Obool), c_fequal), _1396765))), _1396767)), c_Groups_Oone__class_Oone(_1396759))), _1396763) = c_Groups_Oone__class_Oone(_1396759))], (34237 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1396761), _1396765), _1396763)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396761, _1396759), hAPP(hAPP(c_COMBC(_1396761, _1396759, _1396759), hAPP(hAPP(c_COMBS(_1396761, _1396759, tc_fun(_1396759, _1396759)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1396759, tc_fun(_1396759, _1396759)), _1396761), c_If(_1396759)), hAPP(hAPP(c_COMBC(_1396761, _1396761, tc_HOL_Obool), c_fequal), _1396765))), _1396767)), c_Groups_Oone__class_Oone(_1396759))), _1396763) = hAPP(_1396767, _1396765))]]], (45878 ^ _774244) ^ [_1676594, _1676596] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1676594, _1676596) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1676594, _1676596)))], (16987 ^ _774244) ^ [_1064717, _1064719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1064717)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1064719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1064717), _1064719)))], (23657 ^ _774244) ^ [_1184683, _1184685, _1184687, _1184689] : [class_Orderings_Olinorder(_1184683), 23660 ^ _774244 : [(23661 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184683), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184683), _1184685), _1184687)), _1184689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184683), _1184685), _1184689))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184683), _1184687), _1184689)))], (23671 ^ _774244) ^ [] : [23672 ^ _774244 : [(23675 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184683), _1184687), _1184689))], (23673 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184683), _1184685), _1184689))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184683), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184683), _1184685), _1184687)), _1184689)))]]], (29226 ^ _774244) ^ [_1294410, _1294412, _1294414, _1294416] : [class_Orderings_Oorder(_1294410), 29229 ^ _774244 : [(29238 ^ _774244) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1294410, _1294412, _1294414) = hAPP(hAPP(c_Set_Oinsert(_1294410), _1294416), c_Orderings_Obot__class_Obot(tc_fun(_1294410, tc_HOL_Obool)))), _1294412 = _1294414, _1294414 = _1294416], (29230 ^ _774244) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1294410, _1294412, _1294414) = hAPP(hAPP(c_Set_Oinsert(_1294410), _1294416), c_Orderings_Obot__class_Obot(tc_fun(_1294410, tc_HOL_Obool))), 29233 ^ _774244 : [(29236 ^ _774244) ^ [] : [-(_1294414 = _1294416)], (29234 ^ _774244) ^ [] : [-(_1294412 = _1294414)]]]]], (51285 ^ _774244) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (25635 ^ _774244) ^ [_1221497, _1221499, _1221501] : [class_Divides_Osemiring__div(_1221497), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221497), _1221499), _1221501)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221497), _1221499), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1221497), _1221501), _1221499)) = _1221501)], (49410 ^ _774244) ^ [_1762859, _1762861, _1762863] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1762859, tc_HOL_Obool)), hAPP(c_List_Oset(_1762859), _1762861)), hAPP(hAPP(c_Set_Oinsert(_1762859), _1762863), c_Orderings_Obot__class_Obot(tc_fun(_1762859, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1762859), hAPP(c_List_Ofilter(_1762859, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1762859), c_fNot), hAPP(hAPP(c_COMBC(_1762859, _1762859, tc_HOL_Obool), c_fequal), _1762863))), _1762861)))], (23419 ^ _774244) ^ [_1179923, _1179925, _1179927] : [_1179923 = _1179925, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179927, tc_HOL_Obool)), _1179925), _1179923)))], (30007 ^ _774244) ^ [_1308874] : [c_Nat__Transfer_Onat__set(_1308874), 30010 ^ _774244 : [(30017 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1308874))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1308874)))], (30011 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1308874)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1308874))))]]], (16567 ^ _774244) ^ [_1056361, _1056363, _1056365] : [class_Rings_Ocomm__semiring__1(_1056361), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1056361), _1056363), hAPP(c_Nat_OSuc, _1056365)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056361), _1056363), hAPP(hAPP(c_Power_Opower__class_Opower(_1056361), _1056363), _1056365)))], (24441 ^ _774244) ^ [_1199253] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1199253)) = _1199253)], (12758 ^ _774244) ^ [_986204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _986204), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _986204) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18275 ^ _774244) ^ [_1086180, _1086182] : [18276 ^ _774244 : [(18279 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086180), c_Int_OPls))], (18277 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086180), _1086182))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086180)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086182))))], (47690 ^ _774244) ^ [_1722408, _1722410, _1722412] : [-(hAPP(hAPP(c_List_Oappend(_1722408), _1722410), _1722412) = c_List_Olist_ONil(_1722408)), _1722410 = c_List_Olist_ONil(_1722408), _1722412 = c_List_Olist_ONil(_1722408)], (46908 ^ _774244) ^ [_1703654, _1703656, _1703658, _1703660] : [class_Orderings_Olinorder(_1703654), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1703656, _1703654, _1703658), _1703660), c_List_Olist_ONil(_1703656)) = hAPP(hAPP(c_List_Olist_OCons(_1703656), _1703660), c_List_Olist_ONil(_1703656)))], (9208 ^ _774244) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (44231 ^ _774244) ^ [_1637544, _1637546, _1637548, _1637550] : [-(hAPP(_1637544, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1637546, _1637546), _1637548), _1637544), _1637550)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1637546, _1637546), _1637548), _1637544), hAPP(_1637544, _1637550)))], (48958 ^ _774244) ^ [_1753518] : [-(c_List_Olists(_1753518, c_Orderings_Obot__class_Obot(tc_fun(_1753518, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1753518)), c_List_Olist_ONil(_1753518)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1753518), tc_HOL_Obool))))], (6862 ^ _774244) ^ [_885347, _885349, _885351] : [-(hBOOL(hAPP(_885347, _885349))), -(c_Natural_Oevalc(c_Com_Ocom_OWhile(_885347, _885351), _885349, _885349))], (47744 ^ _774244) ^ [_1723344, _1723346] : [-(hAPP(hAPP(c_List_Oappend(_1723344), c_List_Olist_ONil(_1723344)), _1723346) = _1723346)], (51357 ^ _774244) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (51163 ^ _774244) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (20771 ^ _774244) ^ [_1129976, _1129978, _1129980, _1129982] : [class_Fields_Olinordered__field(_1129976), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129976), _1129978), c_Groups_Ozero__class_Ozero(_1129976))), 20778 ^ _774244 : [(20785 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129976), _1129982), _1129978)), _1129980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129976), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129976), _1129980), _1129978)), _1129982)))], (20779 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129976), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129976), _1129980), _1129978)), _1129982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129976), _1129982), _1129978)), _1129980)))]]], (6252 ^ _774244) ^ [_874585, _874587] : [class_Groups_Ozero(_874585), 6255 ^ _774244 : [(6262 ^ _774244) ^ [] : [_874587 = c_Groups_Ozero__class_Ozero(_874585), -(c_Groups_Ozero__class_Ozero(_874585) = _874587)], (6256 ^ _774244) ^ [] : [c_Groups_Ozero__class_Ozero(_874585) = _874587, -(_874587 = c_Groups_Ozero__class_Ozero(_874585))]]], (29336 ^ _774244) ^ [_1296207, _1296209, _1296211, _1296213] : [-(_1296207 = c_Orderings_Obot__class_Obot(tc_fun(_1296209, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1296209, _1296211, hAPP(c_COMBK(_1296211, _1296209), _1296213)), _1296207) = hAPP(hAPP(c_Set_Oinsert(_1296211), _1296213), c_Orderings_Obot__class_Obot(tc_fun(_1296211, tc_HOL_Obool))))], (29144 ^ _774244) ^ [_1293023, _1293025, _1293027] : [class_Orderings_Oorder(_1293023), 29147 ^ _774244 : [(29154 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293023), _1293025), _1293027))), -(c_Orderings_Obot__class_Obot(tc_fun(_1293023, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1293023, _1293025, _1293027))], (29148 ^ _774244) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1293023, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1293023, _1293025, _1293027), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293023), _1293025), _1293027))]]], (1374 ^ _774244) ^ [_794143, _794145] : [-(class_Rings_Olinordered__comm__semiring__strict(_794143)), _794145 = _794143, class_Rings_Olinordered__comm__semiring__strict(_794145)], (44646 ^ _774244) ^ [_1647547, _1647549, _1647551] : [class_Complete__Lattice_Ocomplete__lattice(_1647547), class_Orderings_Olinorder(_1647547), 44653 ^ _774244 : [(44663 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1647547), _1647549), c_Complete__Lattice_OSup__class_OSup(_1647547, _1647551)))), 44664 ^ _774244 : [(44665 ^ _774244) ^ [_1647853] : [hBOOL(hAPP(hAPP(c_member(_1647547), _1647853), _1647551)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1647547), _1647549), _1647853))]]], (44654 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1647547), _1647549), c_Complete__Lattice_OSup__class_OSup(_1647547, _1647551))), 44658 ^ _774244 : [(44661 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1647547), _1647549), 44657 ^ [_1647547, _1647549, _1647551])))], (44659 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1647547), 44657 ^ [_1647547, _1647549, _1647551]), _1647551)))]]]]], (19109 ^ _774244) ^ [_1100352] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1100352)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1100352)))], (49306 ^ _774244) ^ [_1760732, _1760734, _1760736, _1760738] : [-(hAPP(c_List_Ofilter(_1760732, _1760734), hAPP(hAPP(c_List_Oappend(_1760732), _1760736), _1760738)) = hAPP(hAPP(c_List_Oappend(_1760732), hAPP(c_List_Ofilter(_1760732, _1760734), _1760736)), hAPP(c_List_Ofilter(_1760732, _1760734), _1760738)))], (47130 ^ _774244) ^ [_1709073, _1709075, _1709077] : [-(_1709073 = _1709075), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709077)), _1709073) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709077)), _1709075), 47136 ^ _774244 : [(47139 ^ _774244) ^ [] : [hAPP(hAPP(c_List_Onth(_1709077), _1709073), 47135 ^ [_1709073, _1709075, _1709077]) = hAPP(hAPP(c_List_Onth(_1709077), _1709075), 47135 ^ [_1709073, _1709075, _1709077])], (47137 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47135 ^ [_1709073, _1709075, _1709077]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709077)), _1709073))))]]], (10456 ^ _774244) ^ [_946521, _946523, _946525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _946521), _946523)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _946525), _946523))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _946523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946521), _946525)))], (48390 ^ _774244) ^ [_1740736, _1740738, _1740740, _1740742] : [-(hAPP(hAPP(c_List_Odrop(_1740736), _1740738), hAPP(hAPP(c_List_Otake(_1740736), _1740740), _1740742)) = hAPP(hAPP(c_List_Otake(_1740736), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1740740), _1740738)), hAPP(hAPP(c_List_Odrop(_1740736), _1740738), _1740742)))], (10640 ^ _774244) ^ [_949299, _949301, _949303] : [class_Orderings_Olinorder(_949299), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949299), _949301), _949303))), 10647 ^ _774244 : [(10654 ^ _774244) ^ [] : [_949301 = _949303, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949299), _949301), _949303)))], (10648 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949299), _949301), _949303)), -(_949301 = _949303)]]], (41745 ^ _774244) ^ [_1577052, _1577054] : [c_Wellfounded_OwfP(_1577052, _1577054), 41748 ^ _774244 : [(41749 ^ _774244) ^ [_1577116] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1577052, _1577054), _1577116)))]]], (12724 ^ _774244) ^ [_985663, _985665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _985663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _985665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985665), _985663))))], (12354 ^ _774244) ^ [_978799, _978801, _978803, _978805] : [class_Groups_Oordered__comm__monoid__add(_978799), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978799), c_Groups_Ozero__class_Ozero(_978799)), _978801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978799), _978803), _978805)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978799), _978803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978799), _978801), _978805))))], (9768 ^ _774244) ^ [_935105, _935107, _935109] : [class_Rings_Olinordered__idom(_935105), 9771 ^ _774244 : [(9778 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _935107), _935109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935105), hAPP(c_Int_Oring__1__class_Oof__int(_935105), _935107)), hAPP(c_Int_Oring__1__class_Oof__int(_935105), _935109))))], (9772 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935105), hAPP(c_Int_Oring__1__class_Oof__int(_935105), _935107)), hAPP(c_Int_Oring__1__class_Oof__int(_935105), _935109))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _935107), _935109)))]]], (11140 ^ _774244) ^ [_957455, _957457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957455), _957457)), -(_957455 = _957457), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957455), _957457)))], (7764 ^ _774244) ^ [_901047, _901049, _901051] : [-(hAPP(c_Nat_Osize__class_Osize(tc_sum(_901047, _901049)), hAPP(c_Sum__Type_OInl(_901047, _901049), _901051)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6764 ^ _774244) ^ [_883458, _883460, _883462] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_883458, _883460, _883462)], (29752 ^ _774244) ^ [_1304151, _1304153] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1304151, _1304153))))], (17637 ^ _774244) ^ [_1076183, _1076185] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076183) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076185), 17640 ^ _774244 : [(17647 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076183)))), 17650 ^ _774244 : [(17657 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076185)))), -(_1076183 = _1076185)], (17651 ^ _774244) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076185))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076183) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (17641 ^ _774244) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076185)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (41130 ^ _774244) ^ [_1561078, _1561080] : [-(c_Product__Type_Omap__pair(_1561078, _1561078, _1561080, _1561080, c_Fun_Oid(_1561078), c_Fun_Oid(_1561080)) = c_Fun_Oid(tc_prod(_1561078, _1561080)))], (38181 ^ _774244) ^ [_1486059, _1486061, _1486063, _1486065, _1486067, _1486069] : [c_Fun_Oinj__on(_1486059, _1486061, _1486063, _1486065), -(_1486067 = _1486069), hBOOL(hAPP(hAPP(c_member(_1486059), _1486067), _1486065)), hBOOL(hAPP(hAPP(c_member(_1486059), _1486069), _1486065)), hAPP(_1486063, _1486067) = hAPP(_1486063, _1486069)], (18227 ^ _774244) ^ [_1085409] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085409), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085409), c_Int_OPls)))], (10209 ^ _774244) ^ [_942451, _942453, _942455, _942457] : [class_Orderings_Opreorder(_942451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942451), _942453), _942455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942451), _942455), _942457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942451), _942453), _942457)))], (46409 ^ _774244) ^ [_1691662, _1691664, _1691666, _1691668, _1691670, _1691672] : [hBOOL(hAPP(hAPP(_1691662, _1691664), _1691666)), c_List_Olistrelp(_1691668, _1691662, _1691670, _1691672), -(c_List_Olistrelp(_1691668, _1691662, hAPP(hAPP(c_List_Olist_OCons(_1691668), _1691664), _1691670), hAPP(hAPP(c_List_Olist_OCons(_1691668), _1691666), _1691672)))], (2620 ^ _774244) ^ [_813906, _813908] : [_813908 = _813906, -(c_Nitpick_Ozero__frac(_813908) = c_Nitpick_Ozero__frac(_813906))], (10492 ^ _774244) ^ [_947217, _947219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947219)), 10499 ^ _774244 : [(10506 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _947217), _947219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _947217)), hAPP(c_Int_Onat, _947219))))], (10500 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _947217)), hAPP(c_Int_Onat, _947219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _947217), _947219)))]]], (51327 ^ _774244) ^ [_1800227, _1800229] : [-(class_Smallcheck_Osmall(tc_prod(_1800227, _1800229))), class_Smallcheck_Osmall(_1800227), class_Smallcheck_Osmall(_1800229)], (15320 ^ _774244) ^ [_1032180, _1032182, _1032184] : [hBOOL(hAPP(_1032180, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1032182), _1032184)))), 15323 ^ _774244 : [(15330 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1032182), _1032184)), -(hBOOL(hAPP(_1032180, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15324 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032184), _1032182)), -(hBOOL(hAPP(_1032180, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1032182)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1032184)))))]]], (49232 ^ _774244) ^ [_1759035, _1759037, _1759039, _1759041] : [49233 ^ _774244 : [(49236 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1759035), _1759037), hAPP(c_List_Oset(_1759035), c_List_Obutlast(_1759035, _1759041))))], (49234 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1759035), _1759037), hAPP(c_List_Oset(_1759035), c_List_Obutlast(_1759035, _1759039))))]], -(hBOOL(hAPP(hAPP(c_member(_1759035), _1759037), hAPP(c_List_Oset(_1759035), c_List_Obutlast(_1759035, hAPP(hAPP(c_List_Oappend(_1759035), _1759039), _1759041))))))], (47467 ^ _774244) ^ [_1717367, _1717369, _1717371, _1717373, _1717375] : [hAPP(hAPP(c_List_Oappend(_1717367), _1717369), hAPP(hAPP(c_List_Olist_OCons(_1717367), _1717371), c_List_Olist_ONil(_1717367))) = hAPP(hAPP(c_List_Oappend(_1717367), _1717373), hAPP(hAPP(c_List_Olist_OCons(_1717367), _1717375), c_List_Olist_ONil(_1717367))), 47470 ^ _774244 : [(47473 ^ _774244) ^ [] : [-(_1717371 = _1717375)], (47471 ^ _774244) ^ [] : [-(_1717369 = _1717373)]]], (48769 ^ _774244) ^ [_1748915, _1748917] : [-(c_List_Olist_Olist__size(_1748915, _1748917, c_List_Olist_ONil(_1748915)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42902 ^ _774244) ^ [_1603119, _1603121, _1603123, _1603125, _1603127, _1603129] : [c_Finite__Set_Ofun__left__comm(_1603119, _1603121, _1603123), hBOOL(hAPP(c_Finite__Set_Ofinite(_1603119), _1603125)), hBOOL(hAPP(hAPP(c_member(_1603119), _1603127), _1603125)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1603119, _1603121, _1603123), _1603129), _1603125) = hAPP(hAPP(_1603123, _1603127), hAPP(hAPP(c_Finite__Set_Ofold(_1603119, _1603121, _1603123), _1603129), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1603119, tc_HOL_Obool)), _1603125), hAPP(hAPP(c_Set_Oinsert(_1603119), _1603127), c_Orderings_Obot__class_Obot(tc_fun(_1603119, tc_HOL_Obool)))))))], (18743 ^ _774244) ^ [_1093881, _1093883] : [class_Int_Onumber__ring(_1093881), class_Rings_Olinordered__idom(_1093881), 18750 ^ _774244 : [(18757 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1093883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093881), c_Groups_Oone__class_Oone(_1093881)), hAPP(c_Int_Onumber__class_Onumber__of(_1093881), _1093883))))], (18751 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093881), c_Groups_Oone__class_Oone(_1093881)), hAPP(c_Int_Onumber__class_Onumber__of(_1093881), _1093883))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1093883)))]]], (7086 ^ _774244) ^ [_889312, _889314, _889316, _889318] : [c_Natural_Oevalc(c_Com_Ocom_OWhile(_889312, _889314), _889316, _889318), 7091 ^ _774244 : [(7094 ^ _774244) ^ [] : [hBOOL(hAPP(_889312, _889316))], (7092 ^ _774244) ^ [] : [-(_889318 = _889316)]], 7095 ^ _774244 : [(7101 ^ _774244) ^ [] : [-(c_Natural_Oevalc(c_Com_Ocom_OWhile(_889312, _889314), 7097 ^ [_889312, _889314, _889316, _889318], _889318))], (7099 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_889314, _889316, 7097 ^ [_889312, _889314, _889316, _889318]))], (7096 ^ _774244) ^ [] : [-(hBOOL(hAPP(_889312, _889316)))]]], (10061 ^ _774244) ^ [_940043, _940045] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940043), _940045) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940045), _940043))], (13637 ^ _774244) ^ [_1001692, _1001694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001692), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001692), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1001694, _1001692))))], (51371 ^ _774244) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (48432 ^ _774244) ^ [_1741756, _1741758, _1741760, _1741762, _1741764] : [hAPP(hAPP(c_List_Oappend(_1741756), _1741758), _1741760) = hAPP(hAPP(c_List_Oappend(_1741756), _1741762), _1741764), 48435 ^ _774244 : [(48444 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741756)), _1741758)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741756)), _1741762)))), 48447 ^ _774244 : [(48450 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1741756), hAPP(hAPP(c_List_Odrop(_1741756), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741756)), _1741762)), _1741758)), _1741760) = _1741764)], (48448 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1741756), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741756)), _1741762)), _1741758) = _1741762)]]], (48436 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741756)), _1741758)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741756)), _1741762))), 48439 ^ _774244 : [(48442 ^ _774244) ^ [] : [-(_1741760 = hAPP(hAPP(c_List_Oappend(_1741756), hAPP(hAPP(c_List_Odrop(_1741756), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741756)), _1741758)), _1741762)), _1741764))], (48440 ^ _774244) ^ [] : [-(_1741758 = hAPP(hAPP(c_List_Otake(_1741756), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741756)), _1741758)), _1741762))]]]]], (8708 ^ _774244) ^ [_916344, _916346, _916348] : [class_Groups_Ogroup__add(_916344), 8711 ^ _774244 : [(8718 ^ _774244) ^ [] : [_916346 = _916348, -(hAPP(c_Groups_Ouminus__class_Ouminus(_916344), _916346) = hAPP(c_Groups_Ouminus__class_Ouminus(_916344), _916348))], (8712 ^ _774244) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_916344), _916346) = hAPP(c_Groups_Ouminus__class_Ouminus(_916344), _916348), -(_916346 = _916348)]]], (5568 ^ _774244) ^ [_860188, _860190, _860192, _860194, _860196, _860198] : [-(c_COMBS(_860198, _860194, _860190) = c_COMBS(_860196, _860192, _860188)), _860198 = _860196, _860194 = _860192, _860190 = _860188], (25383 ^ _774244) ^ [_1216976, _1216978, _1216980, _1216982] : [class_Rings_Ocomm__semiring__1(_1216976), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216976), _1216978), _1216980)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216976), _1216978), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216976), _1216980), _1216982))))], (36721 ^ _774244) ^ [_1454024, _1454026, _1454028] : [class_Orderings_Oorder(_1454024), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454024, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1454024, _1454026), _1454028)), hAPP(c_SetInterval_Oord__class_OatLeast(_1454024), _1454028)) = c_Orderings_Obot__class_Obot(tc_fun(_1454024, tc_HOL_Obool)))], (3916 ^ _774244) ^ [_834552, _834554, _834556, _834558, _834560, _834562, _834564, _834566, _834568, _834570] : [-(c_Finite__Set_Ofold__graph(_834570, _834566, _834562, _834558, _834554) = c_Finite__Set_Ofold__graph(_834568, _834564, _834560, _834556, _834552)), _834570 = _834568, _834566 = _834564, _834562 = _834560, _834558 = _834556, _834554 = _834552], (38858 ^ _774244) ^ [_1500842, _1500844, _1500846, _1500848] : [hAPP(c_Set_Oimage(_1500842, _1500844, _1500846), c_Orderings_Otop__class_Otop(tc_fun(_1500842, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1500844, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1500842, _1500844, _1500846), hAPP(c_Set_Ovimage(_1500842, _1500844, _1500846), _1500848)) = _1500848)], (44755 ^ _774244) ^ [_1649856, _1649858] : [class_Complete__Lattice_Ocomplete__lattice(_1649856), -(c_Complete__Lattice_OSup__class_OSup(_1649856, hAPP(hAPP(c_Set_Oinsert(_1649856), _1649858), c_Orderings_Obot__class_Obot(tc_fun(_1649856, tc_HOL_Obool)))) = _1649858)], (38796 ^ _774244) ^ [_1499324, _1499326, _1499328, _1499330] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1499324, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1499326, _1499324, _1499328), hAPP(c_Set_Ovimage(_1499326, _1499324, _1499328), _1499330))), _1499330)))], (804 ^ _774244) ^ [_786668, _786670, _786672, _786674, _786676, _786678, _786680, _786682] : [-(c_List_Olistrelp(_786680, _786676, _786672, _786668)), c_List_Olistrelp(_786682, _786678, _786674, _786670), _786682 = _786680, _786678 = _786676, _786674 = _786672, _786670 = _786668], (2748 ^ _774244) ^ [_815886, _815888, _815890, _815892, _815894, _815896] : [-(c_Nitpick_Oof__frac(_815896, _815892, _815888) = c_Nitpick_Oof__frac(_815894, _815890, _815886)), _815896 = _815894, _815892 = _815890, _815888 = _815886], (24717 ^ _774244) ^ [_1205256, _1205258, _1205260, _1205262] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1205256), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1205258, _1205260, _1205256, _1205262) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1205258, 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(_1205258)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1205260, _1205262)), 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(_1205258)))), 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(_1205258)))), 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(_1205258)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1205258, 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(_1205258)))), 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(_1205258)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1205258, _1205260, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1205256), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1205262))), 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(_1205258)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1205258))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1205258)))), 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(_1205258)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1205258, 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(_1205258)))), 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(_1205258)))), 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(_1205258))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1205258)))), 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(_1205258)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1205258)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1205258))))), tc_prod(_1205258, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1205258)), hAPP(hAPP(c_COMBB(_1205258, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1205258)))), tc_prod(_1205258, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1205258)), c_Product__Type_Ofst(_1205258, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (48644 ^ _774244) ^ [_1746255, _1746257, _1746259] : [-(hAPP(c_List_Orotate1(_1746255), hAPP(c_List_Orotate(_1746255, _1746257), _1746259)) = hAPP(c_List_Orotate(_1746255, _1746257), hAPP(c_List_Orotate1(_1746255), _1746259)))], (41609 ^ _774244) ^ [_1573519, _1573521] : [-(hAPP(c_List_Olexn(_1573519, _1573521), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1573519), tc_List_Olist(_1573519)), tc_HOL_Obool)))], (27872 ^ _774244) ^ [_1266433, _1266435] : [class_Lattices_Osemilattice__sup(_1266433), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266433), _1266435), _1266435) = _1266435)], (46112 ^ _774244) ^ [_1682406, _1682408, _1682410, _1682412] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682406)), hAPP(hAPP(c_List_Omap(_1682408, _1682406), _1682410), _1682412)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682408)), _1682412))], (1044 ^ _774244) ^ [_790018, _790020] : [-(class_Rings_Oordered__ring__abs(_790018)), _790020 = _790018, class_Rings_Oordered__ring__abs(_790020)], (45419 ^ _774244) ^ [_1665471, _1665473] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1665471), _1665473) = c_Smallcheck_Osmall_H(_1665471, hAPP(c_Code__Numeral_Oint__of, _1665473), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1665473))))], (18265 ^ _774244) ^ [_1086050, _1086052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086050)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086052))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086050), _1086052))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086050), c_Int_OPls)))], (51379 ^ _774244) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (7239 ^ _774244) ^ [_891640, _891642, _891644, _891646, _891648, _891650] : [-(c_Nitpick_Opair__box_OPairBox(_891640, _891642, _891644, _891646) = c_Nitpick_Opair__box_OPairBox(_891640, _891642, _891648, _891650)), _891644 = _891648, _891646 = _891650], (4102 ^ _774244) ^ [_837609, _837611, _837613, _837615] : [-(c_List_Olenlex(_837615, _837611) = c_List_Olenlex(_837613, _837609)), _837615 = _837613, _837611 = _837609], (8842 ^ _774244) ^ [_919034, _919036, _919038] : [class_Rings_Osemiring__1(_919034), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919034), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _919036), _919038)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919034), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919034), _919036)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919034), _919038)))], (40759 ^ _774244) ^ [_1545852, _1545854, _1545856, _1545858, _1545860] : [-(c_Map_Odom(_1545852, _1545854, hAPP(hAPP(c_COMBS(_1545852, tc_Option_Ooption(_1545854), tc_Option_Ooption(_1545854)), hAPP(hAPP(c_COMBS(_1545852, tc_Option_Ooption(_1545854), tc_fun(tc_Option_Ooption(_1545854), tc_Option_Ooption(_1545854))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1545854), tc_fun(tc_Option_Ooption(_1545854), tc_Option_Ooption(_1545854))), _1545852), c_If(tc_Option_Ooption(_1545854))), _1545856)), _1545858)), _1545860)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1545852, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545852, tc_HOL_Obool)), c_Map_Odom(_1545852, _1545854, _1545858)), hAPP(c_Set_OCollect(_1545852), _1545856))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545852, tc_HOL_Obool)), c_Map_Odom(_1545852, _1545854, _1545860)), hAPP(c_Set_OCollect(_1545852), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1545852), c_fNot), _1545856)))))], (34146 ^ _774244) ^ [_1395078, _1395080, _1395082, _1395084, _1395086] : [class_Groups_Ocomm__monoid__mult(_1395078), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395080), _1395082)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395080, _1395078), hAPP(hAPP(c_COMBS(_1395080, _1395078, _1395078), hAPP(hAPP(c_COMBB(_1395078, tc_fun(_1395078, _1395078), _1395080), c_Groups_Otimes__class_Otimes(_1395078)), _1395084)), _1395086)), _1395082) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395078), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395080, _1395078), _1395084), _1395082)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395080, _1395078), _1395086), _1395082)))], (15818 ^ _774244) ^ [_1042324, _1042326, _1042328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042324), _1042326)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042326), _1042324))), _1042328) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1042326)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042324), _1042328)))], (4122 ^ _774244) ^ [_837907, _837909, _837911, _837913] : [-(c_Nitpick_Ocard_H(_837913, _837909) = c_Nitpick_Ocard_H(_837911, _837907)), _837913 = _837911, _837909 = _837907], (28685 ^ _774244) ^ [_1283314, _1283316, _1283318, _1283320, _1283322] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1283314, tc_fun(_1283316, tc_HOL_Obool)), _1283318), hAPP(hAPP(c_COMBS(_1283314, tc_fun(_1283316, tc_HOL_Obool), tc_fun(_1283316, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1283316, tc_HOL_Obool), tc_fun(tc_fun(_1283316, tc_HOL_Obool), tc_fun(_1283316, tc_HOL_Obool)), _1283314), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283316, tc_HOL_Obool))), _1283320)), _1283322)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283316, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1283314, tc_fun(_1283316, tc_HOL_Obool)), _1283318), _1283320)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1283314, tc_fun(_1283316, tc_HOL_Obool)), _1283318), _1283322)))], (18221 ^ _774244) ^ [_1085304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085304), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085304) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15262 ^ _774244) ^ [_1030978, _1030980, _1030982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030978), _1030980)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030978), _1030982)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030980), _1030978)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030982), _1030978)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030980), _1030982))], (10438 ^ _774244) ^ [_946225, _946227] : [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), _946225), _946227))), 10441 ^ _774244 : [(10444 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _946227)))], (10442 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _946225)))]]], (27830 ^ _774244) ^ [_1265640, _1265642, _1265644] : [class_Lattices_Osemilattice__sup(_1265640), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265640), _1265642), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265640), _1265642), _1265644)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265640), _1265642), _1265644))], (51087 ^ _774244) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (36137 ^ _774244) ^ [_1440409, _1440411, _1440413, _1440415] : [hBOOL(hAPP(hAPP(c_member(_1440409), _1440411), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440409, tc_HOL_Obool)), _1440413), _1440415))), -(hBOOL(hAPP(hAPP(c_member(_1440409), _1440411), _1440413)))], (40713 ^ _774244) ^ [_1544203, _1544205, _1544207] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1544203, tc_HOL_Obool)), _1544205), _1544207) = hAPP(c_Set_OCollect(_1544203), hAPP(hAPP(c_COMBS(_1544203, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1544203), c_fconj), hAPP(hAPP(c_COMBC(_1544203, tc_fun(_1544203, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544203)), _1544205))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1544203), c_fNot), hAPP(hAPP(c_COMBC(_1544203, tc_fun(_1544203, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544203)), _1544207)))))], (28086 ^ _774244) ^ [_1270206, _1270208, _1270210] : [class_Lattices_Osemilattice__sup(_1270206), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270206), _1270208), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1270206), _1270208), _1270210))))], (12788 ^ _774244) ^ [_986623, _986625] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _986623) = _986625, 12791 ^ _774244 : [(12794 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986625)))], (12792 ^ _774244) ^ [] : [-(_986623 = hAPP(c_Int_Onat, _986625))]]], (43257 ^ _774244) ^ [_1611339, _1611341, _1611343, _1611345] : [c_Wellfounded_Owf(_1611339, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1611339, _1611339)), hAPP(hAPP(c_Product__Type_OPair(_1611339, _1611339), _1611341), _1611343)), _1611345)), 43260 ^ _774244 : [(43263 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611339, _1611339)), hAPP(hAPP(c_Product__Type_OPair(_1611339, _1611339), _1611343), _1611341)), c_Transitive__Closure_Ortrancl(_1611339, _1611345)))], (43261 ^ _774244) ^ [] : [-(c_Wellfounded_Owf(_1611339, _1611345))]]], (44354 ^ _774244) ^ [_1640802, _1640804] : [-(c_Transitive__Closure_Ortrancl(_1640802, _1640804) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1640802, _1640802), 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(_1640802, _1640802), tc_HOL_Obool), tc_fun(tc_prod(_1640802, _1640802), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1640802, _1640802), tc_HOL_Obool)), _1640804)))], (47957 ^ _774244) ^ [_1728812, _1728814, _1728816, _1728818] : [-(hAPP(hAPP(c_List_Otake(_1728812), hAPP(c_Nat_OSuc, _1728814)), hAPP(hAPP(c_List_Olist_OCons(_1728812), _1728816), _1728818)) = hAPP(hAPP(c_List_Olist_OCons(_1728812), _1728816), hAPP(hAPP(c_List_Otake(_1728812), _1728814), _1728818)))], (31717 ^ _774244) ^ [_1346910, _1346912, _1346914] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1346910), _1346912)), 31720 ^ _774244 : [(31727 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1346910), _1346914), _1346912))), -(hAPP(c_Finite__Set_Ocard(_1346910), hAPP(hAPP(c_Set_Oinsert(_1346910), _1346914), _1346912)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1346910), _1346912)))], (31721 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1346910), _1346914), _1346912)), -(hAPP(c_Finite__Set_Ocard(_1346910), hAPP(hAPP(c_Set_Oinsert(_1346910), _1346914), _1346912)) = hAPP(c_Finite__Set_Ocard(_1346910), _1346912))]]], (30428 ^ _774244) ^ [_1316952, _1316954, _1316956, _1316958, _1316960] : [c_Typedef_Otype__definition(_1316952, _1316954, _1316956, _1316958, _1316960), -(hAPP(c_Set_Oimage(_1316954, _1316952, _1316958), _1316960) = c_Orderings_Otop__class_Otop(tc_fun(_1316952, tc_HOL_Obool)))], (27406 ^ _774244) ^ [_1257484, _1257486] : [-(hAPP(c_Finite__Set_Ocard(_1257484), _1257486) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1257484, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1257484), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1257486))], (8514 ^ _774244) ^ [_913039, _913041] : [-(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, _913039)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913041))))], (29754 ^ _774244) ^ [_1304182, _1304184] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1304182, _1304184))))], (50681 ^ _774244) ^ [_1790952, _1790954] : [c_List_Oremdups(_1790952, _1790954) = c_List_Olist_ONil(_1790952), -(_1790954 = c_List_Olist_ONil(_1790952))], (41206 ^ _774244) ^ [_1562946, _1562948, _1562950, _1562952, _1562954, _1562956, _1562958, _1562960] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562946, _1562948)), hAPP(hAPP(c_Product__Type_OPair(_1562946, _1562948), _1562950), _1562952)), _1562954)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562948, _1562956)), hAPP(hAPP(c_Product__Type_OPair(_1562948, _1562956), _1562952), _1562958)), _1562960)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562946, _1562956)), hAPP(hAPP(c_Product__Type_OPair(_1562946, _1562956), _1562950), _1562958)), hAPP(hAPP(c_Relation_Orel__comp(_1562946, _1562948, _1562956), _1562954), _1562960))))], (39588 ^ _774244) ^ [_1518026, _1518028, _1518030, _1518032, _1518034] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518026, _1518028), _1518030), hAPP(hAPP(c_COMBS(_1518026, tc_fun(_1518028, tc_HOL_Obool), tc_fun(_1518028, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518028, tc_HOL_Obool), tc_fun(tc_fun(_1518028, tc_HOL_Obool), tc_fun(_1518028, tc_HOL_Obool)), _1518026), c_Groups_Ominus__class_Ominus(tc_fun(_1518028, tc_HOL_Obool))), _1518032)), _1518034)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1518026, _1518028), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518026, _1518028), _1518030), _1518032)), hAPP(hAPP(c_Product__Type_OSigma(_1518026, _1518028), _1518030), _1518034)))], (12480 ^ _774244) ^ [_981170, _981172, _981174, _981176, _981178] : [class_Rings_Olinordered__semiring__strict(_981170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981170), _981172), _981174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981170), _981176), _981178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981170), c_Groups_Ozero__class_Ozero(_981170)), _981172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981170), c_Groups_Ozero__class_Ozero(_981170)), _981176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981170), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981170), _981172), _981176)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981170), _981174), _981178))))], (34132 ^ _774244) ^ [_1394833, _1394835, _1394837] : [class_Groups_Ocomm__monoid__add(_1394833), class_Groups_Ocomm__monoid__mult(_1394833), c_Nat__Transfer_Onat__set(_1394835), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1394833), _1394837), _1394835) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1394833), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1394833, tc_Nat_Onat), _1394837), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1394835)))], (44737 ^ _774244) ^ [_1649541, _1649543, _1649545, _1649547] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649541, tc_HOL_Obool), hAPP(c_Set_Oimage(_1649543, tc_fun(_1649541, tc_HOL_Obool), _1649545), _1649547)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1649543, tc_fun(_1649541, tc_HOL_Obool)), _1649547), _1649545))], (31861 ^ _774244) ^ [_1350024, _1350026, _1350028, _1350030, _1350032] : [class_Rings_Oring(_1350024), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350026), _1350028)), hBOOL(hAPP(hAPP(c_member(_1350026), _1350030), _1350028)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350026, _1350024), _1350032), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350026, tc_HOL_Obool)), _1350028), hAPP(hAPP(c_Set_Oinsert(_1350026), _1350030), c_Orderings_Obot__class_Obot(tc_fun(_1350026, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1350024), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350026, _1350024), _1350032), _1350028)), hAPP(_1350032, _1350030)))], (40047 ^ _774244) ^ [_1531043, _1531045, _1531047, _1531049, _1531051] : [c_Relation_Orefl__on(_1531043, _1531045, _1531047), c_Relation_Orefl__on(_1531043, _1531049, _1531051), -(c_Relation_Orefl__on(_1531043, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1531043, tc_HOL_Obool)), _1531045), _1531049), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1531043, _1531043), tc_HOL_Obool)), _1531047), _1531051)))], (5725 ^ _774244) ^ [_865481, _865483, _865485] : [c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _865481)), _865483, _865485), -(c_Natural_Oevalc(c_Com_Ocom_OBODY(_865481), _865483, _865485))], (12764 ^ _774244) ^ [_986309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _986309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986309)))], (16289 ^ _774244) ^ [_1051301, _1051303, _1051305] : [-(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, _1051301, _1051303)), _1051305), _1051303) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1051301), _1051305), _1051303))], (30781 ^ _774244) ^ [_1325463, _1325465, _1325467, _1325469, _1325471, _1325473] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1325463, _1325465)), hAPP(hAPP(c_Product__Type_OPair(_1325463, _1325465), _1325471), _1325473)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool)), _1325467), _1325469))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325463, tc_fun(_1325465, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1325463, tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_fun(_1325465, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1325465, tc_fun(tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_fun(_1325465, tc_HOL_Obool)), _1325463), c_COMBC(_1325465, tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1325465, tc_prod(_1325463, _1325465)), tc_fun(_1325465, tc_fun(tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_HOL_Obool)), _1325463), hAPP(c_COMBB(tc_prod(_1325463, _1325465), tc_fun(tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_HOL_Obool), _1325465), c_member(tc_prod(_1325463, _1325465)))), c_Product__Type_OPair(_1325463, _1325465)))), _1325467)), hAPP(hAPP(c_COMBC(_1325463, tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_fun(_1325465, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1325465, tc_fun(tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_fun(_1325465, tc_HOL_Obool)), _1325463), c_COMBC(_1325465, tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1325465, tc_prod(_1325463, _1325465)), tc_fun(_1325465, tc_fun(tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_HOL_Obool)), _1325463), hAPP(c_COMBB(tc_prod(_1325463, _1325465), tc_fun(tc_fun(tc_prod(_1325463, _1325465), tc_HOL_Obool), tc_HOL_Obool), _1325465), c_member(tc_prod(_1325463, _1325465)))), c_Product__Type_OPair(_1325463, _1325465)))), _1325469)), _1325471), _1325473)))], (34002 ^ _774244) ^ [_1392424, _1392426, _1392428] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392424, tc_Nat_Onat), _1392426), _1392428)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392424, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1392424), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1392426)), _1392428))], (30059 ^ _774244) ^ [_1309563, _1309565, _1309567, _1309569] : [class_Groups_Ocomm__monoid__add(_1309563), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1309565), _1309567))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1309565, _1309563), _1309569), _1309567) = c_Groups_Ozero__class_Ozero(_1309563))], (6752 ^ _774244) ^ [_883089, _883091, _883093, _883095, _883097, _883099] : [c_Com_Ocom_OCond(_883089, _883091, _883093) = c_Com_Ocom_OLocal(_883095, _883097, _883099)], (41128 ^ _774244) ^ [_1561037, _1561039] : [-(c_Product__Type_Omap__pair(_1561037, _1561037, _1561039, _1561039, c_COMBI(_1561037), c_COMBI(_1561039)) = c_Fun_Oid(tc_prod(_1561037, _1561039)))], (24781 ^ _774244) ^ [_1207027, _1207029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1207027)), 24784 ^ _774244 : [(24791 ^ _774244) ^ [] : [_1207029 = 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), _1207029), _1207027)), _1207027)))], (24785 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1207029), _1207027)), _1207027)), -(_1207029 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (25501 ^ _774244) ^ [_1219064] : [_1219064 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219064), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (23211 ^ _774244) ^ [_1175427, _1175429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175427), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1175429), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1175427, _1175429) = 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), _1175427), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1175429)))))], (29356 ^ _774244) ^ [_1296641, _1296643, _1296645, _1296647, _1296649] : [_1296641 = c_Orderings_Obot__class_Obot(tc_fun(_1296643, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1296645), _1296647), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296643, tc_fun(_1296645, tc_HOL_Obool)), _1296641), _1296649)) = hAPP(hAPP(c_Set_Oinsert(_1296645), _1296647), c_Orderings_Obot__class_Obot(tc_fun(_1296645, tc_HOL_Obool))))], (1916 ^ _774244) ^ [_802150, _802152] : [_802152 = _802150, -(c_Com_Ocom_Ocom__size(_802152) = c_Com_Ocom_Ocom__size(_802150))], (42063 ^ _774244) ^ [_1585269, _1585271] : [42065 ^ _774244 : [(42068 ^ _774244) ^ [] : [hBOOL(hAPP(_1585269, hAPP(c_Int_OAbs__Integ, 42064 ^ [_1585269, _1585271])))], (42066 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 42064 ^ [_1585269, _1585271]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1585269, _1585271)))], (22442 ^ _774244) ^ [_1160908, _1160910] : [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), _1160908))), 22445 ^ _774244 : [(22452 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160910)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160908)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160910), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160908)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160908)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160910), 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), _1160908)))))], (22446 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160910)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160908))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160910), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160908)) = 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), _1160910)))]]], (23151 ^ _774244) ^ [_1174352, _1174354, _1174356, _1174358] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1174352, _1174354), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1174356), _1174358))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1174352), _1174354), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1174358), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1174356)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1174356)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1174358), 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), _1174354), _1174358))))))], (15940 ^ _774244) ^ [_1045052, _1045054] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1045052), _1045054))), -(c_Nat__Transfer_Otsub(_1045054, _1045052) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24281 ^ _774244) ^ [_1195923, _1195925, _1195927, _1195929] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1195923), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195923), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195923), _1195925), _1195927)), _1195929) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195923), _1195925), _1195929)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195923), _1195927), _1195929)))], (11086 ^ _774244) ^ [_956612, _956614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956612), _956614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _956612)), hAPP(c_Nat_OSuc, _956614))))], (24323 ^ _774244) ^ [_1196784, _1196786, _1196788, _1196790] : [class_Orderings_Olinorder(_1196784), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196784), _1196786), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196784), _1196788), _1196790)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196784), _1196788), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196784), _1196786), _1196790)))], (17081 ^ _774244) ^ [_1066274, _1066276] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1066274)), _1066276) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1066274), _1066276)))], (49351 ^ _774244) ^ [_1761641, _1761643, _1761645] : [hBOOL(hAPP(c_List_Odistinct(_1761641), _1761643)), -(hBOOL(hAPP(c_List_Odistinct(_1761641), hAPP(c_List_Ofilter(_1761641, _1761645), _1761643))))], (48566 ^ _774244) ^ [_1744866, _1744868] : [-(_1744866 = c_List_Olist_ONil(_1744868)), -(hAPP(c_List_Ohd(_1744868), _1744866) = hAPP(hAPP(c_List_Onth(_1744868), _1744866), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18203 ^ _774244) ^ [_1085053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085053), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085053)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9150 ^ _774244) ^ [_923950, _923952, _923954, _923956] : [class_Rings_Ocomm__semiring__1(_923950), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923950), _923952), _923954)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923950), _923956), _923954)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923950), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923950), _923952), _923956)), _923954))], (46639 ^ _774244) ^ [_1697812, _1697814, _1697816] : [class_Groups_Omonoid__add(_1697812), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1697812), hAPP(hAPP(c_List_Omap(_1697814, _1697812), hAPP(c_COMBK(_1697812, _1697814), c_Groups_Ozero__class_Ozero(_1697812))), _1697816)) = c_Groups_Ozero__class_Ozero(_1697812))], (8324 ^ _774244) ^ [_909933, _909935, _909937, _909939] : [class_Orderings_Oord(_909933), _909935 = _909937, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909933), _909937), _909939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909933), _909935), _909939)))], (24521 ^ _774244) ^ [_1200874, _1200876] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1200874), _1200876) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1200874)), hAPP(c_Code__Numeral_Onat__of, _1200876))))], (50344 ^ _774244) ^ [_1782546, _1782548, _1782550] : [_1782548 = _1782550, -(hAPP(c_List_Orev(_1782546), _1782548) = hAPP(c_List_Orev(_1782546), _1782550))], (42061 ^ _774244) ^ [_1585234] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 42057 ^ [_1585234]), c_Int_OInteg)))], (14896 ^ _774244) ^ [_1024289, _1024291] : [-(_1024289 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14899 ^ _774244 : [(14906 ^ _774244) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024291, _1024289) = 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), _1024291)), _1024289) = 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), _1024291), _1024289))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (14900 ^ _774244) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024291, _1024289) = 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), _1024291)), _1024289) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024291), _1024289)))]]], (46383 ^ _774244) ^ [_1690823, _1690825, _1690827] : [-(hAPP(c_List_Olexn(_1690823, _1690825), hAPP(c_Nat_OSuc, _1690827)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1690823), tc_List_Olist(_1690823)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1690823, tc_List_Olist(_1690823)), tc_prod(_1690823, tc_List_Olist(_1690823))), tc_prod(tc_List_Olist(_1690823), tc_List_Olist(_1690823)), c_Product__Type_Omap__pair(tc_prod(_1690823, tc_List_Olist(_1690823)), tc_List_Olist(_1690823), tc_prod(_1690823, tc_List_Olist(_1690823)), tc_List_Olist(_1690823), hAPP(c_Product__Type_Oprod_Oprod__case(_1690823, tc_List_Olist(_1690823), tc_List_Olist(_1690823)), c_List_Olist_OCons(_1690823)), hAPP(c_Product__Type_Oprod_Oprod__case(_1690823, tc_List_Olist(_1690823), tc_List_Olist(_1690823)), c_List_Olist_OCons(_1690823)))), c_Wellfounded_Olex__prod(_1690823, tc_List_Olist(_1690823), _1690825, hAPP(c_List_Olexn(_1690823, _1690825), _1690827)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1690823), tc_List_Olist(_1690823))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1690823), tc_List_Olist(_1690823), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690823), tc_fun(tc_List_Olist(_1690823), tc_HOL_Obool), tc_fun(tc_List_Olist(_1690823), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1690823), tc_HOL_Obool), tc_fun(tc_List_Olist(_1690823), tc_HOL_Obool)), tc_List_Olist(_1690823)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1690823))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1690823)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690823), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1690823)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1690823)))), hAPP(c_Nat_OSuc, _1690827))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690823), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1690823)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1690823)))), hAPP(c_Nat_OSuc, _1690827)))))))], (36583 ^ _774244) ^ [_1451000, _1451002, _1451004] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1451000, tc_HOL_Obool)), _1451002), _1451004) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451000, tc_HOL_Obool)), _1451002), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1451000, tc_HOL_Obool)), _1451004)))], (38091 ^ _774244) ^ [_1484453, _1484455, _1484457, _1484459, _1484461, _1484463] : [c_Fun_Oinj__on(_1484453, _1484455, hAPP(c_Fun_Ocomp(_1484457, _1484455, _1484453, _1484459), _1484461), _1484463), -(c_Fun_Oinj__on(_1484457, _1484455, _1484459, hAPP(c_Set_Oimage(_1484453, _1484457, _1484461), _1484463)))], (44819 ^ _774244) ^ [_1651126, _1651128, _1651130, _1651132] : [-(_1651126 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1651128, tc_HOL_Obool), tc_HOL_Obool))), 44825 ^ _774244 : [(44828 ^ _774244) ^ [] : [c_Fun_Oinj__on(_1651128, _1651130, _1651132, 44824 ^ [_1651126, _1651128, _1651130, _1651132])], (44826 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1651128, tc_HOL_Obool)), 44824 ^ [_1651126, _1651128, _1651130, _1651132]), _1651126)))]], -(c_Fun_Oinj__on(_1651128, _1651130, _1651132, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1651128, tc_HOL_Obool), _1651126)))], (50597 ^ _774244) ^ [_1789349, _1789351, _1789353, _1789355] : [-(hBOOL(hAPP(_1789349, _1789351))), -(c_List_OtakeWhile(_1789353, _1789349, hAPP(hAPP(c_List_Olist_OCons(_1789353), _1789351), _1789355)) = c_List_Olist_ONil(_1789353))], (19141 ^ _774244) ^ [_1100928] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1100928)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1100928))))], (25455 ^ _774244) ^ [_1218279, _1218281, _1218283] : [class_Rings_Ocomm__ring__1(_1218279), 25458 ^ _774244 : [(25465 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1218279), _1218281), _1218283)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1218279), _1218281), hAPP(c_Groups_Ouminus__class_Ouminus(_1218279), _1218283))))], (25459 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1218279), _1218281), hAPP(c_Groups_Ouminus__class_Ouminus(_1218279), _1218283))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1218279), _1218281), _1218283)))]]], (16711 ^ _774244) ^ [_1059363, _1059365, _1059367] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1059363), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1059365), _1059367)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1059363), _1059365)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1059363), _1059367)))], (31025 ^ _774244) ^ [_1330646, _1330648, _1330650, _1330652] : [_1330646 = _1330648, hBOOL(hAPP(hAPP(c_member(_1330650), _1330648), _1330652)), -(hBOOL(hAPP(hAPP(c_member(_1330650), _1330646), _1330652)))], (13609 ^ _774244) ^ [_1001254, _1001256] : [class_Divides_Osemiring__div(_1001254), -(c_Divides_Odiv__class_Omod(_1001254, _1001256, c_Groups_Oone__class_Oone(_1001254)) = c_Groups_Ozero__class_Ozero(_1001254))], (9730 ^ _774244) ^ [_934566, _934568] : [class_Int_Oring__char__0(_934566), 9733 ^ _774244 : [(9740 ^ _774244) ^ [] : [_934568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_934566), _934568) = c_Groups_Ozero__class_Ozero(_934566))], (9734 ^ _774244) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_934566), _934568) = c_Groups_Ozero__class_Ozero(_934566), -(_934568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (5334 ^ _774244) ^ [_856701, _856703] : [_856703 = _856701, -(c_Groups_Oplus__class_Oplus(_856703) = c_Groups_Oplus__class_Oplus(_856701))], (40027 ^ _774244) ^ [_1530681, _1530683, _1530685, _1530687] : [c_Finite__Set_Ofolding__one(_1530681, _1530683, _1530685), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530681), _1530687)), -(hAPP(_1530685, _1530687) = hAPP(c_Finite__Set_Ofold1(_1530681, _1530683), _1530687))], (33426 ^ _774244) ^ [_1380827, _1380829, _1380831] : [class_Orderings_Olinorder(_1380827), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380827), _1380829)), hBOOL(hAPP(hAPP(c_member(_1380827), _1380831), _1380829)), 33437 ^ _774244 : [(33444 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1380827, tc_HOL_Obool)), _1380829), hAPP(hAPP(c_Set_Oinsert(_1380827), _1380831), c_Orderings_Obot__class_Obot(tc_fun(_1380827, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1380827, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1380827, c_Orderings_Oord__class_Omax(_1380827), _1380829) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1380827), _1380831), c_Big__Operators_Olattice_OSup__fin(_1380827, c_Orderings_Oord__class_Omax(_1380827), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1380827, tc_HOL_Obool)), _1380829), hAPP(hAPP(c_Set_Oinsert(_1380827), _1380831), c_Orderings_Obot__class_Obot(tc_fun(_1380827, tc_HOL_Obool)))))))], (33438 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1380827, tc_HOL_Obool)), _1380829), hAPP(hAPP(c_Set_Oinsert(_1380827), _1380831), c_Orderings_Obot__class_Obot(tc_fun(_1380827, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1380827, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1380827, c_Orderings_Oord__class_Omax(_1380827), _1380829) = _1380831)]]], (20631 ^ _774244) ^ [_1127342, _1127344, _1127346, _1127348] : [class_Fields_Olinordered__field__inverse__zero(_1127342), 20634 ^ _774244 : [(20635 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127342), _1127344), _1127346)), _1127348)), 20638 ^ _774244 : [(20645 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), c_Groups_Ozero__class_Ozero(_1127342)), _1127346))), 20648 ^ _774244 : [(20655 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), _1127346), c_Groups_Ozero__class_Ozero(_1127342)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), c_Groups_Ozero__class_Ozero(_1127342)), _1127348)))], (20649 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), _1127346), c_Groups_Ozero__class_Ozero(_1127342))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127342), _1127348), _1127346)), _1127344)))]]], (20639 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), c_Groups_Ozero__class_Ozero(_1127342)), _1127346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), _1127344), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127342), _1127348), _1127346))))]]], (20661 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127342), _1127344), _1127346)), _1127348))), 20664 ^ _774244 : [(20667 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), _1127344), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127342), _1127348), _1127346)))], (20665 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), c_Groups_Ozero__class_Ozero(_1127342)), _1127346)))]], 20668 ^ _774244 : [(20671 ^ _774244) ^ [] : [20672 ^ _774244 : [(20675 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127342), _1127348), _1127346)), _1127344))], (20673 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), _1127346), c_Groups_Ozero__class_Ozero(_1127342))))]], 20676 ^ _774244 : [(20679 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), c_Groups_Ozero__class_Ozero(_1127342)), _1127348))], (20677 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), _1127346), c_Groups_Ozero__class_Ozero(_1127342)))]]], (20669 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127342), c_Groups_Ozero__class_Ozero(_1127342)), _1127346))]]]]], (40830 ^ _774244) ^ [_1548591, _1548593] : [-(hAPP(c_Set_OPow(_1548591), _1548593) = hAPP(c_Set_OCollect(tc_fun(_1548591, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1548591, tc_HOL_Obool), tc_fun(_1548591, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1548591, tc_HOL_Obool))), _1548593)))], (36591 ^ _774244) ^ [_1451184, _1451186, _1451188] : [-(hAPP(c_Relation_OImage(_1451184, _1451184, c_Relation_OId__on(_1451184, _1451186)), _1451188) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451184, tc_HOL_Obool)), _1451186), _1451188))], (35211 ^ _774244) ^ [_1419446, _1419448, _1419450, _1419452, _1419454, _1419456, _1419458] : [-(hAPP(c_Product__Type_Oapsnd(_1419446, _1419448, _1419450, _1419452), hAPP(c_Product__Type_Oapsnd(_1419454, _1419446, _1419450, _1419456), _1419458)) = hAPP(c_Product__Type_Oapsnd(_1419454, _1419448, _1419450, hAPP(c_Fun_Ocomp(_1419446, _1419448, _1419454, _1419452), _1419456)), _1419458))], (40069 ^ _774244) ^ [_1531437, _1531439] : [class_Lattices_Olattice(_1531437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531437), _1531439)), -(c_Big__Operators_Olattice__class_OInf__fin(_1531437, _1531439) = hAPP(c_Finite__Set_Ofold1(_1531437, c_Lattices_Osemilattice__inf__class_Oinf(_1531437)), _1531439))], (45397 ^ _774244) ^ [_1665115, _1665117, _1665119] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1665115), _1665117))), -(c_Smallcheck_Osmall_H(_1665119, _1665115, _1665117) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1665119, _1665115, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1665117), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1665119, _1665117)))], (6698 ^ _774244) ^ [_882127, _882129, _882131, _882133] : [-(hAPP(c_Option_Ooption_Ooption__case(_882127, _882129, _882131, _882133), c_Option_Ooption_ONone(_882129)) = _882131)], (5180 ^ _774244) ^ [_854352, _854354] : [_854354 = _854352, -(c_Nat_Osemiring__1__class_Oof__nat(_854354) = c_Nat_Osemiring__1__class_Oof__nat(_854352))], (28871 ^ _774244) ^ [_1287617, _1287619, _1287621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287617, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1287617, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28872 ^ [_1287617, _1287619, _1287621])), _1287619)), _1287621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287617, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1287617, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1287619)), _1287621)))], (7591 ^ _774244) ^ [_897948, _897950] : [class_Groups_Olinordered__ab__group__add(_897948), 7594 ^ _774244 : [(7601 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897948), c_Groups_Ozero__class_Ozero(_897948)), _897950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897948), c_Groups_Ozero__class_Ozero(_897948)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897948), _897950), _897950))))], (7595 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897948), c_Groups_Ozero__class_Ozero(_897948)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897948), _897950), _897950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897948), c_Groups_Ozero__class_Ozero(_897948)), _897950)))]]], (30023 ^ _774244) ^ [_1309094] : [-(c_Finite__Set_Ofun__left__comm__idem(_1309094, tc_fun(_1309094, tc_HOL_Obool), c_Set_Oinsert(_1309094)))], (24029 ^ _774244) ^ [_1191533, _1191535, _1191537] : [class_Orderings_Olinorder(_1191533), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191533), _1191535), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191533), _1191535), _1191537)) = _1191535)], (18403 ^ _774244) ^ [_1088290, _1088292] : [class_Int_Onumber__ring(_1088290), 18406 ^ _774244 : [(18413 ^ _774244) ^ [] : [c_Int_Oiszero(_1088290, hAPP(c_Int_Onumber__class_Onumber__of(_1088290), 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), _1088292)))), -(c_Groups_Oone__class_Oone(_1088290) = hAPP(c_Int_Onumber__class_Onumber__of(_1088290), _1088292))], (18407 ^ _774244) ^ [] : [c_Groups_Oone__class_Oone(_1088290) = hAPP(c_Int_Onumber__class_Onumber__of(_1088290), _1088292), -(c_Int_Oiszero(_1088290, hAPP(c_Int_Onumber__class_Onumber__of(_1088290), 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), _1088292)))))]]], (40631 ^ _774244) ^ [_1542107, _1542109, _1542111] : [hBOOL(hAPP(hAPP(c_member(_1542107), _1542109), hAPP(c_Set_OCollect(_1542107), _1542111))), -(hBOOL(hAPP(_1542111, _1542109)))], (16825 ^ _774244) ^ [_1061608] : [_1061608 = 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), _1061608)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (48388 ^ _774244) ^ [_1740669, _1740671, _1740673, _1740675] : [-(hAPP(hAPP(c_List_Otake(_1740669), _1740671), hAPP(hAPP(c_List_Odrop(_1740669), _1740673), _1740675)) = hAPP(hAPP(c_List_Odrop(_1740669), _1740673), hAPP(hAPP(c_List_Otake(_1740669), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1740671), _1740673)), _1740675)))], (51423 ^ _774244) ^ [_1801130, _1801132] : [-(hAPP(c_COMBI(_1801130), _1801132) = _1801132)], (35189 ^ _774244) ^ [_1418832, _1418834, _1418836, _1418838, _1418840, _1418842] : [-(hAPP(c_Relation_OImage(_1418832, _1418834, _1418836), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418838, tc_fun(_1418832, tc_HOL_Obool)), _1418840), _1418842)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418838, tc_fun(_1418834, tc_HOL_Obool)), _1418840), hAPP(hAPP(c_COMBB(tc_fun(_1418832, tc_HOL_Obool), tc_fun(_1418834, tc_HOL_Obool), _1418838), c_Relation_OImage(_1418832, _1418834, _1418836)), _1418842)))], (51067 ^ _774244) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (16901 ^ _774244) ^ [_1063097, _1063099, _1063101, _1063103] : [class_Rings_Olinordered__semidom(_1063097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063097), c_Groups_Oone__class_Oone(_1063097)), _1063099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063097), hAPP(hAPP(c_Power_Opower__class_Opower(_1063097), _1063099), _1063101)), hAPP(hAPP(c_Power_Opower__class_Opower(_1063097), _1063099), _1063103))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1063101), _1063103)))], (46982 ^ _774244) ^ [_1705005, _1705007, _1705009] : [-(_1705005 = c_List_Olist_ONil(_1705007)), -(hBOOL(hAPP(hAPP(c_member(_1705007), hAPP(c_Product__Type_Ofst(_1705007, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1705007, _1705005), _1705009))), hAPP(c_List_Oset(_1705007), _1705005))))], (37837 ^ _774244) ^ [_1479007, _1479009] : [class_Lattices_Olattice(_1479007), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479007), _1479009)), -(_1479009 = c_Orderings_Obot__class_Obot(tc_fun(_1479007, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1479007), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1479007), 37850 ^ [_1479007, _1479009]), 37851 ^ [_1479007, _1479009])), hAPP(hAPP(c_Set_Oinsert(_1479007), 37850 ^ [_1479007, _1479009]), hAPP(hAPP(c_Set_Oinsert(_1479007), 37851 ^ [_1479007, _1479009]), c_Orderings_Obot__class_Obot(tc_fun(_1479007, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1479007), c_Big__Operators_Olattice__class_OInf__fin(_1479007, _1479009)), _1479009)))], (30851 ^ _774244) ^ [_1327547, _1327549, _1327551, _1327553] : [hBOOL(hAPP(hAPP(c_member(_1327547), _1327549), _1327551)), -(hBOOL(hAPP(hAPP(c_member(_1327547), _1327549), hAPP(hAPP(c_Set_Oinsert(_1327547), _1327553), _1327551))))], (9218 ^ _774244) ^ [_925510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _925510)), -(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, _925510))))], (6321 ^ _774244) ^ [_875757, _875759, _875761, _875763] : [c_Com_Ocom_OBODY(_875757) = c_Com_Ocom_OCall(_875759, _875761, _875763)], (39696 ^ _774244) ^ [_1521473, _1521475, _1521477, _1521479, _1521481, _1521483] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1521473, _1521475)), hAPP(hAPP(c_Product__Type_OPair(_1521473, _1521475), _1521477), _1521479)), hAPP(hAPP(c_Product__Type_OSigma(_1521473, _1521475), _1521481), _1521483))), 39699 ^ _774244 : [(39702 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1521475), _1521479), hAPP(_1521483, _1521477))))], (39700 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1521473), _1521477), _1521481)))]]], (51171 ^ _774244) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (46998 ^ _774244) ^ [_1705288, _1705290, _1705292, _1705294, _1705296] : [-(_1705288 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Lazy__Sequence_Oanamorph(_1705290, _1705292, _1705294, _1705288), _1705296) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1705292), _1705290), tc_prod(_1705292, _1705290), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1705292), _1705290), c_List_Olist_ONil(_1705292)), _1705296), hAPP(c_Product__Type_Oprod_Oprod__case(_1705292, _1705290, tc_prod(tc_List_Olist(_1705292), _1705290)), hAPP(hAPP(c_COMBC(_1705292, tc_fun(_1705290, tc_prod(tc_List_Olist(_1705292), _1705290)), tc_fun(_1705290, tc_prod(tc_List_Olist(_1705292), _1705290))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1705292), _1705290), tc_prod(tc_List_Olist(_1705292), _1705290)), tc_fun(tc_fun(_1705290, tc_prod(tc_List_Olist(_1705292), _1705290)), tc_fun(_1705290, tc_prod(tc_List_Olist(_1705292), _1705290))), _1705292), c_COMBB(tc_prod(tc_List_Olist(_1705292), _1705290), tc_prod(tc_List_Olist(_1705292), _1705290), _1705290)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1705292), tc_fun(_1705290, tc_prod(tc_List_Olist(_1705292), _1705290))), tc_fun(tc_prod(tc_List_Olist(_1705292), _1705290), tc_prod(tc_List_Olist(_1705292), _1705290)), _1705292), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1705292), _1705290, tc_prod(tc_List_Olist(_1705292), _1705290))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1705292), tc_List_Olist(_1705292)), tc_fun(tc_List_Olist(_1705292), tc_fun(_1705290, tc_prod(tc_List_Olist(_1705292), _1705290))), _1705292), hAPP(c_COMBB(tc_List_Olist(_1705292), tc_fun(_1705290, tc_prod(tc_List_Olist(_1705292), _1705290)), tc_List_Olist(_1705292)), c_Product__Type_OPair(tc_List_Olist(_1705292), _1705290))), c_List_Olist_OCons(_1705292))))), c_Lazy__Sequence_Oanamorph(_1705290, _1705292, _1705294, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1705288), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1705294, _1705296)))], (38459 ^ _774244) ^ [_1491709] : [-(c_Fun_Oinj__on(_1491709, tc_fun(_1491709, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1491709, tc_fun(_1491709, tc_HOL_Obool), tc_fun(_1491709, tc_HOL_Obool)), c_Set_Oinsert(_1491709)), c_Orderings_Obot__class_Obot(tc_fun(_1491709, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1491709, tc_HOL_Obool))))], (46737 ^ _774244) ^ [_1700442, _1700444, _1700446, _1700448] : [class_Groups_Ocomm__monoid__add(_1700442), 46740 ^ _774244 : [(46747 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1700444), _1700446))), -(c_Nitpick_Osetsum_H(_1700444, _1700442, _1700448, _1700446) = c_Groups_Ozero__class_Ozero(_1700442))], (46741 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1700444), _1700446)), -(c_Nitpick_Osetsum_H(_1700444, _1700442, _1700448, _1700446) = hAPP(c_List_Omonoid__add__class_Olistsum(_1700442), hAPP(hAPP(c_List_Omap(_1700444, _1700442), _1700448), c_Hilbert__Choice_OEps(tc_List_Olist(_1700444), hAPP(hAPP(c_COMBS(tc_List_Olist(_1700444), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1700444)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700444), tc_fun(_1700444, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1700444, tc_HOL_Obool), tc_fun(tc_fun(_1700444, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1700444)), c_fequal), c_List_Oset(_1700444))), _1700446))), c_List_Odistinct(_1700444))))))]]], (41622 ^ _774244) ^ [_1573822, _1573824, _1573826, _1573828, _1573830] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573822, _1573824)), hAPP(hAPP(c_Product__Type_OPair(_1573822, _1573824), _1573826), _1573828)), _1573830)), -(hBOOL(hAPP(hAPP(c_member(_1573824), _1573828), hAPP(c_Relation_ORange(_1573822, _1573824), _1573830))))], (13585 ^ _774244) ^ [_1000790, _1000792, _1000794] : [class_Divides_Osemiring__div(_1000790), -(c_Divides_Odiv__class_Omod(_1000790, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000790), _1000792), _1000794), _1000792) = c_Groups_Ozero__class_Ozero(_1000790))], (32634 ^ _774244) ^ [_1365668, _1365670] : [class_Int_Oring__char__0(_1365668), hBOOL(hAPP(hAPP(c_member(_1365668), _1365670), c_Int_Oring__1__class_OInts(_1365668))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1365668), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1365668), c_Groups_Oone__class_Oone(_1365668)), _1365670)), _1365670) = c_Groups_Ozero__class_Ozero(_1365668)], (46164 ^ _774244) ^ [_1683539, _1683541, _1683543, _1683545, _1683547] : [class_Orderings_Olinorder(_1683539), 46167 ^ _774244 : [(46176 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1683541), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1683541, _1683539, _1683543), _1683545), _1683547)))), -(hBOOL(hAPP(hAPP(c_member(_1683541), _1683545), hAPP(c_List_Oset(_1683541), _1683547)))), hBOOL(hAPP(c_List_Odistinct(_1683541), _1683547))], (46168 ^ _774244) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1683541), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1683541, _1683539, _1683543), _1683545), _1683547))), 46171 ^ _774244 : [(46174 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1683541), _1683547)))], (46172 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1683541), _1683545), hAPP(c_List_Oset(_1683541), _1683547)))]]]]], (49860 ^ _774244) ^ [_1772202, _1772204] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1772202, _1772204)))], (15044 ^ _774244) ^ [_1027134, _1027136] : [class_Groups_Ogroup__add(_1027134), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1027134), _1027136), c_Groups_Ozero__class_Ozero(_1027134)) = _1027136)], (19153 ^ _774244) ^ [_1101124] : [-(c_Int_Opred(c_Int_OBit0(_1101124)) = c_Int_OBit1(c_Int_Opred(_1101124)))], (10968 ^ _774244) ^ [_954543] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _954543) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34505 ^ _774244) ^ [_1402971] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1402971)), -(_1402971 = 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))), _1402971)), c_FunDef_Omax__strict)))], (18029 ^ _774244) ^ [_1082490] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1082490), 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), _1082490)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1082490)))], (33974 ^ _774244) ^ [_1391857, _1391859, _1391861] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1391857), _1391859), _1391861) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1391857), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1391857, tc_Int_Oint), _1391859), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1391861))), class_Groups_Ocomm__monoid__add(_1391857), class_Groups_Ocomm__monoid__mult(_1391857)], (21109 ^ _774244) ^ [_1135796, _1135798, _1135800] : [class_Fields_Olinordered__field__inverse__zero(_1135796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135796), c_Groups_Ozero__class_Ozero(_1135796)), _1135798)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135796), hAPP(c_Groups_Oabs__class_Oabs(_1135796), _1135800)), _1135798) = hAPP(c_Groups_Oabs__class_Oabs(_1135796), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135796), _1135800), _1135798)))], (18685 ^ _774244) ^ [_1093064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1093064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1093064)))], (49858 ^ _774244) ^ [_1772174, _1772176] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1772174, _1772176)))], (7651 ^ _774244) ^ [_899039, _899041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _899039), hAPP(c_Nat_OSuc, _899041))), -(_899039 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7659 ^ _774244 : [(7662 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 7658 ^ [_899039, _899041]), _899041)))], (7660 ^ _774244) ^ [] : [-(_899039 = hAPP(c_Nat_OSuc, 7658 ^ [_899039, _899041]))]]], (31158 ^ _774244) ^ [_1333599, _1333601, _1333603, _1333605, _1333607] : [hBOOL(hAPP(hAPP(c_member(_1333599), _1333601), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1333603, tc_fun(_1333599, tc_HOL_Obool)), _1333605), _1333607))), 31162 ^ _774244 : [(31165 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333599), _1333601), hAPP(_1333607, 31161 ^ [_1333599, _1333601, _1333603, _1333605, _1333607]))))], (31163 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333603), 31161 ^ [_1333599, _1333601, _1333603, _1333605, _1333607]), _1333605)))]]], (39938 ^ _774244) ^ [_1528360, _1528362, _1528364, _1528366, _1528368, _1528370] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1528360, _1528362), _1528362, tc_prod(_1528364, _1528366), c_Product__Type_Osnd(_1528360, _1528362)), c_Product__Type_Omap__pair(_1528364, _1528360, _1528366, _1528362, _1528368, _1528370)) = hAPP(c_Fun_Ocomp(_1528366, _1528362, tc_prod(_1528364, _1528366), _1528370), c_Product__Type_Osnd(_1528364, _1528366)))], (40149 ^ _774244) ^ [_1532815, _1532817, _1532819] : [class_Lattices_Osemilattice__inf(_1532815), hBOOL(hAPP(c_Finite__Set_Ofinite(_1532815), _1532817)), hBOOL(hAPP(hAPP(c_member(_1532815), _1532819), _1532817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1532815), hAPP(c_Finite__Set_Ofold1(_1532815, c_Lattices_Osemilattice__inf__class_Oinf(_1532815)), _1532817)), _1532819)))], (51251 ^ _774244) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (4988 ^ _774244) ^ [_851304, _851306, _851308, _851310, _851312, _851314, _851316, _851318, _851320, _851322] : [-(c_List_Ofoldr(_851322, _851318, _851314, _851310, _851306) = c_List_Ofoldr(_851320, _851316, _851312, _851308, _851304)), _851322 = _851320, _851318 = _851316, _851314 = _851312, _851310 = _851308, _851306 = _851304], (16131 ^ _774244) ^ [_1048480, _1048482, _1048484] : [class_Rings_Oring__1(_1048480), -(hAPP(c_Int_Oring__1__class_Oof__int(_1048480), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1048482), _1048484)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1048480), hAPP(c_Int_Oring__1__class_Oof__int(_1048480), _1048482)), _1048484))], (9310 ^ _774244) ^ [_927046, _927048] : [class_Groups_Ogroup__add(_927046), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927046), hAPP(c_Groups_Ouminus__class_Ouminus(_927046), _927048)), _927048) = c_Groups_Ozero__class_Ozero(_927046))], (13543 ^ _774244) ^ [_999929, _999931, _999933, _999935] : [class_Divides_Osemiring__div(_999929), -(c_Divides_Odiv__class_Omod(_999929, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999929), _999931), _999933), _999935) = c_Divides_Odiv__class_Omod(_999929, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999929), c_Divides_Odiv__class_Omod(_999929, _999931, _999935)), _999933), _999935))], (51127 ^ _774244) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (22078 ^ _774244) ^ [_1153563, _1153565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1153563), _1153565)), -(c_Divides_Odivmod__nat(_1153563, _1153565) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1153563))], (12672 ^ _774244) ^ [_984815, _984817] : [class_Rings_Olinordered__idom(_984815), 12675 ^ _774244 : [(12682 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984815), c_Groups_Ozero__class_Ozero(_984815)), _984817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984815), c_Groups_Ozero__class_Ozero(_984815)), c_Groups_Osgn__class_Osgn(_984815, _984817))))], (12676 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984815), c_Groups_Ozero__class_Ozero(_984815)), c_Groups_Osgn__class_Osgn(_984815, _984817))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984815), c_Groups_Ozero__class_Ozero(_984815)), _984817)))]]], (7473 ^ _774244) ^ [_895444, _895446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _895444)), hAPP(c_Nat_OSuc, _895446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _895444), _895446)))], (16343 ^ _774244) ^ [_1052203, _1052205] : [16344 ^ _774244 : [(16347 ^ _774244) ^ [] : [_1052205 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16345 ^ _774244) ^ [] : [-(_1052203 = 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), _1052203)), _1052205))))], (49302 ^ _774244) ^ [_1760627, _1760629, _1760631] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1760627, tc_HOL_Obool)), hAPP(c_List_Oset(_1760627), hAPP(c_List_Ofilter(_1760627, _1760629), _1760631))), hAPP(c_List_Oset(_1760627), _1760631))))], (36233 ^ _774244) ^ [_1442753, _1442755] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442753, tc_HOL_Obool)), _1442755), c_Orderings_Obot__class_Obot(tc_fun(_1442753, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1442753, tc_HOL_Obool)))], (46236 ^ _774244) ^ [_1685806, _1685808, _1685810] : [-(_1685806 = _1685808), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685810)), _1685806) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685810)), _1685808), 46242 ^ _774244 : [(46245 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1685810, _1685810, tc_HOL_Obool), c_fequal), 46241 ^ [_1685806, _1685808, _1685810]))], (46243 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1685810, _1685810)), 46241 ^ [_1685806, _1685808, _1685810]), hAPP(c_List_Oset(tc_prod(_1685810, _1685810)), hAPP(hAPP(c_List_Ozip(_1685810, _1685810), _1685806), _1685808)))))]]], (24583 ^ _774244) ^ [_1202296, _1202298, _1202300] : [-(c_Product__Type_Ointernal__split(_1202296, _1202298, _1202300) = c_Product__Type_Oprod_Oprod__case(_1202296, _1202298, _1202300))], (49892 ^ _774244) ^ [_1772654, _1772656, _1772658, _1772660, _1772662] : [class_Orderings_Olinorder(_1772654), 49895 ^ _774244 : [(49902 ^ _774244) ^ [] : [c_List_Olinorder__class_Osorted(_1772654, hAPP(hAPP(c_List_Omap(_1772656, _1772654), _1772658), _1772662)), -(c_List_Olinorder__class_Osorted(_1772654, hAPP(hAPP(c_List_Omap(_1772656, _1772654), _1772658), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1772656, _1772654, _1772658), _1772660), _1772662))))], (49896 ^ _774244) ^ [] : [c_List_Olinorder__class_Osorted(_1772654, hAPP(hAPP(c_List_Omap(_1772656, _1772654), _1772658), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1772656, _1772654, _1772658), _1772660), _1772662))), -(c_List_Olinorder__class_Osorted(_1772654, hAPP(hAPP(c_List_Omap(_1772656, _1772654), _1772658), _1772662)))]]], (3344 ^ _774244) ^ [_825604, _825606] : [_825606 = _825604, -(c_Nitpick_ORep__Frac(_825606) = c_Nitpick_ORep__Frac(_825604))], (21887 ^ _774244) ^ [] : [-(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))], (1004 ^ _774244) ^ [_789518, _789520] : [-(class_Rings_Olinordered__ring__strict(_789518)), _789520 = _789518, class_Rings_Olinordered__ring__strict(_789520)], (22094 ^ _774244) ^ [_1153866, _1153868, _1153870] : [class_Int_Onumber__ring(_1153866), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1153866), _1153868), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1153870))) = hAPP(hAPP(c_HOL_OLet(_1153866, _1153866), hAPP(hAPP(c_Power_Opower__class_Opower(_1153866), _1153868), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1153870))), hAPP(hAPP(c_COMBS(_1153866, _1153866, _1153866), c_Groups_Otimes__class_Otimes(_1153866)), c_COMBI(_1153866))))], (8896 ^ _774244) ^ [_919869, _919871] : [class_Groups_Olinordered__ab__group__add(_919869), 8899 ^ _774244 : [(8906 ^ _774244) ^ [] : [_919871 = c_Groups_Ozero__class_Ozero(_919869), -(hAPP(c_Groups_Ouminus__class_Ouminus(_919869), _919871) = _919871)], (8900 ^ _774244) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_919869), _919871) = _919871, -(_919871 = c_Groups_Ozero__class_Ozero(_919869))]]], (44394 ^ _774244) ^ [_1641785, _1641787] : [class_Complete__Lattice_Ocomplete__lattice(_1641785), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641785), _1641787)), -(c_Complete__Lattice_OInf__class_OInf(_1641785, _1641787) = hAPP(hAPP(c_Finite__Set_Ofold(_1641785, _1641785, c_Lattices_Osemilattice__inf__class_Oinf(_1641785)), c_Orderings_Otop__class_Otop(_1641785)), _1641787))], (15292 ^ _774244) ^ [_1031532, _1031534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031532), _1031534)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1031534, _1031532) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031534), _1031532), _1031532))], (26602 ^ _774244) ^ [_1240916, _1240918] : [hAPP(_1240916, 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), _1240916), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1240918)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1240916), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1240918)))], (45563 ^ _774244) ^ [_1668967, _1668969, _1668971, _1668973, _1668975, _1668977] : [-(hAPP(hAPP(c_List_Omap(_1668967, _1668969), _1668971), hAPP(hAPP(c_List_Omap(_1668973, _1668967), _1668975), _1668977)) = hAPP(hAPP(c_List_Omap(_1668973, _1668969), hAPP(c_Fun_Ocomp(_1668967, _1668969, _1668973, _1668971), _1668975)), _1668977))], (50332 ^ _774244) ^ [_1782332, _1782334, _1782336] : [_1782334 = hAPP(c_List_Orev(_1782332), _1782336), -(hAPP(c_List_Orev(_1782332), _1782334) = _1782336)], (24939 ^ _774244) ^ [_1209675, _1209677, _1209679] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209675), _1209677)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209677), _1209675))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209677), _1209679)), 24950 ^ _774244 : [(24953 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209679), _1209675))], (24951 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209675), _1209679)))]]], (6502 ^ _774244) ^ [_879065, _879067] : [class_Groups_Ocomm__monoid__add(_879065), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879065), c_Groups_Ozero__class_Ozero(_879065)), _879067) = _879067)], (15398 ^ _774244) ^ [_1033707, _1033709, _1033711, _1033713, _1033715, _1033717] : [class_Rings_Oring(_1033707), 15401 ^ _774244 : [(15408 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033707), _1033709), _1033715)), _1033711)), _1033713) = _1033717, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033709), _1033711)), _1033713) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033715), _1033711)), _1033717))], (15402 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033709), _1033711)), _1033713) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033715), _1033711)), _1033717), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033707), _1033709), _1033715)), _1033711)), _1033713) = _1033717)]]], (19569 ^ _774244) ^ [_1108282, _1108284, _1108286] : [class_Rings_Olinordered__idom(_1108282), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108282), c_Groups_Ozero__class_Ozero(_1108282)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108282), hAPP(hAPP(c_Power_Opower__class_Opower(_1108282), _1108284), 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(_1108282), _1108286), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (19183 ^ _774244) ^ [_1101555, _1101557] : [class_Int_Onumber__ring(_1101555), -(hAPP(c_Int_Onumber__class_Onumber__of(_1101555), c_Int_OBit0(_1101557)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101555), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101555), c_Groups_Ozero__class_Ozero(_1101555)), hAPP(c_Int_Onumber__class_Onumber__of(_1101555), _1101557))), hAPP(c_Int_Onumber__class_Onumber__of(_1101555), _1101557)))], (344 ^ _774244) ^ [_779392, _779394, _779396, _779398, _779400, _779402, _779404, _779406, _779408, _779410] : [-(c_Typedef_Otype__definition(_779408, _779404, _779400, _779396, _779392)), c_Typedef_Otype__definition(_779410, _779406, _779402, _779398, _779394), _779410 = _779408, _779406 = _779404, _779402 = _779400, _779398 = _779396, _779394 = _779392], (9870 ^ _774244) ^ [_936944] : [class_Rings_Olinordered__semidom(_936944), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936944), c_Groups_Ozero__class_Ozero(_936944)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936944), c_Groups_Oone__class_Oone(_936944)), c_Groups_Oone__class_Oone(_936944)))))], (11264 ^ _774244) ^ [_959626, _959628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959626), _959628)), -(_959628 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959626), 11267 ^ [_959626, _959628]))], (29002 ^ _774244) ^ [_1290371, _1290373] : [class_Orderings_Obot(_1290371), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290371), c_Orderings_Obot__class_Obot(_1290371)), _1290373)))], (36529 ^ _774244) ^ [_1449459, _1449461, _1449463, _1449465] : [-(hBOOL(hAPP(hAPP(c_member(_1449459), _1449461), _1449463))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449459, tc_HOL_Obool)), _1449463), hAPP(hAPP(c_Set_Oinsert(_1449459), _1449461), _1449465)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449459, tc_HOL_Obool)), _1449463), _1449465))], (13463 ^ _774244) ^ [_998181, _998183, _998185, _998187] : [class_Divides_Osemiring__div(_998181), -(c_Divides_Odiv__class_Omod(_998181, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998181), c_Divides_Odiv__class_Omod(_998181, _998183, _998185)), _998187), _998185) = c_Divides_Odiv__class_Omod(_998181, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998181), _998183), _998187), _998185))], (41806 ^ _774244) ^ [_1578241, _1578243, _1578245, _1578247] : [hBOOL(hAPP(hAPP(c_member(_1578241), _1578243), hAPP(c_Relation_ODomain(_1578241, _1578245), _1578247))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578241, _1578245)), hAPP(hAPP(c_Product__Type_OPair(_1578241, _1578245), _1578243), 41809 ^ [_1578241, _1578243, _1578245, _1578247])), _1578247)))], (33272 ^ _774244) ^ [_1377348, _1377350, _1377352, _1377354, _1377356, _1377358, _1377360, _1377362] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1377348, _1377350), tc_prod(_1377348, _1377350))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1377348, _1377350), tc_prod(_1377348, _1377350)), hAPP(hAPP(c_Product__Type_OPair(_1377348, _1377350), _1377352), _1377354)), hAPP(hAPP(c_Product__Type_OPair(_1377348, _1377350), _1377356), _1377358))), c_Wellfounded_Olex__prod(_1377348, _1377350, _1377360, _1377362))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1377348, _1377348)), hAPP(hAPP(c_Product__Type_OPair(_1377348, _1377348), _1377352), _1377356)), _1377360))), 33279 ^ _774244 : [(33282 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1377350, _1377350)), hAPP(hAPP(c_Product__Type_OPair(_1377350, _1377350), _1377354), _1377358)), _1377362)))], (33280 ^ _774244) ^ [] : [-(_1377352 = _1377356)]]], (13597 ^ _774244) ^ [_1001000, _1001002, _1001004, _1001006] : [class_Divides_Osemiring__div(_1001000), -(c_Divides_Odiv__class_Omod(_1001000, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001000), _1001002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001000), _1001004), _1001006)), _1001006) = c_Divides_Odiv__class_Omod(_1001000, _1001002, _1001006))], (15158 ^ _774244) ^ [_1029194, _1029196] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029194), _1029196) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029196), _1029194) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1029194 = _1029196)], (37239 ^ _774244) ^ [_1465103, _1465105, _1465107] : [class_Orderings_Olinorder(_1465103), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465103), _1465105)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465103), _1465107)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465103, tc_HOL_Obool)), _1465105), _1465107) = c_Orderings_Obot__class_Obot(tc_fun(_1465103, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1465103), c_Big__Operators_Olattice_OSup__fin(_1465103, c_Orderings_Oord__class_Omax(_1465103), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1465103, tc_HOL_Obool)), _1465105), _1465107))), c_Big__Operators_Olattice_OSup__fin(_1465103, c_Orderings_Oord__class_Omax(_1465103), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465103, tc_HOL_Obool)), _1465105), _1465107))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1465103), c_Big__Operators_Olattice_OSup__fin(_1465103, c_Orderings_Oord__class_Omax(_1465103), _1465105)), c_Big__Operators_Olattice_OSup__fin(_1465103, c_Orderings_Oord__class_Omax(_1465103), _1465107)))], (46567 ^ _774244) ^ [_1695935, _1695937, _1695939, _1695941, _1695943] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695935), tc_List_Olist(_1695935))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695935), tc_List_Olist(_1695935)), hAPP(hAPP(c_List_Olist_OCons(_1695935), _1695937), _1695939)), _1695941)), c_List_Olistrel(_1695935, _1695943))), 46572 ^ _774244 : [(46577 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695935), tc_List_Olist(_1695935))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695935), tc_List_Olist(_1695935)), _1695939), 46571 ^ [_1695935, _1695937, _1695939, _1695941, _1695943])), c_List_Olistrel(_1695935, _1695943))))], (46575 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1695935, _1695935)), hAPP(hAPP(c_Product__Type_OPair(_1695935, _1695935), _1695937), 46570 ^ [_1695935, _1695937, _1695939, _1695941, _1695943])), _1695943)))], (46573 ^ _774244) ^ [] : [-(_1695941 = hAPP(hAPP(c_List_Olist_OCons(_1695935), 46570 ^ [_1695935, _1695937, _1695939, _1695941, _1695943]), 46571 ^ [_1695935, _1695937, _1695939, _1695941, _1695943]))]]], (50386 ^ _774244) ^ [_1783602, _1783604, _1783606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1783602), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783604)), _1783606))), -(hAPP(hAPP(c_List_Onth(_1783604), hAPP(c_List_Orev(_1783604), _1783606)), _1783602) = hAPP(hAPP(c_List_Onth(_1783604), _1783606), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783604)), _1783606)), hAPP(c_Nat_OSuc, _1783602))))], (51297 ^ _774244) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (34722 ^ _774244) ^ [_1408550, _1408552] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1408550, _1408550)), hAPP(hAPP(c_Product__Type_OPair(_1408550, _1408550), 34723 ^ [_1408550, _1408552]), 34723 ^ [_1408550, _1408552])), _1408552))), -(c_Relation_Oirrefl(_1408550, _1408552))], (15932 ^ _774244) ^ [_1044897, _1044899] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044897, _1044899) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044897), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1044897), _1044899)), _1044899)))], (4720 ^ _774244) ^ [_847174, _847176, _847178, _847180, _847182, _847184, _847186, _847188] : [-(c_List_Omap__filter(_847188, _847184, _847180, _847176) = c_List_Omap__filter(_847186, _847182, _847178, _847174)), _847188 = _847186, _847184 = _847182, _847180 = _847178, _847176 = _847174], (7732 ^ _774244) ^ [_900338, _900340] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _900338), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900340), _900338)))))], (26067 ^ _774244) ^ [_1229570, _1229572] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1229570))), _1229572)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1229570), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229572))))], (28936 ^ _774244) ^ [_1289082, _1289084, _1289086, _1289088] : [hAPP(c_Set_Oimage(_1289082, _1289084, _1289086), _1289088) = c_Orderings_Obot__class_Obot(tc_fun(_1289084, tc_HOL_Obool)), -(_1289088 = c_Orderings_Obot__class_Obot(tc_fun(_1289082, tc_HOL_Obool)))], (18051 ^ _774244) ^ [_1082801, _1082803] : [class_Int_Onumber__ring(_1082801), 18054 ^ _774244 : [(18061 ^ _774244) ^ [] : [c_Int_Oiszero(_1082801, hAPP(c_Int_Onumber__class_Onumber__of(_1082801), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1082803)))), -(c_Groups_Ozero__class_Ozero(_1082801) = hAPP(c_Int_Onumber__class_Onumber__of(_1082801), _1082803))], (18055 ^ _774244) ^ [] : [c_Groups_Ozero__class_Ozero(_1082801) = hAPP(c_Int_Onumber__class_Onumber__of(_1082801), _1082803), -(c_Int_Oiszero(_1082801, hAPP(c_Int_Onumber__class_Onumber__of(_1082801), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1082803)))))]]], (24527 ^ _774244) ^ [_1201008] : [-(c_Nitpick_Ozero__frac(_1201008) = c_Nitpick_OAbs__Frac(_1201008, 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))))], (24733 ^ _774244) ^ [_1205963, _1205965, _1205967, _1205969, _1205971, _1205973, _1205975] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1205963, _1205965, _1205967, _1205969), _1205971), _1205973), _1205975) = c_New__DSequence_Opos__bind(_1205963, _1205965, hAPP(hAPP(hAPP(_1205967, _1205971), _1205973), _1205975), hAPP(hAPP(c_COMBC(_1205963, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1205965))), hAPP(hAPP(c_COMBC(_1205963, 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(_1205965)))), hAPP(hAPP(c_COMBC(_1205963, 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(_1205965))))), _1205969), _1205971)), _1205973)), _1205975)))], (7758 ^ _774244) ^ [_900888, _900890, _900892, _900894] : [hAPP(c_Sum__Type_OInr(_900888, _900890), _900892) = hAPP(c_Sum__Type_OInl(_900890, _900888), _900894)], (12236 ^ _774244) ^ [_976788] : [-(hBOOL(hAPP(_976788, 12243 ^ [_976788]))), 12237 ^ _774244 : [(12238 ^ _774244) ^ [_976840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _976840)), hBOOL(hAPP(_976788, hAPP(c_Int_Onat, _976840)))]]], (29049 ^ _774244) ^ [_1291298, _1291300, _1291302] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291298, tc_fun(_1291300, tc_HOL_Obool)), _1291302), hAPP(c_COMBK(tc_fun(_1291300, tc_HOL_Obool), _1291298), c_Orderings_Obot__class_Obot(tc_fun(_1291300, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1291300, tc_HOL_Obool)))], (22140 ^ _774244) ^ [_1154826, _1154828, _1154830] : [-(hAPP(c_Divides_Oadjust(_1154826), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1154828), _1154830)) = 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), _1154830), _1154826)), 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)))), _1154828)), 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)))), _1154828)), _1154830))))], (50206 ^ _774244) ^ [_1779652, _1779654] : [c_List_Olist_ONil(_1779652) = c_List_Oconcat(_1779652, _1779654), 50209 ^ _774244 : [(50210 ^ _774244) ^ [_1779743] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1779652)), _1779743), hAPP(c_List_Oset(tc_List_Olist(_1779652)), _1779654))), -(_1779743 = c_List_Olist_ONil(_1779652))]]], (50235 ^ _774244) ^ [_1780270, _1780272] : [50237 ^ _774244 : [(50240 ^ _774244) ^ [] : [50236 ^ [_1780270, _1780272] = c_List_Olist_ONil(_1780270)], (50238 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1780270)), 50236 ^ [_1780270, _1780272]), hAPP(c_List_Oset(tc_List_Olist(_1780270)), _1780272))))]], -(c_List_Oconcat(_1780270, _1780272) = c_List_Olist_ONil(_1780270))], (27316 ^ _774244) ^ [_1255665, _1255667, _1255669] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1255665), _1255667), _1255669) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1255665), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1255665, tc_Int_Oint), _1255667), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1255669))), class_Groups_Ocomm__monoid__add(_1255665), class_Groups_Ocomm__monoid__mult(_1255665)], (29462 ^ _774244) ^ [_1298734] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1298734), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1298734)), c_Option_Ooption_ONone(_1298734)), hAPP(c_Set_Oimage(_1298734, tc_Option_Ooption(_1298734), c_Option_Ooption_OSome(_1298734)), c_Orderings_Otop__class_Otop(tc_fun(_1298734, tc_HOL_Obool)))))], (32065 ^ _774244) ^ [_1354597, _1354599] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1354597, _1354597)), hAPP(hAPP(c_Product__Type_OPair(_1354597, _1354597), 32066 ^ [_1354597, _1354599]), 32066 ^ [_1354597, _1354599])), _1354599)), -(c_Nitpick_Orefl_H(_1354597, _1354599))], (12150 ^ _774244) ^ [_975389] : [hBOOL(hAPP(_975389, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12151 ^ [_975389]))), 12154 ^ _774244 : [(12155 ^ _774244) ^ [_975489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975489)), -(hBOOL(hAPP(_975389, _975489)))]]], (26107 ^ _774244) ^ [_1230339, _1230341] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230339), _1230341)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230339), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230341))))], (43293 ^ _774244) ^ [_1612217, _1612219] : [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), _1612217), _1612219)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1612217), _1612219)))], (24113 ^ _774244) ^ [_1193026] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193026) = _1193026)], (49519 ^ _774244) ^ [_1766334] : [class_Orderings_Olinorder(_1766334), -(c_List_Olinorder__class_Osorted(_1766334, c_List_Olist_ONil(_1766334)))], (36185 ^ _774244) ^ [_1441467, _1441469, _1441471, _1441473] : [class_Lattices_Odistrib__lattice(_1441467), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441467), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441467), _1441469), _1441471)), _1441473) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441467), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441467), _1441469), _1441473)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441467), _1441471), _1441473)))], (43433 ^ _774244) ^ [_1615514, _1615516, _1615518, _1615520, _1615522] : [-(hAPP(c_Relation_Oconverse(_1615514, _1615516), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615518, tc_fun(tc_prod(_1615514, _1615516), tc_HOL_Obool)), _1615520), _1615522)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615518, tc_fun(tc_prod(_1615516, _1615514), tc_HOL_Obool)), _1615520), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1615514, _1615516), tc_HOL_Obool), tc_fun(tc_prod(_1615516, _1615514), tc_HOL_Obool), _1615518), c_Relation_Oconverse(_1615514, _1615516)), _1615522)))], (12039 ^ _774244) ^ [_973421, _973423, _973425] : [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, _973421)), _973423)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973421)), _973425))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973423), _973425)))], (5816 ^ _774244) ^ [_867057, _867059, _867061, _867063, _867065, _867067, _867069, _867071, _867073, _867075, _867077] : [-(c_Com_Ocom_Ocom__rec(_867057, _867059, _867061, _867063, _867065, _867067, _867069, _867071, _867073, c_Com_Ocom_OSemi(_867075, _867077)) = hAPP(hAPP(hAPP(hAPP(_867065, _867075), _867077), c_Com_Ocom_Ocom__rec(_867057, _867059, _867061, _867063, _867065, _867067, _867069, _867071, _867073, _867075)), c_Com_Ocom_Ocom__rec(_867057, _867059, _867061, _867063, _867065, _867067, _867069, _867071, _867073, _867077)))], (23597 ^ _774244) ^ [_1183393, _1183395, _1183397, _1183399] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1183393), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183393), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183393), _1183395), _1183397)), _1183399) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183393), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183393), _1183395), _1183399)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183393), _1183397), _1183399)))], (41967 ^ _774244) ^ [_1582169, _1582171, _1582173, _1582175] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1582169), _1582171))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582173), hAPP(c_Set_Oimage(_1582169, _1582173, _1582175), _1582171))), 41975 ^ _774244 : [(41978 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1582169), hAPP(c_Set_OCollect(_1582169), hAPP(hAPP(c_COMBS(_1582169, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1582169), c_fconj), hAPP(hAPP(c_COMBC(_1582169, tc_fun(_1582169, tc_HOL_Obool), tc_HOL_Obool), c_member(_1582169)), _1582171))), hAPP(hAPP(c_COMBC(_1582169, _1582173, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1582173, tc_fun(_1582173, tc_HOL_Obool), _1582169), c_fequal), _1582175)), hAPP(_1582175, 41974 ^ [_1582169, _1582171, _1582173, _1582175]))))))], (41976 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1582169), 41974 ^ [_1582169, _1582171, _1582173, _1582175]), _1582171)))]]], (15174 ^ _774244) ^ [_1029431, _1029433, _1029435] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029431)), _1029433)), hAPP(c_Nat_OSuc, _1029435)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029431), _1029433)), _1029435))], (25081 ^ _774244) ^ [_1211999, _1212001] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211999), _1212001)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212001), _1211999)), -(_1211999 = _1212001)], (18859 ^ _774244) ^ [_1095869, _1095871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095869), 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)))), _1095871)), 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)))), _1095869)) = 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), _1095871), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1095869))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (37502 ^ _774244) ^ [_1472478, _1472480, _1472482, _1472484, _1472486, _1472488] : [hBOOL(hAPP(hAPP(_1472478, _1472480), _1472482)), hBOOL(hAPP(hAPP(_1472484, _1472480), _1472482)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472486, tc_fun(_1472488, tc_HOL_Obool))), _1472478), _1472484), _1472480), _1472482)))], (22406 ^ _774244) ^ [_1160397, _1160399] : [22407 ^ _774244 : [(22410 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1160399), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22408 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160397), _1160399))]], -(c_Divides_OposDivAlg(_1160397, _1160399) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1160397))], (49804 ^ _774244) ^ [_1771375, _1771377, _1771379] : [class_Orderings_Olinorder(_1771375), c_List_Olinorder__class_Osorted(_1771375, _1771377), hBOOL(hAPP(c_List_Odistinct(_1771375), _1771377)), c_List_Olinorder__class_Osorted(_1771375, _1771379), hBOOL(hAPP(c_List_Odistinct(_1771375), _1771379)), hAPP(c_List_Oset(_1771375), _1771377) = hAPP(c_List_Oset(_1771375), _1771379), -(_1771377 = _1771379)], (1334 ^ _774244) ^ [_793643, _793645] : [-(class_Finite__Set_Ofinite(_793643)), _793645 = _793643, class_Finite__Set_Ofinite(_793645)], (3520 ^ _774244) ^ [_828442, _828444, _828446, _828448, _828450, _828452, _828454, _828456] : [-(c_Product__Type_Oapfst(_828456, _828452, _828448, _828444) = c_Product__Type_Oapfst(_828454, _828450, _828446, _828442)), _828456 = _828454, _828452 = _828450, _828448 = _828446, _828444 = _828442], (47965 ^ _774244) ^ [_1729097, _1729099, _1729101, _1729103, _1729105, _1729107, _1729109] : [-(hBOOL(hAPP(hAPP(c_member(_1729097), _1729099), hAPP(c_List_Oset(_1729097), hAPP(hAPP(c_List_Otake(_1729097), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729101)), _1729103)), _1729105))))), -(c_Map_Omap__upds(_1729097, _1729101, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1729097, tc_Option_Ooption(_1729101)), _1729107), _1729099), hAPP(c_Option_Ooption_OSome(_1729101), _1729109)), _1729105, _1729103) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1729097, tc_Option_Ooption(_1729101)), c_Map_Omap__upds(_1729097, _1729101, _1729107, _1729105, _1729103)), _1729099), hAPP(c_Option_Ooption_OSome(_1729101), _1729109)))], (554 ^ _774244) ^ [_782933, _782935, _782937, _782939] : [-(c_FunDef_Oreduction__pair(_782937, _782933)), c_FunDef_Oreduction__pair(_782939, _782935), _782939 = _782937, _782935 = _782933], (34337 ^ _774244) ^ [_1399132, _1399134, _1399136, _1399138, _1399140, _1399142] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1399132, tc_Option_Ooption(_1399134)), c_Map_Orestrict__map(_1399132, _1399134, _1399136, _1399138)), _1399140), _1399142) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1399132, tc_Option_Ooption(_1399134)), c_Map_Orestrict__map(_1399132, _1399134, _1399136, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399132, tc_HOL_Obool)), _1399138), hAPP(hAPP(c_Set_Oinsert(_1399132), _1399140), c_Orderings_Obot__class_Obot(tc_fun(_1399132, tc_HOL_Obool)))))), _1399140), _1399142))], (18139 ^ _774244) ^ [_1084102, _1084104] : [class_Int_Onumber__ring(_1084102), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1084102), _1084104), hAPP(c_Int_Onumber__class_Onumber__of(_1084102), c_Int_OPls)) = _1084104)], (16819 ^ _774244) ^ [_1061521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1061521)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1061521 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48642 ^ _774244) ^ [_1746199, _1746201, _1746203] : [-(hAPP(hAPP(c_List_Otake(_1746199), _1746201), hAPP(c_List_Otl(_1746199), _1746203)) = hAPP(c_List_Otl(_1746199), hAPP(hAPP(c_List_Otake(_1746199), hAPP(c_Nat_OSuc, _1746201)), _1746203)))], (23633 ^ _774244) ^ [_1184249, _1184251, _1184253] : [class_Orderings_Olinorder(_1184249), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184249), _1184251), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184249), _1184251), _1184253)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184249), _1184251), _1184253))], (50512 ^ _774244) ^ [_1787388, _1787390, _1787392, _1787394] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1787388), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1787388))), _1787390))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1787392), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1787388))), c_List_Otranspose(_1787388, _1787390)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1787394), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1787388))), hAPP(c_List_Ofilter(tc_List_Olist(_1787388), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1787388)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1787392)), c_Nat_Osize__class_Osize(tc_List_Olist(_1787388)))), _1787390)))), -(hAPP(hAPP(c_List_Onth(_1787388), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1787388)), c_List_Otranspose(_1787388, _1787390)), _1787392)), _1787394) = hAPP(hAPP(c_List_Onth(_1787388), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1787388)), _1787390), _1787394)), _1787392))], (31128 ^ _774244) ^ [_1332769, _1332771, _1332773, _1332775] : [hBOOL(hAPP(hAPP(c_member(_1332769), _1332771), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332769, tc_HOL_Obool)), _1332773), _1332775))), 31131 ^ _774244 : [(31134 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1332769), _1332771), _1332775))], (31132 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1332769), _1332771), _1332773)))]]], (15646 ^ _774244) ^ [_1038494, _1038496] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1038494), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1038496)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1038494), _1038496))], (46507 ^ _774244) ^ [_1693704, _1693706, _1693708, _1693710, _1693712, _1693714] : [_1693704 = _1693706, -(hAPP(c_Map_Omap__of(_1693708, _1693710, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1693708, _1693710)), hAPP(hAPP(c_Product__Type_OPair(_1693708, _1693710), _1693704), _1693712)), _1693714)), _1693706) = hAPP(c_Option_Ooption_OSome(_1693710), _1693712))], (18067 ^ _774244) ^ [_1083072] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1083072)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083072) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41493 ^ _774244) ^ [_1570908, _1570910] : [41495 ^ _774244 : [(41496 ^ _774244) ^ [_1570933] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570908, _1570908)), hAPP(hAPP(c_Product__Type_OPair(_1570908, _1570908), hAPP(41494 ^ [_1570908, _1570910], hAPP(c_Nat_OSuc, _1570933))), hAPP(41494 ^ [_1570908, _1570910], _1570933))), _1570910)))]], -(c_Wellfounded_Owf(_1570908, _1570910))], (50719 ^ _774244) ^ [_1791574, _1791576] : [hBOOL(hAPP(c_List_Odistinct(_1791574), _1791576)), -(c_List_Oremdups(_1791574, _1791576) = _1791576)], (3680 ^ _774244) ^ [_830960, _830962, _830964, _830966, _830968, _830970, _830972, _830974] : [-(c_New__Random__Sequence_Oneg__map(_830974, _830970, _830966, _830962) = c_New__Random__Sequence_Oneg__map(_830972, _830968, _830964, _830960)), _830974 = _830972, _830970 = _830968, _830966 = _830964, _830962 = _830960], (9804 ^ _774244) ^ [_935768, _935770] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _935768)), hAPP(c_Int_Onat, _935770)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935770)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _935768), _935770))], (45936 ^ _774244) ^ [_1677639, _1677641, _1677643] : [hBOOL(hAPP(c_List_Odistinct(_1677639), _1677641)), -(hBOOL(hAPP(c_List_Odistinct(_1677639), c_List_Oremove1(_1677639, _1677643, _1677641))))], (51295 ^ _774244) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (18967 ^ _774244) ^ [_1097885] : [c_Int_OBit0(_1097885) = c_Int_OPls, -(_1097885 = c_Int_OPls)], (29590 ^ _774244) ^ [] : [-(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))))], (33576 ^ _774244) ^ [_1383719, _1383721, _1383723] : [class_Orderings_Olinorder(_1383719), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383719), _1383721)), -(_1383723 = c_Orderings_Obot__class_Obot(tc_fun(_1383719, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1383719, tc_HOL_Obool)), _1383723), _1383721)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1383719), c_Big__Operators_Olattice_OInf__fin(_1383719, c_Orderings_Oord__class_Omin(_1383719), _1383723)), c_Big__Operators_Olattice_OInf__fin(_1383719, c_Orderings_Oord__class_Omin(_1383719), _1383721)) = c_Big__Operators_Olattice_OInf__fin(_1383719, c_Orderings_Oord__class_Omin(_1383719), _1383721))], (19075 ^ _774244) ^ [_1099719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099719), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1099719)), c_Int_OPls)))], (20683 ^ _774244) ^ [_1128295, _1128297, _1128299, _1128301] : [class_Fields_Olinordered__field(_1128295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128295), c_Groups_Ozero__class_Ozero(_1128295)), _1128297)), 20690 ^ _774244 : [(20697 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128295), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128295), _1128299), _1128297)), _1128301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128295), _1128299), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128295), _1128301), _1128297))))], (20691 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128295), _1128299), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128295), _1128301), _1128297))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128295), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128295), _1128299), _1128297)), _1128301)))]]], (34632 ^ _774244) ^ [_1406048, _1406050, _1406052] : [-(c_Wellfounded_Omlex__prod(_1406048, _1406050, _1406052) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1406048), _1406048), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1406048, c_Wellfounded_Oless__than, _1406052)), hAPP(hAPP(c_COMBS(_1406048, _1406048, tc_prod(tc_Nat_Onat, _1406048)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1406048, tc_prod(tc_Nat_Onat, _1406048)), _1406048), c_Product__Type_OPair(tc_Nat_Onat, _1406048)), _1406050)), c_COMBI(_1406048))))], (27512 ^ _774244) ^ [_1259342, _1259344] : [c_Nat__Transfer_Onat__set(_1259342), c_Nat__Transfer_Onat__set(_1259344), 27519 ^ _774244 : [(27526 ^ _774244) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259342) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259344), -(_1259342 = _1259344)], (27520 ^ _774244) ^ [] : [_1259342 = _1259344, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259342) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259344))]]], (15830 ^ _774244) ^ [_1042622, _1042624, _1042626, _1042628, _1042630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042622), _1042624)), 15833 ^ _774244 : [(15840 ^ _774244) ^ [] : [_1042628 = 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), _1042624), _1042622)), _1042626)), _1042630), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042622), _1042626)), _1042628) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042624), _1042626)), _1042630))], (15834 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042622), _1042626)), _1042628) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042624), _1042626)), _1042630), -(_1042628 = 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), _1042624), _1042622)), _1042626)), _1042630))]]], (42688 ^ _774244) ^ [_1598583, _1598585, _1598587] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1598583), _1598585)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1598583, tc_HOL_Obool)), _1598587), _1598585) = hAPP(hAPP(c_Finite__Set_Ofold(_1598583, tc_fun(_1598583, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1598583, tc_HOL_Obool), tc_fun(tc_fun(_1598583, tc_HOL_Obool), tc_fun(_1598583, tc_HOL_Obool)), _1598583), hAPP(c_COMBC(tc_fun(_1598583, tc_HOL_Obool), tc_fun(_1598583, tc_HOL_Obool), tc_fun(_1598583, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1598583, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1598583, tc_fun(_1598583, tc_HOL_Obool), tc_fun(_1598583, tc_HOL_Obool)), c_Set_Oinsert(_1598583)), c_Orderings_Obot__class_Obot(tc_fun(_1598583, tc_HOL_Obool))))), _1598587), _1598585))], (51195 ^ _774244) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (33382 ^ _774244) ^ [_1379986, _1379988, _1379990, _1379992] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1379986, _1379988)), c_Sum__Type_OPlus(_1379986, _1379988, _1379990, _1379992)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379986), _1379990)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379988), _1379992))], (29886 ^ _774244) ^ [_1306718] : [29888 ^ _774244 : [(29891 ^ _774244) ^ [_1306828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29887 ^ [_1306718, _1306828]), _1306828))], (29889 ^ _774244) ^ [_1306794] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29887 ^ [_1306718, _1306794]), _1306718)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1306718)))], (10826 ^ _774244) ^ [_952061, _952063, _952065, _952067] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_952061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952061), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952061), _952063), _952065)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952061), _952063), _952067))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952061), _952065), _952067)))], (24707 ^ _774244) ^ [_1204970, _1204972, _1204974, _1204976, _1204978] : [-(hAPP(c_New__DSequence_Opos__bind(_1204970, _1204972, _1204974, _1204976), _1204978) = c_Lazy__Sequence_Obind(_1204970, _1204972, hAPP(_1204974, _1204978), hAPP(hAPP(c_COMBC(_1204970, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1204972)), _1204976), _1204978)))], (19121 ^ _774244) ^ [_1100578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100578), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1100578)), c_Int_OMin)))], (3636 ^ _774244) ^ [_830276, _830278, _830280, _830282, _830284, _830286, _830288, _830290] : [-(c_New__Random__Sequence_Opos__bind(_830290, _830286, _830282, _830278) = c_New__Random__Sequence_Opos__bind(_830288, _830284, _830280, _830276)), _830290 = _830288, _830286 = _830284, _830282 = _830280, _830278 = _830276], (35496 ^ _774244) ^ [_1426834, _1426836, _1426838] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1426834), _1426836), _1426838) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426834, tc_fun(tc_fun(_1426834, tc_HOL_Obool), tc_HOL_Obool)), _1426836), hAPP(hAPP(c_COMBC(_1426834, tc_fun(tc_fun(_1426834, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1426834, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1426834, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1426834, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1426834, tc_HOL_Obool), tc_HOL_Obool)), _1426834), c_Set_Oinsert(tc_fun(_1426834, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1426834, tc_HOL_Obool), tc_fun(_1426834, tc_HOL_Obool), _1426834), c_Relation_OImage(_1426834, _1426834, _1426838)), hAPP(hAPP(c_COMBC(_1426834, tc_fun(_1426834, tc_HOL_Obool), tc_fun(_1426834, tc_HOL_Obool)), c_Set_Oinsert(_1426834)), c_Orderings_Obot__class_Obot(tc_fun(_1426834, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1426834, tc_HOL_Obool), tc_HOL_Obool)))))], (24705 ^ _774244) ^ [_1204847, _1204849, _1204851, _1204853, _1204855, _1204857, _1204859] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1204847, _1204849, _1204851, _1204853), _1204855), _1204857), _1204859) = c_New__DSequence_Oneg__bind(_1204847, _1204849, hAPP(hAPP(hAPP(_1204851, _1204855), _1204857), _1204859), hAPP(hAPP(c_COMBC(_1204847, 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(_1204849)))), hAPP(hAPP(c_COMBC(_1204847, 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(_1204849))))), hAPP(hAPP(c_COMBC(_1204847, 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(_1204849)))))), _1204853), _1204855)), _1204857)), _1204859)))], (36259 ^ _774244) ^ [_1443416, _1443418, _1443420, _1443422] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443416, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443416, tc_HOL_Obool)), _1443418), _1443420)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443416, tc_HOL_Obool)), _1443422), _1443420)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443416, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443416, tc_HOL_Obool)), _1443418), _1443420)), _1443422))], (14175 ^ _774244) ^ [_1011773, _1011775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011773)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011775)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1011773)), hAPP(c_Int_Onat, _1011775)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1011773), _1011775)))], (24269 ^ _774244) ^ [_1195709, _1195711, _1195713] : [class_Orderings_Olinorder(_1195709), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195709), _1195711), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195709), _1195713), _1195711))))], (19239 ^ _774244) ^ [_1102651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1102651)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102651), c_Int_OMin)))], (23495 ^ _774244) ^ [_1181334, _1181336, _1181338, _1181340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1181334, tc_HOL_Obool)), _1181336), _1181338)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1181334, tc_HOL_Obool)), _1181338), _1181340)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1181334, tc_HOL_Obool)), _1181336), _1181340)))], (23365 ^ _774244) ^ [_1178765, _1178767, _1178769, _1178771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1178765, tc_HOL_Obool)), _1178767), _1178769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1178765, tc_HOL_Obool)), _1178769), _1178771)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1178765, tc_HOL_Obool)), _1178769), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1178765, tc_HOL_Obool)), _1178771), _1178767)) = _1178767)], (41642 ^ _774244) ^ [_1574253, _1574255] : [-(hAPP(c_Relation_ORange(_1574253, _1574255), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1574253, _1574255), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1574255, tc_HOL_Obool)))], (15744 ^ _774244) ^ [_1040921, _1040923, _1040925] : [hBOOL(hAPP(_1040921, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040923), _1040925))), 15747 ^ _774244 : [(15754 ^ _774244) ^ [_1041106] : [_1040923 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040925), _1041106), -(hBOOL(hAPP(_1040921, _1041106)))], (15748 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040923), _1040925)), -(hBOOL(hAPP(_1040921, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (40284 ^ _774244) ^ [_1535265, _1535267, _1535269] : [class_Lattices_Oab__semigroup__idem__mult(_1535265), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535265), _1535267)), -(_1535267 = c_Orderings_Obot__class_Obot(tc_fun(_1535265, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535265), _1535269)), -(_1535269 = c_Orderings_Obot__class_Obot(tc_fun(_1535265, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1535265, c_Groups_Otimes__class_Otimes(_1535265)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1535265, tc_HOL_Obool)), _1535267), _1535269)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1535265), hAPP(c_Finite__Set_Ofold1(_1535265, c_Groups_Otimes__class_Otimes(_1535265)), _1535267)), hAPP(c_Finite__Set_Ofold1(_1535265, c_Groups_Otimes__class_Otimes(_1535265)), _1535269)))], (39291 ^ _774244) ^ [_1510687, _1510689, _1510691, _1510693, _1510695] : [-(_1510687 = c_Option_Ooption_ONone(_1510689)), -(c_Map_Odom(_1510691, _1510689, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1510691, tc_Option_Ooption(_1510689)), _1510693), _1510695), _1510687)) = hAPP(hAPP(c_Set_Oinsert(_1510691), _1510695), c_Map_Odom(_1510691, _1510689, _1510693)))], (47893 ^ _774244) ^ [_1727505, _1727507, _1727509] : [-(hAPP(hAPP(c_List_Otake(_1727505), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1727505), _1727507), _1727509)) = hAPP(hAPP(c_List_Olist_OCons(_1727505), _1727507), c_List_Olist_ONil(_1727505)))], (51365 ^ _774244) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (48738 ^ _774244) ^ [_1748330, _1748332, _1748334] : [class_Groups_Omonoid__add(_1748330), -(hAPP(c_List_Ofoldl(_1748330, _1748330, c_Groups_Oplus__class_Oplus(_1748330), _1748332), _1748334) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1748330), _1748332), c_List_Ofoldr(_1748330, _1748330, c_Groups_Oplus__class_Oplus(_1748330), _1748334, c_Groups_Ozero__class_Ozero(_1748330))))], (38840 ^ _774244) ^ [_1500427, _1500429, _1500431, _1500433, _1500435] : [hBOOL(hAPP(hAPP(c_member(_1500427), _1500429), hAPP(c_Set_Ovimage(_1500427, _1500431, _1500433), _1500435))), -(hBOOL(hAPP(hAPP(c_member(_1500431), hAPP(_1500433, _1500429)), _1500435)))], (45383 ^ _774244) ^ [_1664611, _1664613, _1664615] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1664611)), hAPP(c_Set_Oimage(_1664613, tc_Option_Ooption(_1664611), c_Map_Omap__of(_1664613, _1664611, _1664615)), c_Orderings_Otop__class_Otop(tc_fun(_1664613, tc_HOL_Obool))))))], (18843 ^ _774244) ^ [_1095535, _1095537] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1095535))), _1095537) = 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)))), _1095535), _1095537))], (46916 ^ _774244) ^ [_1703808, _1703810] : [-(c_List_Osublist(_1703808, c_List_Olist_ONil(_1703808), _1703810) = c_List_Olist_ONil(_1703808))], (46427 ^ _774244) ^ [_1692041, _1692043, _1692045, _1692047, _1692049, _1692051] : [-(c_List_Olistrelp(_1692041, _1692043, hAPP(hAPP(c_List_Olist_OCons(_1692041), _1692045), _1692047), hAPP(hAPP(c_List_Olist_OCons(_1692041), _1692049), _1692051))), hBOOL(hAPP(hAPP(_1692043, _1692045), _1692049)), c_List_Olistrelp(_1692041, _1692043, _1692047, _1692051)], (41126 ^ _774244) ^ [_1561008, _1561010] : [-(c_Fun_Oinj__on(_1561008, _1561008, c_Fun_Oid(_1561008), _1561010))], (43423 ^ _774244) ^ [_1615084] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615084, tc_HOL_Obool) = c_Set_OBall(_1615084))], (47921 ^ _774244) ^ [_1727977, _1727979, _1727981] : [-(c_List_Osublist(_1727977, _1727979, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1727981)) = hAPP(hAPP(c_List_Otake(_1727977), _1727981), _1727979))], (5858 ^ _774244) ^ [_867903, _867905, _867907] : [c_Com_Ocom_OSemi(_867903, _867905) = c_Com_Ocom_OBODY(_867907)], (22470 ^ _774244) ^ [_1161427, _1161429] : [class_Rings_Oring__1(_1161427), 22473 ^ _774244 : [(22480 ^ _774244) ^ [] : [-(_1161429 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22483 ^ _774244 : [(22490 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161429), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1161427), _1161429) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1161427), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1161427, _1161427)), tc_fun(tc_Int_Oint, _1161427)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1161427, _1161427), _1161427), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1161427, _1161427)), tc_fun(tc_Int_Oint, _1161427)), tc_Int_Oint), c_COMBB(tc_fun(_1161427, _1161427), _1161427, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1161427, tc_fun(tc_fun(_1161427, _1161427), _1161427), tc_Int_Oint), c_HOL_OLet(_1161427, _1161427)), c_Int_Oring__1__class_Oof__int(_1161427)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1161427, _1161427), tc_fun(_1161427, _1161427)), hAPP(hAPP(c_COMBB(tc_fun(_1161427, tc_fun(_1161427, _1161427)), tc_fun(tc_fun(_1161427, _1161427), tc_fun(_1161427, _1161427)), tc_Int_Oint), c_COMBS(_1161427, _1161427, _1161427)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1161427, _1161427), tc_fun(_1161427, tc_fun(_1161427, _1161427))), hAPP(hAPP(c_COMBB(tc_fun(_1161427, tc_fun(_1161427, _1161427)), tc_fun(tc_fun(_1161427, _1161427), tc_fun(_1161427, tc_fun(_1161427, _1161427))), tc_Int_Oint), c_COMBB(_1161427, tc_fun(_1161427, _1161427), _1161427)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1161427, tc_fun(_1161427, _1161427)), tc_Int_Oint), c_If(_1161427)), 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(_1161427, _1161427, _1161427), c_Groups_Oplus__class_Oplus(_1161427)), c_COMBI(_1161427))))), hAPP(hAPP(c_COMBC(_1161427, _1161427, _1161427), hAPP(hAPP(c_COMBB(_1161427, tc_fun(_1161427, _1161427), _1161427), c_Groups_Oplus__class_Oplus(_1161427)), hAPP(hAPP(c_COMBS(_1161427, _1161427, _1161427), c_Groups_Oplus__class_Oplus(_1161427)), c_COMBI(_1161427)))), c_Groups_Oone__class_Oone(_1161427))))), c_Divides_Odivmod__int(_1161429, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (22484 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161429), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1161427), _1161429) = hAPP(c_Groups_Ouminus__class_Ouminus(_1161427), hAPP(c_Int_Oring__1__class_Oof__int(_1161427), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1161429))))]]], (22474 ^ _774244) ^ [] : [_1161429 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1161427), _1161429) = c_Groups_Ozero__class_Ozero(_1161427))]]], (27784 ^ _774244) ^ [_1264560, _1264562, _1264564] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264560, tc_HOL_Obool)), _1264562), _1264564) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264560, tc_HOL_Obool)), _1264564), _1264562))], (47026 ^ _774244) ^ [_1706516, _1706518, _1706520] : [-(hAPP(hAPP(c_List_Onth(_1706516), hAPP(hAPP(c_List_Olist_OCons(_1706516), _1706518), _1706520)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1706518)], (32614 ^ _774244) ^ [_1365357, _1365359] : [class_Int_Oring__char__0(_1365357), hBOOL(hAPP(hAPP(c_member(_1365357), _1365359), c_Int_Oring__1__class_OInts(_1365357))), 32621 ^ _774244 : [(32628 ^ _774244) ^ [] : [_1365359 = c_Groups_Ozero__class_Ozero(_1365357), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1365357), _1365359), _1365359) = c_Groups_Ozero__class_Ozero(_1365357))], (32622 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1365357), _1365359), _1365359) = c_Groups_Ozero__class_Ozero(_1365357), -(_1365359 = c_Groups_Ozero__class_Ozero(_1365357))]]], (50338 ^ _774244) ^ [_1782451, _1782453, _1782455] : [hAPP(c_List_Orev(_1782451), _1782453) = hAPP(c_List_Orev(_1782451), _1782455), -(_1782453 = _1782455)], (15414 ^ _774244) ^ [_1034104, _1034106] : [class_Groups_Ogroup__add(_1034104), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034104), c_Groups_Ozero__class_Ozero(_1034104)), _1034106) = hAPP(c_Groups_Ouminus__class_Ouminus(_1034104), _1034106))], (2448 ^ _774244) ^ [_811234, _811236, _811238, _811240] : [-(c_Groups_Osgn__class_Osgn(_811240, _811236) = c_Groups_Osgn__class_Osgn(_811238, _811234)), _811240 = _811238, _811236 = _811234], (47198 ^ _774244) ^ [_1710708, _1710710, _1710712, _1710714] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1710708) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1710710), hAPP(hAPP(c_List_Olist_OCons(_1710710), _1710712), _1710714)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1710708)) = _1710712)], (48414 ^ _774244) ^ [_1741360, _1741362, _1741364, _1741366] : [_1741360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1741362), _1741360), hAPP(hAPP(c_List_Olist_OCons(_1741362), _1741364), _1741366)) = hAPP(hAPP(c_List_Olist_OCons(_1741362), _1741364), _1741366))], (36577 ^ _774244) ^ [_1450797, _1450799, _1450801] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450797, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450797, tc_HOL_Obool)), _1450799), _1450801)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450797, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450797, tc_HOL_Obool)), _1450799)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450797, tc_HOL_Obool)), _1450801)))], (43093 ^ _774244) ^ [_1607518, _1607520, _1607522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607518, _1607518), tc_HOL_Obool)), _1607520), _1607522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607518, _1607518), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1607518, _1607520)), c_Transitive__Closure_Ortrancl(_1607518, _1607522))))], (27245 ^ _774244) ^ [_1254113, _1254115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1254113), _1254115)), -(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)), _1254113)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254115))))], (36203 ^ _774244) ^ [_1442037, _1442039, _1442041, _1442043] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442037, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442037, tc_HOL_Obool)), _1442039), _1442041)), _1442043) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442037, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442037, tc_HOL_Obool)), _1442039), _1442043)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442037, tc_HOL_Obool)), _1442041), _1442043)))], (36045 ^ _774244) ^ [_1438452, _1438454, _1438456] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438452, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438452, tc_HOL_Obool)), _1438454), _1438456)), _1438454)))], (17867 ^ _774244) ^ [_1080146] : [class_Rings_Osemiring__1(_1080146), -(c_Int_Oiszero(_1080146, c_Groups_Ozero__class_Ozero(_1080146)))], (46038 ^ _774244) ^ [_1680621, _1680623, _1680625, _1680627, _1680629, _1680631, _1680633, _1680635] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680621)), _1680623) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680625)), _1680627), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680621)), _1680629) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680625)), _1680627), -(hBOOL(hAPP(hAPP(c_member(_1680625), _1680631), hAPP(c_List_Oset(_1680625), _1680627)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1680625, tc_Option_Ooption(_1680621)), c_Map_Omap__of(_1680625, _1680621, hAPP(hAPP(c_List_Ozip(_1680625, _1680621), _1680627), _1680623))), _1680631), hAPP(c_Option_Ooption_OSome(_1680621), _1680633)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1680625, tc_Option_Ooption(_1680621)), c_Map_Omap__of(_1680625, _1680621, hAPP(hAPP(c_List_Ozip(_1680625, _1680621), _1680627), _1680629))), _1680631), hAPP(c_Option_Ooption_OSome(_1680621), _1680635)), -(c_Map_Omap__of(_1680625, _1680621, hAPP(hAPP(c_List_Ozip(_1680625, _1680621), _1680627), _1680623)) = c_Map_Omap__of(_1680625, _1680621, hAPP(hAPP(c_List_Ozip(_1680625, _1680621), _1680627), _1680629)))], (25071 ^ _774244) ^ [_1211836, _1211838, _1211840] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211836), _1211838)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211838), _1211840)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211836), _1211840)))], (8284 ^ _774244) ^ [_909321, _909323, _909325] : [class_Orderings_Oorder(_909321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909321), _909323), _909325)), _909323 = _909325], (6215 ^ _774244) ^ [_874004, _874006, _874008] : [-(hAPP(c_Nat_Onat_Onat__rec(_874004, _874006, _874008), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _874006)], (17587 ^ _774244) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25029 ^ _774244) ^ [_1211145, _1211147] : [_1211145 = _1211147, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211145), _1211147)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211147), _1211145)))], (17799 ^ _774244) ^ [_1078806, _1078808, _1078810] : [17801 ^ _774244 : [(17804 ^ _774244) ^ [] : [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(_1078808, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 17800 ^ [_1078806, _1078808, _1078810]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1078808, 17800 ^ [_1078806, _1078808, _1078810])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (17802 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17800 ^ [_1078806, _1078808, _1078810]), _1078806)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1078808, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1078810)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1078810), hAPP(_1078808, _1078806))), 17814 ^ _774244 : [(17817 ^ _774244) ^ [] : [-(hAPP(_1078808, 17813 ^ [_1078806, _1078808, _1078810]) = _1078810)], (17815 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 17813 ^ [_1078806, _1078808, _1078810]), _1078806)))]]], (28842 ^ _774244) ^ [_1286916, _1286918, _1286920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1286916), _1286918)), -(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)), _1286916)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1286920), _1286918)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1286920), _1286916)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1286918), _1286916)))], (34004 ^ _774244) ^ [_1392482, _1392484, _1392486, _1392488] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1392482), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392484, tc_Nat_Onat), _1392486), _1392488)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392484, _1392482), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1392482, _1392484), c_Nat_Osemiring__1__class_Oof__nat(_1392482)), _1392486)), _1392488)), class_Groups_Ocomm__monoid__mult(_1392482), class_Rings_Osemiring__1(_1392482)], (21928 ^ _774244) ^ [_1151205, _1151207, _1151209] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1151205), _1151207))), -(c_Random_Ominus__shift(_1151209, _1151205, _1151207) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1151205), _1151207))], (40731 ^ _774244) ^ [_1544615, _1544617, _1544619] : [-(hAPP(hAPP(c_Set_Oinsert(_1544615), _1544617), _1544619) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1544615, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1544615), hAPP(hAPP(c_COMBC(_1544615, _1544615, tc_HOL_Obool), c_fequal), _1544617))), _1544619))], (7551 ^ _774244) ^ [_897020, _897022, _897024, _897026, _897028] : [c_Com_Ocom_OAss(_897020, _897022) = c_Com_Ocom_OCond(_897024, _897026, _897028)], (28266 ^ _774244) ^ [_1273916, _1273918, _1273920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1273916), _1273918)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1273916), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1273918), _1273920)) = 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, _1273916), _1273918)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1273918), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1273918), _1273920))))], (49081 ^ _774244) ^ [_1755814, _1755816, _1755818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755814), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755816)), _1755818))), -(c_List_Olast(_1755816, hAPP(hAPP(c_List_Odrop(_1755816), _1755814), _1755818)) = c_List_Olast(_1755816, _1755818))], (334 ^ _774244) ^ [_779267, _779269] : [-(class_Fields_Ofield(_779267)), _779269 = _779267, class_Fields_Ofield(_779269)], (6125 ^ _774244) ^ [_872381, _872383, _872385, _872387, _872389, _872391] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_872381, _872383, _872385), _872387, _872389, _872391)), 6126 ^ _774244 : [(6133 ^ _774244) ^ [] : [-(hBOOL(hAPP(_872381, _872387))), c_Natural_Oevaln(_872385, _872387, _872389, _872391)], (6127 ^ _774244) ^ [] : [hBOOL(hAPP(_872381, _872387)), c_Natural_Oevaln(_872383, _872387, _872389, _872391)]]], (18543 ^ _774244) ^ [_1090724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1090724)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090724), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40163 ^ _774244) ^ [_1533052, _1533054, _1533056] : [class_Lattices_Osemilattice__inf(_1533052), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533052), _1533054)), -(_1533054 = c_Orderings_Obot__class_Obot(tc_fun(_1533052, tc_HOL_Obool))), 40174 ^ _774244 : [(40175 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1533052), _1533056), hAPP(c_Finite__Set_Ofold1(_1533052, c_Lattices_Osemilattice__inf__class_Oinf(_1533052)), _1533054))), 40178 ^ _774244 : [(40179 ^ _774244) ^ [_1533345] : [hBOOL(hAPP(hAPP(c_member(_1533052), _1533345), _1533054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1533052), _1533056), _1533345)))]]], (40185 ^ _774244) ^ [] : [40187 ^ _774244 : [(40190 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1533052), _1533056), 40186 ^ [_1533052, _1533054, _1533056]))], (40188 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1533052), 40186 ^ [_1533052, _1533054, _1533056]), _1533054)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1533052), _1533056), hAPP(c_Finite__Set_Ofold1(_1533052, c_Lattices_Osemilattice__inf__class_Oinf(_1533052)), _1533054))))]]], (40777 ^ _774244) ^ [_1546531, _1546533, _1546535, _1546537, _1546539, _1546541] : [class_Groups_Ocomm__monoid__add(_1546531), hBOOL(hAPP(c_Finite__Set_Ofinite(_1546533), _1546535)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1546533, _1546531), _1546537), _1546535) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1546539, _1546531), hAPP(hAPP(c_COMBB(tc_fun(_1546533, tc_HOL_Obool), _1546531, _1546539), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1546533, _1546531), _1546537)), hAPP(hAPP(c_COMBB(tc_fun(_1546533, tc_HOL_Obool), tc_fun(_1546533, tc_HOL_Obool), _1546539), c_Set_OCollect(_1546533)), hAPP(hAPP(c_COMBB(tc_fun(_1546533, tc_HOL_Obool), tc_fun(_1546533, tc_HOL_Obool), _1546539), hAPP(c_COMBS(_1546533, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546533), c_fconj), hAPP(hAPP(c_COMBC(_1546533, tc_fun(_1546533, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546533)), _1546535)))), hAPP(c_COMBC(_1546533, _1546539, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1546539, tc_fun(_1546539, tc_HOL_Obool), _1546533), c_fequal), _1546541)))))), hAPP(c_Set_Oimage(_1546533, _1546539, _1546541), _1546535)))], (36351 ^ _774244) ^ [_1445397, _1445399, _1445401] : [class_Lattices_Olattice(_1445397), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445397), _1445399), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445397), _1445399), _1445401)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445397), _1445399), _1445401))], (28711 ^ _774244) ^ [_1283978] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1283978)) = 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), _1283978))))], (4226 ^ _774244) ^ [_839611, _839613, _839615, _839617, _839619, _839621] : [-(c_Relation_OImage(_839621, _839617, _839613) = c_Relation_OImage(_839619, _839615, _839611)), _839621 = _839619, _839617 = _839615, _839613 = _839611], (10039 ^ _774244) ^ [_939719] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _939719) = _939719)], (29456 ^ _774244) ^ [_1298643] : [class_Lattices_Oboolean__algebra(_1298643), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1298643), c_Orderings_Otop__class_Otop(_1298643)) = c_Orderings_Obot__class_Obot(_1298643))], (48402 ^ _774244) ^ [_1741054, _1741056, _1741058, _1741060] : [-(hAPP(hAPP(c_List_Oappend(_1741054), _1741056), _1741058) = _1741060), _1741056 = hAPP(hAPP(c_List_Otake(_1741054), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741054)), _1741056)), _1741060), _1741058 = hAPP(hAPP(c_List_Odrop(_1741054), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741054)), _1741056)), _1741060)], (44235 ^ _774244) ^ [_1637665, _1637667, _1637669] : [c_Wellfounded_Owf(_1637665, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1637665, _1637665), tc_HOL_Obool), _1637667), _1637669)), -(c_Wellfounded_Owf(_1637665, _1637669))], (39660 ^ _774244) ^ [_1520461, _1520463, _1520465, _1520467, _1520469] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1520461, _1520463), _1520465), hAPP(hAPP(c_COMBS(_1520461, tc_fun(_1520463, tc_HOL_Obool), tc_fun(_1520463, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1520463, tc_HOL_Obool), tc_fun(tc_fun(_1520463, tc_HOL_Obool), tc_fun(_1520463, tc_HOL_Obool)), _1520461), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520463, tc_HOL_Obool))), _1520467)), _1520469)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1520461, _1520463), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1520461, _1520463), _1520465), _1520467)), hAPP(hAPP(c_Product__Type_OSigma(_1520461, _1520463), _1520465), _1520469)))], (29907 ^ _774244) ^ [_1307085, _1307087] : [class_Finite__Set_Ofinite(_1307085), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307085), _1307087)))], (41731 ^ _774244) ^ [_1576743, _1576745] : [c_Wellfounded_Owf(_1576743, hAPP(c_Set_OCollect(tc_prod(_1576743, _1576743)), hAPP(c_Product__Type_Oprod_Oprod__case(_1576743, _1576743, tc_HOL_Obool), _1576745))), -(c_Wellfounded_OwfP(_1576743, _1576745))], (18697 ^ _774244) ^ [_1093248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1093248)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093248), c_Int_OPls)))], (7177 ^ _774244) ^ [_890727, _890729, _890731, _890733] : [-(c_Com_Ocom_OAss(_890727, _890729) = c_Com_Ocom_OAss(_890731, _890733)), _890727 = _890731, _890729 = _890733], (22266 ^ _774244) ^ [_1157855, _1157857, _1157859] : [class_Int_Onumber__ring(_1157855), 22269 ^ _774244 : [(22276 ^ _774244) ^ [] : [-(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), _1157857)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1157855), _1157859), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1157857))) = c_Groups_Oone__class_Oone(_1157855))], (22270 ^ _774244) ^ [] : [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), _1157857))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1157855), _1157859), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1157857))) = hAPP(hAPP(c_HOL_OLet(_1157855, _1157855), hAPP(hAPP(c_Power_Opower__class_Opower(_1157855), _1157859), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157857))), hAPP(hAPP(c_COMBS(_1157855, _1157855, _1157855), hAPP(hAPP(c_COMBB(_1157855, tc_fun(_1157855, _1157855), _1157855), c_Groups_Otimes__class_Otimes(_1157855)), hAPP(c_Groups_Otimes__class_Otimes(_1157855), _1157859))), c_COMBI(_1157855))))]]], (27719 ^ _774244) ^ [_1263067, _1263069, _1263071, _1263073] : [27723 ^ _774244 : [(27726 ^ _774244) ^ [] : [hBOOL(hAPP(_1263073, 27722 ^ [_1263067, _1263069, _1263071, _1263073]))], (27724 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1263067), 27722 ^ [_1263067, _1263069, _1263071, _1263073]), _1263069)))]], 27728 ^ _774244 : [(27731 ^ _774244) ^ [] : [hBOOL(hAPP(_1263073, 27727 ^ [_1263067, _1263069, _1263071, _1263073]))], (27729 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1263067), 27727 ^ [_1263067, _1263069, _1263071, _1263073]), _1263071)))]], 27732 ^ _774244 : [(27733 ^ _774244) ^ [_1263400] : [hBOOL(hAPP(hAPP(c_member(_1263067), _1263400), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263067, tc_HOL_Obool)), _1263069), _1263071))), -(hBOOL(hAPP(_1263073, _1263400)))]]], (18883 ^ _774244) ^ [_1096411, _1096413] : [class_Rings_Osemiring__1(_1096411), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096413)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1096411), 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)))), _1096413))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096411), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1096411), hAPP(c_Int_Onat, _1096413))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1096411), hAPP(c_Int_Onat, _1096413))))], (48031 ^ _774244) ^ [_1730558, _1730560, _1730562, _1730564, _1730566, _1730568] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730558)), _1730560) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730562)), _1730564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730558, tc_HOL_Obool)), hAPP(c_List_Oset(_1730558), _1730560)), _1730566)), -(c_Map_Orestrict__map(_1730558, _1730562, c_Map_Omap__upds(_1730558, _1730562, _1730568, _1730560, _1730564), _1730566) = c_Map_Omap__upds(_1730558, _1730562, c_Map_Orestrict__map(_1730558, _1730562, _1730568, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1730558, tc_HOL_Obool)), _1730566), hAPP(c_List_Oset(_1730558), _1730560))), _1730560, _1730564))], (35564 ^ _774244) ^ [_1428382, _1428384, _1428386, _1428388] : [hBOOL(hAPP(hAPP(c_member(_1428382), _1428384), _1428386)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1428382, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1428382, _1428382, _1428388), hAPP(hAPP(c_Set_Oinsert(_1428382), _1428384), c_Orderings_Obot__class_Obot(tc_fun(_1428382, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1428382), _1428386), _1428388))))], (27854 ^ _774244) ^ [_1266124, _1266126, _1266128] : [class_Lattices_Olattice(_1266124), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266124), _1266126), _1266128) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266124), _1266128), _1266126))], (13475 ^ _774244) ^ [_998451, _998453, _998455, _998457] : [class_Divides_Osemiring__div(_998451), -(c_Divides_Odiv__class_Omod(_998451, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998451), _998453), _998455), _998457) = c_Divides_Odiv__class_Omod(_998451, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998451), c_Divides_Odiv__class_Omod(_998451, _998453, _998457)), c_Divides_Odiv__class_Omod(_998451, _998455, _998457)), _998457))], (46806 ^ _774244) ^ [_1701826, _1701828, _1701830, _1701832] : [c_List_Olist_ONil(_1701826) = hAPP(hAPP(c_List_Omap(_1701828, _1701826), _1701830), _1701832), -(_1701832 = c_List_Olist_ONil(_1701828))], (36981 ^ _774244) ^ [_1459916, _1459918, _1459920, _1459922, _1459924] : [class_Groups_Ocomm__monoid__add(_1459916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459918), _1459920)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459918), _1459922)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459918, tc_HOL_Obool)), _1459920), _1459922) = c_Orderings_Obot__class_Obot(tc_fun(_1459918, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459918, _1459916), _1459924), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459918, tc_HOL_Obool)), _1459920), _1459922)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1459916), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459918, _1459916), _1459924), _1459920)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459918, _1459916), _1459924), _1459922)))], (3392 ^ _774244) ^ [_826376, _826378] : [_826378 = _826376, -(c_SetInterval_Oord__class_OatLeast(_826378) = c_SetInterval_Oord__class_OatLeast(_826376))], (4892 ^ _774244) ^ [_849854, _849856] : [_849856 = _849854, -(c_SetInterval_Oord__class_OatMost(_849856) = c_SetInterval_Oord__class_OatMost(_849854))], (6750 ^ _774244) ^ [_883030, _883032, _883034, _883036] : [c_Com_Ocom_OLocal(_883030, _883032, _883034) = c_Com_Ocom_OBODY(_883036)], (39602 ^ _774244) ^ [_1518650, _1518652, _1518654] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518650, _1518652), _1518654), hAPP(c_COMBK(tc_fun(_1518652, tc_HOL_Obool), _1518650), c_Orderings_Obot__class_Obot(tc_fun(_1518652, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518650, _1518652), tc_HOL_Obool)))], (26784 ^ _774244) ^ [_1244566, _1244568, _1244570] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1244566, tc_Nat_Onat), _1244568), _1244570) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1244566, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1244566), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1244568)), _1244570)))], (27818 ^ _774244) ^ [_1265354, _1265356, _1265358, _1265360] : [class_Lattices_Olattice(_1265354), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265354), _1265356), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265354), _1265358), _1265360)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265354), _1265358), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265354), _1265356), _1265360)))], (44620 ^ _774244) ^ [_1646876, _1646878, _1646880, _1646882] : [-(hAPP(c_Set_Ovimage(_1646876, _1646878, _1646880), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646878, tc_HOL_Obool), _1646882)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1646878, tc_HOL_Obool), tc_fun(_1646876, tc_HOL_Obool)), _1646882), c_Set_Ovimage(_1646876, _1646878, _1646880)))], (23043 ^ _774244) ^ [_1172711, _1172713, _1172715] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1172711), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1172713)), _1172715)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1172711, _1172713), hAPP(c_Divides_OnegateSnd, _1172715))))], (30459 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (6335 ^ _774244) ^ [_876154, _876156, _876158] : [c_Com_Ocom_OCall(_876154, _876156, _876158) = c_Com_Ocom_OSKIP], (50182 ^ _774244) ^ [_1779107, _1779109, _1779111] : [hAPP(hAPP(c_List_Olist_OCons(_1779107), _1779109), c_List_Olist_ONil(_1779107)) = hAPP(c_List_Orev(_1779107), _1779111), -(_1779111 = hAPP(hAPP(c_List_Olist_OCons(_1779107), _1779109), c_List_Olist_ONil(_1779107)))], (48392 ^ _774244) ^ [_1740803, _1740805, _1740807] : [-(hAPP(hAPP(c_List_Oappend(_1740803), hAPP(hAPP(c_List_Otake(_1740803), _1740805), _1740807)), hAPP(hAPP(c_List_Odrop(_1740803), _1740805), _1740807)) = _1740807)], (47337 ^ _774244) ^ [_1714278, _1714280, _1714282, _1714284] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1714278, tc_HOL_Obool)), hAPP(c_List_Oset(_1714278), hAPP(hAPP(c_List_Olist__update(_1714278, _1714280), _1714282), _1714284))), hAPP(hAPP(c_Set_Oinsert(_1714278), _1714284), hAPP(c_List_Oset(_1714278), _1714280)))))], (39898 ^ _774244) ^ [_1527118, _1527120, _1527122, _1527124, _1527126, _1527128] : [hAPP(c_Set_Oimage(_1527118, _1527120, _1527122), c_Orderings_Otop__class_Otop(tc_fun(_1527118, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1527120, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1527124, _1527126, _1527128), c_Orderings_Otop__class_Otop(tc_fun(_1527124, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1527126, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1527118, _1527124), tc_prod(_1527120, _1527126), c_Product__Type_Omap__pair(_1527118, _1527120, _1527124, _1527126, _1527122, _1527128)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1527118, _1527124), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1527120, _1527126), tc_HOL_Obool)))], (384 ^ _774244) ^ [_780030, _780032, _780034, _780036, _780038, _780040, _780042, _780044, _780046, _780048] : [-(c_Finite__Set_Ofolding__image(_780046, _780042, _780038, _780034, _780030)), c_Finite__Set_Ofolding__image(_780048, _780044, _780040, _780036, _780032), _780048 = _780046, _780044 = _780042, _780040 = _780038, _780036 = _780034, _780032 = _780030], (41630 ^ _774244) ^ [_1574021, _1574023, _1574025] : [hAPP(c_Relation_ORange(_1574021, _1574023), _1574025) = c_Orderings_Obot__class_Obot(tc_fun(_1574023, tc_HOL_Obool)), -(_1574025 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1574021, _1574023), tc_HOL_Obool)))], (2324 ^ _774244) ^ [_809272, _809274, _809276, _809278] : [-(c_Random_Olog(_809278, _809274) = c_Random_Olog(_809276, _809272)), _809278 = _809276, _809274 = _809272], (19319 ^ _774244) ^ [_1104047] : [class_Rings_Osemiring__1(_1104047), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1104047), c_Groups_Ozero__class_Ozero(_1104047)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1104047))], (46391 ^ _774244) ^ [_1691250, _1691252, _1691254, _1691256] : [hBOOL(hAPP(hAPP(c_member(_1691250), _1691252), hAPP(c_List_Oset(_1691250), hAPP(hAPP(c_List_Olist_OCons(_1691250), _1691254), _1691256)))), -(_1691252 = _1691254), -(hBOOL(hAPP(hAPP(c_member(_1691250), _1691252), hAPP(c_List_Oset(_1691250), _1691256))))], (39908 ^ _774244) ^ [_1527403, _1527405, _1527407, _1527409, _1527411, _1527413, _1527415, _1527417] : [c_Fun_Oinj__on(_1527403, _1527405, _1527407, _1527409), c_Fun_Oinj__on(_1527411, _1527413, _1527415, _1527417), -(c_Fun_Oinj__on(tc_prod(_1527403, _1527411), tc_prod(_1527405, _1527413), c_Product__Type_Omap__pair(_1527403, _1527405, _1527411, _1527413, _1527407, _1527415), hAPP(hAPP(c_Product__Type_OSigma(_1527403, _1527411), _1527409), hAPP(c_COMBK(tc_fun(_1527411, tc_HOL_Obool), _1527403), _1527417))))], (37857 ^ _774244) ^ [_1479466, _1479468] : [c_Equiv__Relations_Oequiv(_1479466, c_Orderings_Otop__class_Otop(tc_fun(_1479466, tc_HOL_Obool)), _1479468), -(c_Equiv__Relations_Oequivp(_1479466, hAPP(hAPP(c_COMBC(_1479466, tc_fun(tc_prod(_1479466, _1479466), tc_HOL_Obool), tc_fun(_1479466, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479466, tc_fun(tc_fun(tc_prod(_1479466, _1479466), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1479466, _1479466), tc_HOL_Obool), tc_fun(_1479466, tc_HOL_Obool)), _1479466), c_COMBC(_1479466, tc_fun(tc_prod(_1479466, _1479466), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479466, tc_prod(_1479466, _1479466)), tc_fun(_1479466, tc_fun(tc_fun(tc_prod(_1479466, _1479466), tc_HOL_Obool), tc_HOL_Obool)), _1479466), hAPP(c_COMBB(tc_prod(_1479466, _1479466), tc_fun(tc_fun(tc_prod(_1479466, _1479466), tc_HOL_Obool), tc_HOL_Obool), _1479466), c_member(tc_prod(_1479466, _1479466)))), c_Product__Type_OPair(_1479466, _1479466)))), _1479468)))], (51369 ^ _774244) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (12740 ^ _774244) ^ [_985921] : [_985921 = 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), _985921)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6970 ^ _774244) ^ [_887147, _887149, _887151] : [c_Natural_Oevalc(c_Com_Ocom_OWhile(_887147, _887149), _887151, _887151), hBOOL(hAPP(_887147, _887151)), 6978 ^ _774244 : [(6981 ^ _774244) ^ [] : [-(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887147, _887149), 6977 ^ [_887147, _887149, _887151], _887151))], (6979 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_887149, _887151, 6977 ^ [_887147, _887149, _887151]))]]], (17055 ^ _774244) ^ [_1065817, _1065819, _1065821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1065817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1065817), _1065819)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1065817), _1065821))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065819), _1065821)))], (32996 ^ _774244) ^ [_1371825, _1371827, _1371829] : [class_Orderings_Olinorder(_1371825), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371825), _1371827)), -(_1371829 = c_Orderings_Obot__class_Obot(tc_fun(_1371825, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1371825, tc_HOL_Obool)), _1371829), _1371827)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371825), c_Big__Operators_Olinorder__class_OMax(_1371825, _1371829)), c_Big__Operators_Olinorder__class_OMax(_1371825, _1371827)) = c_Big__Operators_Olinorder__class_OMax(_1371825, _1371827))], (6478 ^ _774244) ^ [_878627, _878629, _878631] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878627), _878629) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878627), _878631), -(_878629 = _878631)], (51279 ^ _774244) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (46310 ^ _774244) ^ [_1687553, _1687555] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1687553), _1687555)), -(c_Nitpick_Ocard_H(_1687553, _1687555) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687553)), c_Hilbert__Choice_OEps(tc_List_Olist(_1687553), hAPP(hAPP(c_COMBS(tc_List_Olist(_1687553), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1687553)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687553), tc_fun(_1687553, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1687553, tc_HOL_Obool), tc_fun(tc_fun(_1687553, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1687553)), c_fequal), c_List_Oset(_1687553))), _1687555))), c_List_Odistinct(_1687553)))))], (2458 ^ _774244) ^ [_811383, _811385, _811387, _811389] : [-(c_Divides_Opdivmod(_811389, _811385) = c_Divides_Opdivmod(_811387, _811383)), _811389 = _811387, _811385 = _811383], (186 ^ _774244) ^ [_776903, _776905, _776907, _776909, _776911, _776913, _776915, _776917] : [-(c_Orderings_Oorder_Omono(_776915, _776911, _776907, _776903)), c_Orderings_Oorder_Omono(_776917, _776913, _776909, _776905), _776917 = _776915, _776913 = _776911, _776909 = _776907, _776905 = _776903], (42760 ^ _774244) ^ [_1599939, _1599941, _1599943] : [class_Orderings_Olinorder(_1599939), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599939), _1599941)), -(hBOOL(hAPP(hAPP(c_member(_1599939), _1599943), _1599941))), -(c_Big__Operators_Olinorder__class_OMin(_1599939, hAPP(hAPP(c_Set_Oinsert(_1599939), _1599943), _1599941)) = hAPP(hAPP(c_Finite__Set_Ofold(_1599939, _1599939, c_Orderings_Oord__class_Omin(_1599939)), _1599943), _1599941))], (51363 ^ _774244) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (44018 ^ _774244) ^ [_1632483, _1632485, _1632487] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632483, _1632483)), hAPP(hAPP(c_Product__Type_OPair(_1632483, _1632483), _1632485), _1632487)), c_Relation_OId(_1632483))), -(_1632485 = _1632487)], (23565 ^ _774244) ^ [_1182756, _1182758] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1182756, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1182756, tc_HOL_Obool)), _1182758)) = _1182758)], (5524 ^ _774244) ^ [_859512, _859514] : [_859514 = _859512, -(c_COMBI(_859514) = c_COMBI(_859512))], (25015 ^ _774244) ^ [_1210915, _1210917] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210915), _1210917)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210917), _1210915))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210917), _1210915)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210915), _1210917)))], (33860 ^ _774244) ^ [_1389153, _1389155, _1389157, _1389159, _1389161, _1389163] : [_1389153 = _1389155, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1389157, _1389159), _1389161), _1389155), _1389163), _1389153) = _1389163)], (46858 ^ _774244) ^ [_1702757] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702757)), c_List_Olist_ONil(_1702757)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18829 ^ _774244) ^ [_1095246, _1095248] : [class_Int_Onumber__ring(_1095246), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095246), c_Groups_Oone__class_Oone(_1095246)), hAPP(c_Int_Onumber__class_Onumber__of(_1095246), _1095248)) = hAPP(c_Int_Onumber__class_Onumber__of(_1095246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1095248)))], (16783 ^ _774244) ^ [_1060939, _1060941] : [class_Groups_Oordered__ab__group__add__abs(_1060939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060939), _1060941), c_Groups_Ozero__class_Ozero(_1060939))), -(hAPP(c_Groups_Oabs__class_Oabs(_1060939), _1060941) = hAPP(c_Groups_Ouminus__class_Ouminus(_1060939), _1060941))], (49274 ^ _774244) ^ [_1759981, _1759983, _1759985, _1759987] : [-(hAPP(hAPP(c_List_Oappend(_1759981), _1759983), hAPP(hAPP(c_List_Olist_OCons(_1759981), _1759985), c_List_Olist_ONil(_1759981))) = _1759987), -(_1759987 = c_List_Olist_ONil(_1759981)), c_List_Obutlast(_1759981, _1759987) = _1759983, c_List_Olast(_1759981, _1759987) = _1759985], (13012 ^ _774244) ^ [_990337, _990339] : [class_Rings_Oring__1(_990337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990339)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_990337), hAPP(c_Int_Onat, _990339)) = hAPP(c_Int_Oring__1__class_Oof__int(_990337), _990339))], (44530 ^ _774244) ^ [_1644505] : [class_Complete__Lattice_Ocomplete__lattice(_1644505), -(c_Complete__Lattice_OInf__class_OInf(_1644505, c_Orderings_Otop__class_Otop(tc_fun(_1644505, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1644505))], (51035 ^ _774244) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (23395 ^ _774244) ^ [_1179508, _1179510, _1179512] : [_1179508 = _1179510, 23398 ^ _774244 : [(23401 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179512, tc_HOL_Obool)), _1179510), _1179508)))], (23399 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179512, tc_HOL_Obool)), _1179508), _1179510)))]]], (10688 ^ _774244) ^ [_950034, _950036, _950038] : [class_Orderings_Olinorder(_950034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950034), _950036), _950038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950034), _950038), _950036))], (18241 ^ _774244) ^ [_1085622, _1085624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085622)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085624))), 18244 ^ _774244 : [(18245 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085622), _1085624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1085624)))], (18251 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085622), _1085624)))]]], (28735 ^ _774244) ^ [_1284564, _1284566, _1284568] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284564, tc_HOL_Obool)), _1284566), hAPP(hAPP(c_Set_Oinsert(_1284564), _1284568), _1284566))))], (23609 ^ _774244) ^ [_1183695, _1183697, _1183699, _1183701] : [class_Orderings_Olinorder(_1183695), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183695), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183695), _1183697), _1183699)), _1183701) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183695), _1183697), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183695), _1183699), _1183701)))], (6081 ^ _774244) ^ [_871621, _871623, _871625, _871627, _871629, _871631] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_871621, _871623, _871625), _871627, _871629, _871631), 6086 ^ _774244 : [(6089 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_871623, _871627, _871629, _871631))], (6087 ^ _774244) ^ [] : [-(hBOOL(hAPP(_871621, _871627)))]], 6090 ^ _774244 : [(6093 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_871625, _871627, _871629, _871631))], (6091 ^ _774244) ^ [] : [hBOOL(hAPP(_871621, _871627))]]], (31152 ^ _774244) ^ [_1333370, _1333372, _1333374, _1333376] : [hBOOL(hAPP(hAPP(c_member(_1333370), _1333376), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333370, tc_HOL_Obool)), _1333372), _1333374))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333370, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1333370, tc_fun(_1333370, tc_HOL_Obool), tc_HOL_Obool), c_member(_1333370)), _1333372)), hAPP(hAPP(c_COMBC(_1333370, tc_fun(_1333370, tc_HOL_Obool), tc_HOL_Obool), c_member(_1333370)), _1333374)), _1333376)))], (21567 ^ _774244) ^ [_1144416, _1144418, _1144420, _1144422] : [class_Fields_Olinordered__field__inverse__zero(_1144416), class_Int_Onumber(_1144416), 21574 ^ _774244 : [(21575 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), _1144418), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144416), _1144420), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422)))), 21578 ^ _774244 : [(21585 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), c_Groups_Ozero__class_Ozero(_1144416)), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422)))), 21588 ^ _774244 : [(21595 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422)), c_Groups_Ozero__class_Ozero(_1144416)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), _1144418), c_Groups_Ozero__class_Ozero(_1144416))))], (21589 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422)), c_Groups_Ozero__class_Ozero(_1144416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), _1144420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144416), _1144418), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422)))))]]], (21579 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), c_Groups_Ozero__class_Ozero(_1144416)), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144416), _1144418), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422))), _1144420)))]]], (21601 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), _1144418), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144416), _1144420), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422))))), 21604 ^ _774244 : [(21607 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144416), _1144418), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422))), _1144420))], (21605 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), c_Groups_Ozero__class_Ozero(_1144416)), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422))))]], 21608 ^ _774244 : [(21611 ^ _774244) ^ [] : [21612 ^ _774244 : [(21615 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), _1144420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144416), _1144418), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422))))], (21613 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422)), c_Groups_Ozero__class_Ozero(_1144416))))]], 21616 ^ _774244 : [(21619 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), _1144418), c_Groups_Ozero__class_Ozero(_1144416)))], (21617 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422)), c_Groups_Ozero__class_Ozero(_1144416)))]]], (21609 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144416), c_Groups_Ozero__class_Ozero(_1144416)), hAPP(c_Int_Onumber__class_Onumber__of(_1144416), _1144422)))]]]]], (41474 ^ _774244) ^ [_1570286, _1570288, _1570290] : [c_Wellfounded_Owf(_1570286, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570286, _1570286), tc_HOL_Obool)), _1570288), _1570290)), -(c_Wellfounded_Owf(_1570286, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570286, _1570286), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570286, _1570286), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1570286, _1570286, _1570286), _1570288), _1570288)), hAPP(hAPP(c_Relation_Orel__comp(_1570286, _1570286, _1570286), _1570290), _1570288))), _1570290)))], (18905 ^ _774244) ^ [_1096810, _1096812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1096810)), c_Int_OBit0(_1096812))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096810), _1096812)))], (51177 ^ _774244) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (50813 ^ _774244) ^ [_1793570, _1793572, _1793574, _1793576] : [hBOOL(hAPP(_1793570, _1793572)), -(c_List_OdropWhile(_1793574, _1793570, hAPP(hAPP(c_List_Olist_OCons(_1793574), _1793572), _1793576)) = c_List_OdropWhile(_1793574, _1793570, _1793576))], (39684 ^ _774244) ^ [_1521157, _1521159, _1521161, _1521163, _1521165, _1521167] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1521157, _1521159)), hAPP(hAPP(c_Product__Type_OPair(_1521157, _1521159), _1521161), _1521163)), hAPP(hAPP(c_Product__Type_OSigma(_1521157, _1521159), _1521165), _1521167))), -(hBOOL(hAPP(hAPP(c_member(_1521157), _1521161), _1521165)))], (3404 ^ _774244) ^ [_826546, _826548, _826550, _826552] : [-(c_Sum__Type_OInr(_826552, _826548) = c_Sum__Type_OInr(_826550, _826546)), _826552 = _826550, _826548 = _826546], (47949 ^ _774244) ^ [_1728679, _1728681, _1728683, _1728685, _1728687, _1728689] : [-(hBOOL(hAPP(hAPP(c_member(_1728679), _1728681), hAPP(c_List_Oset(_1728679), _1728683)))), -(hAPP(c_Map_Omap__upds(_1728679, _1728685, _1728687, _1728683, _1728689), _1728681) = hAPP(_1728687, _1728681))], (34948 ^ _774244) ^ [_1413495, _1413497, _1413499] : [-(hAPP(c_Set_OPow(_1413495), hAPP(hAPP(c_Set_Oinsert(_1413495), _1413497), _1413499)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1413495, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1413495), _1413499)), hAPP(c_Set_Oimage(tc_fun(_1413495, tc_HOL_Obool), tc_fun(_1413495, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1413495), _1413497)), hAPP(c_Set_OPow(_1413495), _1413499))))], (13958 ^ _774244) ^ [_1007541, _1007543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007541)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1007541, _1007543))))], (12776 ^ _774244) ^ [_986479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986479)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _986479)) = _986479)], (35432 ^ _774244) ^ [_1425271, _1425273, _1425275, _1425277, _1425279, _1425281] : [c_Finite__Set_Ofolding(_1425271, _1425273, _1425275, _1425277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425271), _1425279)), -(hAPP(c_Fun_Ocomp(_1425273, _1425273, _1425273, hAPP(_1425275, _1425281)), hAPP(_1425277, _1425279)) = hAPP(c_Fun_Ocomp(_1425273, _1425273, _1425273, hAPP(_1425277, _1425279)), hAPP(_1425275, _1425281)))], (47004 ^ _774244) ^ [_1705580] : [-(c_List_Olistset(_1705580, c_List_Olist_ONil(tc_fun(_1705580, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1705580)), c_List_Olist_ONil(_1705580)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1705580), tc_HOL_Obool))))], (7766 ^ _774244) ^ [_901088, _901090, _901092] : [-(hAPP(c_Nat_Osize__class_Osize(tc_sum(_901088, _901090)), hAPP(c_Sum__Type_OInr(_901090, _901088), _901092)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51243 ^ _774244) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (37195 ^ _774244) ^ [_1464236, _1464238, _1464240] : [class_Orderings_Olinorder(_1464236), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464236), _1464238)), -(_1464238 = c_Orderings_Obot__class_Obot(tc_fun(_1464236, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464236), _1464240)), -(_1464240 = c_Orderings_Obot__class_Obot(tc_fun(_1464236, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464236, tc_HOL_Obool)), _1464238), _1464240) = c_Orderings_Obot__class_Obot(tc_fun(_1464236, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1464236, c_Orderings_Oord__class_Omin(_1464236), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464236, tc_HOL_Obool)), _1464238), _1464240)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1464236), c_Big__Operators_Olattice_OInf__fin(_1464236, c_Orderings_Oord__class_Omin(_1464236), _1464238)), c_Big__Operators_Olattice_OInf__fin(_1464236, c_Orderings_Oord__class_Omin(_1464236), _1464240)))], (11056 ^ _774244) ^ [_956105, _956107, _956109] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _956107), _956109)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956105), _956107)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956105), _956109)))], (23831 ^ _774244) ^ [_1187708, _1187710, _1187712, _1187714] : [class_Orderings_Olinorder(_1187708), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187708), _1187710), _1187712)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187708), _1187710), _1187714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187708), _1187710), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187708), _1187712), _1187714))))], (4862 ^ _774244) ^ [_849399, _849401, _849403, _849405, _849407, _849409] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_849409, _849405, _849401) = c_SetInterval_Oord__class_OgreaterThanLessThan(_849407, _849403, _849399)), _849409 = _849407, _849405 = _849403, _849401 = _849399], (30326 ^ _774244) ^ [_1314729, _1314731] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1314729), _1314731)))), -(_1314731 = c_Orderings_Obot__class_Obot(tc_fun(_1314729, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314729), _1314731))], (25265 ^ _774244) ^ [_1214914, _1214916, _1214918, _1214920] : [class_Divides_Osemiring__div(_1214914), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214914), _1214916), _1214918)), 25272 ^ _774244 : [(25279 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214914), _1214916), _1214920)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214914), _1214916), c_Divides_Odiv__class_Omod(_1214914, _1214920, _1214918))))], (25273 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214914), _1214916), c_Divides_Odiv__class_Omod(_1214914, _1214920, _1214918))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214914), _1214916), _1214920)))]]], (39431 ^ _774244) ^ [_1514065, _1514067, _1514069, _1514071] : [c_Wellfounded_Omax__extp(_1514065, _1514067, _1514069, _1514071), 39434 ^ _774244 : [(39437 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1514065), _1514071)))], (39439 ^ _774244) ^ [] : [_1514071 = c_Orderings_Obot__class_Obot(tc_fun(_1514065, tc_HOL_Obool))], (39441 ^ _774244) ^ [_1514281] : [hBOOL(hAPP(hAPP(c_member(_1514065), _1514281), _1514069)), 39445 ^ _774244 : [(39448 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1514067, _1514281), 39444 ^ [_1514065, _1514067, _1514069, _1514071, _1514281])))], (39446 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514065), 39444 ^ [_1514065, _1514067, _1514069, _1514071, _1514281]), _1514071)))]]], (39435 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1514065), _1514069)))]]], (36301 ^ _774244) ^ [_1444241, _1444243] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444241, tc_HOL_Obool)), _1444243), _1444243) = _1444243)], (23461 ^ _774244) ^ [_1180731, _1180733, _1180735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1180731, tc_HOL_Obool)), _1180733), _1180735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1180731, tc_HOL_Obool)), _1180733), _1180735))), -(_1180733 = _1180735)], (6644 ^ _774244) ^ [_881242, _881244] : [class_Rings_Ocomm__semiring__1(_881242), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881242), c_Groups_Ozero__class_Ozero(_881242)), _881244) = _881244)], (10940 ^ _774244) ^ [_954129, _954131, _954133] : [10941 ^ _774244 : [(10944 ^ _774244) ^ [] : [_954129 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10942 ^ _774244) ^ [] : [_954131 = _954133]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954129), _954131) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954129), _954133))], (39157 ^ _774244) ^ [_1507756, _1507758, _1507760, _1507762, _1507764] : [hBOOL(hAPP(hAPP(c_member(_1507756), _1507758), hAPP(c_Relation_OImage(_1507760, _1507756, _1507762), _1507764))), 39161 ^ _774244 : [(39164 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1507760), 39160 ^ [_1507756, _1507758, _1507760, _1507762, _1507764]), _1507764)))], (39162 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1507760, _1507756)), hAPP(hAPP(c_Product__Type_OPair(_1507760, _1507756), 39160 ^ [_1507756, _1507758, _1507760, _1507762, _1507764]), _1507758)), _1507762)))]]], (49936 ^ _774244) ^ [_1773533, _1773535] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1773533)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1773535)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1773533), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1773535)) = c_List_Olist_ONil(tc_Nat_Onat))], (51141 ^ _774244) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (32896 ^ _774244) ^ [_1370224, _1370226, _1370228] : [class_Lattices_Olattice(_1370224), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370224), _1370226)), -(_1370226 = c_Orderings_Obot__class_Obot(tc_fun(_1370224, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1370224, hAPP(hAPP(c_Set_Oinsert(_1370224), _1370228), _1370226)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1370224), _1370228), c_Big__Operators_Olattice__class_OSup__fin(_1370224, _1370226)))], (24389 ^ _774244) ^ [_1198318, _1198320] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198318)), _1198320) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1198318), 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), _1198318)), _1198320))], (29720 ^ _774244) ^ [_1303452, _1303454, _1303456] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1303452), _1303454)), -(hAPP(c_Finite__Set_Ocard(_1303452), hAPP(hAPP(c_Set_Oinsert(_1303452), _1303456), _1303454)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1303452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1303452, tc_HOL_Obool)), _1303454), hAPP(hAPP(c_Set_Oinsert(_1303452), _1303456), c_Orderings_Obot__class_Obot(tc_fun(_1303452, tc_HOL_Obool)))))))], (46106 ^ _774244) ^ [_1682255, _1682257, _1682259, _1682261, _1682263, _1682265, _1682267] : [hAPP(hAPP(c_List_Omap(_1682255, _1682257), _1682259), _1682261) = hAPP(hAPP(c_List_Omap(_1682263, _1682257), _1682265), _1682267), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682255)), _1682261) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682263)), _1682267))], (12954 ^ _774244) ^ [_989431, _989433] : [hAPP(c_Int_Onat, _989431) = _989433, 12957 ^ _774244 : [(12964 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989431))), -(_989433 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12958 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989431)), -(_989431 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _989433))]]], (49367 ^ _774244) ^ [_1761918, _1761920, _1761922] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1761918), tc_List_Olist(_1761918)), c_List_Opartition(_1761918, _1761920, _1761922)) = hAPP(c_List_Ofilter(_1761918, _1761920), _1761922))], (34737 ^ _774244) ^ [_1408969] : [-(hAPP(c_Relation_OField(_1408969), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1408969, _1408969), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1408969, tc_HOL_Obool)))], (17927 ^ _774244) ^ [_1081011] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1081011), hAPP(c_Int_Onumber__class_Onumber__of(_1081011), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1081011)), class_Int_Onumber__ring(_1081011), class_Rings_Olinordered__idom(_1081011)], (39650 ^ _774244) ^ [_1520125, _1520127, _1520129] : [c_Equiv__Relations_Oequiv(_1520125, _1520127, _1520129), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520125, _1520125), tc_HOL_Obool)), _1520129), hAPP(hAPP(c_Product__Type_OSigma(_1520125, _1520125), _1520127), hAPP(c_COMBK(tc_fun(_1520125, tc_HOL_Obool), _1520125), _1520127)))))], (48560 ^ _774244) ^ [_1744815, _1744817] : [-(_1744815 = c_List_Olist_ONil(_1744817)), -(hBOOL(hAPP(hAPP(c_member(_1744817), hAPP(c_List_Ohd(_1744817), _1744815)), hAPP(c_List_Oset(_1744817), _1744815))))], (50880 ^ _774244) ^ [_1794903, _1794905, _1794907, _1794909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1794903), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1794905)), c_List_OdropWhile(_1794905, _1794907, _1794909)))), -(hAPP(hAPP(c_List_Onth(_1794905), c_List_OdropWhile(_1794905, _1794907, _1794909)), _1794903) = hAPP(hAPP(c_List_Onth(_1794905), _1794909), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1794903), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1794905)), c_List_OtakeWhile(_1794905, _1794907, _1794909)))))], (16915 ^ _774244) ^ [_1063362, _1063364, _1063366, _1063368] : [class_Rings_Olinordered__semidom(_1063362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063362), c_Groups_Oone__class_Oone(_1063362)), _1063364)), 16922 ^ _774244 : [(16929 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1063366), _1063368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063362), hAPP(hAPP(c_Power_Opower__class_Opower(_1063362), _1063364), _1063366)), hAPP(hAPP(c_Power_Opower__class_Opower(_1063362), _1063364), _1063368))))], (16923 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063362), hAPP(hAPP(c_Power_Opower__class_Opower(_1063362), _1063364), _1063366)), hAPP(hAPP(c_Power_Opower__class_Opower(_1063362), _1063364), _1063368))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1063366), _1063368)))]]], (28218 ^ _774244) ^ [_1273047, _1273049] : [c_Nat__Transfer_Onat__set(_1273047), c_Nat__Transfer_Onat__set(_1273049), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1273047), _1273049) = 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), _1273047)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1273049))))], (25091 ^ _774244) ^ [_1212148, _1212150] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212148), _1212150)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212150), _1212148)), -(_1212148 = _1212150)], (7561 ^ _774244) ^ [_897315, _897317, _897319, _897321, _897323] : [c_Com_Ocom_OCall(_897315, _897317, _897319) = c_Com_Ocom_OAss(_897321, _897323)], (6333 ^ _774244) ^ [_876108, _876110, _876112] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCall(_876108, _876110, _876112)], (31649 ^ _774244) ^ [_1345438, _1345440, _1345442, _1345444, _1345446] : [class_Groups_Ocomm__monoid__add(_1345438), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345440), _1345442)), -(hBOOL(hAPP(hAPP(c_member(_1345440), _1345444), _1345442))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345440, _1345438), _1345446), hAPP(hAPP(c_Set_Oinsert(_1345440), _1345444), _1345442)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1345438), hAPP(_1345446, _1345444)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345440, _1345438), _1345446), _1345442)))], (1014 ^ _774244) ^ [_789643, _789645] : [-(class_Rings_Oring__no__zero__divisors(_789643)), _789645 = _789643, class_Rings_Oring__no__zero__divisors(_789645)], (50819 ^ _774244) ^ [_1793681, _1793683, _1793685, _1793687] : [-(hBOOL(hAPP(_1793681, _1793683))), -(c_List_OdropWhile(_1793685, _1793681, hAPP(hAPP(c_List_Olist_OCons(_1793685), _1793683), _1793687)) = hAPP(hAPP(c_List_Olist_OCons(_1793685), _1793683), _1793687))], (13004 ^ _774244) ^ [_990205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990205)), -(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)), _990205))))], (45906 ^ _774244) ^ [_1677117, _1677119, _1677121] : [-(hBOOL(hAPP(hAPP(c_member(_1677117), _1677119), hAPP(c_List_Oset(_1677117), _1677121)))), -(c_List_Oremove1(_1677117, _1677119, _1677121) = _1677121)], (44467 ^ _774244) ^ [_1643249, _1643251, _1643253] : [class_Complete__Lattice_Ocomplete__lattice(_1643249), class_Orderings_Olinorder(_1643249), 44474 ^ _774244 : [(44484 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1643249), c_Complete__Lattice_OInf__class_OInf(_1643249, _1643251)), _1643253))), 44485 ^ _774244 : [(44486 ^ _774244) ^ [_1643555] : [hBOOL(hAPP(hAPP(c_member(_1643249), _1643555), _1643251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1643249), _1643555), _1643253))]]], (44475 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1643249), c_Complete__Lattice_OInf__class_OInf(_1643249, _1643251)), _1643253)), 44479 ^ _774244 : [(44482 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1643249), 44478 ^ [_1643249, _1643251, _1643253]), _1643253)))], (44480 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1643249), 44478 ^ [_1643249, _1643251, _1643253]), _1643251)))]]]]], (9128 ^ _774244) ^ [_923538, _923540, _923542, _923544, _923546] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_923538), 9131 ^ _774244 : [(9132 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923538), _923540), _923542)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923538), _923544), _923546)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923538), _923540), _923546)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923538), _923544), _923542)), -(_923540 = _923544), -(_923542 = _923546)], (9142 ^ _774244) ^ [] : [9143 ^ _774244 : [(9146 ^ _774244) ^ [] : [_923542 = _923546], (9144 ^ _774244) ^ [] : [_923540 = _923544]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923538), _923540), _923542)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923538), _923544), _923546)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923538), _923540), _923546)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923538), _923544), _923542)))]]], (34574 ^ _774244) ^ [] : [-(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)))))], (22915 ^ _774244) ^ [_1170187, _1170189, _1170191, _1170193, _1170195] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1170187, _1170189, tc_HOL_Obool), _1170191), hAPP(hAPP(c_Product__Type_OPair(_1170187, _1170189), _1170193), _1170195))), -(hBOOL(hAPP(hAPP(_1170191, _1170193), _1170195)))], (32846 ^ _774244) ^ [_1369377, _1369379, _1369381] : [class_Orderings_Olinorder(_1369377), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369377), _1369379)), hBOOL(hAPP(hAPP(c_member(_1369377), _1369381), _1369379)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1369377), _1369381), c_Big__Operators_Olinorder__class_OMax(_1369377, _1369379)) = c_Big__Operators_Olinorder__class_OMax(_1369377, _1369379))], (28827 ^ _774244) ^ [_1286345, _1286347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1286345), hAPP(c_Nat_OSuc, _1286347))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1286345, hAPP(c_Nat_OSuc, _1286347)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1286347)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1286345, _1286347)))], (34172 ^ _774244) ^ [_1395667, _1395669, _1395671, _1395673, _1395675] : [class_Rings_Ocomm__semiring__1(_1395667), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395669), _1395671)), hBOOL(hAPP(hAPP(c_member(_1395669), _1395673), _1395671)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1395667), hAPP(_1395675, _1395673)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395669, _1395667), _1395675), _1395671))))], (19575 ^ _774244) ^ [_1108425, _1108427, _1108429] : [class_Rings_Olinordered__idom(_1108425), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108425), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108425), hAPP(hAPP(c_Power_Opower__class_Opower(_1108425), _1108427), 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(_1108425), _1108429), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1108425)))], (15584 ^ _774244) ^ [_1037287, _1037289, _1037291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037287), _1037289)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037291), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037289), _1037287)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037291), _1037289)), _1037287))], (38820 ^ _774244) ^ [_1499916, _1499918, _1499920, _1499922, _1499924] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1499916, _1499918, _1499920), _1499922), _1499924), c_Orderings_Obot__class_Obot(tc_fun(_1499918, tc_HOL_Obool))) = _1499924)], (41399 ^ _774244) ^ [_1568844, _1568846, _1568848, _1568850, _1568852, _1568854, _1568856] : [c_Predicate_Opred__comp(_1568844, _1568846, _1568848, _1568850, _1568852, _1568854, _1568856), 41403 ^ _774244 : [(41406 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1568852, 41402 ^ [_1568844, _1568846, _1568848, _1568850, _1568852, _1568854, _1568856]), _1568856)))], (41404 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1568850, _1568854), 41402 ^ [_1568844, _1568846, _1568848, _1568850, _1568852, _1568854, _1568856])))]]], (10355 ^ _774244) ^ [_944730, _944732, _944734] : [class_Orderings_Olinorder(_944730), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944730), _944732), _944734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944730), _944734), _944732)))], (29276 ^ _774244) ^ [_1295289, _1295291, _1295293] : [class_Orderings_Oorder(_1295289), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295289), _1295291), _1295293)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1295289, _1295293, _1295291) = c_Orderings_Obot__class_Obot(tc_fun(_1295289, tc_HOL_Obool)))], (31563 ^ _774244) ^ [_1343051, _1343053, _1343055, _1343057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool)), _1343055), _1343057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1343051, tc_fun(_1343053, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1343051, tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_fun(_1343053, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343053, tc_fun(tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_fun(_1343053, tc_HOL_Obool)), _1343051), c_COMBC(_1343053, tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343053, tc_prod(_1343051, _1343053)), tc_fun(_1343053, tc_fun(tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_HOL_Obool)), _1343051), hAPP(c_COMBB(tc_prod(_1343051, _1343053), tc_fun(tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_HOL_Obool), _1343053), c_member(tc_prod(_1343051, _1343053)))), c_Product__Type_OPair(_1343051, _1343053)))), _1343055)), hAPP(hAPP(c_COMBC(_1343051, tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_fun(_1343053, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343053, tc_fun(tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_fun(_1343053, tc_HOL_Obool)), _1343051), c_COMBC(_1343053, tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1343053, tc_prod(_1343051, _1343053)), tc_fun(_1343053, tc_fun(tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_HOL_Obool)), _1343051), hAPP(c_COMBB(tc_prod(_1343051, _1343053), tc_fun(tc_fun(tc_prod(_1343051, _1343053), tc_HOL_Obool), tc_HOL_Obool), _1343053), c_member(tc_prod(_1343051, _1343053)))), c_Product__Type_OPair(_1343051, _1343053)))), _1343057))))], (46473 ^ _774244) ^ [_1692922, _1692924, _1692926, _1692928, _1692930, _1692932] : [class_Orderings_Olinorder(_1692922), 46476 ^ _774244 : [(46483 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1692922), hAPP(_1692924, _1692926)), hAPP(_1692924, _1692928)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1692930, _1692922, _1692924), _1692926), hAPP(hAPP(c_List_Olist_OCons(_1692930), _1692928), _1692932)) = hAPP(hAPP(c_List_Olist_OCons(_1692930), _1692928), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1692930, _1692922, _1692924), _1692926), _1692932)))], (46477 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1692922), hAPP(_1692924, _1692926)), hAPP(_1692924, _1692928))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1692930, _1692922, _1692924), _1692926), hAPP(hAPP(c_List_Olist_OCons(_1692930), _1692928), _1692932)) = hAPP(hAPP(c_List_Olist_OCons(_1692930), _1692926), hAPP(hAPP(c_List_Olist_OCons(_1692930), _1692928), _1692932)))]]], (17663 ^ _774244) ^ [_1076568, _1076570] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076568) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076570)), 17666 ^ _774244 : [(17669 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076570)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (17667 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076568))))]], 17670 ^ _774244 : [(17673 ^ _774244) ^ [] : [17674 ^ _774244 : [(17677 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076568) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (17675 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076570))))]], 17678 ^ _774244 : [(17681 ^ _774244) ^ [] : [_1076568 = _1076570], (17679 ^ _774244) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076570)))]]], (17671 ^ _774244) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076568)))]]], (42648 ^ _774244) ^ [_1597831, _1597833, _1597835] : [class_Orderings_Olinorder(_1597831), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597831), _1597833)), -(c_Big__Operators_Olinorder__class_OMin(_1597831, hAPP(hAPP(c_Set_Oinsert(_1597831), _1597835), _1597833)) = hAPP(hAPP(c_Finite__Set_Ofold(_1597831, _1597831, c_Orderings_Oord__class_Omin(_1597831)), _1597835), _1597833))], (4434 ^ _774244) ^ [_842861, _842863] : [_842863 = _842861, -(c_Groups_Otimes__class_Otimes(_842863) = c_Groups_Otimes__class_Otimes(_842861))], (43139 ^ _774244) ^ [_1608585, _1608587] : [-(c_Transitive__Closure_Otrancl(_1608585, _1608587) = hAPP(hAPP(c_Relation_Orel__comp(_1608585, _1608585, _1608585), _1608587), c_Transitive__Closure_Ortrancl(_1608585, _1608587)))], (22640 ^ _774244) ^ [_1165052, _1165054] : [-(c_Divides_Odivmod__int(_1165052, _1165054) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1165052), _1165054)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1165052, _1165054)))], (3010 ^ _774244) ^ [_820315, _820317] : [_820317 = _820315, -(c_DSequence_Ounion(_820317) = c_DSequence_Ounion(_820315))], (48966 ^ _774244) ^ [_1753711, _1753713, _1753715, _1753717] : [48967 ^ _774244 : [(48968 ^ _774244) ^ [_1753808, _1753810] : [_1753711 = hAPP(hAPP(c_List_Olist_OCons(_1753713), _1753810), _1753808)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753713), tc_List_Olist(_1753713))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753713), tc_List_Olist(_1753713)), _1753715), hAPP(hAPP(c_List_Oappend(_1753713), _1753715), _1753711))), c_List_Olexord(_1753713, _1753717))))], (41937 ^ _774244) ^ [_1581724, _1581726] : [c_Nitpick_Owf_H(_1581724, _1581726), 41940 ^ _774244 : [(41943 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1581724, _1581724)), _1581726))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (41941 ^ _774244) ^ [] : [-(c_Wellfounded_Oacyclic(_1581724, _1581726))]]], (11198 ^ _774244) ^ [_958329, _958331, _958333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _958329), _958331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _958329), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958333), _958331))))], (24293 ^ _774244) ^ [_1196173, _1196175, _1196177] : [class_Orderings_Olinorder(_1196173), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196173), _1196175), _1196177) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196173), _1196177), _1196175))], (12093 ^ _774244) ^ [_974456, _974458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974456), _974458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974456), hAPP(c_Nat_OSuc, _974458))))], (13264 ^ _774244) ^ [_994653, _994655, _994657] : [13265 ^ _774244 : [(13268 ^ _774244) ^ [] : [_994655 = _994657], (13266 ^ _774244) ^ [] : [_994653 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994653), _994655) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994653), _994657))], (49136 ^ _774244) ^ [_1757025, _1757027, _1757029] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1757025)), _1757027), c_List_Olists(_1757025, _1757029)))), 49137 ^ _774244 : [(49140 ^ _774244) ^ [_1757153, _1757155] : [_1757027 = hAPP(hAPP(c_List_Olist_OCons(_1757025), _1757155), _1757153), hBOOL(hAPP(hAPP(c_member(_1757025), _1757155), _1757029)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1757025)), _1757153), c_List_Olists(_1757025, _1757029)))], (49138 ^ _774244) ^ [] : [_1757027 = c_List_Olist_ONil(_1757025)]]], (46623 ^ _774244) ^ [_1697388, _1697390, _1697392] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1697388, tc_HOL_Obool)), hAPP(c_List_Oset(_1697388), c_List_Osublist(_1697388, _1697390, _1697392))), hAPP(c_List_Oset(_1697388), _1697390))))], (8854 ^ _774244) ^ [_919256, _919258] : [class_Rings_Oring__1(_919256), 8857 ^ _774244 : [(8864 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _919258), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_919256), _919258) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919256), hAPP(c_Int_Onat, _919258)))], (8858 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _919258), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_919256), _919258) = hAPP(c_Groups_Ouminus__class_Ouminus(_919256), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919256), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _919258)))))]]], (19477 ^ _774244) ^ [_1106735, _1106737] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1106735), hAPP(c_Int_Onumber__class_Onumber__of(_1106735), _1106737)), 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(_1106735), hAPP(c_Int_Onumber__class_Onumber__of(_1106735), _1106737)), hAPP(c_Int_Onumber__class_Onumber__of(_1106735), _1106737))), class_Groups_Omonoid__mult(_1106735), class_Int_Onumber(_1106735)], (45775 ^ _774244) ^ [_1674050, _1674052, _1674054] : [hBOOL(hAPP(c_List_Odistinct(_1674050), hAPP(hAPP(c_List_Omap(tc_prod(_1674050, _1674052), _1674050), c_Product__Type_Ofst(_1674050, _1674052)), _1674054))), -(c_Map_Oran(_1674050, _1674052, c_Map_Omap__of(_1674050, _1674052, _1674054)) = hAPP(c_Set_Oimage(tc_prod(_1674050, _1674052), _1674052, c_Product__Type_Osnd(_1674050, _1674052)), hAPP(c_List_Oset(tc_prod(_1674050, _1674052)), _1674054)))], (40557 ^ _774244) ^ [_1540586, _1540588, _1540590] : [40558 ^ _774244 : [(40561 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1540586), hAPP(c_Set_OCollect(_1540586), _1540590)))], (40559 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1540586), hAPP(c_Set_OCollect(_1540586), _1540588)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1540586), hAPP(c_Set_OCollect(_1540586), hAPP(hAPP(c_COMBS(_1540586, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540586), c_fconj), _1540588)), _1540590)))))], (9973 ^ _774244) ^ [_938549, _938551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _938549)), 9976 ^ _774244 : [(9983 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _938549), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _938551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _938549)), _938551)))], (9977 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _938549)), _938551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _938549), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _938551))))]]], (24517 ^ _774244) ^ [_1200782, _1200784] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1200782), _1200784) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1200782)), hAPP(c_Code__Numeral_Onat__of, _1200784))))], (40856 ^ _774244) ^ [_1549158, _1549160, _1549162, _1549164, _1549166, _1549168] : [-(hBOOL(hAPP(hAPP(c_member(_1549158), _1549160), _1549162))), -(hAPP(c_Fun_Ooverride__on(_1549158, _1549164, _1549166, _1549168, _1549162), _1549160) = hAPP(_1549166, _1549160))], (44498 ^ _774244) ^ [_1643879, _1643881, _1643883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1643879, tc_HOL_Obool), tc_HOL_Obool)), _1643881), _1643883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1643879, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1643879, tc_HOL_Obool), _1643883)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1643879, tc_HOL_Obool), _1643881))))], (7740 ^ _774244) ^ [_900508, _900510, _900512, _900514, _900516, _900518] : [-(c_Nitpick_Opair__box_Opair__box__rec(_900508, _900510, _900512, _900514, c_Nitpick_Opair__box_OPairBox(_900508, _900510, _900516, _900518)) = hAPP(hAPP(_900514, _900516), _900518))], (14722 ^ _774244) ^ [_1021103, _1021105, _1021107] : [hBOOL(hAPP(_1021103, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021105), _1021107))), 14725 ^ _774244 : [(14732 ^ _774244) ^ [] : [-(_1021107 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14735 ^ _774244 : [(14736 ^ _774244) ^ [_1021355, _1021357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1021355), _1021107)), _1021105 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021107), _1021357)), _1021355), -(hBOOL(hAPP(_1021103, _1021357)))]]], (14726 ^ _774244) ^ [] : [_1021107 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1021103, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (14646 ^ _774244) ^ [_1019473, _1019475, _1019477] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1019473), _1019475)), _1019477) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1019473), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019475), _1019477))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1019473), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019475, _1019477))), _1019477)))], (51213 ^ _774244) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (37659 ^ _774244) ^ [_1475954, _1475956, _1475958] : [class_Lattices_Olattice(_1475954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475954), _1475956)), hBOOL(hAPP(hAPP(c_member(_1475954), _1475958), _1475956)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1475954), _1475958), c_Big__Operators_Olattice__class_OInf__fin(_1475954, _1475956)) = _1475958)], (27372 ^ _774244) ^ [_1256826, _1256828] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1256826, _1256828)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1256828), _1256826)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (4 ^ _774244) ^ [_774294, _774296] : [_774296 = _774294, -(_774294 = _774296)], (49766 ^ _774244) ^ [_1770772, _1770774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770772), _1770774)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1770772, _1770774)) = _1770772)], (29170 ^ _774244) ^ [_1293405, _1293407, _1293409] : [-(hAPP(hAPP(c_Set_Oinsert(_1293405), _1293407), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1293405, tc_HOL_Obool)), _1293409), hAPP(hAPP(c_Set_Oinsert(_1293405), _1293407), c_Orderings_Obot__class_Obot(tc_fun(_1293405, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_1293405), _1293407), _1293409))], (42190 ^ _774244) ^ [_1588010, _1588012] : [42191 ^ _774244 : [(42192 ^ _774244) ^ [_1588056] : [hBOOL(hAPP(_1588010, _1588056))]], -(hBOOL(hAPP(_1588010, c_Hilbert__Choice_OEps(_1588012, _1588010))))], (3144 ^ _774244) ^ [_822396, _822398, _822400, _822402, _822404, _822406, _822408, _822410, _822412, _822414] : [-(c_SetInterval_Oord_OatLeastLessThan(_822414, _822410, _822406, _822402, _822398) = c_SetInterval_Oord_OatLeastLessThan(_822412, _822408, _822404, _822400, _822396)), _822414 = _822412, _822410 = _822408, _822406 = _822404, _822402 = _822400, _822398 = _822396], (7682 ^ _774244) ^ [_899534] : [_899534 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _899534), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (5856 ^ _774244) ^ [_867856, _867858, _867860] : [c_Com_Ocom_OBODY(_867856) = c_Com_Ocom_OSemi(_867858, _867860)], (31271 ^ _774244) ^ [_1335857, _1335859, _1335861, _1335863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1335857, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1335857), _1335859), _1335861)), _1335863)), 31274 ^ _774244 : [(31277 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1335857, tc_HOL_Obool)), _1335861), _1335863)))], (31275 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1335857), _1335859), _1335863)))]]], (44068 ^ _774244) ^ [_1633664, _1633666, _1633668, _1633670, _1633672, _1633674] : [c_Relation_Osingle__valued(_1633664, _1633666, hAPP(c_Relation_Oconverse(_1633666, _1633664), _1633668)), -(_1633670 = c_Orderings_Obot__class_Obot(tc_fun(_1633672, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1633666, _1633664, _1633668), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633672, tc_fun(_1633666, tc_HOL_Obool)), _1633670), _1633674)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633672, tc_fun(_1633664, tc_HOL_Obool)), _1633670), hAPP(hAPP(c_COMBB(tc_fun(_1633666, tc_HOL_Obool), tc_fun(_1633664, tc_HOL_Obool), _1633672), c_Relation_OImage(_1633666, _1633664, _1633668)), _1633674)))], (28114 ^ _774244) ^ [_1270774, _1270776, _1270778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270774, tc_HOL_Obool)), _1270776), _1270778)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270774, tc_HOL_Obool)), _1270776), _1270778) = _1270778)], (22142 ^ _774244) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (49398 ^ _774244) ^ [_1762602, _1762604, _1762606] : [-(hAPP(c_List_Oset(_1762602), hAPP(c_List_Ofilter(_1762602, _1762604), _1762606)) = hAPP(c_Set_OCollect(_1762602), hAPP(hAPP(c_COMBS(_1762602, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1762602), c_fconj), hAPP(hAPP(c_COMBC(_1762602, tc_fun(_1762602, tc_HOL_Obool), tc_HOL_Obool), c_member(_1762602)), hAPP(c_List_Oset(_1762602), _1762606)))), _1762604)))], (42974 ^ _774244) ^ [_1604651, _1604653, _1604655, _1604657, _1604659, _1604661] : [c_Finite__Set_Ofun__left__comm(_1604651, _1604653, _1604655), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1604651, _1604653, _1604655, _1604657, _1604659), _1604661)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1604651, _1604653, _1604655), _1604657), _1604659) = _1604661)], (27221 ^ _774244) ^ [_1253584, _1253586, _1253588, _1253590] : [class_Groups_Ocomm__monoid__add(_1253584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253586), _1253588)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1253584), _1253590), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1253586, _1253588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253584), hAPP(_1253590, _1253586)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1253584), _1253590), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1253586, _1253588))))], (41819 ^ _774244) ^ [_1578558, _1578560, _1578562, _1578564, _1578566] : [-(hAPP(c_Relation_ODomain(_1578558, _1578560), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1578558, _1578560)), hAPP(hAPP(c_Product__Type_OPair(_1578558, _1578560), _1578562), _1578564)), _1578566)) = hAPP(hAPP(c_Set_Oinsert(_1578558), _1578562), hAPP(c_Relation_ODomain(_1578558, _1578560), _1578566)))], (24735 ^ _774244) ^ [_1206080, _1206082] : [-(c_HOL_OThe(_1206080, hAPP(c_fequal, _1206082)) = _1206082)], (1694 ^ _774244) ^ [_798143, _798145] : [-(class_Orderings_Oord(_798143)), _798145 = _798143, class_Orderings_Oord(_798145)], (50707 ^ _774244) ^ [_1791357, _1791359, _1791361] : [hBOOL(hAPP(c_List_Odistinct(_1791357), _1791359)), -(c_List_Oremove1(_1791357, _1791361, c_List_Oremdups(_1791357, _1791359)) = c_List_Oremdups(_1791357, c_List_Oremove1(_1791357, _1791361, _1791359)))], (48608 ^ _774244) ^ [_1745567, _1745569] : [hBOOL(hAPP(c_List_Odistinct(_1745567), _1745569)), -(hBOOL(hAPP(c_List_Odistinct(_1745567), hAPP(c_List_Otl(_1745567), _1745569))))], (49412 ^ _774244) ^ [_1762946, _1762948, _1762950, _1762952, _1762954] : [c_List_Opartition(_1762946, _1762948, _1762950) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762946), tc_List_Olist(_1762946)), _1762952), _1762954), 49415 ^ _774244 : [(49422 ^ _774244) ^ [_1763208] : [hBOOL(hAPP(hAPP(c_member(_1762946), _1763208), hAPP(c_List_Oset(_1762946), _1762954))), hBOOL(hAPP(_1762948, _1763208))], (49416 ^ _774244) ^ [_1763099] : [hBOOL(hAPP(hAPP(c_member(_1762946), _1763099), hAPP(c_List_Oset(_1762946), _1762952))), -(hBOOL(hAPP(_1762948, _1763099)))]]], (51273 ^ _774244) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (36769 ^ _774244) ^ [_1455076, _1455078, _1455080] : [class_Orderings_Oorder(_1455076), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455076, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1455076, _1455078, _1455080)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1455076), _1455080)) = c_Orderings_Obot__class_Obot(tc_fun(_1455076, tc_HOL_Obool)))], (40119 ^ _774244) ^ [_1532234, _1532236, _1532238, _1532240, _1532242] : [c_Relation_Orefl__on(_1532234, _1532236, _1532238), hBOOL(hAPP(hAPP(c_member(tc_prod(_1532234, _1532234)), hAPP(hAPP(c_Product__Type_OPair(_1532234, _1532234), _1532240), _1532242)), _1532238)), -(hBOOL(hAPP(hAPP(c_member(_1532234), _1532242), _1532236)))], (10512 ^ _774244) ^ [_947532, _947534, _947536] : [class_Orderings_Olinorder(_947532), 10515 ^ _774244 : [(10522 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947532), _947536), _947534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947532), _947534), _947536))], (10516 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947532), _947534), _947536))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947532), _947536), _947534)))]]], (44119 ^ _774244) ^ [_1634768, _1634770, _1634772, _1634774, _1634776, _1634778] : [c_Relation_Osingle__valued(_1634768, _1634770, _1634772), hBOOL(hAPP(hAPP(c_member(tc_prod(_1634768, _1634770)), hAPP(hAPP(c_Product__Type_OPair(_1634768, _1634770), _1634774), _1634776)), _1634772)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1634768, _1634770)), hAPP(hAPP(c_Product__Type_OPair(_1634768, _1634770), _1634774), _1634778)), _1634772)), -(_1634776 = _1634778)], (51351 ^ _774244) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (40922 ^ _774244) ^ [_1551262, _1551264, _1551266, _1551268] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1551262), hAPP(c_Set_OCollect(_1551262), _1551264))), 40925 ^ _774244 : [(40926 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1551266), hAPP(c_Set_OCollect(_1551266), hAPP(hAPP(c_COMBB(tc_fun(_1551262, tc_HOL_Obool), tc_HOL_Obool, _1551266), c_HOL_OEx(_1551262)), hAPP(hAPP(c_COMBB(tc_fun(_1551262, tc_HOL_Obool), tc_fun(_1551262, tc_HOL_Obool), _1551266), hAPP(c_COMBS(_1551262, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1551262), c_fconj), _1551264))), _1551268))))), 40929 ^ _774244 : [(40930 ^ _774244) ^ [_1551545] : [hBOOL(hAPP(_1551264, _1551545)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1551266), hAPP(c_Set_OCollect(_1551266), hAPP(hAPP(c_COMBC(_1551266, _1551262, tc_HOL_Obool), _1551268), _1551545)))))]]], (40936 ^ _774244) ^ [] : [40938 ^ _774244 : [(40941 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1551266), hAPP(c_Set_OCollect(_1551266), hAPP(hAPP(c_COMBC(_1551266, _1551262, tc_HOL_Obool), _1551268), 40937 ^ [_1551262, _1551264, _1551266, _1551268]))))], (40939 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1551264, 40937 ^ [_1551262, _1551264, _1551266, _1551268])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1551266), hAPP(c_Set_OCollect(_1551266), hAPP(hAPP(c_COMBB(tc_fun(_1551262, tc_HOL_Obool), tc_HOL_Obool, _1551266), c_HOL_OEx(_1551262)), hAPP(hAPP(c_COMBB(tc_fun(_1551262, tc_HOL_Obool), tc_fun(_1551262, tc_HOL_Obool), _1551266), hAPP(c_COMBS(_1551262, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1551262), c_fconj), _1551264))), _1551268))))))]]], (30356 ^ _774244) ^ [_1315329, _1315331, _1315333] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1315329), _1315331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315329, tc_HOL_Obool)), _1315331), _1315333)), -(hAPP(c_Finite__Set_Ocard(_1315329), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1315329, tc_HOL_Obool)), _1315333), _1315331)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1315329), _1315333)), hAPP(c_Finite__Set_Ocard(_1315329), _1315331)))], (51085 ^ _774244) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (52 ^ _774244) ^ [_774966, _774968, _774970, _774972] : [-(c_Int_Oiszero(_774970, _774966)), c_Int_Oiszero(_774972, _774968), _774972 = _774970, _774968 = _774966], (15432 ^ _774244) ^ [_1034447, _1034449, _1034451] : [class_Groups_Ogroup__add(_1034447), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034447), _1034449), _1034451) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034447), _1034449), hAPP(c_Groups_Ouminus__class_Ouminus(_1034447), _1034451)))], (45507 ^ _774244) ^ [_1667758] : [-(hAPP(c_List_Omap(_1667758, _1667758), c_COMBI(_1667758)) = c_Fun_Oid(tc_List_Olist(_1667758)))], (39802 ^ _774244) ^ [_1524429, _1524431, _1524433, _1524435, _1524437, _1524439] : [-(hAPP(c_Set_Ovimage(_1524429, tc_prod(_1524431, _1524433), _1524435), hAPP(hAPP(c_Product__Type_OSigma(_1524431, _1524433), _1524437), hAPP(c_COMBK(tc_fun(_1524433, tc_HOL_Obool), _1524431), _1524439))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1524429, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1524429, _1524431, hAPP(c_Fun_Ocomp(tc_prod(_1524431, _1524433), _1524431, _1524429, c_Product__Type_Ofst(_1524431, _1524433)), _1524435)), _1524437)), hAPP(c_Set_Ovimage(_1524429, _1524433, hAPP(c_Fun_Ocomp(tc_prod(_1524431, _1524433), _1524433, _1524429, c_Product__Type_Osnd(_1524431, _1524433)), _1524435)), _1524439)))], (26401 ^ _774244) ^ [_1235597, _1235599, _1235601] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1235597, _1235599) = _1235601, -(_1235597 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1235601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), 26404 ^ [_1235597, _1235599, _1235601]), _1235599)))], (35526 ^ _774244) ^ [_1427560, _1427562, _1427564] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1427560), _1427562), _1427564) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427560, tc_HOL_Obool), tc_HOL_Obool)), -(_1427562 = c_Orderings_Obot__class_Obot(tc_fun(_1427560, tc_HOL_Obool)))], (5248 ^ _774244) ^ [_855414, _855416] : [_855416 = _855414, -(c_List_Oreturn__list(_855416) = c_List_Oreturn__list(_855414))], (19263 ^ _774244) ^ [_1103031] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1103031)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1103031)))], (45952 ^ _774244) ^ [_1677967, _1677969, _1677971, _1677973, _1677975] : [hBOOL(hAPP(hAPP(c_member(_1677967), _1677969), hAPP(c_List_Oset(_1677967), _1677971))), -(hAPP(c_Map_Omap__of(_1677967, _1677973, hAPP(hAPP(c_List_Ozip(_1677967, _1677973), _1677971), hAPP(hAPP(c_List_Omap(_1677967, _1677973), _1677975), _1677971))), _1677969) = hAPP(c_Option_Ooption_OSome(_1677973), hAPP(_1677975, _1677969)))], (25787 ^ _774244) ^ [_1224272, _1224274, _1224276, _1224278, _1224280] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1224272, _1224274, tc_HOL_Obool, _1224276), _1224278), _1224280)), -(hBOOL(hAPP(_1224276, hAPP(hAPP(c_Product__Type_OPair(_1224272, _1224274), _1224278), _1224280))))], (30366 ^ _774244) ^ [_1315554, _1315556, _1315558] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1315554), _1315556)), -(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(_1315554), _1315558)), hAPP(c_Finite__Set_Ocard(_1315554), _1315556))), hAPP(c_Finite__Set_Ocard(_1315554), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1315554, tc_HOL_Obool)), _1315558), _1315556)))))], (6219 ^ _774244) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1788 ^ _774244) ^ [_799336, _799338, _799340, _799342, _799344, _799346, _799348, _799350] : [-(c_Natural_Oevaln(_799348, _799344, _799340, _799336)), c_Natural_Oevaln(_799350, _799346, _799342, _799338), _799350 = _799348, _799346 = _799344, _799342 = _799340, _799338 = _799336], (4938 ^ _774244) ^ [_850543, _850545, _850547, _850549, _850551, _850553] : [-(c_Divides_Odiv__class_Omod(_850553, _850549, _850545) = c_Divides_Odiv__class_Omod(_850551, _850547, _850543)), _850553 = _850551, _850549 = _850547, _850545 = _850543], (3574 ^ _774244) ^ [_829283, _829285] : [_829285 = _829283, -(c_Wellfounded_Ofinite__psubset(_829285) = c_Wellfounded_Ofinite__psubset(_829283))], (51517 ^ _774244) ^ [_1802392, _1802394] : [hBOOL(hAPP(hAPP(c_fimplies, _1802392), _1802394)), hBOOL(_1802392), -(hBOOL(_1802394))], (15812 ^ _774244) ^ [_1042213, _1042215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1042213), _1042215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1042213), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042215), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (40222 ^ _774244) ^ [_1534137, _1534139, _1534141] : [class_Orderings_Olinorder(_1534137), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534137), _1534139)), -(_1534139 = c_Orderings_Obot__class_Obot(tc_fun(_1534137, tc_HOL_Obool))), 40233 ^ _774244 : [(40234 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1534137), _1534141), hAPP(c_Finite__Set_Ofold1(_1534137, c_Orderings_Oord__class_Omin(_1534137)), _1534139))), 40237 ^ _774244 : [(40238 ^ _774244) ^ [_1534430] : [hBOOL(hAPP(hAPP(c_member(_1534137), _1534430), _1534139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1534137), _1534141), _1534430)))]]], (40244 ^ _774244) ^ [] : [40246 ^ _774244 : [(40249 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1534137), _1534141), 40245 ^ [_1534137, _1534139, _1534141]))], (40247 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1534137), 40245 ^ [_1534137, _1534139, _1534141]), _1534139)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1534137), _1534141), hAPP(c_Finite__Set_Ofold1(_1534137, c_Orderings_Oord__class_Omin(_1534137)), _1534139))))]]], (29740 ^ _774244) ^ [_1303969, _1303971] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1303969, _1303971))))], (51381 ^ _774244) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (51391 ^ _774244) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (6275 ^ _774244) ^ [_874980, _874982, _874984] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_874980, _874982, _874984))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OBODY(_874982))))], (9044 ^ _774244) ^ [_922340, _922342] : [class_Rings_Ocomm__semiring__1(_922340), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922340), c_Groups_Ozero__class_Ozero(_922340)), _922342) = c_Groups_Ozero__class_Ozero(_922340))], (40593 ^ _774244) ^ [_1541443, _1541445, _1541447] : [-(hAPP(hAPP(c_Set_Oinsert(_1541443), _1541445), hAPP(c_Set_OCollect(_1541443), _1541447)) = hAPP(c_Set_OCollect(_1541443), hAPP(hAPP(c_COMBS(_1541443, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541443), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1541443), c_fNot), hAPP(hAPP(c_COMBC(_1541443, _1541443, tc_HOL_Obool), c_fequal), _1541445)))), _1541447)))], (51047 ^ _774244) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (31035 ^ _774244) ^ [_1330829, _1330831, _1330833] : [hBOOL(hAPP(hAPP(c_member(_1330829), _1330831), hAPP(c_fequal, _1330833))), -(_1330831 = _1330833)], (4832 ^ _774244) ^ [_848944, _848946] : [_848946 = _848944, -(c_SetInterval_Oord__class_OlessThan(_848946) = c_SetInterval_Oord__class_OlessThan(_848944))], (49264 ^ _774244) ^ [_1759792, _1759794, _1759796, _1759798] : [hAPP(hAPP(c_List_Oappend(_1759792), _1759794), hAPP(hAPP(c_List_Olist_OCons(_1759792), _1759796), c_List_Olist_ONil(_1759792))) = _1759798, 49267 ^ _774244 : [(49272 ^ _774244) ^ [] : [-(c_List_Olast(_1759792, _1759798) = _1759796)], (49270 ^ _774244) ^ [] : [-(c_List_Obutlast(_1759792, _1759798) = _1759794)], (49268 ^ _774244) ^ [] : [_1759798 = c_List_Olist_ONil(_1759792)]]], (4534 ^ _774244) ^ [_844367, _844369, _844371, _844373] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_844373, _844369) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_844371, _844367)), _844373 = _844371, _844369 = _844367], (50409 ^ _774244) ^ [_1784420, _1784422, _1784424] : [50411 ^ _774244 : [(50414 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1784420), tc_List_Olist(_1784420), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1784420), tc_fun(tc_List_Olist(_1784420), tc_Nat_Onat), tc_fun(tc_List_Olist(_1784420), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1784420), tc_Nat_Onat), tc_fun(tc_List_Olist(_1784420), tc_HOL_Obool)), tc_List_Olist(_1784420)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1784420))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1784420)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1784420))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1784420)))), 50410 ^ [_1784420, _1784422, _1784424]))], (50412 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1784420), tc_List_Olist(_1784420))), 50410 ^ [_1784420, _1784422, _1784424]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1784420), tc_List_Olist(_1784420))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1784420), tc_List_Olist(_1784420)), _1784422), _1784424)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1784420))), _1784422) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1784420))), _1784424), 50419 ^ _774244 : [(50426 ^ _774244) ^ [] : [_1784422 = _1784424, -(c_List_Oconcat(_1784420, _1784422) = c_List_Oconcat(_1784420, _1784424))], (50420 ^ _774244) ^ [] : [c_List_Oconcat(_1784420, _1784422) = c_List_Oconcat(_1784420, _1784424), -(_1784422 = _1784424)]]], (35468 ^ _774244) ^ [_1425975] : [-(_1425975 = 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), 35465 ^ [_1425975]), 35466 ^ [_1425975])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (19389 ^ _774244) ^ [_1105216] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1105216))), 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), _1105216), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (7060 ^ _774244) ^ [_888749, _888751, _888753, _888755] : [c_Com_Ocom_OSemi(_888749, _888751) = c_Com_Ocom_OWhile(_888753, _888755)], (21275 ^ _774244) ^ [_1138877, _1138879, _1138881, _1138883] : [class_Fields_Olinordered__field(_1138877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138877), c_Groups_Ozero__class_Ozero(_1138877)), _1138879)), 21282 ^ _774244 : [(21289 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138877), _1138881), _1138879)), _1138883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138877), _1138881), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138877), _1138883), _1138879))))], (21283 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138877), _1138881), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138877), _1138883), _1138879))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138877), _1138881), _1138879)), _1138883)))]]], (2334 ^ _774244) ^ [_809421, _809423, _809425, _809427, _809429, _809431] : [-(c_Random_Ominus__shift(_809431, _809427, _809423) = c_Random_Ominus__shift(_809429, _809425, _809421)), _809431 = _809429, _809427 = _809425, _809423 = _809421], (39114 ^ _774244) ^ [_1506812, _1506814] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506812), _1506814)), -(hAPP(c_Finite__Set_Ocard(_1506812), _1506814) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1506812, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1506812), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1506814))], (14868 ^ _774244) ^ [_1023869, _1023871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023869)), -(c_SMT_Oz3div(_1023871, _1023869) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023871), _1023869))], (9746 ^ _774244) ^ [_934792, _934794] : [class_Int_Oring__char__0(_934792), 9749 ^ _774244 : [(9756 ^ _774244) ^ [] : [_934794 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_934792) = hAPP(c_Int_Oring__1__class_Oof__int(_934792), _934794))], (9750 ^ _774244) ^ [] : [c_Groups_Ozero__class_Ozero(_934792) = hAPP(c_Int_Oring__1__class_Oof__int(_934792), _934794), -(_934794 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (47321 ^ _774244) ^ [_1713826, _1713828, _1713830, _1713832, _1713834] : [-(hAPP(hAPP(c_List_Olist__update(_1713826, hAPP(hAPP(c_List_Olist_OCons(_1713826), _1713828), _1713830)), hAPP(c_Nat_OSuc, _1713832)), _1713834) = hAPP(hAPP(c_List_Olist_OCons(_1713826), _1713828), hAPP(hAPP(c_List_Olist__update(_1713826, _1713830), _1713832), _1713834)))], (262 ^ _774244) ^ [_778119, _778121] : [-(class_Fields_Ofield__inverse__zero(_778119)), _778121 = _778119, class_Fields_Ofield__inverse__zero(_778121)], (15008 ^ _774244) ^ [_1026451, _1026453, _1026455] : [class_Rings_Oring__1(_1026451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026453), _1026455)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1026451), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026455), _1026453)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1026451), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1026451), _1026455)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1026451), _1026453)))], (39632 ^ _774244) ^ [_1519513, _1519515, _1519517, _1519519, _1519521] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519513, _1519515), _1519517), hAPP(hAPP(c_COMBS(_1519513, tc_fun(_1519515, tc_HOL_Obool), tc_fun(_1519515, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519515, tc_HOL_Obool), tc_fun(tc_fun(_1519515, tc_HOL_Obool), tc_fun(_1519515, tc_HOL_Obool)), _1519513), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1519515, tc_HOL_Obool))), _1519519)), _1519521)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1519513, _1519515), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519513, _1519515), _1519517), _1519519)), hAPP(hAPP(c_Product__Type_OSigma(_1519513, _1519515), _1519517), _1519521)))], (9886 ^ _774244) ^ [_937235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _937235), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_937235 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 9889 ^ [_937235]))))], (16855 ^ _774244) ^ [_1062156, _1062158] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1062156), _1062158))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1062156))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1062158))))], (51119 ^ _774244) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (30857 ^ _774244) ^ [_1327672, _1327674, _1327676] : [hBOOL(hAPP(hAPP(c_member(_1327672), _1327674), _1327676)), -(hAPP(hAPP(c_Set_Oinsert(_1327672), _1327674), _1327676) = _1327676)], (17527 ^ _774244) ^ [_1074509, _1074511] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1074509), _1074511) = 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), _1074509)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1074511)))))], (15868 ^ _774244) ^ [_1043575, _1043577, _1043579, _1043581, _1043583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043575), _1043577)), 15871 ^ _774244 : [(15878 ^ _774244) ^ [] : [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), _1043577), _1043575)), _1043579)), _1043581) = _1043583, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043577), _1043579)), _1043581) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043575), _1043579)), _1043583))], (15872 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043577), _1043579)), _1043581) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043575), _1043579)), _1043583), -(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), _1043577), _1043575)), _1043579)), _1043581) = _1043583)]]], (49800 ^ _774244) ^ [_1771301, _1771303] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1771301, _1771303)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1771301), _1771303))], (29362 ^ _774244) ^ [_1296794, _1296796, _1296798, _1296800, _1296802] : [-(_1296794 = c_Orderings_Obot__class_Obot(tc_fun(_1296796, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1296798), _1296800), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296796, tc_fun(_1296798, tc_HOL_Obool)), _1296794), _1296802)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296796, tc_fun(_1296798, tc_HOL_Obool)), _1296794), hAPP(hAPP(c_COMBB(tc_fun(_1296798, tc_HOL_Obool), tc_fun(_1296798, tc_HOL_Obool), _1296796), hAPP(c_Set_Oinsert(_1296798), _1296800)), _1296802)))], (47955 ^ _774244) ^ [_1728747, _1728749, _1728751, _1728753, _1728755] : [-(hAPP(hAPP(c_List_Otake(_1728747), _1728749), hAPP(hAPP(c_List_Omap(_1728751, _1728747), _1728753), _1728755)) = hAPP(hAPP(c_List_Omap(_1728751, _1728747), _1728753), hAPP(hAPP(c_List_Otake(_1728751), _1728749), _1728755)))], (23333 ^ _774244) ^ [_1177929, _1177931, _1177933, _1177935, _1177937] : [-(hAPP(c_Product__Type_Ofst(_1177929, _1177931), hAPP(c_Product__Type_Oapsnd(_1177933, _1177931, _1177929, _1177935), _1177937)) = hAPP(c_Product__Type_Ofst(_1177929, _1177933), _1177937))], (3982 ^ _774244) ^ [_835617, _835619, _835621, _835623, _835625, _835627] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_835627, _835623, _835619) = c_Smallcheck_Ofull__small__class_Ofull__small(_835625, _835621, _835617)), _835627 = _835625, _835623 = _835621, _835619 = _835617], (48510 ^ _774244) ^ [_1743783, _1743785, _1743787, _1743789, _1743791] : [-(hAPP(hAPP(c_List_Ozip(_1743783, _1743785), hAPP(hAPP(c_List_Oappend(_1743783), _1743787), _1743789)), _1743791) = hAPP(hAPP(c_List_Oappend(tc_prod(_1743783, _1743785)), hAPP(hAPP(c_List_Ozip(_1743783, _1743785), _1743787), hAPP(hAPP(c_List_Otake(_1743785), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743783)), _1743787)), _1743791))), hAPP(hAPP(c_List_Ozip(_1743783, _1743785), _1743789), hAPP(hAPP(c_List_Odrop(_1743785), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743783)), _1743787)), _1743791))))], (36393 ^ _774244) ^ [_1446156, _1446158, _1446160, _1446162, _1446164] : [class_Lattices_Olattice(_1446156), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446158, _1446156)), _1446160), _1446162), _1446164) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1446156), hAPP(_1446160, _1446164)), hAPP(_1446162, _1446164)))], (24423 ^ _774244) ^ [_1198971, _1198973] : [_1198971 = _1198973, -(hAPP(c_Code__Numeral_Onat__of, _1198971) = hAPP(c_Code__Numeral_Onat__of, _1198973))], (34397 ^ _774244) ^ [_1400675, _1400677, _1400679, _1400681] : [-(c_Map_Orestrict__map(_1400675, _1400677, _1400679, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1400675, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1400675), _1400681), c_Orderings_Obot__class_Obot(tc_fun(_1400675, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1400675, tc_Option_Ooption(_1400677)), _1400679), _1400681), c_Option_Ooption_ONone(_1400677)))], (29474 ^ _774244) ^ [] : [-(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))))], (46934 ^ _774244) ^ [_1704147, _1704149, _1704151] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1704147), tc_List_Olist(_1704147))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1704147), tc_List_Olist(_1704147)), _1704149), c_List_Olist_ONil(_1704147))), c_List_Olex(_1704147, _1704151)))], (3216 ^ _774244) ^ [_823624, _823626, _823628, _823630, _823632, _823634] : [-(c_SetInterval_Oord_OlessThan(_823634, _823630, _823626) = c_SetInterval_Oord_OlessThan(_823632, _823628, _823624)), _823634 = _823632, _823630 = _823628, _823626 = _823624], (14235 ^ _774244) ^ [_1012735, _1012737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1012735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1012737, _1012735)), _1012735)))], (17839 ^ _774244) ^ [_1079706, _1079708, _1079710] : [class_Int_Onumber__ring(_1079706), 17842 ^ _774244 : [(17849 ^ _774244) ^ [] : [c_Int_Oiszero(_1079706, hAPP(c_Int_Onumber__class_Onumber__of(_1079706), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1079708), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1079710)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1079706), _1079708) = hAPP(c_Int_Onumber__class_Onumber__of(_1079706), _1079710))], (17843 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1079706), _1079708) = hAPP(c_Int_Onumber__class_Onumber__of(_1079706), _1079710), -(c_Int_Oiszero(_1079706, hAPP(c_Int_Onumber__class_Onumber__of(_1079706), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1079708), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1079710)))))]]], (35201 ^ _774244) ^ [_1419182, _1419184, _1419186, _1419188, _1419190, _1419192, _1419194, _1419196, _1419198] : [hAPP(c_Fun_Ocomp(_1419182, _1419184, _1419186, _1419188), _1419190) = hAPP(c_Fun_Ocomp(_1419192, _1419184, _1419186, _1419194), _1419196), -(hAPP(_1419188, hAPP(_1419190, _1419198)) = hAPP(_1419194, hAPP(_1419196, _1419198)))], (11122 ^ _774244) ^ [_957174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _957174)), _957174))], (18107 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (18199 ^ _774244) ^ [_1084988] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1084988) = c_Int_Opred(_1084988))], (11279 ^ _774244) ^ [_959883, _959885] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959883), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959885), _959883))))], (6287 ^ _774244) ^ [_875176, _875178, _875180] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OBODY(_875176))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_875178, _875176, _875180))))], (32408 ^ _774244) ^ [_1361552, _1361554, _1361556] : [hAPP(c_Finite__Set_Ocard(_1361552), _1361554) = hAPP(c_Nat_OSuc, _1361556), 32413 ^ _774244 : [(32416 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1361552), 32411 ^ [_1361552, _1361554, _1361556]), 32412 ^ [_1361552, _1361554, _1361556]))], (32418 ^ _774244) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1361552), 32412 ^ [_1361552, _1361554, _1361556]) = _1361556)], (32420 ^ _774244) ^ [] : [_1361556 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(32412 ^ [_1361552, _1361554, _1361556] = c_Orderings_Obot__class_Obot(tc_fun(_1361552, tc_HOL_Obool)))], (32414 ^ _774244) ^ [] : [-(_1361554 = hAPP(hAPP(c_Set_Oinsert(_1361552), 32411 ^ [_1361552, _1361554, _1361556]), 32412 ^ [_1361552, _1361554, _1361556]))]]], (40667 ^ _774244) ^ [_1543221, _1543223, _1543225, _1543227] : [hBOOL(hAPP(hAPP(c_member(_1543221), _1543223), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1543221, tc_HOL_Obool)), _1543225), hAPP(c_Set_OCollect(_1543221), _1543227)))), 40670 ^ _774244 : [(40673 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1543227, _1543223)))], (40671 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543221), _1543223), _1543225)))]]], (2468 ^ _774244) ^ [_811532, _811534, _811536, _811538] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_811538, _811534) = c_Code__Numeral_Odiv__mod__code__numeral(_811536, _811532)), _811538 = _811536, _811534 = _811532], (7447 ^ _774244) ^ [_895054, _895056, _895058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _895054), _895056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _895056), _895058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _895054)), _895058)))], (12045 ^ _774244) ^ [_973552, _973554, _973556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973554), _973556)), -(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, _973552)), _973554)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973552)), _973556))))], (43141 ^ _774244) ^ [_1608626, _1608628] : [-(c_Transitive__Closure_Ortrancl(_1608626, c_Transitive__Closure_Otrancl(_1608626, _1608628)) = c_Transitive__Closure_Ortrancl(_1608626, _1608628))], (520 ^ _774244) ^ [_782280, _782282, _782284, _782286, _782288, _782290, _782292, _782294, _782296, _782298, _782300, _782302, _782304, _782306] : [-(c_Predicate_Opred__comp(_782304, _782300, _782296, _782292, _782288, _782284, _782280)), c_Predicate_Opred__comp(_782306, _782302, _782298, _782294, _782290, _782286, _782282), _782306 = _782304, _782302 = _782300, _782298 = _782296, _782294 = _782292, _782290 = _782288, _782286 = _782284, _782282 = _782280], (40850 ^ _774244) ^ [_1549041, _1549043, _1549045, _1549047, _1549049, _1549051] : [hBOOL(hAPP(hAPP(c_member(_1549041), _1549043), _1549045)), -(hAPP(c_Fun_Ooverride__on(_1549041, _1549047, _1549049, _1549051, _1549045), _1549043) = hAPP(_1549051, _1549043))], (19039 ^ _774244) ^ [_1099098, _1099100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099098), _1099100)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1099098)), c_Int_OBit1(_1099100))))], (34075 ^ _774244) ^ [_1393898, _1393900, _1393902] : [class_Groups_Ocomm__monoid__mult(_1393898), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1393900, _1393898), _1393902), c_Orderings_Obot__class_Obot(tc_fun(_1393900, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1393898))], (8772 ^ _774244) ^ [_917450, _917452, _917454] : [class_Rings_Ocomm__semiring__1(_917450), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917450), _917452), _917454) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917450), _917454), _917452))], (29160 ^ _774244) ^ [_1293242, _1293244, _1293246] : [class_Orderings_Oorder(_1293242), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293242), _1293244), _1293246)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1293242, _1293246, _1293244) = c_Orderings_Obot__class_Obot(tc_fun(_1293242, tc_HOL_Obool)))], (5985 ^ _774244) ^ [_870076, _870078, _870080] : [hBOOL(hAPP(c_Com_OWT, _870076)), hBOOL(hAPP(c_Com_OWT, _870078)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_870080, _870076, _870078))))], (28234 ^ _774244) ^ [_1273317, _1273319] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1273317)), _1273319) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1273317, _1273319))], (50025 ^ _774244) ^ [_1775295, _1775297] : [class_Orderings_Olinorder(_1775295), hBOOL(hAPP(c_Finite__Set_Ofinite(_1775295), _1775297)), 50032 ^ _774244 : [(50037 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1775295), c_List_Olinorder__class_Osorted__list__of__set(_1775295, _1775297))))], (50035 ^ _774244) ^ [] : [-(c_List_Olinorder__class_Osorted(_1775295, c_List_Olinorder__class_Osorted__list__of__set(_1775295, _1775297)))], (50033 ^ _774244) ^ [] : [-(hAPP(c_List_Oset(_1775295), c_List_Olinorder__class_Osorted__list__of__set(_1775295, _1775297)) = _1775297)]]], (18459 ^ _774244) ^ [_1089311, _1089313] : [_1089311 = _1089313, -(c_Int_OBit1(_1089311) = c_Int_OBit1(_1089313))], (10 ^ _774244) ^ [_774367, _774369, _774371] : [-(_774371 = _774367), _774371 = _774369, _774369 = _774367], (31249 ^ _774244) ^ [_1335408, _1335410, _1335412] : [_1335410 = _1335412, -(hBOOL(hAPP(hAPP(c_member(_1335408), _1335410), hAPP(hAPP(c_Set_Oinsert(_1335408), _1335412), c_Orderings_Obot__class_Obot(tc_fun(_1335408, tc_HOL_Obool))))))], (5719 ^ _774244) ^ [_865386, _865388, _865390] : [c_Natural_Oevalc(c_Com_Ocom_OBODY(_865386), _865388, _865390), -(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _865386)), _865388, _865390))], (9020 ^ _774244) ^ [_921864, _921866, _921868] : [class_Groups_Ogroup__add(_921864), -(hAPP(c_Groups_Ouminus__class_Ouminus(_921864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921864), _921866), _921868)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921864), hAPP(c_Groups_Ouminus__class_Ouminus(_921864), _921868)), hAPP(c_Groups_Ouminus__class_Ouminus(_921864), _921866)))], (7120 ^ _774244) ^ [_889880, _889882, _889884, _889886, _889888, _889890] : [-(c_Nitpick_Opair__box_Opair__box__size(_889880, _889882, _889884, _889886, c_Nitpick_Opair__box_OPairBox(_889880, _889882, _889888, _889890)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_889884, _889888)), hAPP(_889886, _889890))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42489 ^ _774244) ^ [_1594665, _1594667, _1594669, _1594671] : [class_Orderings_Olinorder(_1594665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594665), _1594667)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1594665, _1594665, c_Orderings_Oord__class_Omin(_1594665)), _1594669), hAPP(hAPP(c_Set_Oinsert(_1594665), _1594671), _1594667)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1594665), _1594671), hAPP(hAPP(c_Finite__Set_Ofold(_1594665, _1594665, c_Orderings_Oord__class_Omin(_1594665)), _1594669), _1594667)))], (32022 ^ _774244) ^ [_1353574, _1353576, _1353578, _1353580, _1353582, _1353584] : [hBOOL(hAPP(hAPP(_1353574, _1353576), _1353578)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353580, tc_fun(_1353582, tc_HOL_Obool))), _1353574), _1353584), _1353576), _1353578)))], (1414 ^ _774244) ^ [_794643, _794645] : [-(class_Groups_Oordered__comm__monoid__add(_794643)), _794645 = _794643, class_Groups_Oordered__comm__monoid__add(_794645)], (13916 ^ _774244) ^ [_1006653, _1006655, _1006657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006653), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13919 ^ _774244 : [(13920 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1006655, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1006657), _1006653)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006657, _1006653))), 13923 ^ _774244 : [(13924 ^ _774244) ^ [_1006863, _1006865] : [-(hBOOL(hAPP(hAPP(_1006655, _1006865), _1006863))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006653), _1006863)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006863), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1006657 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1006653), _1006865)), _1006863)]]], (13938 ^ _774244) ^ [] : [13941 ^ _774244 : [(13944 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 13940 ^ [_1006653, _1006655, _1006657]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13946 ^ _774244) ^ [] : [-(_1006657 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1006653), 13939 ^ [_1006653, _1006655, _1006657])), 13940 ^ [_1006653, _1006655, _1006657]))], (13948 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1006655, 13939 ^ [_1006653, _1006655, _1006657]), 13940 ^ [_1006653, _1006655, _1006657]))], (13942 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006653), 13940 ^ [_1006653, _1006655, _1006657])))]], -(hBOOL(hAPP(hAPP(_1006655, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1006657), _1006653)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006657, _1006653))))]]], (7058 ^ _774244) ^ [_888696, _888698, _888700, _888702] : [c_Com_Ocom_OWhile(_888696, _888698) = c_Com_Ocom_OSemi(_888700, _888702)], (50935 ^ _774244) ^ [_1796211, _1796213] : [class_Lattices_Obounded__lattice(_1796211), -(class_Lattices_Obounded__lattice__top(tc_fun(_1796213, _1796211)))], (46152 ^ _774244) ^ [_1683225, _1683227, _1683229, _1683231] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683225)), _1683227) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683229)), _1683231), -(hAPP(hAPP(c_List_Omap(tc_prod(_1683225, _1683229), _1683225), c_Product__Type_Ofst(_1683225, _1683229)), hAPP(hAPP(c_List_Ozip(_1683225, _1683229), _1683227), _1683231)) = _1683227)], (45835 ^ _774244) ^ [_1675573, _1675575, _1675577, _1675579, _1675581] : [hBOOL(hAPP(c_List_Odistinct(_1675573), hAPP(hAPP(c_List_Omap(tc_prod(_1675573, _1675575), _1675573), c_Product__Type_Ofst(_1675573, _1675575)), _1675577))), 45838 ^ _774244 : [(45845 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1675573, _1675575)), hAPP(hAPP(c_Product__Type_OPair(_1675573, _1675575), _1675579), _1675581)), hAPP(c_List_Oset(tc_prod(_1675573, _1675575)), _1675577))), -(hAPP(c_Map_Omap__of(_1675573, _1675575, _1675577), _1675579) = hAPP(c_Option_Ooption_OSome(_1675575), _1675581))], (45839 ^ _774244) ^ [] : [hAPP(c_Map_Omap__of(_1675573, _1675575, _1675577), _1675579) = hAPP(c_Option_Ooption_OSome(_1675575), _1675581), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1675573, _1675575)), hAPP(hAPP(c_Product__Type_OPair(_1675573, _1675575), _1675579), _1675581)), hAPP(c_List_Oset(tc_prod(_1675573, _1675575)), _1675577))))]]], (16203 ^ _774244) ^ [_1049651, _1049653] : [class_Groups_Oordered__ab__group__add__abs(_1049651), 16206 ^ _774244 : [(16213 ^ _774244) ^ [] : [_1049653 = c_Groups_Ozero__class_Ozero(_1049651), -(hAPP(c_Groups_Oabs__class_Oabs(_1049651), _1049653) = c_Groups_Ozero__class_Ozero(_1049651))], (16207 ^ _774244) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1049651), _1049653) = c_Groups_Ozero__class_Ozero(_1049651), -(_1049653 = c_Groups_Ozero__class_Ozero(_1049651))]]], (44316 ^ _774244) ^ [_1639731, _1639733, _1639735] : [c_Relation_Ototal__on(_1639731, _1639733, _1639735), 44319 ^ _774244 : [(44320 ^ _774244) ^ [_1639875] : [hBOOL(hAPP(hAPP(c_member(_1639731), _1639875), _1639733)), 44323 ^ _774244 : [(44324 ^ _774244) ^ [_1640015] : [hBOOL(hAPP(hAPP(c_member(_1639731), _1640015), _1639733)), -(_1639875 = _1640015), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639731, _1639731)), hAPP(hAPP(c_Product__Type_OPair(_1639731, _1639731), _1639875), _1640015)), _1639735))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639731, _1639731)), hAPP(hAPP(c_Product__Type_OPair(_1639731, _1639731), _1640015), _1639875)), _1639735)))]]]]], (43521 ^ _774244) ^ [_1618768, _1618770, _1618772, _1618774] : [c_Orderings_Otop__class_Otop(tc_fun(_1618768, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618770, tc_fun(_1618768, tc_HOL_Obool)), _1618772), _1618774), 43524 ^ _774244 : [(43525 ^ _774244) ^ [_1618884] : [hBOOL(hAPP(hAPP(c_member(_1618770), _1618884), _1618772)), -(hAPP(_1618774, _1618884) = c_Orderings_Otop__class_Otop(tc_fun(_1618768, tc_HOL_Obool)))]]], (36493 ^ _774244) ^ [_1448703, _1448705, _1448707, _1448709] : [hBOOL(hAPP(hAPP(c_member(_1448703), _1448705), _1448707)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448703, tc_HOL_Obool)), _1448707), hAPP(hAPP(c_Set_Oinsert(_1448703), _1448705), _1448709)) = hAPP(hAPP(c_Set_Oinsert(_1448703), _1448705), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448703, tc_HOL_Obool)), _1448707), _1448709)))], (18679 ^ _774244) ^ [_1092965] : [class_Int_Onumber__ring(_1092965), -(c_Groups_Oone__class_Oone(_1092965) = hAPP(c_Int_Onumber__class_Onumber__of(_1092965), c_Int_OBit1(c_Int_OPls)))], (38764 ^ _774244) ^ [_1498654, _1498656, _1498658] : [class_Lattices_Olattice(_1498654), hAPP(_1498656, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1498654), 38769 ^ [_1498654, _1498656, _1498658]), 38770 ^ [_1498654, _1498656, _1498658])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1498654), hAPP(_1498656, 38769 ^ [_1498654, _1498656, _1498658])), hAPP(_1498656, 38770 ^ [_1498654, _1498656, _1498658])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1498654), _1498658)), -(_1498658 = c_Orderings_Obot__class_Obot(tc_fun(_1498654, tc_HOL_Obool))), -(hAPP(_1498656, c_Big__Operators_Olattice__class_OInf__fin(_1498654, _1498658)) = c_Big__Operators_Olattice__class_OInf__fin(_1498654, hAPP(c_Set_Oimage(_1498654, _1498654, _1498656), _1498658)))], (43425 ^ _774244) ^ [_1615112, _1615114, _1615116, _1615118] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1615112, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615114, tc_fun(_1615112, tc_HOL_Obool)), _1615116), _1615118)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615114, tc_fun(_1615112, tc_HOL_Obool)), _1615116), hAPP(hAPP(c_COMBB(tc_fun(_1615112, tc_HOL_Obool), tc_fun(_1615112, tc_HOL_Obool), _1615114), c_Groups_Ouminus__class_Ouminus(tc_fun(_1615112, tc_HOL_Obool))), _1615118)))], (33192 ^ _774244) ^ [_1375402, _1375404] : [class_Orderings_Olinorder(_1375402), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375402), _1375404)), -(_1375404 = c_Orderings_Obot__class_Obot(tc_fun(_1375402, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1375402), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1375402), 33205 ^ [_1375402, _1375404]), 33206 ^ [_1375402, _1375404])), hAPP(hAPP(c_Set_Oinsert(_1375402), 33205 ^ [_1375402, _1375404]), hAPP(hAPP(c_Set_Oinsert(_1375402), 33206 ^ [_1375402, _1375404]), c_Orderings_Obot__class_Obot(tc_fun(_1375402, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1375402), c_Big__Operators_Olinorder__class_OMin(_1375402, _1375404)), _1375404)))], (26177 ^ _774244) ^ [_1231461, _1231463, _1231465] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231461), _1231463)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231461), _1231465))), -(_1231461 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231463), _1231465)))], (4928 ^ _774244) ^ [_850394, _850396, _850398, _850400] : [-(c_List_Orotate(_850400, _850396) = c_List_Orotate(_850398, _850394)), _850400 = _850398, _850396 = _850394], (19621 ^ _774244) ^ [_1109429, _1109431, _1109433] : [class_Rings_Ocomm__semiring__1(_1109429), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1109429), _1109431), 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)))), _1109433))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109429), _1109431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109429), hAPP(hAPP(c_Power_Opower__class_Opower(_1109429), _1109431), _1109433)), hAPP(hAPP(c_Power_Opower__class_Opower(_1109429), _1109431), _1109433))))], (7533 ^ _774244) ^ [_896628, _896630, _896632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _896628), _896630)), _896632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _896628), _896632)))], (9578 ^ _774244) ^ [_931951, _931953, _931955, _931957] : [class_Rings_Olinordered__ring__strict(_931951), 9581 ^ _774244 : [(9596 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931951), _931953), _931955)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931951), _931957), _931955)))), 9597 ^ _774244 : [(9604 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931951), _931955), c_Groups_Ozero__class_Ozero(_931951))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931951), _931957), _931953))], (9598 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931951), c_Groups_Ozero__class_Ozero(_931951)), _931955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931951), _931953), _931957))]]], (9582 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931951), _931953), _931955)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931951), _931957), _931955))), 9587 ^ _774244 : [(9590 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931951), _931953), _931957)))], (9588 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931951), c_Groups_Ozero__class_Ozero(_931951)), _931955)))]], 9591 ^ _774244 : [(9594 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931951), _931957), _931953)))], (9592 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931951), _931955), c_Groups_Ozero__class_Ozero(_931951))))]]]]], (19127 ^ _774244) ^ [_1100691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1100691))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1100691)))], (28972 ^ _774244) ^ [_1289760, _1289762] : [_1289762 = c_Orderings_Obot__class_Obot(tc_fun(_1289760, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1289760, tc_HOL_Obool)), _1289762), c_Orderings_Obot__class_Obot(tc_fun(_1289760, tc_HOL_Obool)))))], (24495 ^ _774244) ^ [_1200428, _1200430] : [-(c_Code__Numeral_Onat__of__aux(_1200428, _1200430) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1200428)), _1200430))], (28194 ^ _774244) ^ [_1272528, _1272530, _1272532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272528, tc_HOL_Obool)), _1272530), _1272532)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272528, tc_HOL_Obool)), _1272530), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272528, tc_HOL_Obool)), _1272532), _1272530)) = _1272532)], (27942 ^ _774244) ^ [_1267684, _1267686, _1267688, _1267690] : [class_Lattices_Osemilattice__sup(_1267684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267684), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267684), _1267686), _1267688)), _1267690)), 27949 ^ _774244 : [(27952 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267684), _1267688), _1267690)))], (27950 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267684), _1267686), _1267690)))]]], (1314 ^ _774244) ^ [_793393, _793395] : [-(class_Orderings_Obot(_793393)), _793395 = _793393, class_Orderings_Obot(_793395)], (7211 ^ _774244) ^ [_891140, _891142, _891144] : [7212 ^ _774244 : [(7215 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_891144, _891142), _891140))], (7213 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891140), _891142)))]], 7218 ^ _774244 : [(7221 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_891144, _891142), _891140))], (7219 ^ _774244) ^ [] : [-(_891140 = _891142)]], 7224 ^ _774244 : [(7227 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_891144, _891142), _891140))], (7225 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891142), _891140)))]], -(hBOOL(hAPP(hAPP(_891144, _891142), _891140)))], (4756 ^ _774244) ^ [_847730, _847732, _847734, _847736, _847738, _847740] : [-(c_List_Osublist(_847740, _847736, _847732) = c_List_Osublist(_847738, _847734, _847730)), _847740 = _847738, _847736 = _847734, _847732 = _847730], (44461 ^ _774244) ^ [_1643118, _1643120, _1643122] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1643118, tc_HOL_Obool)), _1643120), _1643122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1643118, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1643118, tc_HOL_Obool), _1643122)), _1643120)))], (39856 ^ _774244) ^ [_1526002, _1526004, _1526006, _1526008, _1526010, _1526012] : [class_Groups_Ocomm__monoid__add(_1526002), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526004), _1526006)), 39866 ^ _774244 : [(39869 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526008), hAPP(_1526010, 39865 ^ [_1526002, _1526004, _1526006, _1526008, _1526010, _1526012])))], (39867 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526004), 39865 ^ [_1526002, _1526004, _1526006, _1526008, _1526010, _1526012]), _1526006)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526004, _1526002), hAPP(hAPP(c_COMBS(_1526004, tc_fun(_1526008, tc_HOL_Obool), _1526002), hAPP(hAPP(c_COMBB(tc_fun(_1526008, _1526002), tc_fun(tc_fun(_1526008, tc_HOL_Obool), _1526002), _1526004), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526008, _1526002)), _1526012)), _1526010)), _1526006) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1526004, _1526008), _1526002), hAPP(c_Product__Type_Oprod_Oprod__case(_1526004, _1526008, _1526002), _1526012)), hAPP(hAPP(c_Product__Type_OSigma(_1526004, _1526008), _1526006), _1526010)))], (38353 ^ _774244) ^ [_1489476, _1489478, _1489480, _1489482, _1489484] : [c_Fun_Oinj__on(_1489476, _1489478, _1489480, c_Orderings_Otop__class_Otop(tc_fun(_1489476, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1489476, _1489478, _1489480), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1489476, tc_HOL_Obool)), _1489482), _1489484)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1489478, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1489476, _1489478, _1489480), _1489482)), hAPP(c_Set_Oimage(_1489476, _1489478, _1489480), _1489484)))], (23175 ^ _774244) ^ [_1174900, _1174902] : [-(c_Divides_Odivmod__nat(_1174902, _1174900) = 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), _1174902), _1174900), _1174900))), -(_1174900 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174902), _1174900)))], (15300 ^ _774244) ^ [_1031704, _1031706, _1031708] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1031704), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1031706), _1031708)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1031704), _1031706)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1031704), _1031708)))], (51039 ^ _774244) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (21940 ^ _774244) ^ [_1151346, _1151348] : [-(_1151346 = _1151348), -(c_Random_Oinc__shift(_1151346, _1151348) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1151348), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (14157 ^ _774244) ^ [_1011480, _1011482] : [class_Divides_Osemiring__div(_1011480), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1011480), _1011482), c_Groups_Ozero__class_Ozero(_1011480)) = c_Groups_Ozero__class_Ozero(_1011480))], (39622 ^ _774244) ^ [_1519084, _1519086, _1519088] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1519084, _1519086), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519084, _1519086), c_Orderings_Otop__class_Otop(tc_fun(_1519084, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1519086, tc_HOL_Obool), _1519084), _1519088))) = hAPP(hAPP(c_Product__Type_OSigma(_1519084, _1519086), c_Orderings_Otop__class_Otop(tc_fun(_1519084, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1519086, tc_HOL_Obool), _1519084), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1519086, tc_HOL_Obool)), _1519088))))], (42196 ^ _774244) ^ [_1588114, _1588116, _1588118] : [-(c_Hilbert__Choice_OEps(tc_prod(_1588114, _1588116), _1588118) = c_Hilbert__Choice_OEps(tc_prod(_1588114, _1588116), hAPP(c_Product__Type_Oprod_Oprod__case(_1588114, _1588116, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1588116, tc_prod(_1588114, _1588116)), tc_fun(_1588116, tc_HOL_Obool), _1588114), hAPP(c_COMBB(tc_prod(_1588114, _1588116), tc_HOL_Obool, _1588116), _1588118)), c_Product__Type_OPair(_1588114, _1588116)))))], (27571 ^ _774244) ^ [_1260288] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1260288) = 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)), _1260288)))], (36437 ^ _774244) ^ [_1447200, _1447202, _1447204, _1447206, _1447208] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447200, tc_HOL_Obool)), _1447202), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447204, tc_fun(_1447200, tc_HOL_Obool)), _1447206), _1447208)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447204, tc_fun(_1447200, tc_HOL_Obool)), _1447206), hAPP(hAPP(c_COMBB(tc_fun(_1447200, tc_HOL_Obool), tc_fun(_1447200, tc_HOL_Obool), _1447204), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447200, tc_HOL_Obool)), _1447202)), _1447208)))], (51425 ^ _774244) ^ [_1801160, _1801162, _1801164, _1801166] : [-(hAPP(hAPP(c_COMBK(_1801160, _1801162), _1801164), _1801166) = _1801164)], (34753 ^ _774244) ^ [_1409331, _1409333, _1409335, _1409337] : [_1409331 = _1409333, hBOOL(hAPP(hAPP(c_member(_1409335), _1409331), _1409337)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1409335, _1409335)), hAPP(hAPP(c_Product__Type_OPair(_1409335, _1409335), _1409331), _1409333)), c_Relation_OId__on(_1409335, _1409337))))], (35316 ^ _774244) ^ [_1422284, _1422286, _1422288, _1422290, _1422292, _1422294, _1422296] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1422284, _1422286, _1422288), hAPP(c_Fun_Ocomp(_1422290, tc_fun(_1422286, _1422288), _1422284, _1422292), _1422294)), _1422296) = hAPP(hAPP(_1422292, hAPP(_1422294, hAPP(c_Product__Type_Ofst(_1422284, _1422286), _1422296))), hAPP(c_Product__Type_Osnd(_1422284, _1422286), _1422296)))], (48496 ^ _774244) ^ [_1743356, _1743358, _1743360, _1743362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1743356), _1743358)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743360)), _1743362))), -(hAPP(hAPP(c_List_Otake(_1743360), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1743356), _1743358)), _1743362) = hAPP(hAPP(c_List_Oappend(_1743360), hAPP(hAPP(c_List_Otake(_1743360), _1743356), _1743362)), hAPP(hAPP(c_List_Otake(_1743360), _1743358), hAPP(hAPP(c_List_Odrop(_1743360), _1743356), _1743362))))], (34964 ^ _774244) ^ [_1413956, _1413958, _1413960] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1413956, tc_HOL_Obool)), _1413958), hAPP(c_Set_OPow(_1413956), _1413960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413956, tc_HOL_Obool)), _1413958), _1413960)))], (25703 ^ _774244) ^ [_1222793, _1222795, _1222797, _1222799] : [class_Divides_Osemiring__div(_1222793), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222793), _1222795), _1222797)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1222793), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1222793), _1222797), _1222795)), _1222799) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1222793), hAPP(hAPP(c_Power_Opower__class_Opower(_1222793), _1222797), _1222799)), hAPP(hAPP(c_Power_Opower__class_Opower(_1222793), _1222795), _1222799)))], (43421 ^ _774244) ^ [_1614950, _1614952, _1614954, _1614956] : [-(hAPP(c_Set_OCollect(_1614950), hAPP(hAPP(c_COMBB(tc_fun(_1614952, tc_HOL_Obool), tc_HOL_Obool, _1614950), c_HOL_OAll(_1614952)), hAPP(hAPP(c_COMBB(tc_fun(_1614952, tc_HOL_Obool), tc_fun(_1614952, tc_HOL_Obool), _1614950), hAPP(c_COMBS(_1614952, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1614952), c_fimplies), hAPP(hAPP(c_COMBC(_1614952, tc_fun(_1614952, tc_HOL_Obool), tc_HOL_Obool), c_member(_1614952)), _1614954)))), _1614956))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614952, tc_fun(_1614950, tc_HOL_Obool)), _1614954), hAPP(hAPP(c_COMBB(tc_fun(_1614950, tc_HOL_Obool), tc_fun(_1614950, tc_HOL_Obool), _1614952), c_Set_OCollect(_1614950)), hAPP(c_COMBC(_1614950, _1614952, tc_HOL_Obool), _1614956))))], (28795 ^ _774244) ^ [_1285619, _1285621, _1285623, _1285625] : [hAPP(c_Set_Oimage(_1285619, _1285621, _1285623), c_Orderings_Otop__class_Otop(tc_fun(_1285619, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1285621, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1285621, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1285621, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1285619, _1285621, _1285623), _1285625))), hAPP(c_Set_Oimage(_1285619, _1285621, _1285623), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1285619, tc_HOL_Obool)), _1285625)))))], (37913 ^ _774244) ^ [_1481069, _1481071, _1481073, _1481075, _1481077] : [c_Fun_Oinj__on(_1481069, _1481071, _1481073, c_Orderings_Otop__class_Otop(tc_fun(_1481069, tc_HOL_Obool))), 37916 ^ _774244 : [(37923 ^ _774244) ^ [] : [_1481075 = _1481077, -(hAPP(_1481073, _1481075) = hAPP(_1481073, _1481077))], (37917 ^ _774244) ^ [] : [hAPP(_1481073, _1481075) = hAPP(_1481073, _1481077), -(_1481075 = _1481077)]]], (15648 ^ _774244) ^ [_1038534, _1038536] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1038534), _1038536) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1038534), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1038536)))], (33968 ^ _774244) ^ [_1391738, _1391740, _1391742, _1391744, _1391746] : [hBOOL(hAPP(hAPP(c_member(_1391738), _1391740), _1391742)), -(hAPP(c_Map_Orestrict__map(_1391738, _1391744, _1391746, _1391742), _1391740) = hAPP(_1391746, _1391740))], (51121 ^ _774244) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (1454 ^ _774244) ^ [_795143, _795145] : [-(class_Groups_Ocancel__semigroup__add(_795143)), _795145 = _795143, class_Groups_Ocancel__semigroup__add(_795145)], (45456 ^ _774244) ^ [] : [-(c_Com_Obody = c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom, c_Com_Obodies))], (37133 ^ _774244) ^ [_1463063, _1463065, _1463067] : [class_Orderings_Olinorder(_1463063), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463063), _1463065)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463063), _1463067)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463063, tc_HOL_Obool)), _1463065), _1463067) = c_Orderings_Obot__class_Obot(tc_fun(_1463063, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1463063), c_Big__Operators_Olinorder__class_OMin(_1463063, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463063, tc_HOL_Obool)), _1463065), _1463067))), c_Big__Operators_Olinorder__class_OMin(_1463063, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463063, tc_HOL_Obool)), _1463065), _1463067))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1463063), c_Big__Operators_Olinorder__class_OMin(_1463063, _1463065)), c_Big__Operators_Olinorder__class_OMin(_1463063, _1463067)))], (27806 ^ _774244) ^ [_1265068, _1265070, _1265072, _1265074] : [class_Lattices_Osemilattice__sup(_1265068), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265068), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265068), _1265070), _1265072)), _1265074) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265068), _1265070), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265068), _1265072), _1265074)))], (38025 ^ _774244) ^ [_1483264, _1483266] : [-(c_Fun_Oinj__on(_1483264, _1483264, c_COMBI(_1483264), _1483266))], (18125 ^ _774244) ^ [_1083901] : [-(c_Int_Osucc(c_Int_Opred(_1083901)) = _1083901)], (32668 ^ _774244) ^ [_1366360, _1366362, _1366364] : [class_Orderings_Olinorder(_1366360), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366360), _1366362)), hBOOL(hAPP(hAPP(c_member(_1366360), _1366364), _1366362)), 32679 ^ _774244 : [(32686 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366360, tc_HOL_Obool)), _1366362), hAPP(hAPP(c_Set_Oinsert(_1366360), _1366364), c_Orderings_Obot__class_Obot(tc_fun(_1366360, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1366360, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1366360, _1366362) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366360), _1366364), c_Big__Operators_Olinorder__class_OMax(_1366360, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366360, tc_HOL_Obool)), _1366362), hAPP(hAPP(c_Set_Oinsert(_1366360), _1366364), c_Orderings_Obot__class_Obot(tc_fun(_1366360, tc_HOL_Obool)))))))], (32680 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366360, tc_HOL_Obool)), _1366362), hAPP(hAPP(c_Set_Oinsert(_1366360), _1366364), c_Orderings_Obot__class_Obot(tc_fun(_1366360, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1366360, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1366360, _1366362) = _1366364)]]], (11299 ^ _774244) ^ [_960215, _960217, _960219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _960215), _960217)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _960219), _960215)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _960219), _960217))))], (5388 ^ _774244) ^ [_857496, _857498] : [_857498 = _857496, -(c_Nat_Osize__class_Osize(_857498) = c_Nat_Osize__class_Osize(_857496))], (36363 ^ _774244) ^ [_1445647, _1445649, _1445651] : [class_Lattices_Osemilattice__inf(_1445647), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445647), _1445649), _1445651) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445647), _1445651), _1445649))], (16935 ^ _774244) ^ [_1063737, _1063739, _1063741, _1063743] : [class_Rings_Olinordered__semidom(_1063737), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1063739), _1063741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063737), c_Groups_Ozero__class_Ozero(_1063737)), _1063743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063737), _1063743), c_Groups_Oone__class_Oone(_1063737))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063737), hAPP(hAPP(c_Power_Opower__class_Opower(_1063737), _1063743), _1063741)), hAPP(hAPP(c_Power_Opower__class_Opower(_1063737), _1063743), _1063739))))], (16119 ^ _774244) ^ [_1048355, _1048357] : [_1048355 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1048357, _1048355) = _1048357)], (36727 ^ _774244) ^ [_1454155, _1454157, _1454159] : [class_Orderings_Oorder(_1454155), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454155, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1454155, _1454157, _1454159)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1454155), _1454159)) = c_Orderings_Obot__class_Obot(tc_fun(_1454155, tc_HOL_Obool)))], (39271 ^ _774244) ^ [_1510158, _1510160, _1510162] : [_1510162 = hAPP(c_COMBK(tc_Option_Ooption(_1510160), _1510158), c_Option_Ooption_ONone(_1510160)), -(c_Map_Odom(_1510158, _1510160, _1510162) = c_Orderings_Obot__class_Obot(tc_fun(_1510158, tc_HOL_Obool)))], (18119 ^ _774244) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (8770 ^ _774244) ^ [_917421] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _917421), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _917421)], (43680 ^ _774244) ^ [_1623013, _1623015, _1623017, _1623019, _1623021] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623013, tc_fun(_1623015, tc_HOL_Obool)), _1623017), hAPP(hAPP(c_COMBC(_1623013, tc_fun(_1623015, tc_HOL_Obool), tc_fun(_1623015, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1623015, tc_HOL_Obool), tc_fun(tc_fun(_1623015, tc_HOL_Obool), tc_fun(_1623015, tc_HOL_Obool)), _1623013), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623015, tc_HOL_Obool))), _1623019)), _1623021)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623015, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623013, tc_fun(_1623015, tc_HOL_Obool)), _1623017), _1623019)), _1623021))], (3308 ^ _774244) ^ [_825048, _825050] : [_825050 = _825048, -(c_Power_Opower__class_Opower(_825050) = c_Power_Opower__class_Opower(_825048))], (2578 ^ _774244) ^ [_813289, _813291] : [_813291 = _813289, -(c_Int_Opred(_813291) = c_Int_Opred(_813289))], (13868 ^ _774244) ^ [_1005799, _1005801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005799)), -(c_SMT_Oz3mod(_1005801, _1005799) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005801, _1005799))], (2956 ^ _774244) ^ [_819412, _819414, _819416, _819418, _819420, _819422, _819424, _819426] : [-(c_New__DSequence_Oneg__bind(_819426, _819422, _819418, _819414) = c_New__DSequence_Oneg__bind(_819424, _819420, _819416, _819412)), _819426 = _819424, _819422 = _819420, _819418 = _819416, _819414 = _819412], (46056 ^ _774244) ^ [_1681165, _1681167, _1681169, _1681171] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1681165, _1681167))), hAPP(hAPP(c_List_Ozip(_1681165, _1681167), _1681169), _1681171)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681165)), _1681169)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681167)), _1681171)))], (33806 ^ _774244) ^ [_1388191, _1388193, _1388195, _1388197, _1388199, _1388201] : [-(hBOOL(hAPP(hAPP(c_member(_1388191), _1388193), _1388195))), -(hAPP(c_Set_Oimage(_1388191, _1388197, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388191, _1388197), _1388199), _1388193), _1388201)), _1388195) = hAPP(c_Set_Oimage(_1388191, _1388197, _1388199), _1388195))], (36817 ^ _774244) ^ [_1456132, _1456134, _1456136, _1456138, _1456140] : [class_Groups_Ocomm__monoid__mult(_1456132), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456134), _1456136)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456134), _1456138)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1456132), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456134, _1456132), _1456140), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1456134, tc_HOL_Obool)), _1456136), _1456138))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456134, _1456132), _1456140), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456134, tc_HOL_Obool)), _1456136), _1456138))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1456132), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456134, _1456132), _1456140), _1456136)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456134, _1456132), _1456140), _1456138)))], (16028 ^ _774244) ^ [_1046636, _1046638] : [_1046636 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046636), _1046638) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33898 ^ _774244) ^ [_1390022, _1390024, _1390026, _1390028, _1390030, _1390032, _1390034] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1390022, tc_Option_Ooption(_1390024)), _1390026), _1390028), hAPP(c_Option_Ooption_OSome(_1390024), _1390030)), _1390032) = hAPP(c_Option_Ooption_OSome(_1390024), _1390034), 33903 ^ _774244 : [(33906 ^ _774244) ^ [] : [-(_1390030 = _1390034)], (33904 ^ _774244) ^ [] : [-(_1390032 = _1390028)]], 33907 ^ _774244 : [(33910 ^ _774244) ^ [] : [-(hAPP(_1390026, _1390032) = hAPP(c_Option_Ooption_OSome(_1390024), _1390034))], (33908 ^ _774244) ^ [] : [_1390032 = _1390028]]], (49454 ^ _774244) ^ [_1764464, _1764466, _1764468, _1764470, _1764472] : [-(c_List_Omap__filter(_1764464, _1764466, _1764468, hAPP(hAPP(c_List_Olist_OCons(_1764464), _1764470), _1764472)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1764466), _1764466, c_List_Omap__filter(_1764464, _1764466, _1764468, _1764472), hAPP(hAPP(c_COMBC(_1764466, tc_List_Olist(_1764466), tc_List_Olist(_1764466)), c_List_Olist_OCons(_1764466)), c_List_Omap__filter(_1764464, _1764466, _1764468, _1764472))), hAPP(_1764468, _1764470)))], (22901 ^ _774244) ^ [_1169885, _1169887, _1169889, _1169891, _1169893, _1169895] : [_1169885 = _1169887, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1169889, _1169891, _1169893), _1169895), _1169885) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1169889, _1169891, _1169893), _1169895), _1169887))], (46904 ^ _774244) ^ [_1703565, _1703567, _1703569] : [hAPP(hAPP(c_List_Olist_OCons(_1703565), _1703567), _1703569) = c_List_Olist_ONil(_1703565)], (29750 ^ _774244) ^ [_1304120, _1304122] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1304120, _1304122))))], (35048 ^ _774244) ^ [_1415849, _1415851, _1415853, _1415855] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1415849), _1415851)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1415849, tc_HOL_Obool)), _1415851), _1415853)), hBOOL(hAPP(_1415855, c_Orderings_Obot__class_Obot(tc_fun(_1415849, tc_HOL_Obool)))), 35063 ^ _774244 : [(35064 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1415849), 35062 ^ [_1415849, _1415851, _1415853, _1415855])))], (35068 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1415849), 35061 ^ [_1415849, _1415851, _1415853, _1415855]), 35062 ^ [_1415849, _1415851, _1415853, _1415855]))], (35072 ^ _774244) ^ [] : [hBOOL(hAPP(_1415855, hAPP(hAPP(c_Set_Oinsert(_1415849), 35061 ^ [_1415849, _1415851, _1415853, _1415855]), 35062 ^ [_1415849, _1415851, _1415853, _1415855])))], (35070 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1415855, 35062 ^ [_1415849, _1415851, _1415853, _1415855])))], (35066 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415849), 35061 ^ [_1415849, _1415851, _1415853, _1415855]), _1415853)))]], -(hBOOL(hAPP(_1415855, _1415851)))], (36445 ^ _774244) ^ [_1447579, _1447581, _1447583, _1447585] : [class_Lattices_Olattice(_1447579), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1447579), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1447579), _1447581), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1447579), _1447583), _1447585))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1447579), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1447579), _1447581), _1447583)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1447579), _1447581), _1447585)))))], (36253 ^ _774244) ^ [_1443175, _1443177, _1443179, _1443181] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443175, tc_HOL_Obool)), _1443177), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443175, tc_HOL_Obool)), _1443179), _1443181)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443175, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443175, tc_HOL_Obool)), _1443177), _1443179)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443175, tc_HOL_Obool)), _1443177), _1443181)))], (49986 ^ _774244) ^ [_1774527, _1774529] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1774527, _1774529) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1774527), hAPP(c_Nat_OSuc, _1774529))))], (21207 ^ _774244) ^ [_1137577, _1137579, _1137581, _1137583] : [class_Fields_Olinordered__field(_1137577), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137577), _1137579), c_Groups_Ozero__class_Ozero(_1137577))), 21214 ^ _774244 : [(21221 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137577), _1137583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137577), _1137581), _1137579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137577), _1137581), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137577), _1137583), _1137579))))], (21215 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137577), _1137581), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137577), _1137583), _1137579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137577), _1137583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137577), _1137581), _1137579))))]]], (22458 ^ _774244) ^ [_1161226] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1161226) = 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)))], (48025 ^ _774244) ^ [_1730469, _1730471, _1730473, _1730475] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730469) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1730471), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730469)), hAPP(hAPP(c_List_Olist_OCons(_1730471), _1730473), _1730475)) = hAPP(hAPP(c_List_Olist_OCons(_1730471), _1730473), hAPP(hAPP(c_List_Otake(_1730471), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730469)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1730475)))], (42140 ^ _774244) ^ [_1587086, _1587088, _1587090] : [-(c_Hilbert__Choice_OEps(tc_prod(_1587086, _1587088), hAPP(c_Product__Type_Oprod_Oprod__case(_1587086, _1587088, tc_HOL_Obool), _1587090)) = c_Hilbert__Choice_OEps(tc_prod(_1587086, _1587088), hAPP(hAPP(c_COMBS(tc_prod(_1587086, _1587088), _1587088, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1587086, tc_fun(_1587088, tc_HOL_Obool), tc_prod(_1587086, _1587088)), _1587090), c_Product__Type_Ofst(_1587086, _1587088))), c_Product__Type_Osnd(_1587086, _1587088))))], (24435 ^ _774244) ^ [_1199162, _1199164] : [_1199162 = _1199164, -(hAPP(c_Code__Numeral_Onat__of, _1199162) = hAPP(c_Code__Numeral_Onat__of, _1199164))], (5594 ^ _774244) ^ [_860575, _860577, _860579, _860581] : [-(hAPP(_860581, _860577) = hAPP(_860579, _860575)), _860581 = _860579, _860577 = _860575], (1846 ^ _774244) ^ [_800981, _800983, _800985, _800987, _800989, _800991] : [-(c_Option_Ooption_Ooption__size(_800991, _800987, _800983) = c_Option_Ooption_Ooption__size(_800989, _800985, _800981)), _800991 = _800989, _800987 = _800985, _800983 = _800981], (32562 ^ _774244) ^ [_1364451, _1364453] : [class_Rings_Oring__1(_1364451), -(hBOOL(hAPP(hAPP(c_member(_1364451), hAPP(c_Int_Oring__1__class_Oof__int(_1364451), _1364453)), c_Int_Oring__1__class_OInts(_1364451))))], (22390 ^ _774244) ^ [_1160128] : [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), _1160128))), 22393 ^ _774244 : [(22400 ^ _774244) ^ [] : [-(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), _1160128)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160128)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160128)), 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), _1160128)))))], (22394 ^ _774244) ^ [] : [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), _1160128))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160128)) = 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)))]]], (7575 ^ _774244) ^ [_897665, _897667] : [class_Rings_Olinordered__idom(_897665), 7578 ^ _774244 : [(7585 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897665), _897667), c_Groups_Ozero__class_Ozero(_897665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897665), _897667), _897667)), c_Groups_Ozero__class_Ozero(_897665))))], (7579 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_897665), _897667), _897667)), c_Groups_Ozero__class_Ozero(_897665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_897665), _897667), c_Groups_Ozero__class_Ozero(_897665))))]]], (2518 ^ _774244) ^ [_812277, _812279, _812281, _812283] : [-(c_Divides_OnegDivAlg(_812283, _812279) = c_Divides_OnegDivAlg(_812281, _812277)), _812283 = _812281, _812279 = _812277], (22212 ^ _774244) ^ [_1156382, _1156384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1156382)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156384))), -(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(_1156384))), 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), _1156382)), c_Int_Onat))))))], (33416 ^ _774244) ^ [_1380616, _1380618, _1380620, _1380622] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1380616), _1380618)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380620), _1380622)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1380616, _1380620)), c_Sum__Type_OPlus(_1380616, _1380620, _1380618, _1380622)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1380616), _1380618)), hAPP(c_Finite__Set_Ocard(_1380620), _1380622)))], (42455 ^ _774244) ^ [_1593915, _1593917, _1593919, _1593921] : [-(hAPP(c_Finite__Set_Ofold__image(_1593915, _1593917, _1593919), _1593921) = c_Finite__Set_Ofold(_1593917, _1593915, hAPP(hAPP(c_COMBB(_1593915, tc_fun(_1593915, _1593915), _1593917), _1593919), _1593921)))], (34156 ^ _774244) ^ [_1395345, _1395347, _1395349, _1395351, _1395353] : [class_Fields_Ofield__inverse__zero(_1395345), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395347), _1395349)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395347, _1395345), hAPP(hAPP(c_COMBS(_1395347, _1395345, _1395345), hAPP(hAPP(c_COMBB(_1395345, tc_fun(_1395345, _1395345), _1395347), c_Rings_Oinverse__class_Odivide(_1395345)), _1395351)), _1395353)), _1395349) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1395345), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395347, _1395345), _1395351), _1395349)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395347, _1395345), _1395353), _1395349)))], (32910 ^ _774244) ^ [_1370432, _1370434, _1370436] : [class_Orderings_Olinorder(_1370432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370432), _1370434)), -(_1370434 = c_Orderings_Obot__class_Obot(tc_fun(_1370432, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1370432, hAPP(hAPP(c_Set_Oinsert(_1370432), _1370436), _1370434)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1370432), _1370436), c_Big__Operators_Olinorder__class_OMin(_1370432, _1370434)))], (38950 ^ _774244) ^ [_1502887, _1502889, _1502891, _1502893, _1502895] : [class_Groups_Ocomm__monoid__mult(_1502887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502889), _1502891)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1502887, _1502889, c_Groups_Otimes__class_Otimes(_1502887)), hAPP(hAPP(c_COMBS(_1502889, _1502887, _1502887), hAPP(hAPP(c_COMBB(_1502887, tc_fun(_1502887, _1502887), _1502889), c_Groups_Otimes__class_Otimes(_1502887)), _1502893)), _1502895)), c_Groups_Oone__class_Oone(_1502887)), _1502891) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1502887), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1502887, _1502889, c_Groups_Otimes__class_Otimes(_1502887)), _1502893), c_Groups_Oone__class_Oone(_1502887)), _1502891)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1502887, _1502889, c_Groups_Otimes__class_Otimes(_1502887)), _1502895), c_Groups_Oone__class_Oone(_1502887)), _1502891)))], (33828 ^ _774244) ^ [_1388631, _1388633, _1388635, _1388637, _1388639] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388631, _1388633), _1388635), _1388637), _1388639), _1388637) = _1388639)], (49365 ^ _774244) ^ [_1761851, _1761853, _1761855, _1761857] : [-(hAPP(c_List_Ofilter(_1761851, _1761853), hAPP(c_List_Ofilter(_1761851, _1761855), _1761857)) = hAPP(c_List_Ofilter(_1761851, hAPP(hAPP(c_COMBS(_1761851, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1761851), c_fconj), _1761855)), _1761853)), _1761857))], (51143 ^ _774244) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (8562 ^ _774244) ^ [_914028, _914030, _914032] : [class_Rings_Oring(_914028), -(hAPP(c_Groups_Ouminus__class_Ouminus(_914028), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914028), _914030), _914032)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914028), _914030), hAPP(c_Groups_Ouminus__class_Ouminus(_914028), _914032)))], (51245 ^ _774244) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (28687 ^ _774244) ^ [] : [-(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))))], (24571 ^ _774244) ^ [_1202026, _1202028, _1202030, _1202032, _1202034, _1202036] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1202026, _1202028, _1202030, _1202032, _1202034), hAPP(c_Sum__Type_OInr(_1202030, _1202026), _1202036)) = hAPP(_1202034, _1202036))], (19651 ^ _774244) ^ [_1110039] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1110039, 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, _1110039, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (12051 ^ _774244) ^ [_973689, _973691] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973689), hAPP(c_Nat_OSuc, _973691)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973689), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973689), _973691)))], (51029 ^ _774244) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (35332 ^ _774244) ^ [_1422676] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1422676) = 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, _1422676)), 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))))))))], (736 ^ _774244) ^ [_785612, _785614, _785616, _785618] : [-(c_Wellfounded_Oacyclic(_785616, _785612)), c_Wellfounded_Oacyclic(_785618, _785614), _785618 = _785616, _785614 = _785612], (17989 ^ _774244) ^ [_1081866, _1081868] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1081866), hAPP(hAPP(c_Power_Opower__class_Opower(_1081866), hAPP(c_Int_Onumber__class_Onumber__of(_1081866), c_Int_OMin)), _1081868)) = c_Groups_Oone__class_Oone(_1081866)), class_Int_Onumber__ring(_1081866), class_Rings_Olinordered__idom(_1081866)], (16831 ^ _774244) ^ [_1061701, _1061703, _1061705, _1061707] : [class_Int_Onumber__ring(_1061701), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061701), hAPP(c_Int_Onumber__class_Onumber__of(_1061701), _1061703)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1061701), hAPP(c_Int_Onumber__class_Onumber__of(_1061701), _1061705)), _1061707)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1061701), hAPP(c_Int_Onumber__class_Onumber__of(_1061701), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1061703), _1061705))), _1061707))], (6067 ^ _774244) ^ [_871409, _871411] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_871409, _871411)))), hBOOL(hAPP(c_Com_OWT, _871409)), hBOOL(hAPP(c_Com_OWT, _871411))], (29408 ^ _774244) ^ [_1297519, _1297521, _1297523, _1297525, _1297527] : [-(_1297519 = c_Orderings_Obot__class_Obot(tc_fun(_1297521, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297523, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297521, tc_fun(_1297523, tc_HOL_Obool)), _1297519), _1297525)), _1297527) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297521, tc_fun(_1297523, tc_HOL_Obool)), _1297519), hAPP(hAPP(c_COMBC(_1297521, tc_fun(_1297523, tc_HOL_Obool), tc_fun(_1297523, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297523, tc_HOL_Obool), tc_fun(tc_fun(_1297523, tc_HOL_Obool), tc_fun(_1297523, tc_HOL_Obool)), _1297521), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297523, tc_HOL_Obool))), _1297525)), _1297527)))], (50878 ^ _774244) ^ [_1794853, _1794855, _1794857] : [-(c_List_OdropWhile(_1794853, _1794855, _1794857) = hAPP(hAPP(c_List_Odrop(_1794853), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1794853)), c_List_OtakeWhile(_1794853, _1794855, _1794857))), _1794857))], (36803 ^ _774244) ^ [_1455771, _1455773, _1455775, _1455777, _1455779] : [class_Groups_Ocomm__monoid__add(_1455771), hBOOL(hAPP(c_Finite__Set_Ofinite(_1455773), _1455775)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1455773), _1455777)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1455771), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1455773, _1455771), _1455779), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1455773, tc_HOL_Obool)), _1455775), _1455777))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1455773, _1455771), _1455779), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455773, tc_HOL_Obool)), _1455775), _1455777))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1455771), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1455773, _1455771), _1455779), _1455775)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1455773, _1455771), _1455779), _1455777)))], (36375 ^ _774244) ^ [_1445865, _1445867, _1445869] : [class_Lattices_Osemilattice__inf(_1445865), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445865), _1445867), _1445869) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445865), _1445869), _1445867))], (46531 ^ _774244) ^ [_1694317, _1694319, _1694321, _1694323] : [-(c_Map_Omap__of(_1694317, _1694319, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1694317, _1694319)), _1694321), _1694323)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1694317, tc_Option_Ooption(_1694319)), c_Map_Omap__of(_1694317, _1694319, _1694323)), hAPP(c_Product__Type_Ofst(_1694317, _1694319), _1694321)), hAPP(c_Option_Ooption_OSome(_1694319), hAPP(c_Product__Type_Osnd(_1694317, _1694319), _1694321))))], (9989 ^ _774244) ^ [_938808, _938810, _938812, _938814, _938816, _938818] : [class_Rings_Olinordered__semiring__1__strict(_938808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938808), _938810), _938812)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938808), _938814), _938812)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938808), c_Groups_Ozero__class_Ozero(_938808)), _938816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938808), c_Groups_Ozero__class_Ozero(_938808)), _938818)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938808), _938816), _938818) = c_Groups_Oone__class_Oone(_938808), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938808), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938808), _938816), _938810)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938808), _938818), _938814))), _938812)))], (9696 ^ _774244) ^ [_934005, _934007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _934005)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _934007))))], (24557 ^ _774244) ^ [_1201726, _1201728, _1201730, _1201732, _1201734, _1201736, _1201738] : [c_Sum__Type_Osum_Osum__case(_1201726, _1201728, _1201730, _1201732, _1201734) = c_Sum__Type_Osum_Osum__case(_1201726, _1201728, _1201730, _1201736, _1201738), 24560 ^ _774244 : [(24563 ^ _774244) ^ [] : [-(_1201734 = _1201738)], (24561 ^ _774244) ^ [] : [-(_1201732 = _1201736)]]], (16357 ^ _774244) ^ [_1052442, _1052444] : [class_Groups_Oordered__ab__group__add__abs(_1052442), 16360 ^ _774244 : [(16367 ^ _774244) ^ [] : [_1052444 = c_Groups_Ozero__class_Ozero(_1052442), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052442), hAPP(c_Groups_Oabs__class_Oabs(_1052442), _1052444)), c_Groups_Ozero__class_Ozero(_1052442))))], (16361 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052442), hAPP(c_Groups_Oabs__class_Oabs(_1052442), _1052444)), c_Groups_Ozero__class_Ozero(_1052442))), -(_1052444 = c_Groups_Ozero__class_Ozero(_1052442))]]], (43237 ^ _774244) ^ [_1610876, _1610878, _1610880, _1610882] : [hBOOL(hAPP(hAPP(c_member(_1610876), _1610878), c_Wellfounded_Oacc(_1610876, _1610880))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1610876, _1610876)), hAPP(hAPP(c_Product__Type_OPair(_1610876, _1610876), _1610882), _1610878)), c_Transitive__Closure_Ortrancl(_1610876, _1610880))), -(hBOOL(hAPP(hAPP(c_member(_1610876), _1610882), c_Wellfounded_Oacc(_1610876, _1610880))))], (15056 ^ _774244) ^ [_1027324, _1027326, _1027328] : [class_Groups_Oab__group__add(_1027324), 15059 ^ _774244 : [(15066 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1027324), _1027326), _1027328) = c_Groups_Ozero__class_Ozero(_1027324), -(_1027326 = _1027328)], (15060 ^ _774244) ^ [] : [_1027326 = _1027328, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1027324), _1027326), _1027328) = c_Groups_Ozero__class_Ozero(_1027324))]]], (1524 ^ _774244) ^ [_796018, _796020] : [-(class_Rings_Ono__zero__divisors(_796018)), _796020 = _796018, class_Rings_Ono__zero__divisors(_796020)], (44494 ^ _774244) ^ [_1643709, _1643711] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1643709, tc_HOL_Obool), _1643711) = hAPP(c_Set_OCollect(_1643709), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1643709, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1643709), c_HOL_OAll(tc_fun(_1643709, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1643709, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1643709, tc_HOL_Obool), tc_HOL_Obool), _1643709), hAPP(c_COMBS(tc_fun(_1643709, 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(_1643709, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1643709, tc_HOL_Obool), tc_fun(tc_fun(_1643709, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1643709, tc_HOL_Obool))), _1643711)))), c_member(_1643709)))))], (1114 ^ _774244) ^ [_790893, _790895] : [-(class_Divides_Oring__div(_790893)), _790895 = _790893, class_Divides_Oring__div(_790895)], (15924 ^ _774244) ^ [_1044791, _1044793] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044791, _1044793) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044791, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1044793)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044791, _1044793)), _1044793))], (43275 ^ _774244) ^ [_1611781, _1611783, _1611785, _1611787] : [c_Wellfounded_Oacyclic(_1611781, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1611781, _1611781)), hAPP(hAPP(c_Product__Type_OPair(_1611781, _1611781), _1611783), _1611785)), _1611787)), 43278 ^ _774244 : [(43281 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611781, _1611781)), hAPP(hAPP(c_Product__Type_OPair(_1611781, _1611781), _1611785), _1611783)), c_Transitive__Closure_Ortrancl(_1611781, _1611787)))], (43279 ^ _774244) ^ [] : [-(c_Wellfounded_Oacyclic(_1611781, _1611787))]]], (48316 ^ _774244) ^ [_1739143, _1739145, _1739147, _1739149] : [hBOOL(hAPP(hAPP(c_member(_1739143), _1739145), hAPP(c_List_Oset(_1739143), hAPP(hAPP(c_List_Odrop(_1739143), _1739147), _1739149)))), -(hBOOL(hAPP(hAPP(c_member(_1739143), _1739145), hAPP(c_List_Oset(_1739143), _1739149))))], (36237 ^ _774244) ^ [_1442845, _1442847] : [class_Lattices_Obounded__lattice__bot(_1442845), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1442845), _1442847), c_Orderings_Obot__class_Obot(_1442845)) = c_Orderings_Obot__class_Obot(_1442845))], (28709 ^ _774244) ^ [_1283944, _1283946] : [-(hAPP(c_Set_Oimage(_1283944, _1283944, c_COMBI(_1283944)), _1283946) = _1283946)], (44604 ^ _774244) ^ [_1646279, _1646281] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1646279, tc_HOL_Obool), _1646281) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1646279, tc_HOL_Obool), tc_fun(_1646279, tc_HOL_Obool)), _1646281), c_COMBI(tc_fun(_1646279, tc_HOL_Obool))))], (35290 ^ _774244) ^ [_1421530, _1421532, _1421534, _1421536, _1421538] : [hBOOL(hAPP(hAPP(c_member(_1421530), _1421532), hAPP(c_Relation_OImage(_1421534, _1421530, _1421536), hAPP(hAPP(c_Set_Oinsert(_1421534), _1421538), c_Orderings_Obot__class_Obot(tc_fun(_1421534, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1421534, _1421530)), hAPP(hAPP(c_Product__Type_OPair(_1421534, _1421530), _1421538), _1421532)), _1421536)))], (15472 ^ _774244) ^ [_1035189, _1035191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035191), _1035189)), -(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), _1035189), _1035191))))], (36691 ^ _774244) ^ [_1453289, _1453291, _1453293, _1453295, _1453297] : [class_Orderings_Olinorder(_1453289), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453289, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1453289, _1453291, _1453293)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1453289, _1453295, _1453297)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1453289, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1453289), _1453291), _1453295), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1453289), _1453293), _1453297)))], (18917 ^ _774244) ^ [_1097033, _1097035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1097033)), c_Int_OBit0(_1097035))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097033), _1097035)))], (36631 ^ _774244) ^ [_1451897, _1451899, _1451901] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451897, tc_HOL_Obool)), _1451899), _1451901) = c_Orderings_Obot__class_Obot(tc_fun(_1451897, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1451897, tc_HOL_Obool)), _1451899), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1451897, tc_HOL_Obool)), _1451901))))], (43265 ^ _774244) ^ [_1611534, _1611536, _1611538, _1611540] : [-(c_Wellfounded_Owf(_1611534, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1611534, _1611534)), hAPP(hAPP(c_Product__Type_OPair(_1611534, _1611534), _1611536), _1611538)), _1611540))), c_Wellfounded_Owf(_1611534, _1611540), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611534, _1611534)), hAPP(hAPP(c_Product__Type_OPair(_1611534, _1611534), _1611538), _1611536)), c_Transitive__Closure_Ortrancl(_1611534, _1611540))))], (26353 ^ _774244) ^ [_1234629, _1234631] : [-(_1234629 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26356 ^ _774244 : [(26363 ^ _774244) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1234631) = 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), _1234629), _1234631)), _1234629)))], (26357 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234629), _1234631)), _1234629)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1234631) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (38515 ^ _774244) ^ [_1492812, _1492814, _1492816, _1492818] : [c_Fun_Oinj__on(_1492812, _1492814, _1492816, c_Orderings_Otop__class_Otop(tc_fun(_1492812, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492814, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492812, _1492814, _1492816), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1492812, tc_HOL_Obool)), _1492818))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1492814, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492812, _1492814, _1492816), _1492818)))))], (51115 ^ _774244) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (26095 ^ _774244) ^ [_1230120, _1230122] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230120), _1230122)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230120)), _1230122)))], (15310 ^ _774244) ^ [_1031977, _1031979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031977)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1031977), _1031979)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1031979), _1031977)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1031979)), hAPP(c_Int_Onat, _1031977)))], (35308 ^ _774244) ^ [] : [-(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))))))], (41949 ^ _774244) ^ [_1581844, _1581846] : [-(c_Nitpick_Owf_H(_1581844, _1581846)), c_Wellfounded_Oacyclic(_1581844, _1581846), 41954 ^ _774244 : [(41957 ^ _774244) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (41955 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1581844, _1581844)), _1581846))]]], (24001 ^ _774244) ^ [_1190787, _1190789] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1190787), _1190789) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1190787, 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)))), _1190789))))], (6770 ^ _774244) ^ [_883618, _883620, _883622, _883624, _883626, _883628, _883630, _883632, _883634, _883636, _883638, _883640] : [-(c_Com_Ocom_Ocom__case(_883618, _883620, _883622, _883624, _883626, _883628, _883630, _883632, _883634, c_Com_Ocom_OLocal(_883636, _883638, _883640)) = hAPP(hAPP(hAPP(_883624, _883636), _883638), _883640))], (47016 ^ _774244) ^ [_1706200, _1706202] : [-(c_Random_Oselect(_1706200, _1706202) = 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(_1706200, 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(_1706200)), _1706202)))), hAPP(hAPP(c_COMBB(_1706200, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1706200, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1706200, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1706200, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1706200), _1706202)), c_Code__Numeral_Onat__of))))], (43871 ^ _774244) ^ [_1628121, _1628123, _1628125, _1628127] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1628121, _1628121)), hAPP(hAPP(c_Product__Type_OPair(_1628121, _1628121), _1628123), _1628125)), hAPP(c_Relation_Oconverse(_1628121, _1628121), c_Transitive__Closure_Otrancl(_1628121, _1628127)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628121, _1628121)), hAPP(hAPP(c_Product__Type_OPair(_1628121, _1628121), _1628123), _1628125)), c_Transitive__Closure_Otrancl(_1628121, hAPP(c_Relation_Oconverse(_1628121, _1628121), _1628127)))))], (43439 ^ _774244) ^ [_1615786, _1615788, _1615790, _1615792, _1615794, _1615796] : [-(hAPP(c_Set_Ovimage(_1615786, _1615788, _1615790), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615792, tc_fun(_1615788, tc_HOL_Obool)), _1615794), _1615796)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615792, tc_fun(_1615786, tc_HOL_Obool)), _1615794), hAPP(hAPP(c_COMBB(tc_fun(_1615788, tc_HOL_Obool), tc_fun(_1615786, tc_HOL_Obool), _1615792), c_Set_Ovimage(_1615786, _1615788, _1615790)), _1615796)))], (30919 ^ _774244) ^ [_1328728, _1328730, _1328732, _1328734] : [30920 ^ _774244 : [(30923 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1328728), _1328730), _1328734))], (30921 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1328728), _1328730), _1328732))]], -(hBOOL(hAPP(hAPP(c_member(_1328728), _1328730), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328728, tc_HOL_Obool)), _1328732), _1328734))))], (6562 ^ _774244) ^ [_879978] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _879978) = _879978)], (9698 ^ _774244) ^ [_934044, _934046, _934048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934044), _934046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934048)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _934048), _934044)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _934048), _934046))))], (22132 ^ _774244) ^ [_1154664] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1154664) = 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), _1154664), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (12984 ^ _774244) ^ [_989847, _989849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989849)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _989847)), hAPP(c_Int_Onat, _989849)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _989847), _989849)))], (30813 ^ _774244) ^ [_1326904, _1326906, _1326908, _1326910] : [hBOOL(hAPP(hAPP(c_member(_1326904), _1326906), hAPP(hAPP(c_Set_Oinsert(_1326904), _1326908), _1326910))), -(_1326906 = _1326908), -(hBOOL(hAPP(hAPP(c_member(_1326904), _1326906), _1326910)))], (38157 ^ _774244) ^ [_1485658, _1485660, _1485662, _1485664, _1485666, _1485668] : [c_Fun_Oinj__on(_1485658, _1485660, _1485662, _1485664), hBOOL(hAPP(hAPP(c_member(_1485658), _1485666), _1485664)), hBOOL(hAPP(hAPP(c_member(_1485658), _1485668), _1485664)), 38168 ^ _774244 : [(38175 ^ _774244) ^ [] : [_1485666 = _1485668, -(hAPP(_1485662, _1485666) = hAPP(_1485662, _1485668))], (38169 ^ _774244) ^ [] : [hAPP(_1485662, _1485666) = hAPP(_1485662, _1485668), -(_1485666 = _1485668)]]], (21990 ^ _774244) ^ [_1152140, _1152142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152140), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152142)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152140)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152142))], (1654 ^ _774244) ^ [_797643, _797645] : [-(class_Rings_Osemiring__0(_797643)), _797645 = _797643, class_Rings_Osemiring__0(_797645)], (11791 ^ _774244) ^ [_969004, _969006, _969008] : [class_Rings_Oordered__ring(_969004), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969004), c_Groups_Ozero__class_Ozero(_969004)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969004), _969006), _969008)))), 11796 ^ _774244 : [(11803 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969004), _969006), c_Groups_Ozero__class_Ozero(_969004))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969004), _969008), c_Groups_Ozero__class_Ozero(_969004)))], (11797 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969004), c_Groups_Ozero__class_Ozero(_969004)), _969006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969004), c_Groups_Ozero__class_Ozero(_969004)), _969008))]]], (12312 ^ _774244) ^ [_978036, _978038, _978040] : [class_Groups_Oordered__comm__monoid__add(_978036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978036), c_Groups_Ozero__class_Ozero(_978036)), _978038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978036), c_Groups_Ozero__class_Ozero(_978036)), _978040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978036), c_Groups_Ozero__class_Ozero(_978036)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978036), _978038), _978040))))], (6211 ^ _774244) ^ [_873927, _873929, _873931] : [c_Com_Ocom_OCond(_873927, _873929, _873931) = c_Com_Ocom_OSKIP], (31243 ^ _774244) ^ [_1335293, _1335295, _1335297] : [hBOOL(hAPP(hAPP(c_member(_1335293), _1335295), hAPP(hAPP(c_Set_Oinsert(_1335293), _1335297), c_Orderings_Obot__class_Obot(tc_fun(_1335293, tc_HOL_Obool))))), -(_1335295 = _1335297)], (47216 ^ _774244) ^ [_1711041, _1711043, _1711045] : [-(hAPP(c_List_Oset(_1711041), c_List_Osublist(_1711041, _1711043, _1711045)) = hAPP(c_Set_OCollect(_1711041), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1711041), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1711041, 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)), _1711041), 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)), _1711041), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1711041, tc_fun(tc_Nat_Onat, _1711041), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711041, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1711041), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1711041), c_COMBB(_1711041, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1711041), _1711043))))), 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(_1711041)), _1711043)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1711045))))))], (47399 ^ _774244) ^ [_1715520, _1715522, _1715524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715520), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1715522))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1715522), _1715520), _1715524)) = 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), _1715522)), _1715524)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1715522), _1715520)))], (47301 ^ _774244) ^ [_1713406, _1713408, _1713410, _1713412, _1713414] : [-(hAPP(hAPP(c_List_Olist__update(_1713406, hAPP(hAPP(c_List_Olist__update(_1713406, _1713408), _1713410), _1713412)), _1713410), _1713414) = hAPP(hAPP(c_List_Olist__update(_1713406, _1713408), _1713410), _1713414))], (39010 ^ _774244) ^ [_1504191, _1504193, _1504195, _1504197, _1504199, _1504201] : [hBOOL(hAPP(hAPP(c_member(_1504191), _1504193), _1504195)), 39013 ^ _774244 : [(39020 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504191), _1504197), _1504195))), -(hAPP(c_Set_Ovimage(_1504199, _1504191, hAPP(hAPP(c_COMBC(_1504199, _1504191, _1504191), hAPP(hAPP(c_COMBC(_1504199, _1504191, tc_fun(_1504191, _1504191)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1504191, tc_fun(_1504191, _1504191)), _1504199), c_If(_1504191)), hAPP(hAPP(c_COMBC(_1504199, tc_fun(_1504199, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504199)), _1504201))), _1504193)), _1504197)), _1504195) = _1504201)], (39014 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1504191), _1504197), _1504195)), -(hAPP(c_Set_Ovimage(_1504199, _1504191, hAPP(hAPP(c_COMBC(_1504199, _1504191, _1504191), hAPP(hAPP(c_COMBC(_1504199, _1504191, tc_fun(_1504191, _1504191)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1504191, tc_fun(_1504191, _1504191)), _1504199), c_If(_1504191)), hAPP(hAPP(c_COMBC(_1504199, tc_fun(_1504199, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504199)), _1504201))), _1504193)), _1504197)), _1504195) = c_Orderings_Otop__class_Otop(tc_fun(_1504199, tc_HOL_Obool)))]]], (41370 ^ _774244) ^ [_1568346, _1568348] : [hBOOL(hAPP(hAPP(c_member(_1568346), 41371 ^ [_1568346, _1568348]), c_Wellfounded_Oacc(_1568346, _1568348))), -(c_Wellfounded_Owf(_1568346, _1568348))], (36201 ^ _774244) ^ [_1441953, _1441955, _1441957, _1441959] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441953, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441953, tc_HOL_Obool)), _1441955), _1441957)), _1441959) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441953, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441953, tc_HOL_Obool)), _1441955), _1441959)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441953, tc_HOL_Obool)), _1441957), _1441959)))], (22086 ^ _774244) ^ [_1153694, _1153696] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1153694), hAPP(c_Nat_OSuc, _1153696)) = 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), _1153694), _1153696)))], (6398 ^ _774244) ^ [_877213, _877215, _877217, _877219] : [class_Groups_Ocancel__semigroup__add(_877213), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877213), _877215), _877217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877213), _877219), _877217), -(_877215 = _877219)], (11607 ^ _774244) ^ [_965538, _965540, _965542] : [class_Rings_Oordered__cancel__semiring(_965538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965538), c_Groups_Ozero__class_Ozero(_965538)), _965540)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965538), c_Groups_Ozero__class_Ozero(_965538)), _965542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965538), c_Groups_Ozero__class_Ozero(_965538)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965538), _965540), _965542))))], (41109 ^ _774244) ^ [_1560298, _1560300, _1560302, _1560304, _1560306, _1560308] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1560298), _1560300)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560302), _1560304)), 41119 ^ _774244 : [(41122 ^ _774244) ^ [] : [hAPP(c_Finite__Set_Ocard(_1560298), hAPP(c_Set_OCollect(_1560298), hAPP(hAPP(c_COMBS(_1560298, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560298), c_fconj), hAPP(hAPP(c_COMBC(_1560298, tc_fun(_1560298, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560298)), _1560300))), hAPP(hAPP(c_COMBC(_1560298, _1560302, tc_HOL_Obool), _1560306), 41118 ^ [_1560298, _1560300, _1560302, _1560304, _1560306, _1560308])))) = hAPP(_1560308, 41118 ^ [_1560298, _1560300, _1560302, _1560304, _1560306, _1560308])], (41120 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560302), 41118 ^ [_1560298, _1560300, _1560302, _1560304, _1560306, _1560308]), _1560304)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560298, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1560302, tc_HOL_Obool), tc_Nat_Onat, _1560298), c_Finite__Set_Ocard(_1560302)), hAPP(hAPP(c_COMBB(tc_fun(_1560302, tc_HOL_Obool), tc_fun(_1560302, tc_HOL_Obool), _1560298), c_Set_OCollect(_1560302)), hAPP(hAPP(c_COMBB(tc_fun(_1560302, tc_HOL_Obool), tc_fun(_1560302, tc_HOL_Obool), _1560298), hAPP(c_COMBS(_1560302, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560302), c_fconj), hAPP(hAPP(c_COMBC(_1560302, tc_fun(_1560302, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560302)), _1560304)))), _1560306)))), _1560300) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560302, tc_Nat_Onat), _1560308), _1560304))], (39285 ^ _774244) ^ [_1510514, _1510516, _1510518, _1510520, _1510522] : [_1510514 = c_Option_Ooption_ONone(_1510516), -(c_Map_Odom(_1510518, _1510516, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1510518, tc_Option_Ooption(_1510516)), _1510520), _1510522), _1510514)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1510518, tc_HOL_Obool)), c_Map_Odom(_1510518, _1510516, _1510520)), hAPP(hAPP(c_Set_Oinsert(_1510518), _1510522), c_Orderings_Obot__class_Obot(tc_fun(_1510518, tc_HOL_Obool)))))], (6472 ^ _774244) ^ [_878504, _878506, _878508] : [_878504 = _878508, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878504), _878506) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878508), _878506))], (4470 ^ _774244) ^ [_843393, _843395, _843397, _843399] : [-(c_Big__Operators_Olattice__class_OInf__fin(_843399, _843395) = c_Big__Operators_Olattice__class_OInf__fin(_843397, _843393)), _843399 = _843397, _843395 = _843393], (47204 ^ _774244) ^ [_1710827, _1710829, _1710831, _1710833] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1710827) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1710829), hAPP(hAPP(c_List_Olist_OCons(_1710829), _1710831), _1710833)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1710827)) = hAPP(hAPP(c_List_Onth(_1710829), _1710833), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1710827)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (30641 ^ _774244) ^ [_1321276, _1321278, _1321280] : [-(hBOOL(hAPP(hAPP(c_member(_1321276), _1321278), _1321280))), -(hBOOL(hAPP(hAPP(c_member(_1321276), _1321278), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1321276, tc_HOL_Obool)), _1321280))))], (25735 ^ _774244) ^ [_1223374, _1223376, _1223378] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223374), _1223376)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223374), _1223378))), -(_1223374 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223376), _1223378)))], (37947 ^ _774244) ^ [_1481662, _1481664] : [-(c_Equiv__Relations_Oequivp(_1481662, _1481664)), 37952 ^ _774244 : [(37955 ^ _774244) ^ [] : [hAPP(_1481664, 37948 ^ [_1481662, _1481664]) = hAPP(_1481664, 37949 ^ [_1481662, _1481664])], (37953 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1481664, 37948 ^ [_1481662, _1481664]), 37949 ^ [_1481662, _1481664])))]], 37956 ^ _774244 : [(37959 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1481664, 37948 ^ [_1481662, _1481664]), 37949 ^ [_1481662, _1481664]))], (37957 ^ _774244) ^ [] : [-(hAPP(_1481664, 37948 ^ [_1481662, _1481664]) = hAPP(_1481664, 37949 ^ [_1481662, _1481664]))]]], (2194 ^ _774244) ^ [_807249, _807251, _807253, _807255, _807257, _807259, _807261, _807263] : [-(c_Sum__Type_OSumr(_807263, _807259, _807255, _807251) = c_Sum__Type_OSumr(_807261, _807257, _807253, _807249)), _807263 = _807261, _807259 = _807257, _807255 = _807253, _807251 = _807249], (9336 ^ _774244) ^ [_927453, _927455, _927457, _927459] : [class_Rings_Olinordered__ring__strict(_927453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927453), _927455), _927457)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927453), _927459), c_Groups_Ozero__class_Ozero(_927453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927453), _927459), _927457)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927453), _927459), _927455))))], (30937 ^ _774244) ^ [_1329098, _1329100, _1329102, _1329104] : [hBOOL(hAPP(hAPP(c_member(_1329098), _1329100), _1329102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329098, tc_HOL_Obool)), _1329102), _1329104)), -(hBOOL(hAPP(hAPP(c_member(_1329098), _1329100), _1329104)))], (25133 ^ _774244) ^ [_1212799, _1212801] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212799), _1212801)), 25138 ^ _774244 : [(25141 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212801), _1212799))], (25139 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212799), _1212801)))]], -(_1212799 = _1212801)], (35422 ^ _774244) ^ [_1425018, _1425020, _1425022, _1425024, _1425026, _1425028, _1425030, _1425032] : [c_Finite__Set_Ofolding(_1425018, _1425020, _1425022, _1425024), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425018), _1425026)), -(hAPP(c_Fun_Ocomp(_1425020, _1425020, _1425028, hAPP(_1425022, _1425030)), hAPP(c_Fun_Ocomp(_1425020, _1425020, _1425028, hAPP(_1425024, _1425026)), _1425032)) = hAPP(c_Fun_Ocomp(_1425020, _1425020, _1425028, hAPP(_1425024, _1425026)), hAPP(c_Fun_Ocomp(_1425020, _1425020, _1425028, hAPP(_1425022, _1425030)), _1425032)))], (14125 ^ _774244) ^ [_1010817, _1010819, _1010821] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1010817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010819), _1010821)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010819), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1010817), _1010819), _1010821))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1010817, _1010819)))], (50318 ^ _774244) ^ [_1782079, _1782081] : [class_Groups_Ocomm__monoid__add(_1782079), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1782079), hAPP(c_List_Orev(_1782079), _1782081)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1782079), _1782081))], (18717 ^ _774244) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (26474 ^ _774244) ^ [_1237342, _1237344, _1237346] : [class_Groups_Ocomm__monoid__add(_1237342), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237344, _1237342), hAPP(c_COMBK(_1237342, _1237344), c_Groups_Ozero__class_Ozero(_1237342))), _1237346) = c_Groups_Ozero__class_Ozero(_1237342))], (19343 ^ _774244) ^ [_1104412] : [-(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)))), _1104412) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1104412)))], (38501 ^ _774244) ^ [_1492537, _1492539, _1492541, _1492543, _1492545] : [class_Groups_Ocomm__monoid__mult(_1492537), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492539), _1492541)), c_Fun_Oinj__on(_1492539, _1492539, _1492543, _1492541), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1492539, _1492537), _1492545), hAPP(c_Set_Oimage(_1492539, _1492539, _1492543), _1492541)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1492539, _1492537), hAPP(c_Fun_Ocomp(_1492539, _1492537, _1492539, _1492545), _1492543)), _1492541))], (9712 ^ _774244) ^ [_934299, _934301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934299), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _934301), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934299), _934301))), -(_934299 = _934301)], (15212 ^ _774244) ^ [_1030035, _1030037, _1030039] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030035), _1030037)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030039), _1030037)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030035), _1030039))], (43775 ^ _774244) ^ [_1625511, _1625513, _1625515] : [c_Equiv__Relations_Oequiv(_1625511, _1625513, _1625515), -(hAPP(hAPP(c_Relation_Orel__comp(_1625511, _1625511, _1625511), hAPP(c_Relation_Oconverse(_1625511, _1625511), _1625515)), _1625515) = _1625515)], (30146 ^ _774244) ^ [_1311137, _1311139, _1311141, _1311143, _1311145] : [class_Groups_Ocomm__monoid__add(_1311137), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311139), _1311141)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1311139, _1311137), hAPP(hAPP(c_COMBS(_1311139, _1311137, _1311137), hAPP(hAPP(c_COMBB(_1311137, tc_fun(_1311137, _1311137), _1311139), c_Groups_Oplus__class_Oplus(_1311137)), _1311143)), _1311145)), _1311141) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1311137), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1311139, _1311137), _1311143), _1311141)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1311139, _1311137), _1311145), _1311141)))], (29472 ^ _774244) ^ [_1299041] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1299041), hAPP(c_Nat_OSuc, _1299041)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1299041), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (5800 ^ _774244) ^ [_866743, _866745, _866747, _866749] : [-(c_Com_Ocom_OSemi(_866743, _866745) = c_Com_Ocom_OSemi(_866747, _866749)), _866743 = _866747, _866745 = _866749], (43690 ^ _774244) ^ [_1623638, _1623640, _1623642, _1623644, _1623646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1623638, tc_HOL_Obool)), _1623640), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623642, tc_fun(_1623638, tc_HOL_Obool)), _1623644), _1623646))), 43693 ^ _774244 : [(43694 ^ _774244) ^ [_1623771] : [hBOOL(hAPP(hAPP(c_member(_1623642), _1623771), _1623644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1623638, tc_HOL_Obool)), _1623640), hAPP(_1623646, _1623771))))]]], (26956 ^ _774244) ^ [_1248024, _1248026] : [26964 ^ _774244 : [(26967 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1248026, 26963 ^ [_1248024, _1248026])))], (26965 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26963 ^ [_1248024, _1248026]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248024))))]], 26957 ^ _774244 : [(26958 ^ _774244) ^ [_1248092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1248092), _1248024)), hBOOL(hAPP(_1248026, _1248092))]]], (18159 ^ _774244) ^ [_1084382, _1084384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1084382)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1084384)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084382)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1084384), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1084382))))], (41154 ^ _774244) ^ [_1561520] : [-(hAPP(c_Set_Oimage(_1561520, _1561520, c_Fun_Oid(_1561520)), c_Orderings_Otop__class_Otop(tc_fun(_1561520, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1561520, tc_HOL_Obool)))], (7695 ^ _774244) ^ [_899724] : [7696 ^ _774244 : [(7697 ^ _774244) ^ [_899766] : [_899724 = hAPP(c_Nat_OSuc, _899766)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _899724)))], (750 ^ _774244) ^ [_785805, _785807, _785809, _785811] : [-(c_Wellfounded_Owf(_785809, _785805)), c_Wellfounded_Owf(_785811, _785807), _785811 = _785809, _785807 = _785805], (16999 ^ _774244) ^ [_1064948, _1064950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1064948)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1064950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1064948), _1064950)))], (15666 ^ _774244) ^ [_1038898, _1038900] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1038898), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1038900)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1038898), _1038900)))], (4520 ^ _774244) ^ [_844146, _844148, _844150, _844152, _844154, _844156] : [-(c_Big__Operators_Olattice_OSup__fin(_844156, _844152, _844148) = c_Big__Operators_Olattice_OSup__fin(_844154, _844150, _844146)), _844156 = _844154, _844152 = _844150, _844148 = _844146], (28553 ^ _774244) ^ [_1279590, _1279592, _1279594, _1279596, _1279598] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279590, tc_fun(_1279592, tc_HOL_Obool)), _1279594), hAPP(hAPP(c_COMBC(_1279590, tc_fun(_1279592, tc_HOL_Obool), tc_fun(_1279592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1279592, tc_HOL_Obool), tc_fun(tc_fun(_1279592, tc_HOL_Obool), tc_fun(_1279592, tc_HOL_Obool)), _1279590), c_Groups_Ominus__class_Ominus(tc_fun(_1279592, tc_HOL_Obool))), _1279596)), _1279598)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279592, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279590, tc_fun(_1279592, tc_HOL_Obool)), _1279594), _1279596)), _1279598))], (16579 ^ _774244) ^ [_1056623, _1056625, _1056627] : [class_Rings_Ocomm__semiring__1(_1056623), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056623), hAPP(hAPP(c_Power_Opower__class_Opower(_1056623), _1056625), _1056627)), _1056625) = hAPP(hAPP(c_Power_Opower__class_Opower(_1056623), _1056625), hAPP(c_Nat_OSuc, _1056627)))], (49258 ^ _774244) ^ [_1759692, _1759694, _1759696, _1759698] : [-(_1759692 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759694)), _1759696)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1759694, hAPP(hAPP(c_List_Olist__update(_1759694, _1759696), _1759692), _1759698)) = hAPP(hAPP(c_List_Olist__update(_1759694, c_List_Obutlast(_1759694, _1759696)), _1759692), _1759698))], (32328 ^ _774244) ^ [_1359697, _1359699, _1359701, _1359703, _1359705, _1359707, _1359709] : [hBOOL(hAPP(hAPP(c_member(_1359697), _1359699), _1359701)), c_Nitpick_Ofold__graph_H(_1359697, _1359703, _1359705, _1359707, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359697, tc_HOL_Obool)), _1359701), hAPP(hAPP(c_Set_Oinsert(_1359697), _1359699), c_Orderings_Obot__class_Obot(tc_fun(_1359697, tc_HOL_Obool)))), _1359709), -(c_Nitpick_Ofold__graph_H(_1359697, _1359703, _1359705, _1359707, _1359701, hAPP(hAPP(_1359705, _1359699), _1359709)))], (29450 ^ _774244) ^ [_1298552] : [class_Lattices_Oboolean__algebra(_1298552), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1298552), c_Orderings_Obot__class_Obot(_1298552)) = c_Orderings_Otop__class_Otop(_1298552))], (1274 ^ _774244) ^ [_792893, _792895] : [-(class_Lattices_Odistrib__lattice(_792893)), _792895 = _792893, class_Lattices_Odistrib__lattice(_792895)], (1434 ^ _774244) ^ [_794893, _794895] : [-(class_Rings_Oordered__cancel__semiring(_794893)), _794895 = _794893, class_Rings_Oordered__cancel__semiring(_794895)], (50103 ^ _774244) ^ [_1776843, _1776845, _1776847, _1776849, _1776851] : [class_Orderings_Olinorder(_1776843), c_Fun_Oinj__on(_1776845, _1776843, _1776847, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1776845, tc_HOL_Obool)), hAPP(c_List_Oset(_1776845), _1776849)), hAPP(c_List_Oset(_1776845), _1776851))), c_List_Olinorder__class_Osorted(_1776843, hAPP(hAPP(c_List_Omap(_1776845, _1776843), _1776847), _1776849)), hBOOL(hAPP(c_List_Odistinct(_1776843), hAPP(hAPP(c_List_Omap(_1776845, _1776843), _1776847), _1776849))), c_List_Olinorder__class_Osorted(_1776843, hAPP(hAPP(c_List_Omap(_1776845, _1776843), _1776847), _1776851)), hBOOL(hAPP(c_List_Odistinct(_1776843), hAPP(hAPP(c_List_Omap(_1776845, _1776843), _1776847), _1776851))), hAPP(c_List_Oset(_1776845), _1776849) = hAPP(c_List_Oset(_1776845), _1776851), -(_1776849 = _1776851)], (49641 ^ _774244) ^ [_1768635, _1768637] : [c_List_Oupt(_1768635, _1768637) = c_List_Olist_ONil(tc_Nat_Onat), -(_1768637 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1768637), _1768635)))], (7044 ^ _774244) ^ [_888373, _888375] : [hBOOL(hAPP(c_Com_OWT, _888375)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_888373, _888375))))], (30753 ^ _774244) ^ [_1323467, _1323469, _1323471, _1323473, _1323475] : [-(hBOOL(hAPP(hAPP(c_member(_1323467), _1323469), c_SetInterval_Oord_OatLeastAtMost(_1323467, _1323471, _1323473, _1323475)))), hBOOL(hAPP(hAPP(_1323471, _1323473), _1323469)), hBOOL(hAPP(hAPP(_1323471, _1323469), _1323475))], (2614 ^ _774244) ^ [_813821, _813823] : [_813823 = _813821, -(c_Code__Numeral_OSuc__code__numeral(_813823) = c_Code__Numeral_OSuc__code__numeral(_813821))], (46812 ^ _774244) ^ [_1701929, _1701931, _1701933, _1701935] : [_1701935 = c_List_Olist_ONil(_1701931), -(c_List_Olist_ONil(_1701929) = hAPP(hAPP(c_List_Omap(_1701931, _1701929), _1701933), _1701935))], (9184 ^ _774244) ^ [_924686, _924688, _924690, _924692] : [class_Rings_Ocomm__semiring__1(_924686), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924686), _924688), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924686), _924690), _924692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924686), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924686), _924688), _924690)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924686), _924688), _924692)))], (31551 ^ _774244) ^ [_1342318, _1342320, _1342322] : [_1342322 = hAPP(c_Option_Ooption_OSome(_1342318), _1342320), -(hBOOL(hAPP(hAPP(c_member(_1342318), _1342320), c_Option_Oset(_1342318, _1342322))))], (28729 ^ _774244) ^ [_1284427, _1284429, _1284431, _1284433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284427, tc_HOL_Obool)), _1284429), _1284431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284427, tc_HOL_Obool)), _1284429), hAPP(hAPP(c_Set_Oinsert(_1284427), _1284433), _1284431))))], (11156 ^ _774244) ^ [_957679, _957681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957679), _957681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957679), _957681))), -(_957679 = _957681)], (3716 ^ _774244) ^ [_831562, _831564] : [_831564 = _831562, -(tc_Lazy__Sequence_Olazy__sequence(_831564) = tc_Lazy__Sequence_Olazy__sequence(_831562))], (5623 ^ _774244) ^ [_863820, _863822, _863824, _863826] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _863820)), _863822, _863824, _863826), -(c_Natural_Oevaln(c_Com_Ocom_OBODY(_863820), _863822, hAPP(c_Nat_OSuc, _863824), _863826))], (50500 ^ _774244) ^ [_1786927, _1786929, _1786931] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1786927), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1786927))), _1786929))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1786931), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1786927))), _1786929))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1786927))), hAPP(c_List_Ofilter(tc_List_Olist(_1786927), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1786927)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1786931)), c_Nat_Osize__class_Osize(tc_List_Olist(_1786927)))), c_List_Otranspose(_1786927, _1786929))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786927)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1786927)), _1786929), _1786931)))], (46914 ^ _774244) ^ [_1703777, _1703779] : [-(c_List_Osublist(_1703777, _1703779, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1703777))], (16125 ^ _774244) ^ [_1048432, _1048434] : [-(_1048432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1048434, _1048432) = c_Nitpick_Onat__gcd(_1048432, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1048434, _1048432)))], (37570 ^ _774244) ^ [_1473986, _1473988, _1473990, _1473992, _1473994] : [class_Groups_Ocomm__monoid__add(_1473986), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473988), _1473990)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473988), _1473992)), 37584 ^ _774244 : [(37587 ^ _774244) ^ [] : [hAPP(_1473994, 37583 ^ [_1473986, _1473988, _1473990, _1473992, _1473994]) = c_Groups_Ozero__class_Ozero(_1473986)], (37585 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473988), 37583 ^ [_1473986, _1473988, _1473990, _1473992, _1473994]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473988, tc_HOL_Obool)), _1473990), _1473992))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473988, _1473986), _1473994), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473988, tc_HOL_Obool)), _1473990), _1473992)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1473986), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473988, _1473986), _1473994), _1473990)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473988, _1473986), _1473994), _1473992)))], (29043 ^ _774244) ^ [_1291230, _1291232, _1291234, _1291236] : [-(_1291230 = c_Orderings_Obot__class_Obot(tc_fun(_1291232, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291232, tc_fun(_1291234, tc_HOL_Obool)), _1291230), hAPP(c_COMBK(tc_fun(_1291234, tc_HOL_Obool), _1291232), _1291236)) = _1291236)], (35498 ^ _774244) ^ [_1426990, _1426992, _1426994, _1426996, _1426998, _1427000] : [c_Finite__Set_Ofolding__idem(_1426990, _1426992, _1426994, _1426996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426990), _1426998)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426990), _1427000)), -(hAPP(_1426996, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426990, tc_HOL_Obool)), _1426998), _1427000)) = hAPP(c_Fun_Ocomp(_1426992, _1426992, _1426992, hAPP(_1426996, _1426998)), hAPP(_1426996, _1427000)))], (43709 ^ _774244) ^ [_1624159, _1624161, _1624163, _1624165] : [-(hAPP(c_Relation_Oconverse(_1624159, _1624161), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1624159, _1624161), tc_HOL_Obool)), _1624163), _1624165)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1624161, _1624159), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1624159, _1624161), _1624163)), hAPP(c_Relation_Oconverse(_1624159, _1624161), _1624165)))], (32310 ^ _774244) ^ [_1359337, _1359339, _1359341, _1359343] : [hBOOL(hAPP(hAPP(_1359341, _1359343), _1359339)), -(hBOOL(hAPP(hAPP(c_member(_1359337), _1359339), c_SetInterval_Oord_OatLeast(_1359337, _1359341, _1359343))))], (12069 ^ _774244) ^ [_974033, _974035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974033), hAPP(c_Nat_OSuc, _974035))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974033), _974035)))], (29496 ^ _774244) ^ [_1299429, _1299431] : [_1299429 = _1299431, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1299429, _1299431) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1299429), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (8586 ^ _774244) ^ [_914544, _914546] : [class_Rings_Oring__1__no__zero__divisors(_914544), 8589 ^ _774244 : [(8590 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914544), _914546), _914546) = c_Groups_Oone__class_Oone(_914544), -(_914546 = c_Groups_Oone__class_Oone(_914544)), -(_914546 = hAPP(c_Groups_Ouminus__class_Ouminus(_914544), c_Groups_Oone__class_Oone(_914544)))], (8600 ^ _774244) ^ [] : [8601 ^ _774244 : [(8604 ^ _774244) ^ [] : [_914546 = hAPP(c_Groups_Ouminus__class_Ouminus(_914544), c_Groups_Oone__class_Oone(_914544))], (8602 ^ _774244) ^ [] : [_914546 = c_Groups_Oone__class_Oone(_914544)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914544), _914546), _914546) = c_Groups_Oone__class_Oone(_914544))]]], (51293 ^ _774244) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (27440 ^ _774244) ^ [_1258151, _1258153] : [-(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)), _1258151)), 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), _1258153), _1258151))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1258151), _1258153))], (46924 ^ _774244) ^ [_1703950, _1703952] : [-(_1703952 = c_List_Olist_ONil(_1703950)), -(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(_1703950)), _1703952))))], (48947 ^ _774244) ^ [_1753220, _1753222, _1753224] : [48949 ^ _774244 : [(48952 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1753220), 48948 ^ [_1753220, _1753222, _1753224]), _1753224))], (48950 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753220), 48948 ^ [_1753220, _1753222, _1753224]), hAPP(c_List_Oset(_1753220), _1753222))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1753220)), _1753222), c_List_Olists(_1753220, _1753224))))], (26456 ^ _774244) ^ [_1236767, _1236769, _1236771] : [class_Groups_Ocomm__monoid__add(_1236767), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1236767), _1236769), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1236771))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236767), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1236767), _1236769), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1236771))), hAPP(_1236769, _1236771)))], (36561 ^ _774244) ^ [_1450350, _1450352, _1450354, _1450356] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1450350, tc_HOL_Obool)), _1450352), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450350, tc_HOL_Obool)), _1450354), _1450356)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450350, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1450350, tc_HOL_Obool)), _1450352), _1450354)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1450350, tc_HOL_Obool)), _1450352), _1450356)))], (44030 ^ _774244) ^ [_1632723] : [-(hAPP(c_Relation_ODomain(_1632723, _1632723), c_Relation_OId(_1632723)) = c_Orderings_Otop__class_Otop(tc_fun(_1632723, tc_HOL_Obool)))], (5530 ^ _774244) ^ [_859597, _859599, _859601, _859603] : [-(c_COMBK(_859603, _859599) = c_COMBK(_859601, _859597)), _859603 = _859601, _859599 = _859597], (6814 ^ _774244) ^ [_884650, _884652] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_884650)), hAPP(c_Option_Ooption_OSome(_884650), _884652)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22836 ^ _774244) ^ [_1168552, _1168554, _1168556] : [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), _1168552), _1168554))), -(hBOOL(hAPP(hAPP(_1168556, _1168552), _1168554))), 22843 ^ _774244 : [(22846 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1168556, 22841 ^ [_1168552, _1168554, _1168556]), 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)))), 22842 ^ [_1168552, _1168554, _1168556])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 22841 ^ [_1168552, _1168554, _1168556]), 22842 ^ [_1168552, _1168554, _1168556]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 22842 ^ [_1168552, _1168554, _1168556]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22856 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1168556, 22841 ^ [_1168552, _1168554, _1168556]), 22842 ^ [_1168552, _1168554, _1168556]))], (22844 ^ _774244) ^ [] : [-(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), 22841 ^ [_1168552, _1168554, _1168556]), 22842 ^ [_1168552, _1168554, _1168556]))))]]], (47427 ^ _774244) ^ [_1716146, _1716148, _1716150, _1716152, _1716154, _1716156] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1716146), tc_List_Olist(_1716146))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716146), tc_List_Olist(_1716146)), hAPP(hAPP(c_List_Olist_OCons(_1716146), _1716148), _1716150)), hAPP(hAPP(c_List_Olist_OCons(_1716146), _1716152), _1716154))), c_List_Olexord(_1716146, _1716156))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1716146, _1716146)), hAPP(hAPP(c_Product__Type_OPair(_1716146, _1716146), _1716148), _1716152)), _1716156))), 47434 ^ _774244 : [(47437 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1716146), tc_List_Olist(_1716146))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716146), tc_List_Olist(_1716146)), _1716150), _1716154)), c_List_Olexord(_1716146, _1716156))))], (47435 ^ _774244) ^ [] : [-(_1716148 = _1716152)]]], (29919 ^ _774244) ^ [_1307251, _1307253, _1307255, _1307257, _1307259] : [c_Finite__Set_Ofun__left__comm__idem(_1307251, _1307253, _1307255), -(hAPP(hAPP(_1307255, _1307257), hAPP(hAPP(_1307255, _1307257), _1307259)) = hAPP(hAPP(_1307255, _1307257), _1307259))], (44109 ^ _774244) ^ [_1634601, _1634603, _1634605, _1634607, _1634609] : [c_Relation_Osingle__valued(_1634601, _1634603, _1634605), c_Relation_Osingle__valued(_1634603, _1634607, _1634609), -(c_Relation_Osingle__valued(_1634601, _1634607, hAPP(hAPP(c_Relation_Orel__comp(_1634601, _1634603, _1634607), _1634605), _1634609)))], (33036 ^ _774244) ^ [_1372488, _1372490, _1372492] : [class_Orderings_Olinorder(_1372488), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372488), _1372490)), -(_1372490 = c_Orderings_Obot__class_Obot(tc_fun(_1372488, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372488), _1372492)), -(_1372492 = c_Orderings_Obot__class_Obot(tc_fun(_1372488, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1372488, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372488, tc_HOL_Obool)), _1372490), _1372492)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372488), c_Big__Operators_Olinorder__class_OMax(_1372488, _1372490)), c_Big__Operators_Olinorder__class_OMax(_1372488, _1372492)))], (45720 ^ _774244) ^ [_1672865, _1672867, _1672869, _1672871] : [c_Map_Omap__of(_1672865, _1672867, _1672869) = c_Map_Omap__of(_1672865, _1672867, _1672871), -(hAPP(c_Set_Oimage(tc_prod(_1672865, _1672867), _1672865, c_Product__Type_Ofst(_1672865, _1672867)), hAPP(c_List_Oset(tc_prod(_1672865, _1672867)), _1672869)) = hAPP(c_Set_Oimage(tc_prod(_1672865, _1672867), _1672865, c_Product__Type_Ofst(_1672865, _1672867)), hAPP(c_List_Oset(tc_prod(_1672865, _1672867)), _1672871)))], (29110 ^ _774244) ^ [_1292462, _1292464, _1292466] : [class_Groups_Ocomm__monoid__add(_1292462), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1292464, _1292462), _1292466), c_Orderings_Obot__class_Obot(tc_fun(_1292464, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1292462))], (41644 ^ _774244) ^ [_1574297, _1574299, _1574301, _1574303] : [-(hAPP(c_Relation_ORange(_1574297, _1574299), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574297, _1574299), tc_HOL_Obool)), _1574301), _1574303)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574299, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1574297, _1574299), _1574301)), hAPP(c_Relation_ORange(_1574297, _1574299), _1574303)))], (46898 ^ _774244) ^ [_1703447, _1703449] : [_1703449 = c_List_Olist_ONil(_1703447), -(hAPP(c_List_Oset(_1703447), _1703449) = c_Orderings_Obot__class_Obot(tc_fun(_1703447, tc_HOL_Obool)))], (45569 ^ _774244) ^ [_1669152, _1669154, _1669156, _1669158, _1669160] : [-(c_Map_Omap__comp(_1669152, _1669154, _1669156, _1669158, hAPP(c_COMBK(tc_Option_Ooption(_1669152), _1669156), c_Option_Ooption_ONone(_1669152)), _1669160) = c_Option_Ooption_ONone(_1669154))], (51179 ^ _774244) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (48706 ^ _774244) ^ [_1747564, _1747566, _1747568, _1747570] : [class_Groups_Osemigroup__add(_1747564), -(hAPP(c_List_Ofoldl(_1747564, _1747564, c_Groups_Oplus__class_Oplus(_1747564), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1747564), _1747566), _1747568)), _1747570) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1747564), _1747566), hAPP(c_List_Ofoldl(_1747564, _1747564, c_Groups_Oplus__class_Oplus(_1747564), _1747568), _1747570)))], (17865 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (26720 ^ _774244) ^ [_1242947, _1242949, _1242951, _1242953] : [class_Groups_Ocomm__monoid__add(_1242947), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1242947), _1242949), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1242951)), hAPP(c_Nat_OSuc, _1242953))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1242947), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1242947, tc_Nat_Onat), _1242949), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1242951), _1242953)))], (35000 ^ _774244) ^ [_1414767, _1414769] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1414767), _1414769)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1414767, tc_HOL_Obool)), hAPP(c_Set_OPow(_1414767), _1414769))))], (6840 ^ _774244) ^ [_885050] : [-(c_Option_Ois__none(_885050, c_Option_Ooption_ONone(_885050)))], (47339 ^ _774244) ^ [_1714344, _1714346, _1714348, _1714350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714344), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714346)), _1714348))), -(hAPP(hAPP(c_List_Onth(_1714346), hAPP(hAPP(c_List_Olist__update(_1714346, _1714348), _1714344), _1714350)), _1714344) = _1714350)], (17777 ^ _774244) ^ [_1078488] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078488)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078488)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1078488)))], (24305 ^ _774244) ^ [_1196391, _1196393, _1196395] : [class_Orderings_Olinorder(_1196391), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196391), _1196393), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196391), _1196393), _1196395)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196391), _1196393), _1196395))], (24149 ^ _774244) ^ [_1193624, _1193626, _1193628, _1193630, _1193632] : [class_Orderings_Olinorder(_1193624), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193624), _1193626), _1193628)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193624), _1193630), _1193632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193624), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1193624), _1193626), _1193630)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1193624), _1193628), _1193632))))], (30947 ^ _774244) ^ [_1329283, _1329285, _1329287, _1329289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329283, tc_HOL_Obool)), _1329285), _1329287)), hBOOL(hAPP(hAPP(c_member(_1329283), _1329289), _1329285)), -(hBOOL(hAPP(hAPP(c_member(_1329283), _1329289), _1329287)))], (20411 ^ _774244) ^ [_1123338, _1123340, _1123342] : [class_Rings_Odivision__ring(_1123338), -(_1123340 = c_Groups_Ozero__class_Ozero(_1123338)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123338), hAPP(c_Groups_Ouminus__class_Ouminus(_1123338), _1123342)), hAPP(c_Groups_Ouminus__class_Ouminus(_1123338), _1123340)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123338), _1123342), _1123340))], (49862 ^ _774244) ^ [_1772230, _1772232] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1772230), _1772232)) = c_List_Oupt(_1772230, _1772232))], (46591 ^ _774244) ^ [_1696713, _1696715, _1696717] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696713)), c_List_Osublist(_1696713, _1696715, _1696717)) = 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(_1696713)), _1696715)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1696717)))))], (8471 ^ _774244) ^ [_912325, _912327] : [hBOOL(hAPP(_912325, hAPP(c_Int_Onat, _912327))), 8474 ^ _774244 : [(8481 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _912327), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_912325, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (8475 ^ _774244) ^ [_912425] : [_912327 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _912425), -(hBOOL(hAPP(_912325, _912425)))]]], (20105 ^ _774244) ^ [_1118372, _1118374, _1118376] : [class_Fields_Olinordered__field(_1118372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118372), c_Groups_Ozero__class_Ozero(_1118372)), _1118374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118372), _1118376), c_Groups_Ozero__class_Ozero(_1118372))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118372), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118372), _1118374), _1118376)), c_Groups_Ozero__class_Ozero(_1118372))))], (45387 ^ _774244) ^ [_1664927, _1664929, _1664931] : [-(c_Smallcheck_Oorelse(_1664927, _1664929, _1664931) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1664927), _1664927, _1664931, c_Option_Ooption_OSome(_1664927)), _1664929))], (51373 ^ _774244) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (8352 ^ _774244) ^ [_910371, _910373, _910375, _910377] : [class_Orderings_Oord(_910371), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910371), _910373), _910375)), _910375 = _910377, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910371), _910373), _910377)))], (32588 ^ _774244) ^ [_1364904, _1364906, _1364908] : [class_Rings_Osemiring__1(_1364904), hBOOL(hAPP(hAPP(c_member(_1364904), _1364906), c_Nat_Osemiring__1__class_ONats(_1364904))), hBOOL(hAPP(hAPP(c_member(_1364904), _1364908), c_Nat_Osemiring__1__class_ONats(_1364904))), -(hBOOL(hAPP(hAPP(c_member(_1364904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364904), _1364906), _1364908)), c_Nat_Osemiring__1__class_ONats(_1364904))))], (13603 ^ _774244) ^ [_1001127, _1001129, _1001131, _1001133] : [class_Divides_Osemiring__div(_1001127), -(c_Divides_Odiv__class_Omod(_1001127, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001127), _1001129), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001127), _1001131), _1001133)), _1001131) = c_Divides_Odiv__class_Omod(_1001127, _1001129, _1001131))], (51215 ^ _774244) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (51201 ^ _774244) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (19051 ^ _774244) ^ [_1099321, _1099323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099321), _1099323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1099321)), c_Int_OBit1(_1099323))))], (15306 ^ _774244) ^ [_1031875, _1031877, _1031879] : [-(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, _1031875, _1031877)), _1031879), _1031877) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1031875), _1031879), _1031877))], (14496 ^ _774244) ^ [_1017065, _1017067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017065), _1017067)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1017065), _1017067) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16165 ^ _774244) ^ [_1049052, _1049054, _1049056] : [class_Int_Onumber__ring(_1049052), class_Int_Oring__char__0(_1049052), 16172 ^ _774244 : [(16179 ^ _774244) ^ [] : [_1049054 = _1049056, -(hAPP(c_Int_Onumber__class_Onumber__of(_1049052), _1049054) = hAPP(c_Int_Onumber__class_Onumber__of(_1049052), _1049056))], (16173 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1049052), _1049054) = hAPP(c_Int_Onumber__class_Onumber__of(_1049052), _1049056), -(_1049054 = _1049056)]]], (48694 ^ _774244) ^ [_1747314, _1747316, _1747318] : [class_Groups_Oab__semigroup__add(_1747314), -(c_List_Ofoldr(_1747314, _1747314, c_Groups_Oplus__class_Oplus(_1747314), _1747316, _1747318) = hAPP(c_List_Ofoldl(_1747314, _1747314, c_Groups_Oplus__class_Oplus(_1747314), _1747318), _1747316))], (35134 ^ _774244) ^ [_1417539, _1417541, _1417543, _1417545, _1417547] : [class_Groups_Ocomm__monoid__add(_1417539), class_Groups_Oordered__cancel__ab__semigroup__add(_1417539), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417541), _1417543)), -(_1417543 = c_Orderings_Obot__class_Obot(tc_fun(_1417541, tc_HOL_Obool))), 35152 ^ _774244 : [(35155 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417539), hAPP(_1417545, 35151 ^ [_1417539, _1417541, _1417543, _1417545, _1417547])), hAPP(_1417547, 35151 ^ [_1417539, _1417541, _1417543, _1417545, _1417547])))], (35153 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417541), 35151 ^ [_1417539, _1417541, _1417543, _1417545, _1417547]), _1417543)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417539), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417541, _1417539), _1417545), _1417543)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417541, _1417539), _1417547), _1417543))))], (50286 ^ _774244) ^ [_1781319, _1781321, _1781323, _1781325] : [-(hAPP(hAPP(c_List_Omap(_1781319, _1781321), _1781323), c_List_Oconcat(_1781319, _1781325)) = c_List_Oconcat(_1781321, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1781319), tc_List_Olist(_1781321)), hAPP(c_List_Omap(_1781319, _1781321), _1781323)), _1781325)))], (33232 ^ _774244) ^ [_1376290, _1376292] : [-(hBOOL(hAPP(hAPP(c_member(_1376290), _1376292), c_Orderings_Otop__class_Otop(tc_fun(_1376290, tc_HOL_Obool)))))], (34618 ^ _774244) ^ [_1405730, _1405732, _1405734, _1405736] : [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), _1405730), _1405732)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1405734), _1405736))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1405730), _1405736) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1405734), _1405732))], (38303 ^ _774244) ^ [_1488410, _1488412] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1488410), c_Orderings_Otop__class_Otop(tc_fun(_1488410, tc_HOL_Obool)))), c_Fun_Oinj__on(_1488410, _1488410, _1488412, c_Orderings_Otop__class_Otop(tc_fun(_1488410, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1488410, _1488410, _1488412), c_Orderings_Otop__class_Otop(tc_fun(_1488410, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1488410, tc_HOL_Obool)))], (6231 ^ _774244) ^ [_874235] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OBODY(_874235)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31453 ^ _774244) ^ [_1339193] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1339193)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (22618 ^ _774244) ^ [_1164652, _1164654] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1164652, _1164654), c_Divides_Odivmod__nat(_1164652, _1164654))))], (43419 ^ _774244) ^ [_1614905, _1614907, _1614909] : [-(hAPP(c_Relation_ORange(_1614905, _1614907), hAPP(c_Relation_Oconverse(_1614907, _1614905), _1614909)) = hAPP(c_Relation_ODomain(_1614907, _1614905), _1614909))], (24803 ^ _774244) ^ [_1207396] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1207396), _1207396)))], (11116 ^ _774244) ^ [_957059, _957061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _957061)), _957059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957059), _957061))], (5792 ^ _774244) ^ [_866628, _866630, _866632, _866634] : [c_Com_Ocom_OSemi(_866628, _866630) = c_Com_Ocom_OSemi(_866632, _866634), 5795 ^ _774244 : [(5798 ^ _774244) ^ [] : [-(_866630 = _866634)], (5796 ^ _774244) ^ [] : [-(_866628 = _866632)]]], (16771 ^ _774244) ^ [_1060673, _1060675, _1060677] : [class_Groups_Oordered__ab__group__add__abs(_1060673), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060673), hAPP(c_Groups_Oabs__class_Oabs(_1060673), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060673), _1060675), _1060677))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060673), hAPP(c_Groups_Oabs__class_Oabs(_1060673), _1060675)), hAPP(c_Groups_Oabs__class_Oabs(_1060673), _1060677)))))], (32072 ^ _774244) ^ [_1354779, _1354781] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1354779), 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)))), _1354781))), 32075 ^ _774244 : [(32078 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354779), _1354781))], (32076 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354781), _1354779)))]]], (33684 ^ _774244) ^ [_1385587, _1385589, _1385591] : [class_Orderings_Olinorder(_1385587), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385587), _1385589)), -(hBOOL(hAPP(hAPP(c_member(_1385587), _1385591), _1385589))), -(_1385589 = c_Orderings_Obot__class_Obot(tc_fun(_1385587, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1385587, c_Orderings_Oord__class_Omin(_1385587), hAPP(hAPP(c_Set_Oinsert(_1385587), _1385591), _1385589)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1385587), _1385591), c_Big__Operators_Olattice_OInf__fin(_1385587, c_Orderings_Oord__class_Omin(_1385587), _1385589)))], (29804 ^ _774244) ^ [_1305157, _1305159] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1305157, _1305159)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1305157, _1305159), tc_HOL_Obool)))), 29807 ^ _774244 : [(29810 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305159), c_Orderings_Otop__class_Otop(tc_fun(_1305159, tc_HOL_Obool)))))], (29808 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305157), c_Orderings_Otop__class_Otop(tc_fun(_1305157, tc_HOL_Obool)))))]]], (8816 ^ _774244) ^ [_918309, _918311, _918313] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _918309), _918311)), _918313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _918309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _918311), _918313)))], (11058 ^ _774244) ^ [_956162, _956164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _956162)), _956164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956162), _956164)))], (7481 ^ _774244) ^ [_895613, _895615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _895613), _895615)), _895615))], (30909 ^ _774244) ^ [_1328574, _1328576, _1328578, _1328580] : [hBOOL(hAPP(hAPP(c_member(_1328574), _1328576), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328574, tc_HOL_Obool)), _1328578), _1328580))), -(hBOOL(hAPP(hAPP(c_member(_1328574), _1328576), _1328578))), -(hBOOL(hAPP(hAPP(c_member(_1328574), _1328576), _1328580)))], (6906 ^ _774244) ^ [_885990] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _885990) = _885990)], (15140 ^ _774244) ^ [_1028781, _1028783, _1028785, _1028787] : [class_Divides_Oring__div(_1028781), -(c_Divides_Odiv__class_Omod(_1028781, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1028781), _1028783), _1028785), _1028787) = c_Divides_Odiv__class_Omod(_1028781, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1028781), c_Divides_Odiv__class_Omod(_1028781, _1028783, _1028787)), c_Divides_Odiv__class_Omod(_1028781, _1028785, _1028787)), _1028787))], (26943 ^ _774244) ^ [_1247753, _1247755] : [26945 ^ _774244 : [(26948 ^ _774244) ^ [] : [hBOOL(hAPP(_1247755, 26944 ^ [_1247753, _1247755]))], (26946 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26944 ^ [_1247753, _1247755]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1247753))))]], 26949 ^ _774244 : [(26950 ^ _774244) ^ [_1247908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1247908), _1247753)), -(hBOOL(hAPP(_1247755, _1247908)))]]], (14097 ^ _774244) ^ [_1010171, _1010173, _1010175] : [-(hBOOL(hAPP(_1010171, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1010173), _1010175)))), 14098 ^ _774244 : [(14105 ^ _774244) ^ [_1010339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010175), _1010339)), _1010173)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1010173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010175), hAPP(c_Nat_OSuc, _1010339)))), hBOOL(hAPP(_1010171, _1010339))], (14099 ^ _774244) ^ [] : [_1010175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1010171, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (13880 ^ _774244) ^ [_1005938, _1005940, _1005942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005938)), 13883 ^ _774244 : [(13884 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1005940, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1005942), _1005938)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005942, _1005938))), 13887 ^ _774244 : [(13888 ^ _774244) ^ [_1006139, _1006141] : [-(hBOOL(hAPP(hAPP(_1005940, _1006141), _1006139))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006139)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006139), _1005938)), _1005942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005938), _1006141)), _1006139)]]], (13902 ^ _774244) ^ [] : [13905 ^ _774244 : [(13908 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 13904 ^ [_1005938, _1005940, _1005942]), _1005938)))], (13910 ^ _774244) ^ [] : [-(_1005942 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005938), 13903 ^ [_1005938, _1005940, _1005942])), 13904 ^ [_1005938, _1005940, _1005942]))], (13912 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1005940, 13903 ^ [_1005938, _1005940, _1005942]), 13904 ^ [_1005938, _1005940, _1005942]))], (13906 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13904 ^ [_1005938, _1005940, _1005942])))]], -(hBOOL(hAPP(hAPP(_1005940, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1005942), _1005938)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005942, _1005938))))]]], (10171 ^ _774244) ^ [_941820, _941822, _941824, _941826, _941828] : [class_Orderings_Oord(_941820), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941822, _941820)), _941824), _941826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941820), hAPP(_941824, _941828)), hAPP(_941826, _941828))))], (7281 ^ _774244) ^ [_892421, _892423, _892425, _892427] : [class_Groups_Oordered__cancel__ab__semigroup__add(_892421), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892421), _892423), _892425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892421), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892421), _892423), _892427)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892421), _892425), _892427))))], (33014 ^ _774244) ^ [_1372139, _1372141, _1372143] : [class_Orderings_Olinorder(_1372139), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372139), _1372141)), -(_1372141 = c_Orderings_Obot__class_Obot(tc_fun(_1372139, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372139), _1372143)), -(_1372143 = c_Orderings_Obot__class_Obot(tc_fun(_1372139, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1372139, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372139, tc_HOL_Obool)), _1372141), _1372143)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1372139), c_Big__Operators_Olinorder__class_OMin(_1372139, _1372141)), c_Big__Operators_Olinorder__class_OMin(_1372139, _1372143)))], (31885 ^ _774244) ^ [_1350578, _1350580, _1350582, _1350584] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1350578), _1350580)), hBOOL(hAPP(hAPP(c_member(_1350578), _1350582), _1350580)), hBOOL(hAPP(hAPP(c_member(_1350578), _1350584), _1350580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1350578), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350578, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350578, tc_HOL_Obool)), _1350580), hAPP(hAPP(c_Set_Oinsert(_1350578), _1350582), c_Orderings_Obot__class_Obot(tc_fun(_1350578, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1350578), _1350584), c_Orderings_Obot__class_Obot(tc_fun(_1350578, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1350578), _1350580))))], (8676 ^ _774244) ^ [_915862, _915864, _915866] : [class_Groups_Ogroup__add(_915862), 8679 ^ _774244 : [(8686 ^ _774244) ^ [] : [_915866 = hAPP(c_Groups_Ouminus__class_Ouminus(_915862), _915864), -(_915864 = hAPP(c_Groups_Ouminus__class_Ouminus(_915862), _915866))], (8680 ^ _774244) ^ [] : [_915864 = hAPP(c_Groups_Ouminus__class_Ouminus(_915862), _915866), -(_915866 = hAPP(c_Groups_Ouminus__class_Ouminus(_915862), _915864))]]], (11192 ^ _774244) ^ [_958218, _958220, _958222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _958218), _958220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _958218), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958220), _958222))))], (17541 ^ _774244) ^ [_1074715] : [class_Power_Opower(_1074715), -(c_Power_Opower__class_Opower(_1074715) = c_Power_Opower_Opower(_1074715, c_Groups_Oone__class_Oone(_1074715), c_Groups_Otimes__class_Otimes(_1074715)))], (43982 ^ _774244) ^ [_1631595, _1631597, _1631599, _1631601, _1631603, _1631605, _1631607] : [43984 ^ _774244 : [(43987 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1631603, 43983 ^ [_1631595, _1631597, _1631599, _1631601, _1631603, _1631605, _1631607]), _1631605), _1631607))], (43985 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1631595), 43983 ^ [_1631595, _1631597, _1631599, _1631601, _1631603, _1631605, _1631607]), _1631601)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631595, tc_fun(_1631597, tc_fun(_1631599, tc_HOL_Obool))), _1631601), _1631603), _1631605), _1631607)))], (23917 ^ _774244) ^ [_1189286, _1189288] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1189286), hAPP(c_Nat_OSuc, _1189288)) = 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)), _1189288)), _1189286))], (50354 ^ _774244) ^ [_1782761, _1782763] : [-(hAPP(c_List_Oset(_1782761), hAPP(c_List_Orev(_1782761), _1782763)) = hAPP(c_List_Oset(_1782761), _1782763))], (18153 ^ _774244) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41603 ^ _774244) ^ [_1573424, _1573426, _1573428] : [c_Wellfounded_Owf(_1573424, _1573426), -(c_Wellfounded_Owf(tc_List_Olist(_1573424), hAPP(c_List_Olexn(_1573424, _1573426), _1573428)))], (6716 ^ _774244) ^ [_882435, _882437, _882439, _882441, _882443, _882445] : [-(c_Com_Ocom_OLocal(_882435, _882437, _882439) = c_Com_Ocom_OLocal(_882441, _882443, _882445)), _882435 = _882441, _882437 = _882443, _882439 = _882445], (38936 ^ _774244) ^ [_1502604, _1502606, _1502608, _1502610] : [hBOOL(hAPP(hAPP(c_member(_1502604), _1502606), _1502608)), -(hAPP(c_Set_Ovimage(_1502610, _1502604, hAPP(c_COMBK(_1502604, _1502610), _1502606)), _1502608) = c_Orderings_Otop__class_Otop(tc_fun(_1502610, tc_HOL_Obool)))], (19245 ^ _774244) ^ [_1102746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102746), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1102746)), c_Int_OMin)))], (50362 ^ _774244) ^ [_1782982, _1782984, _1782986] : [-(hAPP(c_List_Orev(_1782982), hAPP(c_List_Ofilter(_1782982, _1782984), _1782986)) = hAPP(c_List_Ofilter(_1782982, _1782984), hAPP(c_List_Orev(_1782982), _1782986)))], (14746 ^ _774244) ^ [_1021540, _1021542, _1021544] : [-(hBOOL(hAPP(_1021540, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021542), _1021544)))), 14749 ^ _774244 : [(14752 ^ _774244) ^ [] : [hBOOL(hAPP(_1021540, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14750 ^ _774244) ^ [] : [-(_1021544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14753 ^ _774244 : [(14758 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14756 ^ [_1021540, _1021542, _1021544]), _1021544)))], (14760 ^ _774244) ^ [] : [-(_1021542 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021544), 14755 ^ [_1021540, _1021542, _1021544])), 14756 ^ [_1021540, _1021542, _1021544]))], (14762 ^ _774244) ^ [] : [hBOOL(hAPP(_1021540, 14755 ^ [_1021540, _1021542, _1021544]))], (14754 ^ _774244) ^ [] : [_1021544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (51241 ^ _774244) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (39772 ^ _774244) ^ [_1523182, _1523184, _1523186, _1523188, _1523190, _1523192] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1523182, _1523184), hAPP(hAPP(c_Set_Oinsert(_1523182), _1523186), _1523188)), hAPP(c_COMBK(tc_fun(_1523184, tc_HOL_Obool), _1523182), hAPP(hAPP(c_Set_Oinsert(_1523184), _1523190), _1523192))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1523182, _1523184)), hAPP(hAPP(c_Product__Type_OPair(_1523182, _1523184), _1523186), _1523190)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1523182, _1523184), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1523182, _1523184), _1523188), hAPP(c_COMBK(tc_fun(_1523184, tc_HOL_Obool), _1523182), hAPP(hAPP(c_Set_Oinsert(_1523184), _1523190), _1523192)))), hAPP(hAPP(c_Product__Type_OSigma(_1523182, _1523184), hAPP(hAPP(c_Set_Oinsert(_1523182), _1523186), _1523188)), hAPP(c_COMBK(tc_fun(_1523184, tc_HOL_Obool), _1523182), _1523192)))))], (16887 ^ _774244) ^ [_1062856, _1062858, _1062860] : [class_Rings_Olinordered__semidom(_1062856), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062856), c_Groups_Oone__class_Oone(_1062856)), _1062858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062856), c_Groups_Oone__class_Oone(_1062856)), hAPP(hAPP(c_Power_Opower__class_Opower(_1062856), _1062858), _1062860))))], (26017 ^ _774244) ^ [_1228742, _1228744, _1228746, _1228748] : [class_Orderings_Oorder(_1228742), c_Orderings_Oorder_Omono(tc_Nat_Onat, _1228742, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228744), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228746), _1228748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228742), hAPP(_1228744, _1228746)), hAPP(_1228744, _1228748))))], (30593 ^ _774244) ^ [_1320366, _1320368] : [-(hBOOL(hAPP(hAPP(c_member(_1320366), _1320368), c_Orderings_Otop__class_Otop(tc_fun(_1320366, tc_HOL_Obool)))))], (14211 ^ _774244) ^ [_1012397, _1012399] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1012397, _1012399)) = _1012399, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1012397), _1012399) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32156 ^ _774244) ^ [_1356368, _1356370, _1356372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1356368)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1356370), _1356372)), 32163 ^ _774244 : [(32164 ^ _774244) ^ [_1356558] : [32166 ^ _774244 : [(32172 ^ _774244) ^ [] : [-(_1356558 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32168 ^ [_1356368, _1356370, _1356372, _1356558]), 32165 ^ [_1356368, _1356370, _1356372, _1356558]))], (32170 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32168 ^ [_1356368, _1356370, _1356372, _1356558]), _1356372)))], (32167 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32165 ^ [_1356368, _1356370, _1356372, _1356558]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1356368))))]], -(_1356558 = _1356370), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1356558), _1356368) = _1356370]]], (25987 ^ _774244) ^ [_1228235, _1228237, _1228239] : [class_Rings_Ocomm__semiring__1(_1228235), 25992 ^ _774244 : [(25995 ^ _774244) ^ [] : [_1228239 = c_Groups_Oone__class_Oone(_1228235)], (25993 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1228237))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228235), _1228239), hAPP(hAPP(c_Power_Opower__class_Opower(_1228235), _1228239), _1228237))))], (40789 ^ _774244) ^ [_1547045, _1547047, _1547049, _1547051, _1547053, _1547055] : [class_Groups_Ocomm__monoid__add(_1547045), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547047), _1547049)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1547047, _1547045), hAPP(hAPP(c_COMBS(_1547047, _1547045, _1547045), hAPP(hAPP(c_COMBS(_1547047, _1547045, tc_fun(_1547045, _1547045)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1547045, tc_fun(_1547045, _1547045)), _1547047), c_If(_1547045)), _1547051)), _1547053)), _1547055)), _1547049) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1547045), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1547047, _1547045), _1547053), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1547047, tc_HOL_Obool)), _1547049), hAPP(c_Set_OCollect(_1547047), _1547051)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1547047, _1547045), _1547055), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1547047, tc_HOL_Obool)), _1547049), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1547047, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1547047), _1547051))))))], (9482 ^ _774244) ^ [_930199, _930201, _930203] : [class_Rings_Olinordered__semiring__strict(_930199), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930199), c_Groups_Ozero__class_Ozero(_930199)), _930201)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930199), _930203), c_Groups_Ozero__class_Ozero(_930199))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930199), _930203), _930201)), c_Groups_Ozero__class_Ozero(_930199))))], (48600 ^ _774244) ^ [_1745366, _1745368, _1745370] : [-(hAPP(c_List_Otl(_1745366), hAPP(hAPP(c_List_Olist_OCons(_1745366), _1745368), _1745370)) = _1745370)], (14766 ^ _774244) ^ [_1021980, _1021982, _1021984] : [hBOOL(hAPP(_1021980, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1021982, _1021984))), 14769 ^ _774244 : [(14776 ^ _774244) ^ [] : [-(_1021984 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14779 ^ _774244 : [(14780 ^ _774244) ^ [_1022228, _1022230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1022228), _1021984)), _1021982 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021984), _1022230)), _1022228), -(hBOOL(hAPP(_1021980, _1022228)))]]], (14770 ^ _774244) ^ [] : [_1021984 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1021980, _1021982)))]]], (17073 ^ _774244) ^ [_1066124] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066124) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066124)))], (45315 ^ _774244) ^ [_1663016, _1663018, _1663020] : [-(c_Map_Omap__add(_1663016, _1663018, _1663020, hAPP(c_COMBK(tc_Option_Ooption(_1663018), _1663016), c_Option_Ooption_ONone(_1663018))) = _1663020)], (11443 ^ _774244) ^ [_962704, _962706, _962708, _962710] : [class_Groups_Oordered__comm__monoid__add(_962704), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962704), c_Groups_Ozero__class_Ozero(_962704)), _962706)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962704), _962708), _962710)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962704), _962708), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962704), _962706), _962710))))], (16231 ^ _774244) ^ [_1050133, _1050135, _1050137] : [class_Rings_Olinordered__idom(_1050133), -(hAPP(c_Groups_Oabs__class_Oabs(_1050133), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050133), _1050135), _1050137)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050133), hAPP(c_Groups_Oabs__class_Oabs(_1050133), _1050135)), hAPP(c_Groups_Oabs__class_Oabs(_1050133), _1050137)))], (25847 ^ _774244) ^ [_1225568, _1225570, _1225572, _1225574] : [class_Rings_Ocomm__ring(_1225568), class_Rings_Odvd(_1225568), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225568), _1225570), _1225572)), 25858 ^ _774244 : [(25865 ^ _774244) ^ [_1225994, _1225996] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225568), _1225570), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225568), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1225568), _1225996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225568), _1225994), _1225572))), _1225574))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225568), _1225570), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225568), _1225996), _1225574))))], (25859 ^ _774244) ^ [_1225821, _1225823] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225568), _1225570), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225568), _1225823), _1225574))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225568), _1225570), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225568), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1225568), _1225823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225568), _1225821), _1225572))), _1225574))))]]], (5731 ^ _774244) ^ [_865582, _865584, _865586, _865588] : [class_Rings_Osemiring__1(_865582), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_865582, _865584, hAPP(c_Nat_OSuc, _865586), _865588) = c_Nat_Osemiring__1__class_Oof__nat__aux(_865582, _865584, _865586, hAPP(_865584, _865588)))], (8126 ^ _774244) ^ [_907287] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _907287) = _907287)], (18183 ^ _774244) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (26399 ^ _774244) ^ [_1235510, _1235512, _1235514] : [-(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), _1235510)), 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))), _1235512))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1235514))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1235514)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1235510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1235510), 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), _1235514), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1235512)))))], (39839 ^ _774244) ^ [_1525525, _1525527, _1525529, _1525531, _1525533, _1525535] : [class_Groups_Ocomm__monoid__mult(_1525525), hBOOL(hAPP(c_Finite__Set_Ofinite(_1525527), _1525529)), 39849 ^ _774244 : [(39852 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1525531), hAPP(_1525533, 39848 ^ [_1525525, _1525527, _1525529, _1525531, _1525533, _1525535])))], (39850 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525527), 39848 ^ [_1525525, _1525527, _1525529, _1525531, _1525533, _1525535]), _1525529)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1525527, _1525525), hAPP(hAPP(c_COMBS(_1525527, tc_fun(_1525531, tc_HOL_Obool), _1525525), hAPP(hAPP(c_COMBB(tc_fun(_1525531, _1525525), tc_fun(tc_fun(_1525531, tc_HOL_Obool), _1525525), _1525527), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1525531, _1525525)), _1525535)), _1525533)), _1525529) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1525527, _1525531), _1525525), hAPP(c_Product__Type_Oprod_Oprod__case(_1525527, _1525531, _1525525), _1525535)), hAPP(hAPP(c_Product__Type_OSigma(_1525527, _1525531), _1525529), _1525533)))], (24463 ^ _774244) ^ [_1199787, _1199789, _1199791, _1199793, _1199795] : [-(hAPP(c_Product__Type_Osnd(_1199787, _1199789), hAPP(c_Product__Type_Oapfst(_1199791, _1199787, _1199789, _1199793), _1199795)) = hAPP(c_Product__Type_Osnd(_1199791, _1199789), _1199795))], (18535 ^ _774244) ^ [_1090613] : [c_Int_OMin = _1090613, -(c_Int_OMin = c_Int_OBit1(_1090613))], (44178 ^ _774244) ^ [_1636203, _1636205, _1636207, _1636209, _1636211] : [c_Relation_Osingle__valued(_1636203, _1636205, hAPP(c_Relation_Oconverse(_1636205, _1636203), _1636207)), -(hAPP(c_Relation_OImage(_1636205, _1636203, _1636207), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1636205, tc_HOL_Obool)), _1636209), _1636211)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1636203, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1636205, _1636203, _1636207), _1636209)), hAPP(c_Relation_OImage(_1636205, _1636203, _1636207), _1636211)))], (39944 ^ _774244) ^ [_1528625, _1528627, _1528629, _1528631, _1528633, _1528635, _1528637, _1528639, _1528641, _1528643] : [hAPP(c_Set_Oimage(_1528625, _1528627, _1528629), _1528631) = _1528633, hAPP(c_Set_Oimage(_1528635, _1528637, _1528639), _1528641) = _1528643, -(hAPP(c_Set_Oimage(tc_prod(_1528625, _1528635), tc_prod(_1528627, _1528637), c_Product__Type_Omap__pair(_1528625, _1528627, _1528635, _1528637, _1528629, _1528639)), hAPP(hAPP(c_Product__Type_OSigma(_1528625, _1528635), _1528631), hAPP(c_COMBK(tc_fun(_1528635, tc_HOL_Obool), _1528625), _1528641))) = hAPP(hAPP(c_Product__Type_OSigma(_1528627, _1528637), _1528633), hAPP(c_COMBK(tc_fun(_1528637, tc_HOL_Obool), _1528627), _1528643)))], (51427 ^ _774244) ^ [_1801198, _1801200, _1801202, _1801204, _1801206, _1801208] : [-(hAPP(hAPP(hAPP(c_COMBB(_1801198, _1801200, _1801202), _1801204), _1801206), _1801208) = hAPP(_1801204, hAPP(_1801206, _1801208)))], (25951 ^ _774244) ^ [_1227618, _1227620] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227618), _1227620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1227618), _1227620)))], (2860 ^ _774244) ^ [_817750, _817752, _817754, _817756, _817758, _817760, _817762, _817764, _817766, _817768, _817770, _817772, _817774, _817776] : [-(c_New__Random__Sequence_Oneg__decr__bind(_817776, _817772, _817768, _817764, _817760, _817756, _817752) = c_New__Random__Sequence_Oneg__decr__bind(_817774, _817770, _817766, _817762, _817758, _817754, _817750)), _817776 = _817774, _817772 = _817770, _817768 = _817766, _817764 = _817762, _817760 = _817758, _817756 = _817754, _817752 = _817750], (15024 ^ _774244) ^ [_1026779, _1026781, _1026783, _1026785, _1026787] : [class_Groups_Oordered__ab__group__add(_1026779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1026779), _1026781), _1026783) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1026779), _1026785), _1026787), 15031 ^ _774244 : [(15038 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026779), _1026785), _1026787)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026779), _1026781), _1026783)))], (15032 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026779), _1026781), _1026783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1026779), _1026785), _1026787)))]]], (28531 ^ _774244) ^ [_1279135, _1279137] : [class_Groups_Oordered__ab__group__add(_1279135), -(hAPP(c_Set_Oimage(_1279135, _1279135, c_Groups_Ouminus__class_Ouminus(_1279135)), hAPP(c_SetInterval_Oord__class_OatMost(_1279135), _1279137)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1279135), hAPP(c_Groups_Ouminus__class_Ouminus(_1279135), _1279137)))], (28216 ^ _774244) ^ [_1272982, _1272984, _1272986] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272982, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272982, tc_HOL_Obool)), _1272984), _1272986)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272982, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272982, tc_HOL_Obool)), _1272984)), _1272986))], (3036 ^ _774244) ^ [_820698, _820700, _820702, _820704, _820706, _820708] : [-(c_Random__Sequence_Oempty(_820708, _820704, _820700) = c_Random__Sequence_Oempty(_820706, _820702, _820698)), _820708 = _820706, _820704 = _820702, _820700 = _820698], (43055 ^ _774244) ^ [_1606499, _1606501, _1606503, _1606505, _1606507] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606499, _1606499)), hAPP(hAPP(c_Product__Type_OPair(_1606499, _1606499), _1606501), _1606503)), _1606505)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1606499, _1606499)), hAPP(hAPP(c_Product__Type_OPair(_1606499, _1606499), _1606503), _1606507)), c_Transitive__Closure_Ortrancl(_1606499, _1606505))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606499, _1606499)), hAPP(hAPP(c_Product__Type_OPair(_1606499, _1606499), _1606501), _1606507)), c_Transitive__Closure_Ortrancl(_1606499, _1606505))))], (26301 ^ _774244) ^ [_1233753, _1233755] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1233753), _1233755)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233753), _1233755)))], (33892 ^ _774244) ^ [_1389855, _1389857, _1389859, _1389861, _1389863] : [hAPP(_1389855, _1389857) = hAPP(c_Option_Ooption_OSome(_1389859), _1389861), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1389863, tc_Option_Ooption(_1389859)), _1389855), _1389857), hAPP(c_Option_Ooption_OSome(_1389859), _1389861)) = _1389855)], (38908 ^ _774244) ^ [_1501976, _1501978, _1501980, _1501982, _1501984] : [hAPP(c_Set_Oimage(_1501976, _1501978, _1501980), c_Orderings_Otop__class_Otop(tc_fun(_1501976, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1501978, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501976, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1501976, _1501978, _1501980), _1501982)), _1501984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501978, tc_HOL_Obool)), _1501982), hAPP(c_Set_Oimage(_1501976, _1501978, _1501980), _1501984))))], (38722 ^ _774244) ^ [_1497560, _1497562, _1497564, _1497566] : [c_Fun_Oinj__on(_1497560, _1497562, _1497564, _1497566), -(hAPP(c_Set_Oimage(_1497562, _1497560, c_Fun_Othe__inv__into(_1497560, _1497562, _1497566, _1497564)), hAPP(c_Set_Oimage(_1497560, _1497562, _1497564), _1497566)) = _1497566)], (43427 ^ _774244) ^ [_1615194, _1615196, _1615198, _1615200] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1615194, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615196, tc_fun(_1615194, tc_HOL_Obool)), _1615198), _1615200)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615196, tc_fun(_1615194, tc_HOL_Obool)), _1615198), hAPP(hAPP(c_COMBB(tc_fun(_1615194, tc_HOL_Obool), tc_fun(_1615194, tc_HOL_Obool), _1615196), c_Groups_Ouminus__class_Ouminus(tc_fun(_1615194, tc_HOL_Obool))), _1615200)))], (48480 ^ _774244) ^ [_1743028, _1743030, _1743032, _1743034] : [-(hAPP(c_List_Orotate1(_1743028), c_List_Olist_ONil(_1743028)) = c_List_Olist_ONil(_1743028))], (8240 ^ _774244) ^ [_908720, _908722, _908724] : [class_Orderings_Olinorder(_908720), -(_908722 = _908724), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908720), _908722), _908724))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908720), _908724), _908722)))], (9893 ^ _774244) ^ [_937348, _937350] : [class_Groups_Osgn__if(_937348), 9896 ^ _774244 : [(9903 ^ _774244) ^ [] : [-(_937350 = c_Groups_Ozero__class_Ozero(_937348)), 9906 ^ _774244 : [(9913 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937348), c_Groups_Ozero__class_Ozero(_937348)), _937350))), -(c_Groups_Osgn__class_Osgn(_937348, _937350) = hAPP(c_Groups_Ouminus__class_Ouminus(_937348), c_Groups_Oone__class_Oone(_937348)))], (9907 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937348), c_Groups_Ozero__class_Ozero(_937348)), _937350)), -(c_Groups_Osgn__class_Osgn(_937348, _937350) = c_Groups_Oone__class_Oone(_937348))]]], (9897 ^ _774244) ^ [] : [_937350 = c_Groups_Ozero__class_Ozero(_937348), -(c_Groups_Osgn__class_Osgn(_937348, _937350) = c_Groups_Ozero__class_Ozero(_937348))]]], (35442 ^ _774244) ^ [_1425484, _1425486, _1425488, _1425490, _1425492, _1425494] : [c_Finite__Set_Ofolding(_1425484, _1425486, _1425488, _1425490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425484), _1425492)), -(hBOOL(hAPP(hAPP(c_member(_1425484), _1425494), _1425492))), -(hAPP(_1425490, hAPP(hAPP(c_Set_Oinsert(_1425484), _1425494), _1425492)) = hAPP(c_Fun_Ocomp(_1425486, _1425486, _1425486, hAPP(_1425490, _1425492)), hAPP(_1425488, _1425494)))], (9710 ^ _774244) ^ [_934252] : [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)), _934252)), _934252) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (18109 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (48640 ^ _774244) ^ [_1746167] : [-(hAPP(c_List_Otl(_1746167), c_List_Olist_ONil(_1746167)) = c_List_Olist_ONil(_1746167))], (5186 ^ _774244) ^ [_854437, _854439, _854441, _854443, _854445, _854447] : [-(c_List_Oremove1(_854447, _854443, _854439) = c_List_Oremove1(_854445, _854441, _854437)), _854447 = _854445, _854443 = _854441, _854439 = _854437], (51005 ^ _774244) ^ [_1797130, _1797132] : [class_Orderings_Oord(_1797130), -(class_Orderings_Oord(tc_fun(_1797132, _1797130)))], (36571 ^ _774244) ^ [_1450615, _1450617] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450615, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450615, tc_HOL_Obool)), _1450617)), _1450617) = c_Orderings_Obot__class_Obot(tc_fun(_1450615, tc_HOL_Obool)))], (22656 ^ _774244) ^ [_1165457, _1165459] : [-(c_Divides_Opdivmod(_1165457, _1165459) = 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), _1165457)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1165459))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1165457), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1165459))))], (44731 ^ _774244) ^ [_1649381] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649381, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1649381, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1649381, tc_HOL_Obool)))], (5864 ^ _774244) ^ [_867995] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OBODY(_867995)], (17789 ^ _774244) ^ [_1078639, _1078641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1078639), _1078641)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1078639), _1078641) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (2992 ^ _774244) ^ [_820014, _820016, _820018, _820020, _820022, _820024, _820026, _820028] : [-(c_Random__Sequence_ORandom(_820028, _820024, _820020, _820016) = c_Random__Sequence_ORandom(_820026, _820022, _820018, _820014)), _820028 = _820026, _820024 = _820022, _820020 = _820018, _820016 = _820014], (5032 ^ _774244) ^ [_852012, _852014, _852016, _852018, _852020, _852022, _852024, _852026] : [-(c_List_Olist_Olist__case(_852026, _852022, _852018, _852014) = c_List_Olist_Olist__case(_852024, _852020, _852016, _852012)), _852026 = _852024, _852022 = _852020, _852018 = _852016, _852014 = _852012], (29670 ^ _774244) ^ [_1302573] : [-(c_Option_Oset(_1302573, c_Option_Ooption_ONone(_1302573)) = c_Orderings_Obot__class_Obot(tc_fun(_1302573, tc_HOL_Obool)))], (4346 ^ _774244) ^ [_841493, _841495, _841497, _841499, _841501, _841503, _841505, _841507] : [-(c_Map_Orestrict__map(_841507, _841503, _841499, _841495) = c_Map_Orestrict__map(_841505, _841501, _841497, _841493)), _841507 = _841505, _841503 = _841501, _841499 = _841497, _841495 = _841493], (46860 ^ _774244) ^ [_1702804, _1702806] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702804)), _1702806) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1702806 = c_List_Olist_ONil(_1702804))], (24857 ^ _774244) ^ [_1208309, _1208311, _1208313] : [class_Rings_Olinordered__idom(_1208309), hAPP(c_Groups_Oabs__class_Oabs(_1208309), _1208311) = hAPP(c_Groups_Oabs__class_Oabs(_1208309), _1208313), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208309), _1208311), _1208313)))], (28777 ^ _774244) ^ [_1285367, _1285369] : [class_Lattices_Obounded__lattice__top(_1285367), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285367), c_Orderings_Otop__class_Otop(_1285367)), _1285369) = c_Orderings_Otop__class_Otop(_1285367))], (39346 ^ _774244) ^ [_1512208, _1512210, _1512212, _1512214, _1512216] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1512208, _1512210, _1512212, _1512214, c_Orderings_Obot__class_Obot(tc_fun(_1512208, tc_HOL_Obool))), _1512216)), -(_1512216 = _1512214)], (27860 ^ _774244) ^ [_1266233, _1266235, _1266237] : [class_Lattices_Osemilattice__sup(_1266233), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266233), _1266235), _1266237) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266233), _1266237), _1266235))], (51343 ^ _774244) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (40649 ^ _774244) ^ [_1542444, _1542446] : [-(hAPP(c_Set_OCollect(_1542444), hAPP(hAPP(c_COMBC(_1542444, tc_fun(_1542444, tc_HOL_Obool), tc_HOL_Obool), c_member(_1542444)), _1542446)) = _1542446)], (48019 ^ _774244) ^ [_1730346, _1730348, _1730350, _1730352] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730346) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1730348), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730346)), hAPP(hAPP(c_List_Olist_OCons(_1730348), _1730350), _1730352)) = c_List_Olist_ONil(_1730348))], (6694 ^ _774244) ^ [_882043, _882045, _882047, _882049, _882051] : [-(hAPP(c_Option_Ooption_Ooption__case(_882043, _882045, _882047, _882049), hAPP(c_Option_Ooption_OSome(_882045), _882051)) = hAPP(_882049, _882051))], (50174 ^ _774244) ^ [_1778897, _1778899] : [-(c_Fun_Oinj__on(tc_List_Olist(_1778897), tc_List_Olist(_1778897), c_List_Orev(_1778897), _1778899))], (7399 ^ _774244) ^ [_894336, _894338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894336), _894338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _894336)), hAPP(c_Nat_OSuc, _894338))))], (23505 ^ _774244) ^ [_1181531, _1181533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181531), 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)), _1181533)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181531), _1181533) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1181531, _1181533)))], (36439 ^ _774244) ^ [_1447290, _1447292, _1447294, _1447296, _1447298] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447290, tc_HOL_Obool)), _1447292), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447294, tc_fun(_1447290, tc_HOL_Obool)), _1447296), _1447298)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447294, tc_fun(_1447290, tc_HOL_Obool)), _1447296), hAPP(hAPP(c_COMBB(tc_fun(_1447290, tc_HOL_Obool), tc_fun(_1447290, tc_HOL_Obool), _1447294), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447290, tc_HOL_Obool)), _1447292)), _1447298)))], (23531 ^ _774244) ^ [_1181974, _1181976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181976), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181974), _1181976) = 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), _1181974), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181976)))))], (31557 ^ _774244) ^ [_1342450, _1342452, _1342454, _1342456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1342450, tc_fun(_1342452, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1342450, tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_fun(_1342452, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1342452, tc_fun(tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_fun(_1342452, tc_HOL_Obool)), _1342450), c_COMBC(_1342452, tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1342452, tc_prod(_1342450, _1342452)), tc_fun(_1342452, tc_fun(tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_HOL_Obool)), _1342450), hAPP(c_COMBB(tc_prod(_1342450, _1342452), tc_fun(tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_HOL_Obool), _1342452), c_member(tc_prod(_1342450, _1342452)))), c_Product__Type_OPair(_1342450, _1342452)))), _1342454)), hAPP(hAPP(c_COMBC(_1342450, tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_fun(_1342452, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1342452, tc_fun(tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_fun(_1342452, tc_HOL_Obool)), _1342450), c_COMBC(_1342452, tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1342452, tc_prod(_1342450, _1342452)), tc_fun(_1342452, tc_fun(tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_HOL_Obool)), _1342450), hAPP(c_COMBB(tc_prod(_1342450, _1342452), tc_fun(tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool), tc_HOL_Obool), _1342452), c_member(tc_prod(_1342450, _1342452)))), c_Product__Type_OPair(_1342450, _1342452)))), _1342456))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1342450, _1342452), tc_HOL_Obool)), _1342454), _1342456)))], (44614 ^ _774244) ^ [_1646629, _1646631, _1646633] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646629, tc_HOL_Obool)), _1646631), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646629, tc_HOL_Obool), _1646633)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1646629, tc_HOL_Obool), tc_fun(_1646629, tc_HOL_Obool)), _1646633), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1646629, tc_HOL_Obool)), _1646631)))], (20355 ^ _774244) ^ [_1122552, _1122554] : [class_Rings_Odivision__ring__inverse__zero(_1122552), 20358 ^ _774244 : [(20365 ^ _774244) ^ [] : [-(_1122554 = c_Groups_Ozero__class_Ozero(_1122552)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122552), _1122554), _1122554) = c_Groups_Oone__class_Oone(_1122552))], (20359 ^ _774244) ^ [] : [_1122554 = c_Groups_Ozero__class_Ozero(_1122552), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122552), _1122554), _1122554) = c_Groups_Ozero__class_Ozero(_1122552))]]], (1644 ^ _774244) ^ [_797518, _797520] : [-(class_Rings_Osemiring__1(_797518)), _797520 = _797518, class_Rings_Osemiring__1(_797520)], (51301 ^ _774244) ^ [_1799894, _1799896] : [-(class_Finite__Set_Ofinite(tc_sum(_1799894, _1799896))), class_Finite__Set_Ofinite(_1799894), class_Finite__Set_Ofinite(_1799896)], (35610 ^ _774244) ^ [_1429465, _1429467, _1429469, _1429471] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1429465, tc_HOL_Obool)), _1429467), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1429465), _1429469), _1429471))), 35614 ^ _774244 : [(35617 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1429465), 35613 ^ [_1429465, _1429467, _1429469, _1429471]), _1429469)))], (35615 ^ _774244) ^ [] : [-(_1429467 = hAPP(c_Relation_OImage(_1429465, _1429465, _1429471), hAPP(hAPP(c_Set_Oinsert(_1429465), 35613 ^ [_1429465, _1429467, _1429469, _1429471]), c_Orderings_Obot__class_Obot(tc_fun(_1429465, tc_HOL_Obool)))))]]], (46533 ^ _774244) ^ [_1694423, _1694425, _1694427, _1694429, _1694431, _1694433] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694423), tc_List_Olist(_1694423))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694423), tc_List_Olist(_1694423)), hAPP(hAPP(c_List_Olist_OCons(_1694423), _1694425), _1694427)), hAPP(hAPP(c_List_Olist_OCons(_1694423), _1694429), _1694431))), c_List_Olex(_1694423, _1694433))), 46538 ^ _774244 : [(46541 ^ _774244) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694423)), _1694427) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694423)), _1694431))], (46539 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1694423, _1694423)), hAPP(hAPP(c_Product__Type_OPair(_1694423, _1694423), _1694425), _1694429)), _1694433)))]], 46542 ^ _774244 : [(46545 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694423), tc_List_Olist(_1694423))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694423), tc_List_Olist(_1694423)), _1694427), _1694431)), c_List_Olex(_1694423, _1694433))))], (46543 ^ _774244) ^ [] : [-(_1694425 = _1694429)]]], (30993 ^ _774244) ^ [_1330124, _1330126, _1330128, _1330130] : [_1330124 = _1330126, 30996 ^ _774244 : [(31003 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1330128), _1330130), _1330126)), -(hBOOL(hAPP(hAPP(c_member(_1330128), _1330130), _1330124)))], (30997 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1330128), _1330130), _1330124)), -(hBOOL(hAPP(hAPP(c_member(_1330128), _1330130), _1330126)))]]], (6796 ^ _774244) ^ [_884293, _884295, _884297, _884299] : [class_Rings_Ocomm__semiring__1(_884293), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884293), _884295), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884293), _884297), _884299)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884293), _884297), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884293), _884295), _884299)))], (7547 ^ _774244) ^ [_896911, _896913, _896915, _896917] : [c_Com_Ocom_OAss(_896911, _896913) = c_Com_Ocom_OWhile(_896915, _896917)], (3654 ^ _774244) ^ [_830577, _830579] : [_830579 = _830577, -(c_New__Random__Sequence_Opos__single(_830579) = c_New__Random__Sequence_Opos__single(_830577))], (51401 ^ _774244) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (6692 ^ _774244) ^ [_881998, _882000, _882002, _882004, _882006] : [-(c_Option_Ooption_Ooption__rec(_881998, _882000, _882002, _882004, hAPP(c_Option_Ooption_OSome(_882000), _882006)) = hAPP(_882004, _882006))], (19271 ^ _774244) ^ [_1103187, _1103189] : [class_Int_Onumber__ring(_1103187), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103187), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103187), c_Groups_Oone__class_Oone(_1103187)), c_Groups_Oone__class_Oone(_1103187))), hAPP(c_Int_Onumber__class_Onumber__of(_1103187), _1103189)) = hAPP(c_Int_Onumber__class_Onumber__of(_1103187), c_Int_OBit0(_1103189)))], (18877 ^ _774244) ^ [_1096284, _1096286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096284)), -(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)))), _1096286)), 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)))), _1096284)) = 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, _1096286, _1096284))))], (6460 ^ _774244) ^ [_878244, _878246, _878248, _878250] : [class_Groups_Oab__semigroup__add(_878244), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878244), _878246), _878248)), _878250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878244), _878246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878244), _878248), _878250)))], (46693 ^ _774244) ^ [_1699352, _1699354, _1699356, _1699358] : [class_Groups_Ocomm__monoid__add(_1699352), hBOOL(hAPP(c_List_Odistinct(_1699354), _1699356)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1699352), hAPP(hAPP(c_List_Omap(_1699354, _1699352), _1699358), _1699356)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1699354, _1699352), _1699358), hAPP(c_List_Oset(_1699354), _1699356)))], (7143 ^ _774244) ^ [_890249, _890251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890249), _890251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890249)), hAPP(c_Nat_OSuc, _890251))))], (1144 ^ _774244) ^ [_791268, _791270] : [-(class_Int_Onumber__ring(_791268)), _791270 = _791268, class_Int_Onumber__ring(_791270)], (18581 ^ _774244) ^ [_1091358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1091358)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1091358), c_Int_OMin)))], (51239 ^ _774244) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (4586 ^ _774244) ^ [_845133, _845135, _845137, _845139] : [-(c_Wellfounded_Oacc(_845139, _845135) = c_Wellfounded_Oacc(_845137, _845133)), _845139 = _845137, _845135 = _845133], (38798 ^ _774244) ^ [_1499377, _1499379, _1499381, _1499383, _1499385] : [-(hAPP(c_Set_Ovimage(_1499377, _1499379, _1499381), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499379, tc_HOL_Obool)), _1499383), _1499385)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499377, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1499377, _1499379, _1499381), _1499383)), hAPP(c_Set_Ovimage(_1499377, _1499379, _1499381), _1499385)))], (20529 ^ _774244) ^ [_1125456, _1125458, _1125460, _1125462, _1125464] : [class_Fields_Olinordered__field(_1125456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125456), c_Groups_Ozero__class_Ozero(_1125456)), _1125458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125456), _1125458), _1125460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125456), c_Groups_Ozero__class_Ozero(_1125456)), _1125462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125456), _1125462), _1125464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125456), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125456), _1125458), _1125464)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125456), _1125460), _1125462))))], (49113 ^ _774244) ^ [_1756549, _1756551, _1756553] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1756549, _1756549)), hAPP(hAPP(c_Product__Type_OPair(_1756549, _1756549), 49114 ^ [_1756549, _1756551, _1756553]), 49114 ^ [_1756549, _1756551, _1756553])), _1756551))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756549), tc_List_Olist(_1756549))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756549), tc_List_Olist(_1756549)), _1756553), _1756553)), c_List_Olexord(_1756549, _1756551)))], (43131 ^ _774244) ^ [_1608422, _1608424] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1608422, _1608422, _1608422), c_Transitive__Closure_Ortrancl(_1608422, _1608424)), c_Transitive__Closure_Ortrancl(_1608422, _1608424)) = c_Transitive__Closure_Ortrancl(_1608422, _1608424))], (22100 ^ _774244) ^ [_1154037, _1154039] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1154037), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1154039))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1154037), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1154039))), 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))))], (44038 ^ _774244) ^ [_1632878, _1632880] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1632878, _1632878), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1632878, _1632880)), c_Relation_OId(_1632878)) = c_Transitive__Closure_Ortrancl(_1632878, _1632880))], (28884 ^ _774244) ^ [_1287995, _1287997, _1287999] : [hAPP(hAPP(c_Set_Oinsert(_1287995), _1287997), _1287999) = c_Orderings_Obot__class_Obot(tc_fun(_1287995, tc_HOL_Obool))], (40539 ^ _774244) ^ [_1540266, _1540268] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1540266))), -(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)), _1540266))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1540268)))) = 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)), _1540266))), 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, _1540268))))))], (8670 ^ _774244) ^ [_915767, _915769] : [class_Groups_Ocomm__monoid__mult(_915767), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915767), _915769), c_Groups_Oone__class_Oone(_915767)) = _915769)], (23563 ^ _774244) ^ [_1182693, _1182695] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1182693)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1182695)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1182695))), 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), _1182693)), c_Int_Onat)))))], (14938 ^ _774244) ^ [_1025054, _1025056, _1025058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025054)), 14944 ^ _774244 : [(14947 ^ _774244) ^ [] : [hBOOL(hAPP(_1025056, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 14943 ^ [_1025054, _1025056, _1025058]), _1025054)))], (14945 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1025056, 14943 ^ [_1025054, _1025056, _1025058])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025058)), 14952 ^ _774244 : [(14953 ^ _774244) ^ [_1025343] : [hBOOL(hAPP(_1025056, _1025343)), -(hBOOL(hAPP(_1025056, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1025343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1025058), _1025054)))))]]], (43700 ^ _774244) ^ [_1623896, _1623898, _1623900, _1623902, _1623904] : [43702 ^ _774244 : [(43705 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1623896, tc_HOL_Obool)), _1623898), hAPP(_1623904, 43701 ^ [_1623896, _1623898, _1623900, _1623902, _1623904])))], (43703 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623900), 43701 ^ [_1623896, _1623898, _1623900, _1623902, _1623904]), _1623902)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1623896, tc_HOL_Obool)), _1623898), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623900, tc_fun(_1623896, tc_HOL_Obool)), _1623902), _1623904))))], (15656 ^ _774244) ^ [_1038699, _1038701] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1038699), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1038701), _1038699)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1038701), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1038701, _1038699)))], (36093 ^ _774244) ^ [_1439444, _1439446, _1439448] : [class_Lattices_Obounded__lattice__top(_1439444), 36096 ^ _774244 : [(36105 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1439444), _1439446), _1439448) = c_Orderings_Otop__class_Otop(_1439444)), _1439446 = c_Orderings_Otop__class_Otop(_1439444), _1439448 = c_Orderings_Otop__class_Otop(_1439444)], (36097 ^ _774244) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1439444), _1439446), _1439448) = c_Orderings_Otop__class_Otop(_1439444), 36100 ^ _774244 : [(36103 ^ _774244) ^ [] : [-(_1439448 = c_Orderings_Otop__class_Otop(_1439444))], (36101 ^ _774244) ^ [] : [-(_1439446 = c_Orderings_Otop__class_Otop(_1439444))]]]]], (38826 ^ _774244) ^ [_1500083, _1500085, _1500087, _1500089, _1500091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500083, tc_HOL_Obool)), _1500085), _1500087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500089, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1500089, _1500083, _1500091), _1500085)), hAPP(c_Set_Ovimage(_1500089, _1500083, _1500091), _1500087))))], (18369 ^ _774244) ^ [_1087676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1087676)), -(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), _1087676))))], (26119 ^ _774244) ^ [_1230543, _1230545, _1230547] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230543), _1230545)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230543), _1230547)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230543), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230545, _1230547))))], (43469 ^ _774244) ^ [_1617309, _1617311, _1617313, _1617315, _1617317] : [43471 ^ _774244 : [(43474 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1617309), _1617311), hAPP(_1617317, 43470 ^ [_1617309, _1617311, _1617313, _1617315, _1617317])))], (43472 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617313), 43470 ^ [_1617309, _1617311, _1617313, _1617315, _1617317]), _1617315)))]], -(hBOOL(hAPP(hAPP(c_member(_1617309), _1617311), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1617313, tc_fun(_1617309, tc_HOL_Obool)), _1617315), _1617317))))], (10466 ^ _774244) ^ [_946698, _946700, _946702] : [10467 ^ _774244 : [(10470 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946698), _946702))], (10468 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _946700)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _946698), _946700)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _946702), _946700))))], (13308 ^ _774244) ^ [_995421, _995423, _995425] : [class_Lattices_Oboolean__algebra(_995421), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995421), _995423), _995425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995421), hAPP(c_Groups_Ouminus__class_Ouminus(_995421), _995425)), hAPP(c_Groups_Ouminus__class_Ouminus(_995421), _995423))))], (25329 ^ _774244) ^ [_1216003, _1216005, _1216007, _1216009] : [class_Rings_Ocomm__semiring__1(_1216003), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216003), _1216005), _1216007)), _1216009)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216003), _1216007), _1216009)))], (16193 ^ _774244) ^ [_1049482, _1049484, _1049486] : [class_Groups_Oordered__ab__group__add__abs(_1049482), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049482), hAPP(c_Groups_Oabs__class_Oabs(_1049482), _1049484)), _1049486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049482), _1049484), _1049486)))], (50841 ^ _774244) ^ [_1794068, _1794070, _1794072] : [50843 ^ _774244 : [(50846 ^ _774244) ^ [] : [hBOOL(hAPP(_1794070, 50842 ^ [_1794068, _1794070, _1794072]))], (50844 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1794068), 50842 ^ [_1794068, _1794070, _1794072]), hAPP(c_List_Oset(_1794068), _1794072))))]], -(c_List_OdropWhile(_1794068, _1794070, _1794072) = c_List_Olist_ONil(_1794068))], (6367 ^ _774244) ^ [_876661, _876663] : [6368 ^ _774244 : [(6369 ^ _774244) ^ [_876709] : [_876661 = hAPP(c_Option_Ooption_OSome(_876663), _876709)]], _876661 = c_Option_Ooption_ONone(_876663)], (28934 ^ _774244) ^ [_1289017, _1289019, _1289021] : [-(hAPP(c_Set_Oimage(_1289017, _1289019, _1289021), c_Orderings_Obot__class_Obot(tc_fun(_1289017, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1289019, tc_HOL_Obool)))], (51137 ^ _774244) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (33296 ^ _774244) ^ [_1378048, _1378050, _1378052, _1378054, _1378056, _1378058, _1378060] : [hBOOL(hAPP(_1378048, _1378050)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1378052, _1378052)), hAPP(hAPP(c_Product__Type_OPair(_1378052, _1378052), _1378054), _1378056)), hAPP(_1378058, _1378050))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1378060, _1378052), tc_prod(_1378060, _1378052))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1378060, _1378052), tc_prod(_1378060, _1378052)), hAPP(hAPP(c_Product__Type_OPair(_1378060, _1378052), _1378050), _1378054)), hAPP(hAPP(c_Product__Type_OPair(_1378060, _1378052), _1378050), _1378056))), c_Recdef_Osame__fst(_1378060, _1378052, _1378048, _1378058))))], (35185 ^ _774244) ^ [_1418714, _1418716, _1418718] : [-(hAPP(c_Relation_OImage(_1418714, _1418716, _1418718), c_Orderings_Obot__class_Obot(tc_fun(_1418714, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1418716, tc_HOL_Obool)))], (2788 ^ _774244) ^ [_816490, _816492, _816494, _816496, _816498, _816500, _816502, _816504, _816506, _816508, _816510, _816512, _816514, _816516] : [-(c_New__Random__Sequence_Opos__decr__bind(_816516, _816512, _816508, _816504, _816500, _816496, _816492) = c_New__Random__Sequence_Opos__decr__bind(_816514, _816510, _816506, _816502, _816498, _816494, _816490)), _816516 = _816514, _816512 = _816510, _816508 = _816506, _816504 = _816502, _816500 = _816498, _816496 = _816494, _816492 = _816490], (8648 ^ _774244) ^ [_915455, _915457] : [class_Groups_Oone(_915455), 8651 ^ _774244 : [(8658 ^ _774244) ^ [] : [_915457 = c_Groups_Oone__class_Oone(_915455), -(c_Groups_Oone__class_Oone(_915455) = _915457)], (8652 ^ _774244) ^ [] : [c_Groups_Oone__class_Oone(_915455) = _915457, -(_915457 = c_Groups_Oone__class_Oone(_915455))]]], (18495 ^ _774244) ^ [_1089960, _1089962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089960), _1089962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1089960)), c_Int_OBit1(_1089962))))], (41077 ^ _774244) ^ [_1557904, _1557906, _1557908] : [class_Orderings_Olinorder(_1557904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557904), _1557906)), -(_1557906 = c_Orderings_Obot__class_Obot(tc_fun(_1557904, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557904), _1557908)), -(_1557908 = c_Orderings_Obot__class_Obot(tc_fun(_1557904, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1557904), c_Big__Operators_Olattice_OInf__fin(_1557904, c_Orderings_Oord__class_Omin(_1557904), _1557906)), c_Big__Operators_Olattice_OInf__fin(_1557904, c_Orderings_Oord__class_Omin(_1557904), _1557908)) = c_Big__Operators_Olattice_OInf__fin(_1557904, c_Orderings_Oord__class_Omin(_1557904), hAPP(c_Set_OCollect(_1557904), hAPP(hAPP(c_COMBB(tc_fun(_1557904, tc_HOL_Obool), tc_HOL_Obool, _1557904), c_HOL_OEx(_1557904)), hAPP(hAPP(c_COMBB(tc_fun(_1557904, tc_fun(_1557904, tc_HOL_Obool)), tc_fun(_1557904, tc_HOL_Obool), _1557904), hAPP(c_COMBB(tc_fun(_1557904, tc_HOL_Obool), tc_HOL_Obool, _1557904), c_HOL_OEx(_1557904))), hAPP(hAPP(c_COMBC(_1557904, tc_fun(_1557904, tc_fun(_1557904, tc_HOL_Obool)), tc_fun(_1557904, tc_fun(_1557904, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557904, tc_fun(tc_fun(_1557904, tc_HOL_Obool), tc_fun(_1557904, tc_HOL_Obool))), tc_fun(tc_fun(_1557904, tc_fun(_1557904, tc_HOL_Obool)), tc_fun(_1557904, tc_fun(_1557904, tc_HOL_Obool))), _1557904), c_COMBS(_1557904, tc_fun(_1557904, tc_HOL_Obool), tc_fun(_1557904, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557904, tc_fun(_1557904, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1557904, tc_fun(tc_fun(_1557904, tc_HOL_Obool), tc_fun(_1557904, tc_HOL_Obool))), _1557904), hAPP(c_COMBB(tc_fun(_1557904, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1557904, tc_HOL_Obool), tc_fun(_1557904, tc_HOL_Obool)), _1557904), c_COMBS(_1557904, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557904, tc_fun(_1557904, tc_HOL_Obool)), tc_fun(_1557904, tc_fun(_1557904, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1557904), hAPP(c_COMBB(tc_fun(_1557904, tc_HOL_Obool), tc_fun(_1557904, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1557904), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1557904), c_fconj))), hAPP(hAPP(c_COMBC(_1557904, tc_fun(_1557904, tc_fun(_1557904, _1557904)), tc_fun(_1557904, tc_fun(_1557904, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1557904, _1557904), tc_fun(_1557904, tc_HOL_Obool)), tc_fun(tc_fun(_1557904, tc_fun(_1557904, _1557904)), tc_fun(_1557904, tc_fun(_1557904, tc_HOL_Obool))), _1557904), c_COMBB(tc_fun(_1557904, _1557904), tc_fun(_1557904, tc_HOL_Obool), _1557904)), hAPP(hAPP(c_COMBB(tc_fun(_1557904, tc_HOL_Obool), tc_fun(tc_fun(_1557904, _1557904), tc_fun(_1557904, tc_HOL_Obool)), _1557904), c_COMBB(_1557904, tc_HOL_Obool, _1557904)), c_fequal))), c_Orderings_Oord__class_Omax(_1557904)))))), hAPP(hAPP(c_COMBC(_1557904, tc_fun(_1557904, tc_HOL_Obool), tc_fun(_1557904, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1557904, tc_HOL_Obool), tc_fun(_1557904, tc_HOL_Obool)), _1557904), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1557904)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1557904), c_fconj), hAPP(hAPP(c_COMBC(_1557904, tc_fun(_1557904, tc_HOL_Obool), tc_HOL_Obool), c_member(_1557904)), _1557906)))), hAPP(hAPP(c_COMBC(_1557904, tc_fun(_1557904, tc_HOL_Obool), tc_HOL_Obool), c_member(_1557904)), _1557908))))))))], (18617 ^ _774244) ^ [_1091958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1091958))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1091958)))], (36021 ^ _774244) ^ [_1438024, _1438026, _1438028] : [class_Lattices_Osemilattice__inf(_1438024), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438024), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1438024), _1438026), _1438028)), _1438028)))], (47724 ^ _774244) ^ [_1722999, _1723001] : [-(hAPP(hAPP(c_List_Oappend(_1722999), _1723001), c_List_Olist_ONil(_1722999)) = _1723001)], (45214 ^ _774244) ^ [_1660909, _1660911, _1660913, _1660915, _1660917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660909, tc_HOL_Obool)), _1660911), _1660913)), 45220 ^ _774244 : [(45225 ^ _774244) ^ [] : [hBOOL(hAPP(_1660917, 45219 ^ [_1660909, _1660911, _1660913, _1660915, _1660917]))], (45223 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1660915, 45219 ^ [_1660909, _1660911, _1660913, _1660915, _1660917])))], (45221 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1660909), 45219 ^ [_1660909, _1660911, _1660913, _1660915, _1660917]), _1660911)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660909, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660909, tc_HOL_Obool)), _1660911), hAPP(c_Set_OCollect(_1660909), _1660915))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660909, tc_HOL_Obool)), _1660913), hAPP(c_Set_OCollect(_1660909), _1660917)))))], (51271 ^ _774244) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (27278 ^ _774244) ^ [_1254748, _1254750, _1254752, _1254754, _1254756] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254748, tc_HOL_Obool)), _1254750), hAPP(c_Set_Oimage(_1254752, _1254748, _1254754), _1254756)))), 27279 ^ _774244 : [(27280 ^ _774244) ^ [_1254828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254752, tc_HOL_Obool)), _1254828), _1254756)), _1254750 = hAPP(c_Set_Oimage(_1254752, _1254748, _1254754), _1254828)]]], (18979 ^ _774244) ^ [_1098053, _1098055] : [c_Int_OBit0(_1098053) = c_Int_OBit1(_1098055)], (44054 ^ _774244) ^ [_1633219] : [-(c_Relation_OId(_1633219) = hAPP(c_Set_OCollect(tc_prod(_1633219, _1633219)), hAPP(hAPP(c_COMBB(tc_fun(_1633219, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1633219, _1633219)), c_HOL_OEx(_1633219)), hAPP(hAPP(c_COMBC(tc_prod(_1633219, _1633219), tc_fun(_1633219, tc_prod(_1633219, _1633219)), tc_fun(_1633219, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1633219, _1633219), tc_HOL_Obool), tc_fun(tc_fun(_1633219, tc_prod(_1633219, _1633219)), tc_fun(_1633219, tc_HOL_Obool)), tc_prod(_1633219, _1633219)), c_COMBB(tc_prod(_1633219, _1633219), tc_HOL_Obool, _1633219)), c_fequal)), hAPP(hAPP(c_COMBS(_1633219, _1633219, tc_prod(_1633219, _1633219)), c_Product__Type_OPair(_1633219, _1633219)), c_COMBI(_1633219))))))], (40518 ^ _774244) ^ [_1539769, _1539771, _1539773, _1539775, _1539777, _1539779, _1539781, _1539783] : [c_Finite__Set_Ofolding__image__simple(_1539769, _1539771, _1539773, _1539775, _1539777, _1539779), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539771), _1539781)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539771), _1539783)), 40532 ^ _774244 : [(40535 ^ _774244) ^ [] : [hAPP(_1539777, 40531 ^ [_1539769, _1539771, _1539773, _1539775, _1539777, _1539779, _1539781, _1539783]) = _1539775], (40533 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539771), 40531 ^ [_1539769, _1539771, _1539773, _1539775, _1539777, _1539779, _1539781, _1539783]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1539771, tc_HOL_Obool)), _1539781), _1539783))))]], -(hAPP(_1539779, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1539771, tc_HOL_Obool)), _1539781), _1539783)) = hAPP(hAPP(_1539773, hAPP(_1539779, _1539781)), hAPP(_1539779, _1539783)))], (29684 ^ _774244) ^ [_1302819, _1302821] : [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)))), _1302819, _1302821) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1302819), _1302821)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1302821), _1302819)))], (14199 ^ _774244) ^ [_1012215, _1012217, _1012219] : [_1012215 = 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), _1012215), _1012217)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012215), _1012219)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5977 ^ _774244) ^ [_869951, _869953] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_869951, _869953))), 5980 ^ _774244 : [(5983 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _869953)))], (5981 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _869951)))]]], (22184 ^ _774244) ^ [_1155809, _1155811, _1155813, _1155815] : [-(hAPP(c_Nat_Onat_Onat__rec(_1155809, _1155811, _1155813), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155815)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1155809), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1155815))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1155809, _1155809), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1155809, tc_fun(_1155809, _1155809)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1155809, tc_fun(_1155809, _1155809)), tc_Int_Oint), c_If(_1155809)), c_Nat__Numeral_Oneg)), _1155811)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1155809, _1155809), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1155809, _1155809), tc_Int_Oint), _1155813), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1155809, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1155809, _1155811, _1155813)), c_Int_Onat)))))], (3350 ^ _774244) ^ [_825689, _825691, _825693, _825695, _825697, _825699, _825701, _825703] : [-(c_Random__Sequence_Omap(_825703, _825699, _825695, _825691) = c_Random__Sequence_Omap(_825701, _825697, _825693, _825689)), _825703 = _825701, _825699 = _825697, _825695 = _825693, _825691 = _825689], (24503 ^ _774244) ^ [_1200556, _1200558] : [class_Orderings_Olinorder(_1200556), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200556), _1200558), _1200558) = _1200558)], (32371 ^ _774244) ^ [_1360670, _1360672, _1360674, _1360676] : [-(c_Nitpick_Ofold__graph_H(_1360670, _1360672, _1360674, _1360676, c_Orderings_Obot__class_Obot(tc_fun(_1360670, tc_HOL_Obool)), _1360676))], (51263 ^ _774244) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (42552 ^ _774244) ^ [_1596005, _1596007, _1596009, _1596011, _1596013] : [c_Finite__Set_Ofolding__one__idem(_1596005, _1596007, _1596009), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596005), _1596011)), -(hAPP(_1596009, hAPP(hAPP(c_Set_Oinsert(_1596005), _1596013), _1596011)) = hAPP(hAPP(c_Finite__Set_Ofold(_1596005, _1596005, _1596007), _1596013), _1596011))], (34477 ^ _774244) ^ [_1402409, _1402411, _1402413, _1402415] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1402409), _1402411)), 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)), _1402409), _1402413)), 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)), _1402411), _1402415)), 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)), _1402411), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1402413), _1402415))), c_FunDef_Omin__strict)))], (38065 ^ _774244) ^ [_1483974, _1483976, _1483978, _1483980, _1483982, _1483984] : [c_Fun_Oinj__on(_1483974, _1483976, _1483978, _1483980), 38068 ^ _774244 : [(38075 ^ _774244) ^ [] : [c_Fun_Oinj__on(_1483974, _1483982, hAPP(c_Fun_Ocomp(_1483976, _1483982, _1483974, _1483984), _1483978), _1483980), -(c_Fun_Oinj__on(_1483976, _1483982, _1483984, hAPP(c_Set_Oimage(_1483974, _1483976, _1483978), _1483980)))], (38069 ^ _774244) ^ [] : [c_Fun_Oinj__on(_1483976, _1483982, _1483984, hAPP(c_Set_Oimage(_1483974, _1483976, _1483978), _1483980)), -(c_Fun_Oinj__on(_1483974, _1483982, hAPP(c_Fun_Ocomp(_1483976, _1483982, _1483974, _1483984), _1483978), _1483980))]]], (16435 ^ _774244) ^ [_1053788, _1053790, _1053792] : [class_Groups_Oordered__ab__group__add__abs(_1053788), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053788), hAPP(c_Groups_Oabs__class_Oabs(_1053788), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1053788), hAPP(c_Groups_Oabs__class_Oabs(_1053788), _1053790)), hAPP(c_Groups_Oabs__class_Oabs(_1053788), _1053792)))), hAPP(c_Groups_Oabs__class_Oabs(_1053788), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1053788), _1053790), _1053792)))))], (34606 ^ _774244) ^ [_1405493, _1405495] : [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), _1405493), _1405495)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1405493), _1405495)))], (26243 ^ _774244) ^ [_1232720, _1232722] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232720)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232722))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232720), _1232722)))], (39766 ^ _774244) ^ [_1523104, _1523106, _1523108, _1523110] : [-(_1523104 = c_Orderings_Obot__class_Obot(tc_fun(_1523106, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1523106, _1523108), _1523108, c_Product__Type_Osnd(_1523106, _1523108)), hAPP(hAPP(c_Product__Type_OSigma(_1523106, _1523108), _1523104), hAPP(c_COMBK(tc_fun(_1523108, tc_HOL_Obool), _1523106), _1523110))) = _1523110)], (39068 ^ _774244) ^ [_1505654, _1505656, _1505658, _1505660, _1505662] : [class_Groups_Ocomm__monoid__mult(_1505654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505656), _1505658)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505656), _1505660)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1505654), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1505654, _1505656, c_Groups_Otimes__class_Otimes(_1505654)), _1505662), c_Groups_Oone__class_Oone(_1505654)), _1505658)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1505654, _1505656, c_Groups_Otimes__class_Otimes(_1505654)), _1505662), c_Groups_Oone__class_Oone(_1505654)), _1505660)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1505654), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1505654, _1505656, c_Groups_Otimes__class_Otimes(_1505654)), _1505662), c_Groups_Oone__class_Oone(_1505654)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1505656, tc_HOL_Obool)), _1505658), _1505660))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1505654, _1505656, c_Groups_Otimes__class_Otimes(_1505654)), _1505662), c_Groups_Oone__class_Oone(_1505654)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1505656, tc_HOL_Obool)), _1505658), _1505660))))], (27896 ^ _774244) ^ [_1266956] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1266956) = c_Orderings_Oord__class_Omax(_1266956)), class_Lattices_Osemilattice__sup(_1266956), class_Orderings_Olinorder(_1266956)], (47361 ^ _774244) ^ [_1714777, _1714779, _1714781, _1714783, _1714785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714777), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714779)), _1714781))), 47364 ^ _774244 : [(47371 ^ _774244) ^ [] : [-(_1714777 = _1714783), -(hAPP(hAPP(c_List_Onth(_1714779), hAPP(hAPP(c_List_Olist__update(_1714779, _1714781), _1714777), _1714785)), _1714783) = hAPP(hAPP(c_List_Onth(_1714779), _1714781), _1714783))], (47365 ^ _774244) ^ [] : [_1714777 = _1714783, -(hAPP(hAPP(c_List_Onth(_1714779), hAPP(hAPP(c_List_Olist__update(_1714779, _1714781), _1714777), _1714785)), _1714783) = _1714785)]]], (44907 ^ _774244) ^ [_1653333, _1653335, _1653337, _1653339, _1653341, _1653343] : [-(_1653333 = c_Orderings_Obot__class_Obot(tc_fun(_1653335, tc_HOL_Obool))), 44913 ^ _774244 : [(44916 ^ _774244) ^ [] : [c_Fun_Oinj__on(_1653337, _1653339, _1653341, hAPP(_1653343, 44912 ^ [_1653333, _1653335, _1653337, _1653339, _1653341, _1653343]))], (44914 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653335), 44912 ^ [_1653333, _1653335, _1653337, _1653339, _1653341, _1653343]), _1653333)))]], -(c_Fun_Oinj__on(_1653337, _1653339, _1653341, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653335, tc_fun(_1653337, tc_HOL_Obool)), _1653333), _1653343)))], (28791 ^ _774244) ^ [] : [-(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)))], (50901 ^ _774244) ^ [_1795481, _1795483] : [class_Orderings_Olinorder(_1795481), 50908 ^ _774244 : [(50913 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1795481), hAPP(hAPP(c_List_Onth(_1795481), _1795483), 50906 ^ [_1795481, _1795483])), hAPP(hAPP(c_List_Onth(_1795481), _1795483), 50907 ^ [_1795481, _1795483])))], (50911 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50907 ^ [_1795481, _1795483]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795481)), _1795483))))], (50909 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50906 ^ [_1795481, _1795483]), 50907 ^ [_1795481, _1795483])))]], -(c_List_Olinorder__class_Osorted(_1795481, _1795483))], (47901 ^ _774244) ^ [_1727669, _1727671] : [-(hAPP(hAPP(c_List_Otake(_1727669), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1727671) = c_List_Olist_ONil(_1727669))], (2230 ^ _774244) ^ [_807851, _807853, _807855, _807857] : [-(c_Com_Ocom_OAss(_807857, _807853) = c_Com_Ocom_OAss(_807855, _807851)), _807857 = _807855, _807853 = _807851], (18185 ^ _774244) ^ [_1084757, _1084759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084757), _1084759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1084757)), _1084759)))], (37887 ^ _774244) ^ [_1480580, _1480582, _1480584, _1480586, _1480588] : [c_Fun_Oinj__on(_1480580, _1480582, _1480584, _1480586), c_Fun_Oinj__on(_1480580, _1480582, _1480584, _1480588), -(c_Fun_Oinj__on(_1480580, _1480582, _1480584, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1480580, tc_HOL_Obool)), _1480586), _1480588)))], (46080 ^ _774244) ^ [_1681735, _1681737, _1681739, _1681741, _1681743] : [class_Orderings_Olinorder(_1681735), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681737)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681737, _1681735, _1681739), _1681741), _1681743)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681737)), _1681743)))], (5866 ^ _774244) ^ [_868029] : [c_Com_Ocom_OBODY(_868029) = c_Com_Ocom_OSKIP], (47267 ^ _774244) ^ [_1712713, _1712715, _1712717, _1712719, _1712721] : [-(_1712713 = _1712715), -(hAPP(hAPP(c_List_Onth(_1712717), hAPP(hAPP(c_List_Olist__update(_1712717, _1712719), _1712713), _1712721)), _1712715) = hAPP(hAPP(c_List_Onth(_1712717), _1712719), _1712715))], (17077 ^ _774244) ^ [_1066188, _1066190] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1066188)), _1066190) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1066188), _1066190)))], (5416 ^ _774244) ^ [_857900, _857902, _857904, _857906] : [-(c_List_Omap(_857906, _857902) = c_List_Omap(_857904, _857900)), _857906 = _857904, _857902 = _857900], (44729 ^ _774244) ^ [_1649311, _1649313, _1649315] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649311, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1649311, tc_HOL_Obool), tc_HOL_Obool)), _1649313), _1649315)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1649311, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649311, tc_HOL_Obool), _1649313)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649311, tc_HOL_Obool), _1649315)))], (41306 ^ _774244) ^ [_1567271, _1567273, _1567275, _1567277, _1567279, _1567281, _1567283, _1567285] : [hBOOL(hAPP(hAPP(_1567271, _1567273), _1567275)), hBOOL(hAPP(hAPP(_1567277, _1567275), _1567279)), -(c_Predicate_Opred__comp(_1567281, _1567283, _1567285, _1567271, _1567277, _1567273, _1567279))], (10474 ^ _774244) ^ [_946878, _946880, _946882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _946878), _946880)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _946878), _946882))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _946878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946880), _946882)))], (18703 ^ _774244) ^ [_1093343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093343), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1093343)), c_Int_OPls)))], (42576 ^ _774244) ^ [_1596465, _1596467, _1596469, _1596471] : [class_Lattices_Osemilattice__inf(_1596465), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596465), _1596467)), hBOOL(hAPP(hAPP(c_member(_1596465), _1596469), _1596467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1596465), hAPP(hAPP(c_Finite__Set_Ofold(_1596465, _1596465, c_Lattices_Osemilattice__inf__class_Oinf(_1596465)), _1596471), _1596467)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1596465), _1596469), _1596471))))], (10121 ^ _774244) ^ [_941088, _941090, _941092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941090), _941092)), -(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, _941088)), _941090)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _941088)), _941092))))], (43676 ^ _774244) ^ [_1622839, _1622841, _1622843, _1622845, _1622847] : [-(hAPP(hAPP(c_Set_Oinsert(_1622839), _1622841), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622843, tc_fun(_1622839, tc_HOL_Obool)), _1622845), _1622847)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622843, tc_fun(_1622839, tc_HOL_Obool)), _1622845), hAPP(hAPP(c_COMBB(tc_fun(_1622839, tc_HOL_Obool), tc_fun(_1622839, tc_HOL_Obool), _1622843), hAPP(c_Set_Oinsert(_1622839), _1622841)), _1622847)))], (1872 ^ _774244) ^ [_801372, _801374, _801376, _801378, _801380, _801382, _801384, _801386, _801388, _801390] : [-(c_Nitpick_Opair__box_Opair__box__size(_801390, _801386, _801382, _801378, _801374) = c_Nitpick_Opair__box_Opair__box__size(_801388, _801384, _801380, _801376, _801372)), _801390 = _801388, _801386 = _801384, _801382 = _801380, _801378 = _801376, _801374 = _801372], (51227 ^ _774244) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (49440 ^ _774244) ^ [_1764030, _1764032, _1764034, _1764036] : [-(c_List_Omap__filter(_1764030, _1764032, _1764034, _1764036) = hAPP(hAPP(c_List_Omap(_1764030, _1764032), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1764032), _1764032, _1764030, c_Option_Othe(_1764032)), _1764034)), hAPP(c_List_Ofilter(_1764030, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1764030), c_fNot), hAPP(hAPP(c_COMBC(_1764030, tc_Option_Ooption(_1764032), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1764032), tc_fun(tc_Option_Ooption(_1764032), tc_HOL_Obool), _1764030), c_fequal), _1764034)), c_Option_Ooption_ONone(_1764032)))), _1764036)))], (46419 ^ _774244) ^ [_1691884, _1691886, _1691888, _1691890, _1691892, _1691894] : [c_List_Olistrelp(_1691884, _1691886, hAPP(hAPP(c_List_Olist_OCons(_1691884), _1691888), _1691890), hAPP(hAPP(c_List_Olist_OCons(_1691884), _1691892), _1691894)), 46422 ^ _774244 : [(46425 ^ _774244) ^ [] : [-(c_List_Olistrelp(_1691884, _1691886, _1691890, _1691894))], (46423 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1691886, _1691888), _1691892)))]]], (49830 ^ _774244) ^ [_1771758, _1771760, _1771762] : [class_Orderings_Olinorder(_1771758), 49833 ^ _774244 : [(49840 ^ _774244) ^ [] : [c_List_Olinorder__class_Osorted(_1771758, _1771762), -(c_List_Olinorder__class_Osorted(_1771758, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1771758, _1771758, c_COMBI(_1771758)), _1771760), _1771762)))], (49834 ^ _774244) ^ [] : [c_List_Olinorder__class_Osorted(_1771758, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1771758, _1771758, c_COMBI(_1771758)), _1771760), _1771762)), -(c_List_Olinorder__class_Osorted(_1771758, _1771762))]]], (18987 ^ _774244) ^ [_1098197, _1098199] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1098197)), _1098199) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1098197), _1098199)))], (28608 ^ _774244) ^ [_1281430, _1281432, _1281434, _1281436, _1281438] : [class_Complete__Lattice_Ocomplete__lattice(_1281430), 28611 ^ _774244 : [(28612 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281430), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281432, _1281430), _1281434), _1281436)), _1281438)), 28615 ^ _774244 : [(28616 ^ _774244) ^ [_1281611] : [hBOOL(hAPP(hAPP(c_member(_1281432), _1281611), _1281434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281430), hAPP(_1281436, _1281611)), _1281438)))]]], (28622 ^ _774244) ^ [] : [28624 ^ _774244 : [(28627 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281430), hAPP(_1281436, 28623 ^ [_1281430, _1281432, _1281434, _1281436, _1281438])), _1281438))], (28625 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1281432), 28623 ^ [_1281430, _1281432, _1281434, _1281436, _1281438]), _1281434)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281430), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281432, _1281430), _1281434), _1281436)), _1281438)))]]], (25615 ^ _774244) ^ [_1221107, _1221109, _1221111] : [class_Divides_Osemiring__div(_1221107), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221107), _1221109), _1221111)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221107), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1221107), _1221111), _1221109)), _1221109) = _1221111)], (12860 ^ _774244) ^ [_987848] : [-(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), _987848))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35312 ^ _774244) ^ [_1422180, _1422182, _1422184, _1422186, _1422188, _1422190] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1422180, tc_fun(_1422182, tc_HOL_Obool)), _1422184), hAPP(c_Fun_Ocomp(_1422186, tc_fun(_1422182, tc_HOL_Obool), _1422180, _1422188), _1422190)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1422186, tc_fun(_1422182, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1422180, _1422186, _1422190), _1422184)), _1422188))], (34283 ^ _774244) ^ [_1398043, _1398045, _1398047, _1398049] : [class_Groups_Ocomm__monoid__mult(_1398043), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398045), _1398047)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398045, _1398043), hAPP(c_COMBK(_1398043, _1398045), _1398049)), _1398047) = hAPP(hAPP(c_Power_Opower__class_Opower(_1398043), _1398049), hAPP(c_Finite__Set_Ocard(_1398045), _1398047)))], (44616 ^ _774244) ^ [_1646696, _1646698, _1646700, _1646702] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1646696, tc_HOL_Obool), tc_fun(_1646698, tc_HOL_Obool)), _1646700), hAPP(hAPP(c_COMBC(tc_fun(_1646696, tc_HOL_Obool), tc_fun(_1646696, tc_fun(_1646698, tc_HOL_Obool)), tc_fun(_1646698, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1646696, tc_fun(_1646698, tc_HOL_Obool))), _1646702)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1646696, tc_fun(_1646698, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646696, tc_HOL_Obool), _1646700)), _1646702))], (31677 ^ _774244) ^ [_1345959, _1345961, _1345963, _1345965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1345959, tc_HOL_Obool)), _1345961), hAPP(hAPP(c_Set_Oinsert(_1345959), _1345963), _1345965))), 31680 ^ _774244 : [(31687 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1345959), _1345963), _1345961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1345959, tc_HOL_Obool)), _1345961), _1345965)))], (31681 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1345959), _1345963), _1345961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1345959, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345959, tc_HOL_Obool)), _1345961), hAPP(hAPP(c_Set_Oinsert(_1345959), _1345963), c_Orderings_Obot__class_Obot(tc_fun(_1345959, tc_HOL_Obool))))), _1345965)))]]], (36081 ^ _774244) ^ [_1439254, _1439256] : [class_Lattices_Obounded__lattice__top(_1439254), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1439254), c_Orderings_Otop__class_Otop(_1439254)), _1439256) = _1439256)], (35394 ^ _774244) ^ [_1424412, _1424414, _1424416, _1424418, _1424420, _1424422, _1424424, _1424426] : [c_Finite__Set_Ofolding(_1424412, _1424414, _1424416, _1424418), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424412), _1424420)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424412), _1424422)), -(hAPP(c_Fun_Ocomp(_1424414, _1424414, _1424424, hAPP(_1424418, _1424422)), hAPP(c_Fun_Ocomp(_1424414, _1424414, _1424424, hAPP(_1424418, _1424420)), _1424426)) = hAPP(c_Fun_Ocomp(_1424414, _1424414, _1424424, hAPP(_1424418, _1424420)), hAPP(c_Fun_Ocomp(_1424414, _1424414, _1424424, hAPP(_1424418, _1424422)), _1424426)))], (15560 ^ _774244) ^ [_1036809, _1036811, _1036813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036809), _1036811)), _1036813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036813), _1036811))))], (45293 ^ _774244) ^ [_1662670, _1662672, _1662674, _1662676, _1662678] : [hBOOL(hAPP(hAPP(c_member(_1662670), _1662672), c_Map_Odom(_1662670, _1662674, _1662676))), -(hAPP(c_Map_Omap__add(_1662670, _1662674, _1662678, _1662676), _1662672) = hAPP(_1662676, _1662672))], (45557 ^ _774244) ^ [_1668757, _1668759, _1668761, _1668763, _1668765] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1668757), tc_List_Olist(_1668759), tc_List_Olist(_1668761), hAPP(c_List_Omap(_1668757, _1668759), _1668763)), hAPP(c_List_Omap(_1668761, _1668757), _1668765)) = hAPP(c_List_Omap(_1668761, _1668759), hAPP(c_Fun_Ocomp(_1668757, _1668759, _1668761, _1668763), _1668765)))], (24539 ^ _774244) ^ [_1201271, _1201273, _1201275, _1201277, _1201279] : [-(_1201271 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1201273, _1201275, _1201271, _1201277), _1201279) = hAPP(hAPP(c_Product__Type_Oscomp(_1201275, _1201273, _1201275, tc_prod(_1201273, _1201275)), hAPP(_1201277, _1201279)), c_Random_Oiterate(_1201273, _1201275, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1201271), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1201277)))], (20965 ^ _774244) ^ [_1133411, _1133413, _1133415, _1133417] : [class_Fields_Ofield__inverse__zero(_1133411), class_Int_Onumber(_1133411), 20972 ^ _774244 : [(20973 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1133411), _1133413) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133411), _1133415), _1133417), 20976 ^ _774244 : [(20983 ^ _774244) ^ [] : [_1133417 = c_Groups_Ozero__class_Ozero(_1133411), -(hAPP(c_Int_Onumber__class_Onumber__of(_1133411), _1133413) = c_Groups_Ozero__class_Ozero(_1133411))], (20977 ^ _774244) ^ [] : [-(_1133417 = c_Groups_Ozero__class_Ozero(_1133411)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133411), hAPP(c_Int_Onumber__class_Onumber__of(_1133411), _1133413)), _1133417) = _1133415)]]], (20989 ^ _774244) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1133411), _1133413) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133411), _1133415), _1133417)), 20992 ^ _774244 : [(20995 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133411), hAPP(c_Int_Onumber__class_Onumber__of(_1133411), _1133413)), _1133417) = _1133415], (20993 ^ _774244) ^ [] : [_1133417 = c_Groups_Ozero__class_Ozero(_1133411)]], 20996 ^ _774244 : [(20999 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1133411), _1133413) = c_Groups_Ozero__class_Ozero(_1133411)], (20997 ^ _774244) ^ [] : [-(_1133417 = c_Groups_Ozero__class_Ozero(_1133411))]]]]], (18605 ^ _774244) ^ [_1091750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1091750)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091750), c_Int_OMin)))], (13952 ^ _774244) ^ [_1007386, _1007388, _1007390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007386)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007388, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1007390), _1007386)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1007390), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1007388), _1007390), _1007386))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007388, _1007390)))], (5446 ^ _774244) ^ [_858355, _858357, _858359, _858361, _858363, _858365] : [-(c_Set_Oimage(_858365, _858361, _858357) = c_Set_Oimage(_858363, _858359, _858355)), _858365 = _858363, _858361 = _858359, _858357 = _858355], (7607 ^ _774244) ^ [_898231, _898233] : [class_Groups_Olinordered__ab__group__add(_898231), 7610 ^ _774244 : [(7617 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_898231), _898233), c_Groups_Ozero__class_Ozero(_898231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_898231), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898231), _898233), _898233)), c_Groups_Ozero__class_Ozero(_898231))))], (7611 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_898231), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898231), _898233), _898233)), c_Groups_Ozero__class_Ozero(_898231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_898231), _898233), c_Groups_Ozero__class_Ozero(_898231))))]]], (45359 ^ _774244) ^ [_1663991, _1663993, _1663995, _1663997] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1663991, tc_HOL_Obool)), c_Map_Odom(_1663991, _1663993, _1663995)), c_Map_Odom(_1663991, _1663993, _1663997)) = c_Orderings_Obot__class_Obot(tc_fun(_1663991, tc_HOL_Obool)), -(c_Map_Omap__add(_1663991, _1663993, _1663995, _1663997) = c_Map_Omap__add(_1663991, _1663993, _1663997, _1663995))], (18541 ^ _774244) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (10416 ^ _774244) ^ [_945822, _945824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945822), _945824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _945822)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _945824))))], (13682 ^ _774244) ^ [_1002439, _1002441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002439), _1002441)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1002439, _1002441) = _1002439)], (17897 ^ _774244) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20723 ^ _774244) ^ [_1129057, _1129059, _1129061, _1129063] : [class_Fields_Olinordered__field(_1129057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129057), c_Groups_Ozero__class_Ozero(_1129057)), _1129059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129057), _1129061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129057), _1129063), _1129059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129057), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129057), _1129061), _1129059)), _1129063)))], (16725 ^ _774244) ^ [_1059642, _1059644] : [class_Rings_Olinordered__idom(_1059642), -(hAPP(c_Groups_Oabs__class_Oabs(_1059642), _1059644) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059642), _1059644), c_Groups_Osgn__class_Osgn(_1059642, _1059644)))], (50759 ^ _774244) ^ [_1792295, _1792297] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792295)), c_List_Oremdups(_1792295, _1792297)) = hAPP(c_Finite__Set_Ocard(_1792295), hAPP(c_List_Oset(_1792295), _1792297)))], (47923 ^ _774244) ^ [_1728019, _1728021, _1728023, _1728025, _1728027] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1728019, _1728021)), _1728023), hAPP(hAPP(c_List_Ozip(_1728019, _1728021), _1728025), _1728027)) = hAPP(hAPP(c_List_Ozip(_1728019, _1728021), hAPP(hAPP(c_List_Otake(_1728019), _1728023), _1728025)), hAPP(hAPP(c_List_Otake(_1728021), _1728023), _1728027)))], (46403 ^ _774244) ^ [_1691495, _1691497, _1691499] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1691495, tc_HOL_Obool)), hAPP(c_List_Oset(_1691495), _1691497)), hAPP(c_List_Oset(_1691495), hAPP(hAPP(c_List_Olist_OCons(_1691495), _1691499), _1691497)))))], (48837 ^ _774244) ^ [_1750449, _1750451, _1750453, _1750455, _1750457] : [hBOOL(hAPP(hAPP(c_member(_1750449), _1750451), hAPP(c_List_Oset(_1750449), _1750453))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750455), hAPP(_1750457, _1750451))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750455), c_List_Olist_Olist__size(_1750449, _1750457, _1750453))))], (7911 ^ _774244) ^ [_903512] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _903512) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_903512 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27534 ^ _774244) ^ [_1259655, _1259657] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1259655, _1259657)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1259657), _1259655))], (6428 ^ _774244) ^ [_877714, _877716, _877718, _877720] : [class_Groups_Ocancel__semigroup__add(_877714), 6431 ^ _774244 : [(6438 ^ _774244) ^ [] : [_877716 = _877720, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877714), _877716), _877718) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877714), _877720), _877718))], (6432 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877714), _877716), _877718) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877714), _877720), _877718), -(_877716 = _877720)]]], (33402 ^ _774244) ^ [_1380342, _1380344, _1380346, _1380348] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1380342, _1380344)), c_Sum__Type_OPlus(_1380342, _1380344, _1380346, _1380348))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1380342), _1380346)))], (19353 ^ _774244) ^ [_1104576, _1104578] : [class_Rings_Oring__1(_1104576), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1104576), hAPP(c_Groups_Ouminus__class_Ouminus(_1104576), _1104578)), 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(_1104576), _1104578), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (42039 ^ _774244) ^ [_1584457, _1584459, _1584461, _1584463] : [c_Equiv__Relations_Ocongruent(_1584457, _1584459, _1584461, _1584463), 42042 ^ _774244 : [(42043 ^ _774244) ^ [_1584602] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584457, _1584457)), _1584602), _1584461)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1584457, _1584457, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1584457, tc_fun(_1584457, _1584459), tc_fun(_1584457, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584459, tc_HOL_Obool), tc_fun(tc_fun(_1584457, _1584459), tc_fun(_1584457, tc_HOL_Obool)), _1584457), c_COMBB(_1584459, tc_HOL_Obool, _1584457)), hAPP(hAPP(c_COMBB(_1584459, tc_fun(_1584459, tc_HOL_Obool), _1584457), c_fequal), _1584463))), _1584463)), _1584602)))]]], (51317 ^ _774244) ^ [_1800098, _1800100] : [-(class_Finite__Set_Ofinite(tc_prod(_1800098, _1800100))), class_Finite__Set_Ofinite(_1800098), class_Finite__Set_Ofinite(_1800100)], (28188 ^ _774244) ^ [_1272361, _1272363, _1272365, _1272367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272361, tc_HOL_Obool)), _1272363), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272361, tc_HOL_Obool)), _1272365), _1272367))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272361, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272361, tc_HOL_Obool)), _1272363), _1272365)), _1272367)))], (32750 ^ _774244) ^ [_1367879, _1367881] : [class_Orderings_Olinorder(_1367879), -(c_Big__Operators_Olinorder__class_OMin(_1367879, hAPP(hAPP(c_Set_Oinsert(_1367879), _1367881), c_Orderings_Obot__class_Obot(tc_fun(_1367879, tc_HOL_Obool)))) = _1367881)], (4912 ^ _774244) ^ [_850160, _850162] : [_850162 = _850160, -(c_Lattices_Osemilattice__sup__class_Osup(_850162) = c_Lattices_Osemilattice__sup__class_Osup(_850160))], (23305 ^ _774244) ^ [_1177406, _1177408, _1177410, _1177412] : [_1177406 = _1177408, 23308 ^ _774244 : [(23311 ^ _774244) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1177410, _1177412), _1177406) = hAPP(c_Product__Type_Osnd(_1177410, _1177412), _1177408))], (23309 ^ _774244) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1177410, _1177412), _1177406) = hAPP(c_Product__Type_Ofst(_1177410, _1177412), _1177408))]]], (6019 ^ _774244) ^ [_870644, _870646, _870648] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_870644, _870646, _870648))), 6022 ^ _774244 : [(6025 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _870648)))], (6023 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _870646)))]]], (29532 ^ _774244) ^ [_1300107, _1300109, _1300111] : [class_Orderings_Olinorder(_1300107), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300107), _1300109), _1300111)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1300107, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1300107, _1300109), _1300111)), hAPP(hAPP(c_Set_Oinsert(_1300107), _1300111), c_Orderings_Obot__class_Obot(tc_fun(_1300107, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1300107, _1300109, _1300111))], (46521 ^ _774244) ^ [_1693982, _1693984, _1693986, _1693988, _1693990, _1693992] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1693982, _1693982)), hAPP(hAPP(c_Product__Type_OPair(_1693982, _1693982), _1693984), _1693986)), _1693988)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693982), tc_List_Olist(_1693982))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693982), tc_List_Olist(_1693982)), _1693990), _1693992)), c_List_Olistrel(_1693982, _1693988))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693982), tc_List_Olist(_1693982))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1693982), tc_List_Olist(_1693982)), hAPP(hAPP(c_List_Olist_OCons(_1693982), _1693984), _1693990)), hAPP(hAPP(c_List_Olist_OCons(_1693982), _1693986), _1693992))), c_List_Olistrel(_1693982, _1693988))))], (40597 ^ _774244) ^ [_1541582, _1541584] : [c_Orderings_Obot__class_Obot(tc_fun(_1541582, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1541582), _1541584), 40600 ^ _774244 : [(40601 ^ _774244) ^ [_1541667] : [hBOOL(hAPP(_1541584, _1541667))]]], (1384 ^ _774244) ^ [_794268, _794270] : [-(class_Groups_Olinordered__ab__semigroup__add(_794268)), _794270 = _794268, class_Groups_Olinordered__ab__semigroup__add(_794270)], (29658 ^ _774244) ^ [_1302381, _1302383] : [c_Option_Oset(_1302381, _1302383) = c_Orderings_Obot__class_Obot(tc_fun(_1302381, tc_HOL_Obool)), -(_1302383 = c_Option_Ooption_ONone(_1302381))], (8516 ^ _774244) ^ [_913081] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _913081)) = 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), _913081)))], (14682 ^ _774244) ^ [_1020188, _1020190, _1020192] : [class_Divides_Osemiring__div(_1020188), -(_1020190 = c_Groups_Ozero__class_Ozero(_1020188)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020188), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020188), _1020192), _1020190)), _1020190) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020188), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020188), _1020192), _1020190)), c_Groups_Oone__class_Oone(_1020188)))], (5967 ^ _774244) ^ [_869753, _869755, _869757, _869759, _869761, _869763, _869765, _869767, _869769, _869771, _869773, _869775] : [-(c_Com_Ocom_Ocom__case(_869753, _869755, _869757, _869759, _869761, _869763, _869765, _869767, _869769, c_Com_Ocom_OCond(_869771, _869773, _869775)) = hAPP(hAPP(hAPP(_869763, _869771), _869773), _869775))], (5366 ^ _774244) ^ [_857177, _857179, _857181, _857183] : [-(c_List_Ofilter(_857183, _857179) = c_List_Ofilter(_857181, _857177)), _857183 = _857181, _857179 = _857177], (7052 ^ _774244) ^ [_888528, _888530, _888532] : [c_Com_Ocom_OBODY(_888528) = c_Com_Ocom_OWhile(_888530, _888532)], (28092 ^ _774244) ^ [_1270313, _1270315, _1270317] : [class_Lattices_Olattice(_1270313), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270313), _1270315), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1270313), _1270315), _1270317))))], (41685 ^ _774244) ^ [_1575830, _1575832, _1575834, _1575836] : [hBOOL(hAPP(hAPP(c_member(_1575830), _1575832), hAPP(c_Relation_ORange(_1575834, _1575830), _1575836))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575834, _1575830)), hAPP(hAPP(c_Product__Type_OPair(_1575834, _1575830), 41688 ^ [_1575830, _1575832, _1575834, _1575836]), _1575832)), _1575836)))], (49525 ^ _774244) ^ [_1766411, _1766413] : [class_Orderings_Olinorder(_1766411), -(c_List_Olinorder__class_Osorted(_1766411, hAPP(hAPP(c_List_Olist_OCons(_1766411), _1766413), c_List_Olist_ONil(_1766411))))], (12416 ^ _774244) ^ [_979943, _979945, _979947, _979949] : [class_Rings_Olinordered__ring__strict(_979943), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979943), _979945), c_Groups_Ozero__class_Ozero(_979943))), 12423 ^ _774244 : [(12430 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979943), _979949), _979947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979943), _979945), _979947)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979943), _979945), _979949))))], (12424 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979943), _979945), _979947)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979943), _979945), _979949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979943), _979949), _979947)))]]], (19521 ^ _774244) ^ [_1107345, _1107347, _1107349] : [class_Rings_Ocomm__semiring__1(_1107345), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1107345), _1107347), 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)))), _1107349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107345), hAPP(hAPP(c_Power_Opower__class_Opower(_1107345), _1107347), _1107349)), hAPP(hAPP(c_Power_Opower__class_Opower(_1107345), _1107347), _1107349)))], (8778 ^ _774244) ^ [_917559, _917561] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _917559), _917561) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _917561), _917559))], (18157 ^ _774244) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (26408 ^ _774244) ^ [_1235740, _1235742, _1235744] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1235740, _1235742) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1235744, _1235742), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1235740), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235742), 26411 ^ [_1235740, _1235742, _1235744])) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1235744), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235742), 26412 ^ [_1235740, _1235742, _1235744])))], (23413 ^ _774244) ^ [_1179824, _1179826, _1179828] : [_1179824 = _1179826, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179828, tc_HOL_Obool)), _1179824), _1179826)))], (8608 ^ _774244) ^ [_914851, _914853, _914855] : [class_Rings_Oidom(_914851), 8611 ^ _774244 : [(8612 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914851), _914853), _914853) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914851), _914855), _914855), -(_914853 = _914855), -(_914853 = hAPP(c_Groups_Ouminus__class_Ouminus(_914851), _914855))], (8622 ^ _774244) ^ [] : [8623 ^ _774244 : [(8626 ^ _774244) ^ [] : [_914853 = hAPP(c_Groups_Ouminus__class_Ouminus(_914851), _914855)], (8624 ^ _774244) ^ [] : [_914853 = _914855]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914851), _914853), _914853) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914851), _914855), _914855))]]], (19133 ^ _774244) ^ [_1100774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1100774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1100774))))], (22294 ^ _774244) ^ [_1158442, _1158444] : [22295 ^ _774244 : [(22298 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158444), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22296 ^ _774244) ^ [] : [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), _1158442), _1158444)))]], -(c_Divides_OnegDivAlg(_1158442, _1158444) = 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), _1158442), _1158444)))], (18513 ^ _774244) ^ [_1090299] : [c_Int_OBit1(_1090299) = c_Int_OPls], (31581 ^ _774244) ^ [_1343888, _1343890] : [c_Nat__Transfer_Onat__set(_1343888), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1343890), _1343888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1343890)))], (15775 ^ _774244) ^ [_1041508, _1041510, _1041512] : [hBOOL(hAPP(_1041508, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041510), _1041512))), 15778 ^ _774244 : [(15785 ^ _774244) ^ [_1041699] : [_1041510 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041512), _1041699), -(hBOOL(hAPP(_1041508, _1041699)))], (15779 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041510), _1041512)), -(hBOOL(hAPP(_1041508, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (48744 ^ _774244) ^ [_1748478, _1748480] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1748478), _1748480) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 48747 ^ _774244 : [(48750 ^ _774244) ^ [_1748592] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1748592), hAPP(c_List_Oset(tc_Nat_Onat), _1748480))), -(_1748592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48748 ^ _774244) ^ [] : [-(_1748478 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (41334 ^ _774244) ^ [_1567737, _1567739] : [-(c_Wellfounded_Owf(_1567737, hAPP(c_Wellfounded_Omeasure(_1567737), _1567739)))], (44716 ^ _774244) ^ [_1648957, _1648959, _1648961] : [44718 ^ _774244 : [(44721 ^ _774244) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648957, tc_HOL_Obool)), 44717 ^ [_1648957, _1648959, _1648961]), _1648961) = c_Orderings_Obot__class_Obot(tc_fun(_1648957, tc_HOL_Obool))], (44719 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1648957, tc_HOL_Obool)), 44717 ^ [_1648957, _1648959, _1648961]), _1648959)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648957, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1648957, tc_HOL_Obool), _1648959)), _1648961) = c_Orderings_Obot__class_Obot(tc_fun(_1648957, tc_HOL_Obool)))], (23595 ^ _774244) ^ [_1183347, _1183349] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1183347)), hAPP(c_Nat_OSuc, _1183349)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1183347), _1183349)))], (51439 ^ _774244) ^ [_1801446, _1801448] : [_1801446 = _1801448, -(hBOOL(hAPP(hAPP(c_fequal, _1801446), _1801448)))], (10279 ^ _774244) ^ [_943554, _943556, _943558, _943560] : [class_Orderings_Oord(_943554), _943556 = _943558, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943554), _943558), _943560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943554), _943556), _943560)))], (42461 ^ _774244) ^ [_1594062, _1594064, _1594066] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1594062), _1594064)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1594062, tc_HOL_Obool)), _1594064), _1594066) = hAPP(hAPP(c_Finite__Set_Ofold(_1594062, tc_fun(_1594062, tc_HOL_Obool), c_Set_Oinsert(_1594062)), _1594066), _1594064))], (50671 ^ _774244) ^ [_1790804, _1790806] : [class_Orderings_Olinorder(_1790804), c_List_Olinorder__class_Osorted(_1790804, _1790806), -(c_List_Olinorder__class_Osorted(_1790804, c_List_Oremdups(_1790804, _1790806)))], (7992 ^ _774244) ^ [_904925, _904927, _904929] : [class_Rings_Olinordered__semidom(_904925), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _904927), _904929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904925), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904925), _904927)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904925), _904929))))], (128 ^ _774244) ^ [_776012, _776014, _776016, _776018, _776020, _776022] : [-(c_Nitpick_Oless__frac(_776020, _776016, _776012)), c_Nitpick_Oless__frac(_776022, _776018, _776014), _776022 = _776020, _776018 = _776016, _776014 = _776012], (42822 ^ _774244) ^ [_1601081, _1601083] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1601081, _1601081)), c_Transitive__Closure_Otrancl(_1601081, _1601083))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1601081, _1601081)), _1601083)))], (37719 ^ _774244) ^ [_1476940, _1476942, _1476944] : [class_Lattices_Olattice(_1476940), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476940), _1476942)), -(_1476942 = c_Orderings_Obot__class_Obot(tc_fun(_1476940, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476940), _1476944)), -(_1476944 = c_Orderings_Obot__class_Obot(tc_fun(_1476940, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1476940, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476940, tc_HOL_Obool)), _1476942), _1476944)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1476940), c_Big__Operators_Olattice__class_OInf__fin(_1476940, _1476942)), c_Big__Operators_Olattice__class_OInf__fin(_1476940, _1476944)))], (46842 ^ _774244) ^ [_1702479] : [-(hBOOL(hAPP(c_List_Odistinct(_1702479), c_List_Olist_ONil(_1702479))))], (29494 ^ _774244) ^ [_1299395] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1299395, _1299395) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1299395), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (31301 ^ _774244) ^ [_1336513, _1336515, _1336517, _1336519] : [-(hBOOL(hAPP(hAPP(c_member(_1336513), hAPP(_1336515, _1336517)), hAPP(c_Set_Oimage(_1336519, _1336513, _1336515), c_Orderings_Otop__class_Otop(tc_fun(_1336519, tc_HOL_Obool))))))], (36167 ^ _774244) ^ [_1441040, _1441042, _1441044] : [class_Lattices_Olattice(_1441040), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441040), _1441042), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441040), _1441042), _1441044)) = _1441042)], (18641 ^ _774244) ^ [_1092338] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1092338)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1092338))))], (48596 ^ _774244) ^ [_1745269, _1745271, _1745273] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745269)), hAPP(c_List_Orotate(_1745269, _1745271), _1745273)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745269)), _1745273))], (28631 ^ _774244) ^ [_1281924, _1281926, _1281928, _1281930, _1281932] : [class_Complete__Lattice_Ocomplete__lattice(_1281924), class_Orderings_Olinorder(_1281924), 28638 ^ _774244 : [(28648 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281924), _1281926), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281928, _1281924), _1281930), _1281932)))), 28649 ^ _774244 : [(28650 ^ _774244) ^ [_1282272] : [hBOOL(hAPP(hAPP(c_member(_1281928), _1282272), _1281930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281924), _1281926), hAPP(_1281932, _1282272)))]]], (28639 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281924), _1281926), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281928, _1281924), _1281930), _1281932))), 28643 ^ _774244 : [(28646 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281924), _1281926), hAPP(_1281932, 28642 ^ [_1281924, _1281926, _1281928, _1281930, _1281932]))))], (28644 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1281928), 28642 ^ [_1281924, _1281926, _1281928, _1281930, _1281932]), _1281930)))]]]]], (35215 ^ _774244) ^ [_1419580, _1419582, _1419584, _1419586, _1419588, _1419590, _1419592, _1419594, _1419596, _1419598, _1419600] : [hAPP(_1419580, hAPP(_1419582, _1419584)) = hAPP(_1419586, hAPP(_1419588, _1419590)), -(hAPP(hAPP(c_Fun_Ocomp(_1419592, _1419594, _1419596, _1419580), _1419582), _1419584) = hAPP(hAPP(c_Fun_Ocomp(_1419598, _1419594, _1419600, _1419586), _1419588), _1419590))], (4490 ^ _774244) ^ [_843691, _843693, _843695, _843697] : [-(c_Big__Operators_Olinorder__class_OMax(_843697, _843693) = c_Big__Operators_Olinorder__class_OMax(_843695, _843691)), _843697 = _843695, _843693 = _843691], (27555 ^ _774244) ^ [_1260010, _1260012, _1260014] : [class_Groups_Oordered__ab__group__add(_1260010), -(hAPP(c_Set_Oimage(_1260010, _1260010, c_Groups_Ouminus__class_Ouminus(_1260010)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1260010, _1260012, _1260014)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1260010, hAPP(c_Groups_Ouminus__class_Ouminus(_1260010), _1260014), hAPP(c_Groups_Ouminus__class_Ouminus(_1260010), _1260012)))], (17259 ^ _774244) ^ [_1069457, _1069459] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1069457), c_Groups_Ozero__class_Ozero(_1069457)), hAPP(c_Nat_OSuc, _1069459)) = c_Groups_Ozero__class_Ozero(_1069457)), class_Power_Opower(_1069457), class_Rings_Osemiring__0(_1069457)], (38293 ^ _774244) ^ [_1488231, _1488233, _1488235] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1488231), _1488233)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488231, tc_HOL_Obool)), _1488233), hAPP(c_Set_Oimage(_1488231, _1488231, _1488235), _1488233))), -(c_Fun_Oinj__on(_1488231, _1488231, _1488235, _1488233))], (50791 ^ _774244) ^ [_1793187, _1793189, _1793191] : [-(hAPP(hAPP(c_List_Oappend(_1793187), c_List_OtakeWhile(_1793187, _1793189, _1793191)), c_List_OdropWhile(_1793187, _1793189, _1793191)) = _1793191)], (39558 ^ _774244) ^ [_1517192, _1517194, _1517196, _1517198, _1517200, _1517202] : [-(hAPP(c_Set_Oimage(_1517192, tc_prod(_1517194, _1517196), hAPP(hAPP(c_COMBS(_1517192, _1517196, tc_prod(_1517194, _1517196)), hAPP(hAPP(c_COMBB(_1517194, tc_fun(_1517196, tc_prod(_1517194, _1517196)), _1517192), c_Product__Type_OPair(_1517194, _1517196)), _1517198)), _1517200)), _1517202) = hAPP(hAPP(c_Product__Type_OSigma(_1517194, _1517196), hAPP(c_Set_Oimage(_1517192, _1517194, _1517198), _1517202)), hAPP(hAPP(c_COMBB(tc_fun(_1517192, tc_HOL_Obool), tc_fun(_1517196, tc_HOL_Obool), _1517194), c_Set_Oimage(_1517192, _1517196, _1517200)), hAPP(hAPP(c_COMBC(_1517194, tc_fun(_1517192, tc_HOL_Obool), tc_fun(_1517192, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517192, tc_HOL_Obool), tc_fun(tc_fun(_1517192, tc_HOL_Obool), tc_fun(_1517192, tc_HOL_Obool)), _1517194), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1517192, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1517194, tc_HOL_Obool), tc_fun(_1517192, tc_HOL_Obool), _1517194), c_Set_Ovimage(_1517192, _1517194, _1517198)), hAPP(hAPP(c_COMBC(_1517194, tc_fun(_1517194, tc_HOL_Obool), tc_fun(_1517194, tc_HOL_Obool)), c_Set_Oinsert(_1517194)), c_Orderings_Obot__class_Obot(tc_fun(_1517194, tc_HOL_Obool)))))), _1517202))))], (29664 ^ _774244) ^ [_1302474, _1302476] : [_1302476 = c_Option_Ooption_ONone(_1302474), -(c_Option_Oset(_1302474, _1302476) = c_Orderings_Obot__class_Obot(tc_fun(_1302474, tc_HOL_Obool)))], (50779 ^ _774244) ^ [_1792825, _1792827, _1792829] : [hBOOL(hAPP(c_List_Odistinct(_1792825), _1792827)), hBOOL(hAPP(hAPP(c_member(_1792825), _1792829), hAPP(c_List_Oset(_1792825), _1792827))), -(c_List_OdropWhile(_1792825, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1792825), c_fNot), hAPP(hAPP(c_COMBC(_1792825, _1792825, tc_HOL_Obool), c_fequal), _1792829)), hAPP(c_List_Orev(_1792825), _1792827)) = hAPP(hAPP(c_List_Olist_OCons(_1792825), _1792829), hAPP(c_List_Orev(_1792825), c_List_OtakeWhile(_1792825, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1792825), c_fNot), hAPP(hAPP(c_COMBC(_1792825, _1792825, tc_HOL_Obool), c_fequal), _1792829)), _1792827))))], (28960 ^ _774244) ^ [_1289535, _1289537, _1289539] : [class_Orderings_Obot(_1289535), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1289537, _1289535)), _1289539) = c_Orderings_Obot__class_Obot(_1289535))], (36161 ^ _774244) ^ [_1440931, _1440933, _1440935] : [class_Lattices_Olattice(_1440931), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1440931), _1440933), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1440931), _1440933), _1440935)) = _1440933)], (3880 ^ _774244) ^ [_834012, _834014, _834016, _834018] : [-(c_Relation_ORange(_834018, _834014) = c_Relation_ORange(_834016, _834012)), _834018 = _834016, _834014 = _834012], (49974 ^ _774244) ^ [_1774253, _1774255, _1774257, _1774259] : [class_Groups_Ocomm__monoid__add(_1774253), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1774253), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1774253), _1774255), c_List_Oupt(_1774257, _1774259))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1774253), _1774255), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1774257, _1774259))))], (40663 ^ _774244) ^ [_1543014, _1543016, _1543018] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1543014, tc_HOL_Obool)), _1543016), _1543018) = hAPP(c_Set_OCollect(_1543014), hAPP(hAPP(c_COMBS(_1543014, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543014), c_fdisj), hAPP(hAPP(c_COMBC(_1543014, tc_fun(_1543014, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543014)), _1543016))), hAPP(hAPP(c_COMBC(_1543014, tc_fun(_1543014, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543014)), _1543018))))], (45652 ^ _774244) ^ [_1671374, _1671376, _1671378, _1671380, _1671382] : [-(hAPP(hAPP(c_Option_Omap(_1671374, _1671376), _1671378), _1671380) = hAPP(c_Option_Ooption_OSome(_1671376), _1671382)), 45653 ^ _774244 : [(45654 ^ _774244) ^ [_1671442] : [_1671380 = hAPP(c_Option_Ooption_OSome(_1671374), _1671442), hAPP(_1671378, _1671442) = _1671382]]], (1254 ^ _774244) ^ [_792643, _792645] : [-(class_Lattices_Osemilattice__sup(_792643)), _792645 = _792643, class_Lattices_Osemilattice__sup(_792645)], (7064 ^ _774244) ^ [_888864, _888866, _888868, _888870, _888872] : [c_Com_Ocom_OWhile(_888864, _888866) = c_Com_Ocom_OCall(_888868, _888870, _888872)], (51375 ^ _774244) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (43631 ^ _774244) ^ [_1621572, _1621574, _1621576, _1621578, _1621580, _1621582] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1621572, tc_fun(_1621574, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1621576, _1621572, _1621578), _1621580)), _1621582) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1621576, tc_fun(_1621574, tc_HOL_Obool)), _1621580), hAPP(hAPP(c_COMBB(_1621572, tc_fun(_1621574, tc_HOL_Obool), _1621576), _1621582), _1621578)))], (36431 ^ _774244) ^ [_1446821, _1446823, _1446825] : [-(hAPP(c_Set_OPow(_1446821), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446821, tc_HOL_Obool)), _1446823), _1446825)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1446821, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1446821), _1446823)), hAPP(c_Set_OPow(_1446821), _1446825)))], (41679 ^ _774244) ^ [_1575473, _1575475, _1575477, _1575479] : [hBOOL(hAPP(hAPP(c_member(_1575475), _1575479), hAPP(c_Relation_ORange(_1575473, _1575475), _1575477))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1575473, _1575475, hAPP(hAPP(c_COMBC(_1575473, tc_fun(tc_prod(_1575473, _1575475), tc_HOL_Obool), tc_fun(_1575475, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575475, tc_fun(tc_fun(tc_prod(_1575473, _1575475), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1575473, _1575475), tc_HOL_Obool), tc_fun(_1575475, tc_HOL_Obool)), _1575473), c_COMBC(_1575475, tc_fun(tc_prod(_1575473, _1575475), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575475, tc_prod(_1575473, _1575475)), tc_fun(_1575475, tc_fun(tc_fun(tc_prod(_1575473, _1575475), tc_HOL_Obool), tc_HOL_Obool)), _1575473), hAPP(c_COMBB(tc_prod(_1575473, _1575475), tc_fun(tc_fun(tc_prod(_1575473, _1575475), tc_HOL_Obool), tc_HOL_Obool), _1575475), c_member(tc_prod(_1575473, _1575475)))), c_Product__Type_OPair(_1575473, _1575475)))), _1575477)), _1575479)))], (24667 ^ _774244) ^ [_1203902, _1203904] : [-(c_Nitpick_Oinverse__frac(_1203902, _1203904) = hAPP(hAPP(c_Nitpick_Ofrac(_1203902), hAPP(c_Nitpick_Odenom(_1203902), _1203904)), hAPP(c_Nitpick_Onum(_1203902), _1203904)))], (36775 ^ _774244) ^ [_1455203, _1455205, _1455207, _1455209, _1455211, _1455213, _1455215, _1455217] : [c_Finite__Set_Ofolding__image__simple(_1455203, _1455205, _1455207, _1455209, _1455211, _1455213), hBOOL(hAPP(c_Finite__Set_Ofinite(_1455205), _1455215)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1455205), _1455217)), -(hAPP(hAPP(_1455207, hAPP(_1455213, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1455205, tc_HOL_Obool)), _1455215), _1455217))), hAPP(_1455213, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455205, tc_HOL_Obool)), _1455215), _1455217))) = hAPP(hAPP(_1455207, hAPP(_1455213, _1455215)), hAPP(_1455213, _1455217)))], (43109 ^ _774244) ^ [_1607864, _1607866, _1607868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607864, _1607864), tc_HOL_Obool)), _1607866), c_Transitive__Closure_Ortrancl(_1607864, _1607868))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607864, _1607864), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1607864, _1607866)), c_Transitive__Closure_Ortrancl(_1607864, _1607868))))], (39368 ^ _774244) ^ [_1512667, _1512669, _1512671, _1512673, _1512675] : [class_Groups_Oab__semigroup__mult(_1512667), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1512667, _1512667, c_Groups_Otimes__class_Otimes(_1512667), _1512669, _1512671), _1512673)), -(hBOOL(hAPP(hAPP(c_member(_1512667), _1512669), _1512671))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1512667, _1512667, c_Groups_Otimes__class_Otimes(_1512667), _1512675, hAPP(hAPP(c_Set_Oinsert(_1512667), _1512669), _1512671)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1512667), _1512675), _1512673))))], (16731 ^ _774244) ^ [_1059749, _1059751] : [class_Rings_Olinordered__idom(_1059749), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059749), c_Groups_Osgn__class_Osgn(_1059749, _1059751)), hAPP(c_Groups_Oabs__class_Oabs(_1059749), _1059751)) = _1059751)], (32012 ^ _774244) ^ [_1353331, _1353333, _1353335, _1353337, _1353339, _1353341] : [32013 ^ _774244 : [(32016 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1353337, _1353333), _1353335))], (32014 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1353331, _1353333), _1353335))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353339, tc_fun(_1353341, tc_HOL_Obool))), _1353337), _1353331), _1353333), _1353335)))], (40767 ^ _774244) ^ [_1546122, _1546124, _1546126, _1546128, _1546130] : [class_Groups_Ocomm__monoid__add(_1546122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1546124), _1546126)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1546124, _1546122), _1546128), hAPP(c_Set_OCollect(_1546124), hAPP(hAPP(c_COMBS(_1546124, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546124), c_fconj), hAPP(hAPP(c_COMBC(_1546124, tc_fun(_1546124, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546124)), _1546126))), hAPP(hAPP(c_COMBC(_1546124, tc_fun(_1546124, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546124)), _1546130)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1546124, _1546122), hAPP(hAPP(c_COMBC(_1546124, _1546122, _1546122), hAPP(hAPP(c_COMBS(_1546124, _1546122, tc_fun(_1546122, _1546122)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1546122, tc_fun(_1546122, _1546122)), _1546124), c_If(_1546122)), hAPP(hAPP(c_COMBC(_1546124, tc_fun(_1546124, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546124)), _1546130))), _1546128)), c_Groups_Ozero__class_Ozero(_1546122))), _1546126))], (8912 ^ _774244) ^ [_920095, _920097] : [class_Groups_Ogroup__add(_920095), 8915 ^ _774244 : [(8922 ^ _774244) ^ [] : [_920097 = c_Groups_Ozero__class_Ozero(_920095), -(hAPP(c_Groups_Ouminus__class_Ouminus(_920095), _920097) = c_Groups_Ozero__class_Ozero(_920095))], (8916 ^ _774244) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_920095), _920097) = c_Groups_Ozero__class_Ozero(_920095), -(_920097 = c_Groups_Ozero__class_Ozero(_920095))]]], (17529 ^ _774244) ^ [_1074564] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074564))), -(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), _1074564)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11252 ^ _774244) ^ [_959367, _959369, _959371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959367), _959369)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959367), _959371))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959369), _959371)))], (44634 ^ _774244) ^ [_1647289, _1647291, _1647293] : [c_Equiv__Relations_Oequiv(_1647289, _1647291, _1647293), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1647289, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1647289), _1647291), _1647293)) = _1647291)], (19875 ^ _774244) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23287 ^ _774244) ^ [_1177037, _1177039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177037), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177039), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1177037), _1177039) = 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), _1177037), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1177039)))))], (21948 ^ _774244) ^ [_1151430] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1151430)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1151430)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (15791 ^ _774244) ^ [_1041800, _1041802, _1041804] : [-(hBOOL(hAPP(_1041800, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041802), _1041804)))), 15794 ^ _774244 : [(15797 ^ _774244) ^ [] : [hBOOL(hAPP(_1041800, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15795 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041802), _1041804)))]], 15799 ^ _774244 : [(15802 ^ _774244) ^ [] : [hBOOL(hAPP(_1041800, 15798 ^ [_1041800, _1041802, _1041804]))], (15800 ^ _774244) ^ [] : [-(_1041802 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041804), 15798 ^ [_1041800, _1041802, _1041804]))]]], (22104 ^ _774244) ^ [_1154114, _1154116, _1154118] : [class_Int_Onumber__ring(_1154114), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1154114), hAPP(c_Int_Onumber__class_Onumber__of(_1154114), _1154116)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1154118))) = hAPP(hAPP(c_HOL_OLet(_1154114, _1154114), hAPP(hAPP(c_Power_Opower__class_Opower(_1154114), hAPP(c_Int_Onumber__class_Onumber__of(_1154114), _1154116)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1154118))), hAPP(hAPP(c_COMBS(_1154114, _1154114, _1154114), c_Groups_Otimes__class_Otimes(_1154114)), c_COMBI(_1154114))))], (32224 ^ _774244) ^ [_1357629, _1357631, _1357633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357629)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1357631), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1357633)), 32234 ^ _774244 : [(32240 ^ _774244) ^ [] : [-(_1357631 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32236 ^ [_1357629, _1357631, _1357633]), 32233 ^ [_1357629, _1357631, _1357633]))], (32238 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32236 ^ [_1357629, _1357631, _1357633]), _1357633)))], (32235 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32233 ^ [_1357629, _1357631, _1357633]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1357629))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1357631), _1357629) = _1357631)], (51433 ^ _774244) ^ [_1801357, _1801359] : [hBOOL(hAPP(hAPP(c_fequal, _1801357), _1801359)), -(_1801357 = _1801359)], (28922 ^ _774244) ^ [_1288789, _1288791, _1288793, _1288795] : [c_Orderings_Obot__class_Obot(tc_fun(_1288789, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1288791, _1288789, _1288793), _1288795), -(_1288795 = c_Orderings_Obot__class_Obot(tc_fun(_1288791, tc_HOL_Obool)))], (18715 ^ _774244) ^ [_1093498] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1093498)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1093498)))], (31167 ^ _774244) ^ [_1333807, _1333809, _1333811, _1333813, _1333815] : [-(hBOOL(hAPP(hAPP(c_member(_1333807), _1333809), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1333811, tc_fun(_1333807, tc_HOL_Obool)), _1333813), _1333815)))), 31168 ^ _774244 : [(31169 ^ _774244) ^ [_1333889] : [hBOOL(hAPP(hAPP(c_member(_1333811), _1333889), _1333813)), hBOOL(hAPP(hAPP(c_member(_1333807), _1333809), hAPP(_1333815, _1333889)))]]], (25399 ^ _774244) ^ [_1217262, _1217264, _1217266] : [class_Rings_Ocomm__semiring__1(_1217262), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1217262), _1217264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217262), _1217264), _1217266))))], (5969 ^ _774244) ^ [_869822, _869824, _869826] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_869822, _869824, _869826))), 5972 ^ _774244 : [(5975 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _869826)))], (5973 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _869824)))]]], (51149 ^ _774244) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (44777 ^ _774244) ^ [_1650380, _1650382, _1650384] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1650380, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1650380, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1650380, tc_HOL_Obool), tc_HOL_Obool)), _1650382), _1650384))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1650380, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1650380, tc_HOL_Obool), _1650382)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1650380, tc_HOL_Obool), _1650384)))))], (46024 ^ _774244) ^ [_1680136, _1680138, _1680140, _1680142, _1680144, _1680146] : [-(hAPP(hAPP(c_List_Ozip(_1680136, _1680138), hAPP(hAPP(c_List_Omap(_1680140, _1680136), _1680142), _1680144)), _1680146) = hAPP(hAPP(c_List_Omap(tc_prod(_1680140, _1680138), tc_prod(_1680136, _1680138)), hAPP(c_Product__Type_Oprod_Oprod__case(_1680140, _1680138, tc_prod(_1680136, _1680138)), hAPP(hAPP(c_COMBB(_1680136, tc_fun(_1680138, tc_prod(_1680136, _1680138)), _1680140), c_Product__Type_OPair(_1680136, _1680138)), _1680142))), hAPP(hAPP(c_List_Ozip(_1680140, _1680138), _1680144), _1680146)))], (4480 ^ _774244) ^ [_843542, _843544, _843546, _843548] : [-(c_Big__Operators_Olinorder__class_OMin(_843548, _843544) = c_Big__Operators_Olinorder__class_OMin(_843546, _843542)), _843548 = _843546, _843544 = _843542], (51275 ^ _774244) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (4132 ^ _774244) ^ [_838056, _838058, _838060, _838062, _838064, _838066, _838068, _838070, _838072, _838074, _838076, _838078] : [-(c_Product__Type_Omap__pair(_838078, _838074, _838070, _838066, _838062, _838058) = c_Product__Type_Omap__pair(_838076, _838072, _838068, _838064, _838060, _838056)), _838078 = _838076, _838074 = _838072, _838070 = _838068, _838066 = _838064, _838062 = _838060, _838058 = _838056], (8184 ^ _774244) ^ [_908076, _908078, _908080] : [class_Orderings_Olinorder(_908076), 8187 ^ _774244 : [(8188 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908076), _908078), _908080))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908076), _908080), _908078))), -(_908078 = _908080)], (8198 ^ _774244) ^ [] : [8199 ^ _774244 : [(8202 ^ _774244) ^ [] : [_908078 = _908080], (8200 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908076), _908080), _908078))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908076), _908078), _908080))]]], (4192 ^ _774244) ^ [_839076, _839078] : [_839078 = _839076, -(c_Groups_Ouminus__class_Ouminus(_839078) = c_Groups_Ouminus__class_Ouminus(_839076))], (25161 ^ _774244) ^ [_1213225, _1213227] : [_1213225 = _1213227, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1213225), _1213227)))], (16083 ^ _774244) ^ [_1047672, _1047674, _1047676] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1047672, _1047674) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1047676, _1047674), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047676), _1047672)), -(_1047672 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047674), 16090 ^ [_1047672, _1047674, _1047676])))], (45055 ^ _774244) ^ [_1657317, _1657319, _1657321] : [45057 ^ _774244 : [(45060 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1657317), _1657321), 45056 ^ [_1657317, _1657319, _1657321]))], (45058 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1657317, tc_HOL_Obool)), 45056 ^ [_1657317, _1657319, _1657321]), _1657319)))]], -(hBOOL(hAPP(hAPP(c_member(_1657317), _1657321), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657317, tc_HOL_Obool), _1657319))))], (12538 ^ _774244) ^ [_982285, _982287, _982289, _982291] : [class_Rings_Olinordered__semiring__strict(_982285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982285), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982285), _982287), _982289)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982285), _982291), _982289))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982285), c_Groups_Ozero__class_Ozero(_982285)), _982289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982285), _982287), _982291)))], (22993 ^ _774244) ^ [_1172009, _1172011, _1172013, _1172015, _1172017] : [-(hAPP(c_Product__Type_Osnd(_1172009, _1172011), hAPP(c_Product__Type_Oapsnd(_1172013, _1172011, _1172009, _1172015), _1172017)) = hAPP(_1172015, hAPP(c_Product__Type_Osnd(_1172009, _1172013), _1172017)))], (12368 ^ _774244) ^ [_979052, _979054, _979056] : [class_Groups_Oordered__comm__monoid__add(_979052), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979052), _979054), c_Groups_Ozero__class_Ozero(_979052))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979052), _979056), c_Groups_Ozero__class_Ozero(_979052))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979052), _979054), _979056)), c_Groups_Ozero__class_Ozero(_979052))))], (45678 ^ _774244) ^ [_1671910, _1671912, _1671914, _1671916, _1671918] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1671910), tc_Option_Ooption(_1671912), _1671914, hAPP(c_Option_Omap(_1671910, _1671912), _1671916)), hAPP(c_COMBK(tc_Option_Ooption(_1671910), _1671914), c_Option_Ooption_ONone(_1671910))), _1671918) = c_Option_Ooption_ONone(_1671912))], (7541 ^ _774244) ^ [_896769, _896771] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_896769, _896771))))], (26285 ^ _774244) ^ [_1233489, _1233491] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1233489), _1233491)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233491), _1233489)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1233491)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1233489)))], (45606 ^ _774244) ^ [_1670084, _1670086, _1670088, _1670090] : [-(hAPP(c_List_Oset(_1670084), hAPP(hAPP(c_List_Omap(_1670086, _1670084), _1670088), _1670090)) = hAPP(c_Set_Oimage(_1670086, _1670084, _1670088), hAPP(c_List_Oset(_1670086), _1670090)))], (14151 ^ _774244) ^ [_1011341, _1011343, _1011345] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1011341, _1011343)), _1011345) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011341), _1011345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011343), _1011345)))], (43713 ^ _774244) ^ [_1624311, _1624313, _1624315, _1624317, _1624319] : [-(hAPP(c_Relation_Oconverse(_1624311, _1624313), hAPP(hAPP(c_Relation_Orel__comp(_1624311, _1624315, _1624313), _1624317), _1624319)) = hAPP(hAPP(c_Relation_Orel__comp(_1624313, _1624315, _1624311), hAPP(c_Relation_Oconverse(_1624315, _1624313), _1624319)), hAPP(c_Relation_Oconverse(_1624311, _1624315), _1624317)))], (48972 ^ _774244) ^ [_1753925, _1753927, _1753929] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753925), tc_List_Olist(_1753925))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753925), tc_List_Olist(_1753925)), c_List_Olist_ONil(_1753925)), _1753927)), c_List_Olexord(_1753925, _1753929))), -(_1753927 = hAPP(hAPP(c_List_Olist_OCons(_1753925), 48975 ^ [_1753925, _1753927, _1753929]), 48976 ^ [_1753925, _1753927, _1753929]))], (51165 ^ _774244) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (24407 ^ _774244) ^ [_1198668, _1198670, _1198672, _1198674, _1198676, _1198678, _1198680] : [-(hAPP(c_Product__Type_Oapfst(_1198668, _1198670, _1198672, _1198674), hAPP(c_Product__Type_Oapsnd(_1198676, _1198672, _1198668, _1198678), _1198680)) = hAPP(hAPP(c_Product__Type_OPair(_1198670, _1198672), hAPP(_1198674, hAPP(c_Product__Type_Ofst(_1198668, _1198676), _1198680))), hAPP(_1198678, hAPP(c_Product__Type_Osnd(_1198668, _1198676), _1198680))))], (1974 ^ _774244) ^ [_803047, _803049, _803051, _803053] : [-(c_Com_Ocom_OSemi(_803053, _803049) = c_Com_Ocom_OSemi(_803051, _803047)), _803053 = _803051, _803049 = _803047], (41788 ^ _774244) ^ [_1577794, _1577796] : [-(hAPP(c_Relation_ODomain(_1577794, _1577796), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1577794, _1577796), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1577794, tc_HOL_Obool)))], (43741 ^ _774244) ^ [_1624926, _1624928, _1624930, _1624932, _1624934] : [_1624926 = c_Orderings_Obot__class_Obot(tc_fun(_1624928, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624930, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1624928, tc_fun(_1624930, tc_HOL_Obool)), _1624926), _1624932)), _1624934) = _1624934)], (47451 ^ _774244) ^ [_1716846, _1716848, _1716850, _1716852] : [-(hAPP(hAPP(c_List_Onth(_1716846), hAPP(hAPP(c_List_Oappend(_1716846), _1716848), hAPP(hAPP(c_List_Olist_OCons(_1716846), _1716850), _1716852))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716846)), _1716848)) = _1716850)], (29176 ^ _774244) ^ [_1293638, _1293640, _1293642] : [class_Orderings_Oorder(_1293638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293638), _1293640), _1293642)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293638, _1293642), _1293640) = c_Orderings_Obot__class_Obot(tc_fun(_1293638, tc_HOL_Obool)))], (5737 ^ _774244) ^ [_865693, _865695, _865697] : [c_Natural_Oevalc(_865693, _865695, _865697), -(c_Natural_Oevaln(_865693, _865695, 5740 ^ [_865693, _865695, _865697], _865697))], (13631 ^ _774244) ^ [_1001593, _1001595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1001595, _1001593)), _1001593)))], (51403 ^ _774244) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (37492 ^ _774244) ^ [] : [-(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))], (50769 ^ _774244) ^ [_1792534, _1792536, _1792538] : [hBOOL(hAPP(c_List_Odistinct(_1792534), _1792536)), hBOOL(hAPP(hAPP(c_member(_1792534), _1792538), hAPP(c_List_Oset(_1792534), _1792536))), -(c_List_OtakeWhile(_1792534, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1792534), c_fNot), hAPP(hAPP(c_COMBC(_1792534, _1792534, tc_HOL_Obool), c_fequal), _1792538)), hAPP(c_List_Orev(_1792534), _1792536)) = hAPP(c_List_Orev(_1792534), hAPP(c_List_Otl(_1792534), c_List_OdropWhile(_1792534, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1792534), c_fNot), hAPP(hAPP(c_COMBC(_1792534, _1792534, tc_HOL_Obool), c_fequal), _1792538)), _1792536))))], (42884 ^ _774244) ^ [_1602584, _1602586] : [-(c_Transitive__Closure_Otrancl(_1602584, _1602586) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1602584, _1602584), tc_HOL_Obool)), _1602586), hAPP(hAPP(c_Relation_Orel__comp(_1602584, _1602584, _1602584), c_Transitive__Closure_Otrancl(_1602584, _1602586)), _1602586)))], (51065 ^ _774244) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (47670 ^ _774244) ^ [_1722065, _1722067, _1722069] : [hAPP(hAPP(c_List_Oappend(_1722065), _1722067), _1722069) = _1722067, -(_1722069 = c_List_Olist_ONil(_1722065))], (15824 ^ _774244) ^ [_1042473, _1042475, _1042477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042473), _1042475)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042477), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042475), _1042473))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042477), _1042473)), hAPP(c_Nat_OSuc, _1042475)))], (26748 ^ _774244) ^ [_1243679, _1243681, _1243683, _1243685, _1243687] : [class_Groups_Ocomm__monoid__add(_1243679), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1243679), _1243681), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1243683), _1243685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1243687), _1243685))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1243679), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1243679, tc_Nat_Onat), _1243681), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1243685))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1243683, _1243687)))], (40569 ^ _774244) ^ [_1540877, _1540879, _1540881] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1540877), hAPP(c_Set_OCollect(_1540877), hAPP(hAPP(c_COMBS(_1540877, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540877), c_fdisj), _1540879)), _1540881)))), 40572 ^ _774244 : [(40575 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1540877), hAPP(c_Set_OCollect(_1540877), _1540881))))], (40573 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1540877), hAPP(c_Set_OCollect(_1540877), _1540879))))]]], (36703 ^ _774244) ^ [_1453579, _1453581, _1453583, _1453585, _1453587] : [class_Orderings_Olinorder(_1453579), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453579, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1453579, _1453581, _1453583)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1453579, _1453585, _1453587)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1453579, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1453579), _1453581), _1453585), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1453579), _1453583), _1453587)))], (38890 ^ _774244) ^ [_1501546, _1501548, _1501550, _1501552, _1501554] : [hAPP(_1501552, _1501548) = _1501554, -(hBOOL(hAPP(hAPP(c_member(_1501546), _1501548), hAPP(c_Set_Ovimage(_1501546, _1501550, _1501552), hAPP(hAPP(c_Set_Oinsert(_1501550), _1501554), c_Orderings_Obot__class_Obot(tc_fun(_1501550, tc_HOL_Obool)))))))], (26566 ^ _774244) ^ [_1239956, _1239958, _1239960] : [-(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), _1239956)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1239958))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1239960))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239960), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1239956), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1239956), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1239960), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1239958)))))], (34592 ^ _774244) ^ [] : [-(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)))], (19669 ^ _774244) ^ [_1110446, _1110448, _1110450] : [class_Rings_Olinordered__idom(_1110446), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110446), c_Groups_Ozero__class_Ozero(_1110446)), hAPP(hAPP(c_Power_Opower__class_Opower(_1110446), _1110448), 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)))), _1110450))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110446), c_Groups_Ozero__class_Ozero(_1110446)), _1110448)))], (36679 ^ _774244) ^ [_1453035, _1453037, _1453039, _1453041] : [class_Orderings_Oorder(_1453035), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453035, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1453035, _1453037, _1453039)), c_SetInterval_Oord__class_OatLeastAtMost(_1453035, _1453039, _1453041)) = c_Orderings_Obot__class_Obot(tc_fun(_1453035, tc_HOL_Obool)))], (38874 ^ _774244) ^ [_1501182, _1501184, _1501186, _1501188, _1501190, _1501192, _1501194] : [c_Finite__Set_Ofolding__image(_1501182, _1501184, _1501186, _1501188, _1501190), hBOOL(hAPP(c_Finite__Set_Ofinite(_1501184), _1501192)), -(hAPP(hAPP(_1501190, _1501194), _1501192) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1501182, _1501184, _1501186), _1501194), _1501188), _1501192))], (51155 ^ _774244) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (18515 ^ _774244) ^ [_1090333] : [c_Int_OPls = c_Int_OBit1(_1090333)], (18375 ^ _774244) ^ [_1087776, _1087778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087776), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087776)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087778)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087778))], (41548 ^ _774244) ^ [_1572179, _1572181, _1572183, _1572185] : [c_FunDef_Oreduction__pair(_1572179, _1572181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1572179, _1572179), tc_HOL_Obool)), _1572183), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1572179, _1572179), tc_HOL_Obool), tc_fun(tc_prod(_1572179, _1572179), tc_HOL_Obool)), _1572181))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1572179, _1572179), tc_HOL_Obool)), _1572185), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1572179, _1572179), tc_HOL_Obool), tc_fun(tc_prod(_1572179, _1572179), tc_HOL_Obool)), _1572181))), c_Wellfounded_Owf(_1572179, _1572185), -(c_Wellfounded_Owf(_1572179, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572179, _1572179), tc_HOL_Obool)), _1572183), _1572185)))], (43437 ^ _774244) ^ [_1615696, _1615698, _1615700, _1615702, _1615704] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615696, tc_fun(_1615698, tc_HOL_Obool)), _1615700), hAPP(hAPP(c_COMBB(tc_fun(_1615698, tc_HOL_Obool), tc_fun(_1615698, tc_HOL_Obool), _1615696), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615698, tc_HOL_Obool)), _1615702)), _1615704)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615698, tc_HOL_Obool)), _1615702), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615696, tc_fun(_1615698, tc_HOL_Obool)), _1615700), _1615704)))], (19069 ^ _774244) ^ [_1099624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1099624)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099624), c_Int_OPls)))], (4898 ^ _774244) ^ [_849939, _849941, _849943, _849945, _849947, _849949] : [-(c_List_Olinorder__class_Oinsort__key(_849949, _849945, _849941) = c_List_Olinorder__class_Oinsort__key(_849947, _849943, _849939)), _849949 = _849947, _849945 = _849943, _849941 = _849939], (24111 ^ _774244) ^ [_1192997] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1192997), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1192997)], (31116 ^ _774244) ^ [_1332485, _1332487, _1332489, _1332491] : [hBOOL(hAPP(hAPP(c_member(_1332485), _1332487), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332485, tc_HOL_Obool)), _1332489), _1332491))), hBOOL(hAPP(hAPP(c_member(_1332485), _1332487), _1332491))], (22054 ^ _774244) ^ [_1153082, _1153084, _1153086, _1153088] : [class_Groups_Ouminus(_1153082), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1153084, _1153082)), _1153086), _1153088) = hAPP(c_Groups_Ouminus__class_Ouminus(_1153082), hAPP(_1153086, _1153088)))], (31136 ^ _774244) ^ [_1332944, _1332946, _1332948, _1332950] : [-(hBOOL(hAPP(hAPP(c_member(_1332944), _1332946), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332944, tc_HOL_Obool)), _1332948), _1332950)))), hBOOL(hAPP(hAPP(c_member(_1332944), _1332946), _1332948)), -(hBOOL(hAPP(hAPP(c_member(_1332944), _1332946), _1332950)))], (44725 ^ _774244) ^ [_1649220] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649220, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1649220, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1649220, tc_HOL_Obool)))], (28966 ^ _774244) ^ [_1289647, _1289649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1289647, tc_HOL_Obool)), _1289649), c_Orderings_Obot__class_Obot(tc_fun(_1289647, tc_HOL_Obool)))), -(_1289649 = c_Orderings_Obot__class_Obot(tc_fun(_1289647, tc_HOL_Obool)))], (28467 ^ _774244) ^ [_1277866, _1277868, _1277870] : [class_Orderings_Oorder(_1277866), 28470 ^ _774244 : [(28477 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277866), _1277870), _1277868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277866, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1277866), _1277868)), hAPP(c_SetInterval_Oord__class_OatLeast(_1277866), _1277870))))], (28471 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277866, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1277866), _1277868)), hAPP(c_SetInterval_Oord__class_OatLeast(_1277866), _1277870))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277866), _1277870), _1277868)))]]], (50510 ^ _774244) ^ [_1787236, _1787238] : [-(c_List_Oconcat(tc_List_Olist(_1787236), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1787236), tc_List_Olist(tc_List_Olist(_1787236))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1787236)), _1787236, c_List_Olist_ONil(tc_List_Olist(_1787236)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1787236), tc_List_Olist(tc_List_Olist(_1787236))), _1787236), hAPP(hAPP(c_COMBC(tc_List_Olist(_1787236), tc_List_Olist(tc_List_Olist(_1787236)), tc_List_Olist(tc_List_Olist(_1787236))), c_List_Olist_OCons(tc_List_Olist(_1787236))), c_List_Olist_ONil(tc_List_Olist(_1787236)))))), _1787238)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1787236), tc_List_Olist(_1787236)), c_List_Otl(_1787236)), hAPP(c_List_Ofilter(tc_List_Olist(_1787236), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1787236)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1787236), tc_List_Olist(_1787236), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1787236)))), _1787238)))], (974 ^ _774244) ^ [_789143, _789145] : [-(class_Groups_Oordered__ab__group__add__abs(_789143)), _789145 = _789143, class_Groups_Oordered__ab__group__add__abs(_789145)], (51203 ^ _774244) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (29396 ^ _774244) ^ [_1297320, _1297322] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297320), _1297322))), -(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), _1297320, _1297322))], (35360 ^ _774244) ^ [_1423575] : [-(c_Nitpick_Onum(_1423575) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1423575, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1423575)))], (14225 ^ _774244) ^ [_1012582, _1012584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012582)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012584)), -(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), _1012582), _1012584))))], (7483 ^ _774244) ^ [_895667, _895669, _895671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _895667), _895669)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _895667), _895671))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _895669), _895671)))], (6155 ^ _774244) ^ [_872896, _872898, _872900, _872902, _872904] : [-(c_Natural_Oevalc(c_Com_Ocom_OCond(_872896, _872898, _872900), _872902, _872904)), 6156 ^ _774244 : [(6163 ^ _774244) ^ [] : [-(hBOOL(hAPP(_872896, _872902))), c_Natural_Oevalc(_872900, _872902, _872904)], (6157 ^ _774244) ^ [] : [hBOOL(hAPP(_872896, _872902)), c_Natural_Oevalc(_872898, _872902, _872904)]]], (14149 ^ _774244) ^ [_1011288, _1011290, _1011292] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011288), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1011290, _1011292)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011288), _1011290), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011288), _1011292)))], (39344 ^ _774244) ^ [_1512166, _1512168, _1512170, _1512172] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1512166, _1512168, _1512170, _1512172, c_Orderings_Obot__class_Obot(tc_fun(_1512166, tc_HOL_Obool))), _1512172)))], (31122 ^ _774244) ^ [_1332617, _1332619, _1332621, _1332623] : [hBOOL(hAPP(hAPP(c_member(_1332617), _1332619), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332617, tc_HOL_Obool)), _1332621), _1332623))), -(hBOOL(hAPP(hAPP(c_member(_1332617), _1332619), _1332621)))], (50270 ^ _774244) ^ [_1780899] : [-(hAPP(c_List_Orev(_1780899), c_List_Olist_ONil(_1780899)) = c_List_Olist_ONil(_1780899))], (43531 ^ _774244) ^ [_1618997, _1618999, _1619001, _1619003] : [43533 ^ _774244 : [(43536 ^ _774244) ^ [] : [hAPP(_1619003, 43532 ^ [_1618997, _1618999, _1619001, _1619003]) = c_Orderings_Otop__class_Otop(tc_fun(_1618997, tc_HOL_Obool))], (43534 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618999), 43532 ^ [_1618997, _1618999, _1619001, _1619003]), _1619001)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1618997, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618999, tc_fun(_1618997, tc_HOL_Obool)), _1619001), _1619003))], (46405 ^ _774244) ^ [_1691550, _1691552, _1691554] : [-(hAPP(c_List_Oset(_1691550), hAPP(hAPP(c_List_Olist_OCons(_1691550), _1691552), _1691554)) = hAPP(hAPP(c_Set_Oinsert(_1691550), _1691552), hAPP(c_List_Oset(_1691550), _1691554)))], (29172 ^ _774244) ^ [_1293472, _1293474, _1293476, _1293478] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1293472, tc_HOL_Obool)), _1293474), hAPP(hAPP(c_Set_Oinsert(_1293472), _1293476), _1293478)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1293472, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1293472, tc_HOL_Obool)), _1293474), hAPP(hAPP(c_Set_Oinsert(_1293472), _1293476), c_Orderings_Obot__class_Obot(tc_fun(_1293472, tc_HOL_Obool))))), _1293478))], (1244 ^ _774244) ^ [_792518, _792520] : [-(class_Lattices_Obounded__lattice__bot(_792518)), _792520 = _792518, class_Lattices_Obounded__lattice__bot(_792520)], (12940 ^ _774244) ^ [_989192, _989194] : [-(_989192 = hAPP(c_Int_Onat, _989194)), 12943 ^ _774244 : [(12946 ^ _774244) ^ [] : [_989194 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _989192)], (12944 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989194)))]], 12947 ^ _774244 : [(12950 ^ _774244) ^ [] : [_989192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12948 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989194))]]], (37869 ^ _774244) ^ [_1480114, _1480116, _1480118] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1480114), _1480116)), c_Fun_Oinj__on(_1480114, tc_fun(tc_fun(_1480114, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1480114, tc_fun(tc_prod(_1480114, _1480114), tc_HOL_Obool), tc_fun(tc_fun(_1480114, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1480114, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1480114, _1480114), tc_HOL_Obool), tc_fun(tc_fun(_1480114, tc_HOL_Obool), tc_HOL_Obool)), _1480114), c_Equiv__Relations_Oquotient(_1480114)), hAPP(hAPP(c_COMBC(_1480114, tc_fun(_1480114, tc_HOL_Obool), tc_fun(_1480114, tc_HOL_Obool)), c_Set_Oinsert(_1480114)), c_Orderings_Obot__class_Obot(tc_fun(_1480114, tc_HOL_Obool))))), _1480118), _1480116), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1480114, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1480114), _1480116), _1480118)) = hAPP(c_Finite__Set_Ocard(_1480114), _1480116))], (7139 ^ _774244) ^ [_890190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890190), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (28428 ^ _774244) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (51135 ^ _774244) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (46872 ^ _774244) ^ [_1702992] : [class_Orderings_Olinorder(_1702992), -(c_List_Olinorder__class_Osorted__list__of__set(_1702992, c_Orderings_Obot__class_Obot(tc_fun(_1702992, tc_HOL_Obool))) = c_List_Olist_ONil(_1702992))], (49848 ^ _774244) ^ [_1772035, _1772037, _1772039] : [class_Orderings_Olinorder(_1772035), c_List_Olinorder__class_Osorted(_1772035, _1772037), -(c_List_Olinorder__class_Osorted(_1772035, c_List_Oremove1(_1772035, _1772039, _1772037)))], (48310 ^ _774244) ^ [_1738979, _1738981, _1738983] : [-(hAPP(hAPP(c_List_Odrop(_1738979), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1738979), _1738981), _1738983)) = _1738983)], (48722 ^ _774244) ^ [_1747988, _1747990, _1747992, _1747994, _1747996, _1747998] : [-(hAPP(c_List_Ofoldl(_1747988, _1747990, _1747992, _1747994), hAPP(hAPP(c_List_Olist_OCons(_1747990), _1747996), _1747998)) = hAPP(c_List_Ofoldl(_1747988, _1747990, _1747992, hAPP(hAPP(_1747992, _1747994), _1747996)), _1747998))], (44558 ^ _774244) ^ [_1645257, _1645259, _1645261] : [class_Complete__Lattice_Ocomplete__lattice(_1645257), hBOOL(hAPP(c_Finite__Set_Ofinite(_1645257), _1645259)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1645257), _1645261), c_Complete__Lattice_OInf__class_OInf(_1645257, _1645259)) = hAPP(hAPP(c_Finite__Set_Ofold(_1645257, _1645257, c_Lattices_Osemilattice__inf__class_Oinf(_1645257)), _1645261), _1645259))], (1404 ^ _774244) ^ [_794518, _794520] : [-(class_Groups_Oordered__ab__semigroup__add(_794518)), _794520 = _794518, class_Groups_Oordered__ab__semigroup__add(_794520)], (22548 ^ _774244) ^ [_1163361, _1163363] : [-(_1163361 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1163363, _1163361) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1163363), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1163361)))], (23797 ^ _774244) ^ [_1187137, _1187139, _1187141] : [class_Orderings_Olinorder(_1187137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187137), _1187139), _1187141)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187137), _1187139), _1187141) = _1187139)], (48554 ^ _774244) ^ [_1744761, _1744763, _1744765] : [-(_1744761 = c_List_Olist_ONil(_1744763)), -(hAPP(c_List_Ohd(_1744763), hAPP(hAPP(c_List_Oappend(_1744763), _1744761), _1744765)) = hAPP(c_List_Ohd(_1744763), _1744761))], (50352 ^ _774244) ^ [_1782704, _1782706, _1782708, _1782710, _1782712] : [-(c_List_Ofoldr(_1782704, _1782706, _1782708, _1782710, _1782712) = hAPP(c_List_Ofoldl(_1782706, _1782704, hAPP(c_COMBC(_1782704, _1782706, _1782706), _1782708), _1782712), hAPP(c_List_Orev(_1782704), _1782710)))], (18523 ^ _774244) ^ [_1090445] : [_1090445 = c_Int_OMin, -(c_Int_OBit1(_1090445) = c_Int_OMin)], (50665 ^ _774244) ^ [_1790682, _1790684, _1790686, _1790688] : [-(c_List_Oremdups(_1790682, hAPP(hAPP(c_List_Omap(_1790684, _1790682), _1790686), c_List_Oremdups(_1790684, _1790688))) = c_List_Oremdups(_1790682, hAPP(hAPP(c_List_Omap(_1790684, _1790682), _1790686), _1790688)))], (51287 ^ _774244) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (37701 ^ _774244) ^ [_1476626, _1476628, _1476630] : [class_Lattices_Olattice(_1476626), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476626), _1476628)), -(_1476630 = c_Orderings_Obot__class_Obot(tc_fun(_1476626, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1476626, tc_HOL_Obool)), _1476630), _1476628)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1476626), c_Big__Operators_Olattice__class_OInf__fin(_1476626, _1476630)), c_Big__Operators_Olattice__class_OInf__fin(_1476626, _1476628)) = c_Big__Operators_Olattice__class_OInf__fin(_1476626, _1476628))], (3258 ^ _774244) ^ [_824287, _824289, _824291, _824293, _824295, _824297] : [-(c_SetInterval_Oord_OatMost(_824297, _824293, _824289) = c_SetInterval_Oord_OatMost(_824295, _824291, _824287)), _824297 = _824295, _824293 = _824291, _824289 = _824287], (34385 ^ _774244) ^ [_1400381, _1400383, _1400385, _1400387, _1400389, _1400391] : [hBOOL(hAPP(hAPP(c_member(_1400381), _1400383), _1400385)), -(c_Map_Orestrict__map(_1400381, _1400387, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1400381, tc_Option_Ooption(_1400387)), _1400389), _1400383), _1400391), _1400385) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1400381, tc_Option_Ooption(_1400387)), c_Map_Orestrict__map(_1400381, _1400387, _1400389, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400381, tc_HOL_Obool)), _1400385), hAPP(hAPP(c_Set_Oinsert(_1400381), _1400383), c_Orderings_Obot__class_Obot(tc_fun(_1400381, tc_HOL_Obool)))))), _1400383), _1400391))], (10742 ^ _774244) ^ [_950781, _950783, _950785] : [class_Orderings_Oorder(_950781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950781), _950783), _950785)), -(_950783 = _950785), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950781), _950783), _950785)))], (23721 ^ _774244) ^ [_1185770, _1185772, _1185774, _1185776] : [class_Groups_Oordered__ab__group__add(_1185770), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185770), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1185770), _1185772), _1185774)), _1185776) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1185770), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185770), _1185772), _1185776)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185770), _1185774), _1185776)))], (35247 ^ _774244) ^ [_1420368, _1420370, _1420372, _1420374, _1420376, _1420378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1420368, _1420370), tc_HOL_Obool)), _1420372), _1420374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1420368, tc_HOL_Obool)), _1420376), _1420378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1420370, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1420368, _1420370, _1420372), _1420376)), hAPP(c_Relation_OImage(_1420368, _1420370, _1420374), _1420378))))], (50176 ^ _774244) ^ [_1778930, _1778932, _1778934] : [-(hAPP(c_List_Ofilter(_1778930, _1778932), c_List_Oconcat(_1778930, _1778934)) = c_List_Oconcat(_1778930, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1778930), tc_List_Olist(_1778930)), c_List_Ofilter(_1778930, _1778932)), _1778934)))], (16275 ^ _774244) ^ [_1051020, _1051022, _1051024, _1051026] : [class_Rings_Ocomm__semiring__1(_1051020), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1051020), hAPP(hAPP(c_Power_Opower__class_Opower(_1051020), _1051022), _1051024)), _1051026) = hAPP(hAPP(c_Power_Opower__class_Opower(_1051020), _1051022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1051024), _1051026)))], (17181 ^ _774244) ^ [_1068147, _1068149, _1068151, _1068153] : [class_Rings_Olinordered__semidom(_1068147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068147), _1068149), _1068151)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068147), c_Groups_Ozero__class_Ozero(_1068147)), _1068149)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068147), hAPP(hAPP(c_Power_Opower__class_Opower(_1068147), _1068149), _1068153)), hAPP(hAPP(c_Power_Opower__class_Opower(_1068147), _1068151), _1068153))))], (22230 ^ _774244) ^ [_1156820, _1156822] : [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(_1156820))), 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)), _1156822)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156820)), hAPP(c_Nat_OSuc, _1156822))))], (34830 ^ _774244) ^ [_1410910, _1410912, _1410914, _1410916, _1410918] : [class_Groups_Ocomm__monoid__mult(_1410910), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410912), _1410914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1410912, tc_HOL_Obool)), _1410916), _1410914)), 34844 ^ _774244 : [(34847 ^ _774244) ^ [] : [hAPP(_1410918, 34843 ^ [_1410910, _1410912, _1410914, _1410916, _1410918]) = c_Groups_Oone__class_Oone(_1410910)], (34845 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1410912), 34843 ^ [_1410910, _1410912, _1410914, _1410916, _1410918]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410912, tc_HOL_Obool)), _1410914), _1410916))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410912, _1410910), _1410918), _1410916) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410912, _1410910), _1410918), _1410914))], (40824 ^ _774244) ^ [_1548434, _1548436] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1548434), _1548436)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1548434, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1548434, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1548434, tc_HOL_Obool), tc_fun(_1548434, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1548434, tc_HOL_Obool))), _1548436)))))], (14141 ^ _774244) ^ [_1011159, _1011161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1011159), _1011161)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1011159, _1011161) = _1011159)], (46218 ^ _774244) ^ [_1685174, _1685176, _1685178] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1685174), _1685176)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1685174)), hAPP(c_Set_OCollect(tc_List_Olist(_1685174)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1685174), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1685174)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1685174), tc_fun(_1685174, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1685174, tc_HOL_Obool), tc_fun(tc_fun(_1685174, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1685174)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1685174, tc_HOL_Obool))), c_List_Oset(_1685174))), _1685176))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1685174), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1685174)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1685174)))), _1685178))))))], (27788 ^ _774244) ^ [_1264645, _1264647, _1264649, _1264651, _1264653] : [class_Lattices_Olattice(_1264645), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264647, _1264645)), _1264649), _1264651), _1264653) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264645), hAPP(_1264649, _1264653)), hAPP(_1264651, _1264653)))], (46437 ^ _774244) ^ [_1692262, _1692264, _1692266, _1692268, _1692270] : [hAPP(hAPP(c_List_Olist_OCons(_1692262), _1692264), _1692266) = hAPP(hAPP(c_List_Olist_OCons(_1692262), _1692268), _1692270), 46440 ^ _774244 : [(46443 ^ _774244) ^ [] : [-(_1692266 = _1692270)], (46441 ^ _774244) ^ [] : [-(_1692264 = _1692268)]]], (26311 ^ _774244) ^ [_1233921, _1233923] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233921)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233923))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233923), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233921)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29764 ^ _774244) ^ [_1304356, _1304358, _1304360, _1304362] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1304356), _1304358)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1304360), hAPP(c_Set_Oimage(_1304356, _1304360, _1304362), _1304358))))], (40691 ^ _774244) ^ [_1543776, _1543778, _1543780] : [-(hBOOL(hAPP(_1543776, _1543778))), -(hAPP(c_Set_OCollect(_1543780), hAPP(hAPP(c_COMBS(_1543780, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543780), c_fconj), hAPP(hAPP(c_COMBC(_1543780, _1543780, tc_HOL_Obool), c_fequal), _1543778))), _1543776)) = c_Orderings_Obot__class_Obot(tc_fun(_1543780, tc_HOL_Obool)))], (25359 ^ _774244) ^ [_1216526, _1216528, _1216530, _1216532, _1216534] : [class_Rings_Ocomm__semiring__1(_1216526), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216526), _1216528), _1216530)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216526), _1216532), _1216534)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216526), _1216528), _1216532)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216526), _1216530), _1216534))))], (23451 ^ _774244) ^ [_1180535, _1180537, _1180539] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1180535, tc_HOL_Obool)), _1180537), _1180539))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1180535, tc_HOL_Obool)), _1180537), _1180539)), -(_1180537 = _1180539)], (14922 ^ _774244) ^ [_1024748, _1024750, _1024752] : [class_Divides_Osemiring__div(_1024748), -(_1024750 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024748), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024748), _1024750), _1024752)), _1024752)), c_Divides_Odiv__class_Omod(_1024748, _1024750, _1024752)))], (21079 ^ _774244) ^ [_1135211, _1135213, _1135215] : [class_Fields_Olinordered__field(_1135211), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135211), _1135213), _1135215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135211), _1135213), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135211), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135211), _1135213), _1135215)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135211), c_Groups_Oone__class_Oone(_1135211)), c_Groups_Oone__class_Oone(_1135211))))))], (28749 ^ _774244) ^ [_1284879, _1284881, _1284883, _1284885] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1284879), _1284881), _1284883), _1284885)), -(_1284881 = _1284885), -(hBOOL(hAPP(_1284883, _1284885)))], (12207 ^ _774244) ^ [_976282] : [hBOOL(hAPP(_976282, 12208 ^ [_976282])), 12211 ^ _774244 : [(12212 ^ _774244) ^ [_976376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _976376)), -(hBOOL(hAPP(_976282, hAPP(c_Int_Onat, _976376))))]]], (12181 ^ _774244) ^ [_975911] : [-(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), _975911))))], (46459 ^ _774244) ^ [_1692674, _1692676, _1692678, _1692680, _1692682] : [-(hAPP(hAPP(c_List_Omap(_1692674, _1692676), _1692678), hAPP(hAPP(c_List_Olist_OCons(_1692674), _1692680), _1692682)) = hAPP(hAPP(c_List_Olist_OCons(_1692676), hAPP(_1692678, _1692680)), hAPP(hAPP(c_List_Omap(_1692674, _1692676), _1692678), _1692682)))], (48136 ^ _774244) ^ [_1733694, _1733696, _1733698] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733694), tc_List_Olist(_1733694))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733694), tc_List_Olist(_1733694)), c_List_Olist_ONil(_1733694)), _1733696)), c_List_Olistrel1(_1733694, _1733698)))], (51099 ^ _774244) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (35278 ^ _774244) ^ [_1421149, _1421151, _1421153, _1421155, _1421157] : [-(hBOOL(hAPP(hAPP(c_member(_1421149), _1421151), hAPP(c_Relation_OImage(_1421153, _1421149, _1421155), _1421157)))), 35279 ^ _774244 : [(35280 ^ _774244) ^ [_1421235] : [hBOOL(hAPP(hAPP(c_member(_1421153), _1421235), _1421157)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1421153, _1421149)), hAPP(hAPP(c_Product__Type_OPair(_1421153, _1421149), _1421235), _1421151)), _1421155))]]], (21909 ^ _774244) ^ [_1150800, _1150802, _1150804] : [class_Fields_Olinordered__field(_1150800), 21915 ^ _774244 : [(21918 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150800), _1150802), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150800), _1150804), 21914 ^ [_1150800, _1150802, _1150804])))], (21916 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150800), c_Groups_Ozero__class_Ozero(_1150800)), 21914 ^ [_1150800, _1150802, _1150804])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150800), _1150802), _1150804)))], (39826 ^ _774244) ^ [_1525238, _1525240, _1525242, _1525244] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1525238), _1525240)), 39832 ^ _774244 : [(39835 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1525242), hAPP(_1525244, 39831 ^ [_1525238, _1525240, _1525242, _1525244])))], (39833 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525238), 39831 ^ [_1525238, _1525240, _1525242, _1525244]), _1525240)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1525238, _1525242)), hAPP(hAPP(c_Product__Type_OSigma(_1525238, _1525242), _1525240), _1525244))))], (17047 ^ _774244) ^ [_1065680, _1065682] : [17048 ^ _774244 : [(17051 ^ _774244) ^ [] : [_1065682 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17049 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1065680))]], -(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), _1065680), _1065682))))], (5656 ^ _774244) ^ [_864388] : [_864388 = hAPP(c_Nat_OSuc, _864388)], (20893 ^ _774244) ^ [_1132198, _1132200, _1132202, _1132204] : [class_Fields_Ofield(_1132198), -(_1132200 = c_Groups_Ozero__class_Ozero(_1132198)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132198), _1132202), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132198), _1132204), _1132200)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132198), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132198), _1132200), _1132202)), _1132204)), _1132200))], (25295 ^ _774244) ^ [_1215428, _1215430, _1215432, _1215434] : [class_Divides_Osemiring__div(_1215428), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215428), _1215430), _1215432)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215428), _1215430), _1215434)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215428), _1215430), c_Divides_Odiv__class_Omod(_1215428, _1215432, _1215434))))], (43601 ^ _774244) ^ [_1620887, _1620889, _1620891, _1620893] : [hBOOL(hAPP(hAPP(c_member(_1620889), _1620893), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1620887, tc_fun(_1620889, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1620887, tc_HOL_Obool))), _1620891))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1620887, tc_fun(_1620889, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1620887, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1620889, tc_HOL_Obool), tc_fun(_1620889, tc_HOL_Obool), _1620887), hAPP(c_COMBC(_1620889, tc_fun(_1620889, tc_HOL_Obool), tc_HOL_Obool), c_member(_1620889))), _1620891)), _1620893)))], (40951 ^ _774244) ^ [_1552271, _1552273, _1552275] : [-(c_Map_Oran(_1552271, _1552273, _1552275) = hAPP(c_Set_OCollect(_1552273), hAPP(hAPP(c_COMBB(tc_fun(_1552271, tc_HOL_Obool), tc_HOL_Obool, _1552273), c_HOL_OEx(_1552271)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1552273), tc_fun(_1552271, tc_HOL_Obool), _1552273), hAPP(c_COMBC(_1552271, tc_Option_Ooption(_1552273), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1552273), tc_fun(tc_Option_Ooption(_1552273), tc_HOL_Obool), _1552271), c_fequal), _1552275))), c_Option_Ooption_OSome(_1552273)))))], (48003 ^ _774244) ^ [_1729988, _1729990, _1729992, _1729994, _1729996, _1729998, _1730000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729988)), _1729990)), _1729992)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729992), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729994)), _1729996))), -(c_Map_Omap__upds(_1729988, _1729994, _1729998, _1729990, hAPP(hAPP(c_List_Olist__update(_1729994, _1729996), _1729992), _1730000)) = c_Map_Omap__upds(_1729988, _1729994, _1729998, _1729990, _1729996))], (29438 ^ _774244) ^ [_1298275, _1298277, _1298279, _1298281, _1298283] : [_1298275 = c_Orderings_Obot__class_Obot(tc_fun(_1298277, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298277, tc_fun(_1298279, tc_HOL_Obool)), _1298275), hAPP(hAPP(c_COMBB(tc_fun(_1298279, tc_HOL_Obool), tc_fun(_1298279, tc_HOL_Obool), _1298277), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298279, tc_HOL_Obool)), _1298281)), _1298283)) = c_Orderings_Obot__class_Obot(tc_fun(_1298279, tc_HOL_Obool)))], (48602 ^ _774244) ^ [_1745406, _1745408, _1745410, _1745412] : [-(hAPP(hAPP(c_List_Omap(_1745406, _1745408), _1745410), hAPP(c_List_Otl(_1745406), _1745412)) = hAPP(c_List_Otl(_1745408), hAPP(hAPP(c_List_Omap(_1745406, _1745408), _1745410), _1745412)))], (30336 ^ _774244) ^ [_1314895] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1314895), c_Orderings_Otop__class_Otop(tc_fun(_1314895, 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(_1314895), c_Orderings_Otop__class_Otop(tc_fun(_1314895, tc_HOL_Obool))))))], (31933 ^ _774244) ^ [_1351699, _1351701, _1351703, _1351705, _1351707] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1351699, _1351701, _1351703), _1351705), _1351707)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1351699, _1351701)), hAPP(hAPP(c_Product__Type_OPair(_1351699, _1351701), _1351705), _1351707)), _1351703)))], (1634 ^ _774244) ^ [_797393, _797395] : [-(class_Groups_Omonoid__add(_797393)), _797395 = _797393, class_Groups_Omonoid__add(_797395)], (7553 ^ _774244) ^ [_897079, _897081, _897083, _897085, _897087] : [c_Com_Ocom_OCond(_897079, _897081, _897083) = c_Com_Ocom_OAss(_897085, _897087)], (35813 ^ _774244) ^ [_1433977, _1433979, _1433981, _1433983, _1433985, _1433987, _1433989, _1433991, _1433993, _1433995] : [c_Equiv__Relations_Oequiv(_1433977, _1433979, _1433981), c_Equiv__Relations_Oequiv(_1433983, _1433985, _1433987), c_Equiv__Relations_Ocongruent2(_1433977, _1433983, tc_fun(_1433989, tc_HOL_Obool), _1433981, _1433987, _1433991), hBOOL(hAPP(hAPP(c_member(_1433977), _1433993), _1433979)), hBOOL(hAPP(hAPP(c_member(_1433983), _1433995), _1433985)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433977, tc_fun(_1433989, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1433977, _1433977, _1433981), hAPP(hAPP(c_Set_Oinsert(_1433977), _1433993), c_Orderings_Obot__class_Obot(tc_fun(_1433977, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1433983, tc_fun(_1433989, tc_HOL_Obool)), tc_fun(_1433989, tc_HOL_Obool), _1433977), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433983, tc_fun(_1433989, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1433983, _1433983, _1433987), hAPP(hAPP(c_Set_Oinsert(_1433983), _1433995), c_Orderings_Obot__class_Obot(tc_fun(_1433983, tc_HOL_Obool)))))), _1433991)) = hAPP(hAPP(_1433991, _1433993), _1433995))], (2294 ^ _774244) ^ [_808817, _808819, _808821, _808823, _808825, _808827] : [-(c_Power_Opower_Opower(_808827, _808823, _808819) = c_Power_Opower_Opower(_808825, _808821, _808817)), _808827 = _808825, _808823 = _808821, _808819 = _808817], (10948 ^ _774244) ^ [_954287, _954289] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954287), _954289) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_954287 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_954289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47941 ^ _774244) ^ [_1728483, _1728485, _1728487] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1728483, tc_HOL_Obool)), hAPP(c_List_Oset(_1728483), hAPP(hAPP(c_List_Otake(_1728483), _1728485), _1728487))), hAPP(c_List_Oset(_1728483), _1728487))))], (25373 ^ _774244) ^ [_1216797, _1216799, _1216801, _1216803] : [class_Rings_Ocomm__semiring__1(_1216797), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216797), _1216799), _1216801)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216797), _1216799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216797), _1216803), _1216801))))], (48588 ^ _774244) ^ [_1745156, _1745158, _1745160] : [-(hAPP(hAPP(c_List_Odrop(_1745156), hAPP(c_Nat_OSuc, _1745158)), _1745160) = hAPP(hAPP(c_List_Odrop(_1745156), _1745158), hAPP(c_List_Otl(_1745156), _1745160)))], (28318 ^ _774244) ^ [_1274958, _1274960, _1274962, _1274964] : [class_Orderings_Olinorder(_1274958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274958), _1274960), _1274962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274958), _1274962), _1274964)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274958, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1274958, _1274960, _1274962)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1274958, _1274962), _1274964)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1274958, _1274960, _1274964))], (46846 ^ _774244) ^ [_1702541, _1702543, _1702545, _1702547] : [-(c_List_Ofoldr(_1702541, _1702543, _1702545, c_List_Olist_ONil(_1702541), _1702547) = _1702547)], (9112 ^ _774244) ^ [_923327] : [class_Rings_Ozero__neq__one(_923327), c_Groups_Ozero__class_Ozero(_923327) = c_Groups_Oone__class_Oone(_923327)], (14880 ^ _774244) ^ [_1024016, _1024018] : [-(_1024016 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14883 ^ _774244 : [(14890 ^ _774244) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024018, _1024016) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024018), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1024016)) = 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), _1024018), _1024016))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (14884 ^ _774244) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024018, _1024016) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024018), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1024016)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024018), _1024016)))]]], (29786 ^ _774244) ^ [_1304779, _1304781] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1304779, _1304781)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1304779, _1304781), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1304781), c_Orderings_Otop__class_Otop(tc_fun(_1304781, tc_HOL_Obool)))))], (51131 ^ _774244) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (42844 ^ _774244) ^ [_1601574, _1601576, _1601578, _1601580, _1601582] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601574, _1601574)), hAPP(hAPP(c_Product__Type_OPair(_1601574, _1601574), _1601576), _1601578)), c_Transitive__Closure_Otrancl(_1601574, _1601580))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1601574, _1601574)), hAPP(hAPP(c_Product__Type_OPair(_1601574, _1601574), _1601578), _1601582)), _1601580)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601574, _1601574)), hAPP(hAPP(c_Product__Type_OPair(_1601574, _1601574), _1601576), _1601582)), c_Transitive__Closure_Otrancl(_1601574, _1601580))))], (22264 ^ _774244) ^ [_1157703, _1157705, _1157707, _1157709, _1157711] : [-(hAPP(c_Nat_Onat_Onat__rec(_1157703, _1157705, _1157707), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157709)), _1157711)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1157703), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1157709))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1157703, _1157703), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1157703, tc_fun(_1157703, _1157703)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1157703, tc_fun(_1157703, _1157703)), tc_Int_Oint), c_If(_1157703)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1157703, _1157705, _1157707), _1157711))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1157703, _1157703), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1157703, _1157703), tc_Int_Oint), _1157707), 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)), _1157711))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1157703, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1157703, _1157705, _1157707)), 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)), _1157711))))))], (51091 ^ _774244) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (10033 ^ _774244) ^ [_939606, _939608] : [-(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), _939606))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _939608))))], (13010 ^ _774244) ^ [_990303] : [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, _990303)))))], (49980 ^ _774244) ^ [_1774396, _1774398, _1774400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1774396), _1774398)), _1774400)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1774396, _1774400)), _1774398) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1774396), _1774398))], (34461 ^ _774244) ^ [_1402069, _1402071, _1402073, _1402075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1402069), _1402071)), -(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), _1402069), _1402073)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1402071), _1402075))), c_FunDef_Opair__less)))], (7569 ^ _774244) ^ [_897511, _897513] : [c_Com_Ocom_OAss(_897511, _897513) = c_Com_Ocom_OSKIP], (50272 ^ _774244) ^ [_1780931, _1780933, _1780935] : [-(hAPP(c_List_Orev(_1780931), hAPP(hAPP(c_List_Olist_OCons(_1780931), _1780933), _1780935)) = hAPP(hAPP(c_List_Oappend(_1780931), hAPP(c_List_Orev(_1780931), _1780935)), hAPP(hAPP(c_List_Olist_OCons(_1780931), _1780933), c_List_Olist_ONil(_1780931))))], (27536 ^ _774244) ^ [_1259705] : [c_Nat__Transfer_Onat__set(_1259705), 27539 ^ _774244 : [(27540 ^ _774244) ^ [_1259771] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1259771), _1259705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259771)))]]], (5750 ^ _774244) ^ [_865913, _865915] : [c_Natural_Oevalc(c_Com_Ocom_OSKIP, _865913, _865915), -(_865915 = _865913)], (2424 ^ _774244) ^ [_810848, _810850, _810852, _810854, _810856, _810858, _810860, _810862] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_810862, _810858, _810854, _810850) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_810860, _810856, _810852, _810848)), _810862 = _810860, _810858 = _810856, _810854 = _810852, _810850 = _810848], (31423 ^ _774244) ^ [_1338705, _1338707] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1338705), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1338707), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 31430 ^ _774244 : [(31437 ^ _774244) ^ [] : [_1338705 = _1338707, -(hAPP(c_Code__Numeral_Oof__nat, _1338705) = hAPP(c_Code__Numeral_Oof__nat, _1338707))], (31431 ^ _774244) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1338705) = hAPP(c_Code__Numeral_Oof__nat, _1338707), -(_1338705 = _1338707)]]], (30987 ^ _774244) ^ [_1330025, _1330027, _1330029] : [hBOOL(hAPP(_1330029, _1330027)), -(hBOOL(hAPP(hAPP(c_member(_1330025), _1330027), _1330029)))], (30563 ^ _774244) ^ [_1319839, _1319841] : [hBOOL(hAPP(hAPP(c_member(_1319839), _1319841), c_Orderings_Obot__class_Obot(tc_fun(_1319839, tc_HOL_Obool))))], (51207 ^ _774244) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (46334 ^ _774244) ^ [_1688585, _1688587, _1688589, _1688591] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1688585), tc_List_Olist(_1688585))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1688585), tc_List_Olist(_1688585)), _1688587), _1688589)), c_List_Olistrel(_1688585, _1688591)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688585)), _1688587) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688585)), _1688589), 46340 ^ _774244 : [(46343 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1688585, _1688585, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1688585, tc_fun(tc_prod(_1688585, _1688585), tc_HOL_Obool), tc_fun(_1688585, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1688585, tc_fun(tc_fun(tc_prod(_1688585, _1688585), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1688585, _1688585), tc_HOL_Obool), tc_fun(_1688585, tc_HOL_Obool)), _1688585), c_COMBC(_1688585, tc_fun(tc_prod(_1688585, _1688585), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1688585, tc_prod(_1688585, _1688585)), tc_fun(_1688585, tc_fun(tc_fun(tc_prod(_1688585, _1688585), tc_HOL_Obool), tc_HOL_Obool)), _1688585), hAPP(c_COMBB(tc_prod(_1688585, _1688585), tc_fun(tc_fun(tc_prod(_1688585, _1688585), tc_HOL_Obool), tc_HOL_Obool), _1688585), c_member(tc_prod(_1688585, _1688585)))), c_Product__Type_OPair(_1688585, _1688585)))), _1688591)), 46339 ^ [_1688585, _1688587, _1688589, _1688591]))], (46341 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1688585, _1688585)), 46339 ^ [_1688585, _1688587, _1688589, _1688591]), hAPP(c_List_Oset(tc_prod(_1688585, _1688585)), hAPP(hAPP(c_List_Ozip(_1688585, _1688585), _1688587), _1688589)))))]]], (22218 ^ _774244) ^ [_1156527, _1156529] : [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(_1156529))), 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), _1156527)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1156527)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156529))))], (33836 ^ _774244) ^ [_1388807, _1388809, _1388811, _1388813, _1388815, _1388817] : [-(_1388807 = _1388809), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388811, _1388813), _1388815), _1388809), _1388817), _1388807) = hAPP(_1388815, _1388807))], (42445 ^ _774244) ^ [_1593726, _1593728, _1593730, _1593732, _1593734, _1593736] : [c_Finite__Set_Ofolding(_1593726, _1593728, _1593730, _1593732), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593726), _1593734)), -(hAPP(hAPP(_1593732, _1593734), _1593736) = hAPP(hAPP(c_Finite__Set_Ofold(_1593726, _1593728, _1593730), _1593736), _1593734))], (7291 ^ _774244) ^ [_892616, _892618, _892620, _892622] : [class_Groups_Oordered__cancel__ab__semigroup__add(_892616), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892616), _892618), _892620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892616), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892616), _892622), _892618)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892616), _892622), _892620))))], (45918 ^ _774244) ^ [_1677293, _1677295, _1677297, _1677299] : [-(_1677293 = _1677295), 45921 ^ _774244 : [(45928 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1677297), _1677293), hAPP(c_List_Oset(_1677297), _1677299))), -(hBOOL(hAPP(hAPP(c_member(_1677297), _1677293), hAPP(c_List_Oset(_1677297), c_List_Oremove1(_1677297, _1677295, _1677299)))))], (45922 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1677297), _1677293), hAPP(c_List_Oset(_1677297), c_List_Oremove1(_1677297, _1677295, _1677299)))), -(hBOOL(hAPP(hAPP(c_member(_1677297), _1677293), hAPP(c_List_Oset(_1677297), _1677299))))]]], (7187 ^ _774244) ^ [_890874, _890876] : [-(_890874 = _890876), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890874), _890876))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890876), _890874)))], (51399 ^ _774244) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (17713 ^ _774244) ^ [_1077541] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077541)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077541)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077541))], (41408 ^ _774244) ^ [_1569022, _1569024, _1569026, _1569028, _1569030, _1569032, _1569034] : [-(c_Predicate_Opred__comp(_1569022, _1569024, _1569026, _1569028, _1569030, _1569032, _1569034)), 41409 ^ _774244 : [(41410 ^ _774244) ^ [_1569087] : [hBOOL(hAPP(hAPP(_1569028, _1569032), _1569087)), hBOOL(hAPP(hAPP(_1569030, _1569087), _1569034))]]], (39277 ^ _774244) ^ [_1510277, _1510279, _1510281] : [-(c_Map_Odom(_1510277, _1510279, hAPP(hAPP(c_COMBB(_1510279, tc_Option_Ooption(_1510279), _1510277), c_Option_Ooption_OSome(_1510279)), _1510281)) = c_Orderings_Otop__class_Otop(tc_fun(_1510277, tc_HOL_Obool)))], (44271 ^ _774244) ^ [_1638459, _1638461, _1638463, _1638465, _1638467, _1638469] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1638459, _1638459)), hAPP(hAPP(c_Product__Type_OPair(_1638459, _1638459), _1638461), _1638463)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638459, _1638459), tc_HOL_Obool), _1638465), _1638467))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1638459, _1638459)), hAPP(hAPP(c_Product__Type_OPair(_1638459, _1638459), _1638463), _1638469)), _1638467)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638459, _1638459)), hAPP(hAPP(c_Product__Type_OPair(_1638459, _1638459), _1638461), _1638469)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638459, _1638459), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1638465)), _1638467))))], (6856 ^ _774244) ^ [_885304, _885306, _885308, _885310] : [-(hBOOL(hAPP(_885304, _885306))), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_885304, _885308), _885306, _885310, _885306))], (4310 ^ _774244) ^ [_840953, _840955] : [_840955 = _840953, -(c_Random_Orange(_840955) = c_Random_Orange(_840953))], (27300 ^ _774244) ^ [_1255279, _1255281, _1255283] : [class_Groups_Oordered__ab__group__add(_1255279), -(hAPP(c_Set_Oimage(_1255279, _1255279, c_Groups_Ouminus__class_Ouminus(_1255279)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255279, _1255281), _1255283)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1255279, hAPP(c_Groups_Ouminus__class_Ouminus(_1255279), _1255283), hAPP(c_Groups_Ouminus__class_Ouminus(_1255279), _1255281)))], (49794 ^ _774244) ^ [_1771184, _1771186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1771184), _1771186)), -(c_List_Oupt(_1771184, _1771186) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1771184), c_List_Oupt(hAPP(c_Nat_OSuc, _1771184), _1771186)))], (15852 ^ _774244) ^ [_1043184, _1043186, _1043188, _1043190, _1043192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043184), _1043186)), 15855 ^ _774244 : [(15862 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043190), 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), _1043186), _1043184)), _1043188)), _1043192))), -(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), _1043184), _1043188)), _1043190)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043186), _1043188)), _1043192))))], (15856 ^ _774244) ^ [] : [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), _1043184), _1043188)), _1043190)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043186), _1043188)), _1043192))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043190), 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), _1043186), _1043184)), _1043188)), _1043192))))]]], (23859 ^ _774244) ^ [_1188228, _1188230, _1188232, _1188234] : [class_Orderings_Olinorder(_1188228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188228), _1188230), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188228), _1188232), _1188234))), 23866 ^ _774244 : [(23869 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188228), _1188230), _1188234)))], (23867 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188228), _1188230), _1188232)))]]], (11132 ^ _774244) ^ [_957320, _957322] : [11133 ^ _774244 : [(11136 ^ _774244) ^ [] : [_957320 = _957322], (11134 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957320), _957322))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957320), _957322)))], (3826 ^ _774244) ^ [_833225, _833227, _833229, _833231] : [-(c_HOL_OThe(_833231, _833227) = c_HOL_OThe(_833229, _833225)), _833231 = _833229, _833227 = _833225], (34275 ^ _774244) ^ [_1397938, _1397940, _1397942, _1397944, _1397946] : [-(hBOOL(hAPP(hAPP(c_member(_1397938), _1397940), _1397942))), -(hAPP(c_Map_Orestrict__map(_1397938, _1397944, _1397946, _1397942), _1397940) = c_Option_Ooption_ONone(_1397944))], (43447 ^ _774244) ^ [_1616070, _1616072, _1616074, _1616076, _1616078, _1616080] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616070, tc_fun(_1616072, tc_fun(_1616074, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1616070, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1616072, _1616074), tc_HOL_Obool), tc_fun(_1616072, tc_fun(_1616074, tc_HOL_Obool)), _1616070), hAPP(c_COMBC(_1616072, tc_fun(tc_prod(_1616072, _1616074), tc_HOL_Obool), tc_fun(_1616074, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616074, tc_fun(tc_fun(tc_prod(_1616072, _1616074), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1616072, _1616074), tc_HOL_Obool), tc_fun(_1616074, tc_HOL_Obool)), _1616072), c_COMBC(_1616074, tc_fun(tc_prod(_1616072, _1616074), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616074, tc_prod(_1616072, _1616074)), tc_fun(_1616074, tc_fun(tc_fun(tc_prod(_1616072, _1616074), tc_HOL_Obool), tc_HOL_Obool)), _1616072), hAPP(c_COMBB(tc_prod(_1616072, _1616074), tc_fun(tc_fun(tc_prod(_1616072, _1616074), tc_HOL_Obool), tc_HOL_Obool), _1616074), c_member(tc_prod(_1616072, _1616074)))), c_Product__Type_OPair(_1616072, _1616074))))), _1616076)), _1616078), _1616080)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616072, _1616074)), hAPP(hAPP(c_Product__Type_OPair(_1616072, _1616074), _1616078), _1616080)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616070, tc_fun(tc_prod(_1616072, _1616074), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1616070, tc_HOL_Obool))), _1616076))))], (8062 ^ _774244) ^ [_906312, _906314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906312), _906314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _906312)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _906314))))], (45976 ^ _774244) ^ [_1678459, _1678461] : [-(hAPP(hAPP(c_List_Ozip(_1678459, _1678459), _1678461), _1678461) = hAPP(hAPP(c_List_Omap(_1678459, tc_prod(_1678459, _1678459)), hAPP(hAPP(c_COMBS(_1678459, _1678459, tc_prod(_1678459, _1678459)), c_Product__Type_OPair(_1678459, _1678459)), c_COMBI(_1678459))), _1678461))], (8580 ^ _774244) ^ [_914415, _914417, _914419] : [class_Rings_Oring(_914415), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914415), hAPP(c_Groups_Ouminus__class_Ouminus(_914415), _914417)), hAPP(c_Groups_Ouminus__class_Ouminus(_914415), _914419)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914415), _914417), _914419))], (16527 ^ _774244) ^ [_1055548, _1055550, _1055552] : [class_Int_Onumber(_1055548), class_Orderings_Olinorder(_1055548), 16534 ^ _774244 : [(16541 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055548), hAPP(c_Int_Onumber__class_Onumber__of(_1055548), _1055552)), hAPP(c_Int_Onumber__class_Onumber__of(_1055548), _1055550)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055548), hAPP(c_Int_Onumber__class_Onumber__of(_1055548), _1055550)), hAPP(c_Int_Onumber__class_Onumber__of(_1055548), _1055552))))], (16535 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055548), hAPP(c_Int_Onumber__class_Onumber__of(_1055548), _1055550)), hAPP(c_Int_Onumber__class_Onumber__of(_1055548), _1055552))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055548), hAPP(c_Int_Onumber__class_Onumber__of(_1055548), _1055552)), hAPP(c_Int_Onumber__class_Onumber__of(_1055548), _1055550)))]]], (24615 ^ _774244) ^ [_1202926, _1202928, _1202930, _1202932, _1202934, _1202936] : [hBOOL(hAPP(hAPP(_1202926, _1202928), _1202930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1202932, tc_fun(_1202934, tc_HOL_Obool))), _1202926), _1202936)), -(hBOOL(hAPP(hAPP(_1202936, _1202928), _1202930)))], (40739 ^ _774244) ^ [_1544892, _1544894, _1544896] : [-(c_Map_Odom(_1544892, _1544894, _1544896) = hAPP(c_Set_OCollect(_1544892), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1544892), c_fNot), hAPP(hAPP(c_COMBC(_1544892, tc_Option_Ooption(_1544894), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1544894), tc_fun(tc_Option_Ooption(_1544894), tc_HOL_Obool), _1544892), c_fequal), _1544896)), c_Option_Ooption_ONone(_1544894)))))], (40467 ^ _774244) ^ [_1538786, _1538788, _1538790, _1538792, _1538794] : [c_Finite__Set_Ofolding__one__idem(_1538786, _1538788, _1538790), hAPP(_1538792, hAPP(hAPP(_1538788, 40472 ^ [_1538786, _1538788, _1538790, _1538792, _1538794]), 40473 ^ [_1538786, _1538788, _1538790, _1538792, _1538794])) = hAPP(hAPP(_1538788, hAPP(_1538792, 40472 ^ [_1538786, _1538788, _1538790, _1538792, _1538794])), hAPP(_1538792, 40473 ^ [_1538786, _1538788, _1538790, _1538792, _1538794])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538786), _1538794)), -(_1538794 = c_Orderings_Obot__class_Obot(tc_fun(_1538786, tc_HOL_Obool))), -(hAPP(_1538792, hAPP(_1538790, _1538794)) = hAPP(_1538790, hAPP(c_Set_Oimage(_1538786, _1538786, _1538792), _1538794)))], (34527 ^ _774244) ^ [_1403259, _1403261, _1403263, _1403265] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1403259), _1403261)), 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)), _1403263), _1403259)), 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)), _1403265), _1403261)), 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)), _1403263), _1403265)), _1403261)), c_FunDef_Omax__weak)))], (43201 ^ _774244) ^ [_1610035, _1610037, _1610039, _1610041, _1610043] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1610035, _1610035)), hAPP(hAPP(c_Product__Type_OPair(_1610035, _1610035), _1610037), _1610039)), c_Transitive__Closure_Otrancl(_1610035, _1610041))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1610035, _1610035)), hAPP(hAPP(c_Product__Type_OPair(_1610035, _1610035), _1610039), _1610043)), c_Transitive__Closure_Ortrancl(_1610035, _1610041))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610035, _1610035)), hAPP(hAPP(c_Product__Type_OPair(_1610035, _1610035), _1610037), _1610043)), c_Transitive__Closure_Otrancl(_1610035, _1610041))))], (51511 ^ _774244) ^ [_1802309, _1802311] : [hBOOL(_1802309), -(hBOOL(hAPP(hAPP(c_fimplies, _1802311), _1802309)))], (24011 ^ _774244) ^ [_1191056, _1191058, _1191060, _1191062] : [class_Orderings_Olinorder(_1191056), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191056), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191056), _1191058), _1191060)), _1191062) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191056), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191056), _1191058), _1191062)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191056), _1191060), _1191062)))], (29895 ^ _774244) ^ [_1306909] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1306909)), -(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)), _1306909))))], (8750 ^ _774244) ^ [_917070, _917072, _917074] : [class_Rings_Oring__1(_917070), -(hAPP(c_Int_Oring__1__class_Oof__int(_917070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _917072), _917074)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917070), hAPP(c_Int_Oring__1__class_Oof__int(_917070), _917072)), hAPP(c_Int_Oring__1__class_Oof__int(_917070), _917074)))], (7103 ^ _774244) ^ [_889589, _889591, _889593, _889595, _889597] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_889589, _889591), _889593, _889595, _889597), 7108 ^ _774244 : [(7111 ^ _774244) ^ [] : [hBOOL(hAPP(_889589, _889593))], (7109 ^ _774244) ^ [] : [-(_889597 = _889593)]], 7112 ^ _774244 : [(7118 ^ _774244) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_889589, _889591), 7114 ^ [_889589, _889591, _889593, _889595, _889597], _889595, _889597))], (7116 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_889591, _889593, _889595, 7114 ^ [_889589, _889591, _889593, _889595, _889597]))], (7113 ^ _774244) ^ [] : [-(hBOOL(hAPP(_889589, _889593)))]]], (40953 ^ _774244) ^ [_1552365, _1552367] : [-(hAPP(c_Set_OPow(_1552365), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1552365, tc_HOL_Obool)), _1552367)) = hAPP(c_Set_OCollect(tc_fun(_1552365, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1552365, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1552365, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1552365, tc_HOL_Obool), tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1552365, tc_HOL_Obool)), c_COMBS(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1552365, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1552365, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1552365, tc_HOL_Obool), tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_fun(_1552365, tc_HOL_Obool)), tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_fun(_1552365, tc_HOL_Obool)), tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1552365, tc_HOL_Obool)), c_COMBB(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1552365, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1552365, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1552365, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1552365, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1552365, tc_HOL_Obool)), _1552367)), c_Set_OPow(_1552365))))))], (42590 ^ _774244) ^ [_1596732, _1596734, _1596736, _1596738] : [class_Orderings_Olinorder(_1596732), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596732), _1596734)), hBOOL(hAPP(hAPP(c_member(_1596732), _1596736), _1596734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1596732), hAPP(hAPP(c_Finite__Set_Ofold(_1596732, _1596732, c_Orderings_Oord__class_Omin(_1596732)), _1596738), _1596734)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1596732), _1596736), _1596738))))], (19889 ^ _774244) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18835 ^ _774244) ^ [_1095367, _1095369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1095367)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1095369)), _1095367) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1095369), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1095367), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (15480 ^ _774244) ^ [_1035333, _1035335] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035333), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035333), _1035335)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6225 ^ _774244) ^ [_874194] : [-(hAPP(c_Com_Obody, _874194) = c_Option_Ooption_ONone(tc_Com_Ocom)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OBODY(_874194))))], (12630 ^ _774244) ^ [_984026, _984028, _984030] : [class_Rings_Olinordered__ring(_984026), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984026), c_Groups_Ozero__class_Ozero(_984026)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984026), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984026), _984028), _984028)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984026), _984030), _984030)))))], (13481 ^ _774244) ^ [_998594, _998596, _998598, _998600] : [class_Divides_Osemiring__div(_998594), -(c_Divides_Odiv__class_Omod(_998594, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998594), _998596), _998598), _998600) = c_Divides_Odiv__class_Omod(_998594, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998594), c_Divides_Odiv__class_Omod(_998594, _998596, _998600)), _998598), _998600))], (16219 ^ _774244) ^ [_1049883] : [class_Groups_Oordered__ab__group__add__abs(_1049883), -(hAPP(c_Groups_Oabs__class_Oabs(_1049883), c_Groups_Ozero__class_Ozero(_1049883)) = c_Groups_Ozero__class_Ozero(_1049883))], (48859 ^ _774244) ^ [_1751154, _1751156] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1751154), hAPP(c_List_Oset(tc_Nat_Onat), _1751156))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1751154), 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)), _1751156))))], (43502 ^ _774244) ^ [_1618288, _1618290, _1618292, _1618294] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618288, tc_fun(_1618290, tc_HOL_Obool)), _1618292), _1618294) = c_Orderings_Otop__class_Otop(tc_fun(_1618290, tc_HOL_Obool)), 43505 ^ _774244 : [(43506 ^ _774244) ^ [_1618404] : [hBOOL(hAPP(hAPP(c_member(_1618288), _1618404), _1618292)), -(hAPP(_1618294, _1618404) = c_Orderings_Otop__class_Otop(tc_fun(_1618290, tc_HOL_Obool)))]]], (12161 ^ _774244) ^ [_975592] : [-(hBOOL(hAPP(_975592, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12168 ^ [_975592])))), 12162 ^ _774244 : [(12163 ^ _774244) ^ [_975644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975644)), hBOOL(hAPP(_975592, _975644))]]], (34634 ^ _774244) ^ [_1406130, _1406132, _1406134, _1406136] : [c_FunDef_Oreduction__pair(_1406130, _1406132), -(c_FunDef_Oreduction__pair(_1406134, hAPP(hAPP(c_FunDef_Orp__inv__image(_1406130, _1406134), _1406132), _1406136)))], (34249 ^ _774244) ^ [_1397297, _1397299, _1397301, _1397303, _1397305] : [class_Groups_Ocomm__monoid__mult(_1397297), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397299), _1397301)), 34256 ^ _774244 : [(34263 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1397299), _1397303), _1397301))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397299, _1397297), hAPP(hAPP(c_COMBC(_1397299, _1397297, _1397297), hAPP(hAPP(c_COMBS(_1397299, _1397297, tc_fun(_1397297, _1397297)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1397297, tc_fun(_1397297, _1397297)), _1397299), c_If(_1397297)), hAPP(c_fequal, _1397303))), _1397305)), c_Groups_Oone__class_Oone(_1397297))), _1397301) = c_Groups_Oone__class_Oone(_1397297))], (34257 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1397299), _1397303), _1397301)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397299, _1397297), hAPP(hAPP(c_COMBC(_1397299, _1397297, _1397297), hAPP(hAPP(c_COMBS(_1397299, _1397297, tc_fun(_1397297, _1397297)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1397297, tc_fun(_1397297, _1397297)), _1397299), c_If(_1397297)), hAPP(c_fequal, _1397303))), _1397305)), c_Groups_Oone__class_Oone(_1397297))), _1397301) = hAPP(_1397305, _1397303))]]], (47345 ^ _774244) ^ [_1714483, _1714485, _1714487, _1714489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714483), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714485)), _1714487))), 47348 ^ _774244 : [(47355 ^ _774244) ^ [] : [hAPP(hAPP(c_List_Onth(_1714485), _1714487), _1714483) = _1714489, -(hAPP(hAPP(c_List_Olist__update(_1714485, _1714487), _1714483), _1714489) = _1714487)], (47349 ^ _774244) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1714485, _1714487), _1714483), _1714489) = _1714487, -(hAPP(hAPP(c_List_Onth(_1714485), _1714487), _1714483) = _1714489)]]], (22330 ^ _774244) ^ [_1159103, _1159105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1159103)), 22333 ^ _774244 : [(22340 ^ _774244) ^ [] : [-(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), _1159105), _1159103)))), -(c_Divides_OnegDivAlg(_1159105, _1159103) = hAPP(c_Divides_Oadjust(_1159103), c_Divides_OnegDivAlg(_1159105, 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)))), _1159103))))], (22334 ^ _774244) ^ [] : [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), _1159105), _1159103))), -(c_Divides_OnegDivAlg(_1159105, _1159103) = 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), _1159105), _1159103)))]]], (43688 ^ _774244) ^ [_1623411, _1623413, _1623415, _1623417, _1623419, _1623421, _1623423] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623411, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623413, tc_fun(_1623411, tc_HOL_Obool)), _1623415), _1623417)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623419, tc_fun(_1623411, tc_HOL_Obool)), _1623421), _1623423)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623413, tc_fun(_1623411, tc_HOL_Obool)), _1623415), hAPP(hAPP(c_COMBB(tc_fun(_1623419, tc_fun(_1623411, tc_HOL_Obool)), tc_fun(_1623411, tc_HOL_Obool), _1623413), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623419, tc_fun(_1623411, tc_HOL_Obool)), _1623421)), hAPP(hAPP(c_COMBC(_1623413, tc_fun(_1623419, tc_fun(_1623411, tc_HOL_Obool)), tc_fun(_1623419, tc_fun(_1623411, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1623411, tc_HOL_Obool), tc_fun(_1623411, tc_HOL_Obool)), tc_fun(tc_fun(_1623419, tc_fun(_1623411, tc_HOL_Obool)), tc_fun(_1623419, tc_fun(_1623411, tc_HOL_Obool))), _1623413), c_COMBB(tc_fun(_1623411, tc_HOL_Obool), tc_fun(_1623411, tc_HOL_Obool), _1623419)), hAPP(hAPP(c_COMBB(tc_fun(_1623411, tc_HOL_Obool), tc_fun(tc_fun(_1623411, tc_HOL_Obool), tc_fun(_1623411, tc_HOL_Obool)), _1623413), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623411, tc_HOL_Obool))), _1623417))), _1623423))))], (29652 ^ _774244) ^ [_1302275, _1302277] : [_1302275 = _1302277, -(hAPP(c_Int_ORep__Integ, _1302275) = hAPP(c_Int_ORep__Integ, _1302277))], (16573 ^ _774244) ^ [_1056492, _1056494, _1056496] : [class_Rings_Ocomm__semiring__1(_1056492), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056492), _1056494), hAPP(hAPP(c_Power_Opower__class_Opower(_1056492), _1056494), _1056496)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1056492), _1056494), hAPP(c_Nat_OSuc, _1056496)))], (35310 ^ _774244) ^ [_1422055, _1422057, _1422059, _1422061] : [-(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), _1422055), _1422057)), 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), _1422059), _1422061)), 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), _1422055), _1422059)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1422057), _1422061))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1422055), _1422061)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1422057), _1422059)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (18477 ^ _774244) ^ [_1089636, _1089638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1089636)), c_Int_OBit1(_1089638))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1089636), _1089638)))], (44733 ^ _774244) ^ [_1649423, _1649425, _1649427] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649423, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1649423, tc_HOL_Obool)), _1649425), _1649427)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1649423, tc_HOL_Obool)), _1649425), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649423, tc_HOL_Obool), _1649427)))], (42668 ^ _774244) ^ [_1598201, _1598203, _1598205] : [class_Orderings_Olinorder(_1598201), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598201), _1598203)), -(c_Big__Operators_Olattice_OInf__fin(_1598201, c_Orderings_Oord__class_Omin(_1598201), hAPP(hAPP(c_Set_Oinsert(_1598201), _1598205), _1598203)) = hAPP(hAPP(c_Finite__Set_Ofold(_1598201, _1598201, c_Orderings_Oord__class_Omin(_1598201)), _1598205), _1598203))], (43589 ^ _774244) ^ [_1620476, _1620478, _1620480, _1620482, _1620484] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620476, _1620478)), hAPP(hAPP(c_Product__Type_OPair(_1620476, _1620478), _1620480), _1620482)), hAPP(c_Relation_Oconverse(_1620478, _1620476), _1620484))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620478, _1620476)), hAPP(hAPP(c_Product__Type_OPair(_1620478, _1620476), _1620482), _1620480)), _1620484)))], (50392 ^ _774244) ^ [_1783779, _1783781, _1783783] : [c_List_Oconcat(_1783779, _1783781) = c_List_Oconcat(_1783779, _1783783), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1783779))), _1783781) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1783779))), _1783783), 50402 ^ _774244 : [(50405 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1783779), tc_List_Olist(_1783779), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1783779), tc_fun(tc_List_Olist(_1783779), tc_Nat_Onat), tc_fun(tc_List_Olist(_1783779), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1783779), tc_Nat_Onat), tc_fun(tc_List_Olist(_1783779), tc_HOL_Obool)), tc_List_Olist(_1783779)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1783779))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1783779)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1783779))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1783779)))), 50401 ^ [_1783779, _1783781, _1783783]))], (50403 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1783779), tc_List_Olist(_1783779))), 50401 ^ [_1783779, _1783781, _1783783]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1783779), tc_List_Olist(_1783779))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1783779), tc_List_Olist(_1783779)), _1783781), _1783783)))))]], -(_1783781 = _1783783)], (15120 ^ _774244) ^ [_1028379, _1028381, _1028383] : [class_Groups_Oab__group__add(_1028379), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1028379), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1028379), _1028381), _1028383)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1028379), _1028383), _1028381))], (11333 ^ _774244) ^ [_960798, _960800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _960798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _960800)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _960798)), hAPP(c_Int_Onat, _960800)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _960798), _960800)))], (38884 ^ _774244) ^ [_1501407, _1501409, _1501411, _1501413, _1501415] : [hBOOL(hAPP(hAPP(c_member(_1501407), _1501409), hAPP(c_Set_Ovimage(_1501407, _1501411, _1501413), hAPP(hAPP(c_Set_Oinsert(_1501411), _1501415), c_Orderings_Obot__class_Obot(tc_fun(_1501411, tc_HOL_Obool)))))), -(hAPP(_1501413, _1501409) = _1501415)], (37653 ^ _774244) ^ [_1475847, _1475849] : [class_Lattices_Olattice(_1475847), -(c_Big__Operators_Olattice__class_OInf__fin(_1475847, hAPP(hAPP(c_Set_Oinsert(_1475847), _1475849), c_Orderings_Obot__class_Obot(tc_fun(_1475847, tc_HOL_Obool)))) = _1475849)], (49872 ^ _774244) ^ [_1772370, _1772372, _1772374] : [class_Orderings_Olinorder(_1772370), c_List_Olinorder__class_Osorted(_1772370, _1772372), -(c_List_Olinorder__class_Osorted(_1772370, hAPP(hAPP(c_List_Otake(_1772370), _1772374), _1772372)))], (50356 ^ _774244) ^ [_1782801, _1782803, _1782805, _1782807] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782801)), _1782803) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782805)), _1782807), -(hAPP(hAPP(c_List_Ozip(_1782801, _1782805), hAPP(c_List_Orev(_1782801), _1782803)), hAPP(c_List_Orev(_1782805), _1782807)) = hAPP(c_List_Orev(tc_prod(_1782801, _1782805)), hAPP(hAPP(c_List_Ozip(_1782801, _1782805), _1782803), _1782807)))], (12227 ^ _774244) ^ [_976645] : [12228 ^ _774244 : [(12229 ^ _774244) ^ [_976702] : [hBOOL(hAPP(_976645, _976702))]], 12231 ^ _774244 : [(12234 ^ _774244) ^ [] : [-(hBOOL(hAPP(_976645, hAPP(c_Int_Onat, 12230 ^ [_976645]))))], (12232 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12230 ^ [_976645])))]]], (18239 ^ _774244) ^ [] : [-(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))))], (49788 ^ _774244) ^ [_1771138, _1771140] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1771138), _1771140))), -(c_List_Oupt(_1771138, _1771140) = c_List_Olist_ONil(tc_Nat_Onat))], (41190 ^ _774244) ^ [_1562231, _1562233] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562231), _1562233)), -(_1562233 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1562231, 41194 ^ [_1562231, _1562233]), 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)), 41193 ^ [_1562231, _1562233]))))], (19045 ^ _774244) ^ [_1099220, _1099222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1099220)), c_Int_OBit1(_1099222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099220), _1099222)))], (46691 ^ _774244) ^ [_1699268, _1699270] : [-(c_Random_Oselect__weight(_1699268, _1699270) = 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(_1699268, 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, _1699268), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1699268)), _1699270)))), hAPP(hAPP(c_COMBB(_1699268, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1699268, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1699268, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1699268, _1699270))))], (23701 ^ _774244) ^ [_1185412, _1185414, _1185416, _1185418] : [class_Orderings_Olinorder(_1185412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185412), _1185414), _1185416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185412), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1185412), _1185414), _1185418)), _1185416)))], (23777 ^ _774244) ^ [_1186779, _1186781, _1186783, _1186785] : [class_Orderings_Olinorder(_1186779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186779), _1186781), _1186783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186779), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186779), _1186781), _1186785)), _1186783)))], (3968 ^ _774244) ^ [_835396, _835398, _835400, _835402, _835404, _835406] : [-(c_Smallcheck_Oorelse(_835406, _835402, _835398) = c_Smallcheck_Oorelse(_835404, _835400, _835396)), _835406 = _835404, _835402 = _835400, _835398 = _835396], (4500 ^ _774244) ^ [_843840, _843842, _843844, _843846, _843848, _843850] : [-(c_Big__Operators_Olattice_OInf__fin(_843850, _843846, _843842) = c_Big__Operators_Olattice_OInf__fin(_843848, _843844, _843840)), _843850 = _843848, _843846 = _843844, _843842 = _843840], (33612 ^ _774244) ^ [_1384383, _1384385, _1384387] : [class_Orderings_Olinorder(_1384383), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384383), _1384385)), hBOOL(hAPP(hAPP(c_member(_1384383), _1384387), _1384385)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1384383), _1384387), c_Big__Operators_Olattice_OSup__fin(_1384383, c_Orderings_Oord__class_Omax(_1384383), _1384385)) = _1384387)], (14652 ^ _774244) ^ [_1019668, _1019670, _1019672, _1019674] : [class_Divides_Osemiring__div(_1019668), -(_1019670 = c_Groups_Ozero__class_Ozero(_1019668)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019668), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019668), _1019672), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019668), _1019674), _1019670))), _1019670) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019668), _1019674), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019668), _1019672), _1019670)))], (32132 ^ _774244) ^ [_1355918, _1355920, _1355922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1355918)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1355920), _1355922)), 32139 ^ _774244 : [(32140 ^ _774244) ^ [_1356108] : [32142 ^ _774244 : [(32148 ^ _774244) ^ [] : [-(_1356108 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32144 ^ [_1355918, _1355920, _1355922, _1356108]), 32141 ^ [_1355918, _1355920, _1355922, _1356108]))], (32146 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32144 ^ [_1355918, _1355920, _1355922, _1356108]), _1355922)))], (32143 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32141 ^ [_1355918, _1355920, _1355922, _1356108]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1355918))))]], -(_1356108 = _1355920), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1356108), _1355918) = _1355920]]], (24669 ^ _774244) ^ [_1203948, _1203950] : [-(c_Nitpick_Ouminus__frac(_1203948, _1203950) = c_Nitpick_OAbs__Frac(_1203948, 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(_1203948), _1203950))), hAPP(c_Nitpick_Odenom(_1203948), _1203950))))], (14644 ^ _774244) ^ [_1019426, _1019428] : [-(_1019426 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1019428), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019426), _1019428))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019426, _1019428)))], (14810 ^ _774244) ^ [_1022822, _1022824, _1022826, _1022828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1022822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1022824), _1022826)), -(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), _1022826), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1022828, _1022822))), _1022824)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022826), _1022822))))], (19427 ^ _774244) ^ [_1105917, _1105919] : [class_Rings_Olinordered__idom(_1105917), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105917), c_Groups_Ozero__class_Ozero(_1105917)), hAPP(hAPP(c_Power_Opower__class_Opower(_1105917), _1105919), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (49725 ^ _774244) ^ [_1770055, _1770057, _1770059] : [class_Orderings_Olinorder(_1770055), 49728 ^ _774244 : [(49741 ^ _774244) ^ [] : [-(c_List_Olinorder__class_Osorted(_1770055, hAPP(hAPP(c_List_Olist_OCons(_1770055), _1770057), _1770059))), c_List_Olinorder__class_Osorted(_1770055, _1770059), 49747 ^ _774244 : [(49750 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1770055), _1770057), 49746 ^ [_1770055, _1770057, _1770059]))], (49748 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770055), 49746 ^ [_1770055, _1770057, _1770059]), hAPP(c_List_Oset(_1770055), _1770059))))]]], (49729 ^ _774244) ^ [] : [c_List_Olinorder__class_Osorted(_1770055, hAPP(hAPP(c_List_Olist_OCons(_1770055), _1770057), _1770059)), 49732 ^ _774244 : [(49735 ^ _774244) ^ [_1770241] : [hBOOL(hAPP(hAPP(c_member(_1770055), _1770241), hAPP(c_List_Oset(_1770055), _1770059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1770055), _1770057), _1770241)))], (49733 ^ _774244) ^ [] : [-(c_List_Olinorder__class_Osorted(_1770055, _1770059))]]]]], (13290 ^ _774244) ^ [_995150, _995152, _995154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _995150)), 13293 ^ _774244 : [(13300 ^ _774244) ^ [] : [_995152 = _995154, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995150), _995152) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995150), _995154))], (13294 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995150), _995152) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995150), _995154), -(_995152 = _995154)]]], (410 ^ _774244) ^ [_780475, _780477, _780479, _780481, _780483, _780485, _780487, _780489, _780491, _780493] : [-(c_Big__Operators_Ocomm__monoid__big(_780491, _780487, _780483, _780479, _780475)), c_Big__Operators_Ocomm__monoid__big(_780493, _780489, _780485, _780481, _780477), _780493 = _780491, _780489 = _780487, _780485 = _780483, _780481 = _780479, _780477 = _780475], (48482 ^ _774244) ^ [_1743063, _1743065, _1743067, _1743069] : [-(hAPP(c_List_Orotate1(_1743065), hAPP(hAPP(c_List_Olist_OCons(_1743065), _1743067), _1743069)) = hAPP(hAPP(c_List_Oappend(_1743065), _1743069), hAPP(hAPP(c_List_Olist_OCons(_1743065), _1743067), c_List_Olist_ONil(_1743065))))], (44588 ^ _774244) ^ [_1645841, _1645843] : [class_Complete__Lattice_Ocomplete__lattice(_1645841), -(c_Complete__Lattice_OSup__class_OSup(_1645841, _1645843) = c_Complete__Lattice_OInf__class_OInf(_1645841, hAPP(c_Set_OCollect(_1645841), hAPP(hAPP(c_COMBB(tc_fun(_1645841, tc_HOL_Obool), tc_HOL_Obool, _1645841), c_HOL_OAll(_1645841)), hAPP(hAPP(c_COMBB(tc_fun(_1645841, tc_HOL_Obool), tc_fun(_1645841, tc_HOL_Obool), _1645841), hAPP(c_COMBS(_1645841, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1645841), c_fimplies), hAPP(hAPP(c_COMBC(_1645841, tc_fun(_1645841, tc_HOL_Obool), tc_HOL_Obool), c_member(_1645841)), _1645843)))), hAPP(c_COMBC(_1645841, _1645841, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1645841)))))))], (5272 ^ _774244) ^ [_855754, _855756, _855758, _855760, _855762, _855764, _855766, _855768] : [-(c_Fun_Ocomp(_855768, _855764, _855760, _855756) = c_Fun_Ocomp(_855766, _855762, _855758, _855754)), _855768 = _855766, _855764 = _855762, _855760 = _855758, _855756 = _855754], (48290 ^ _774244) ^ [_1738380, _1738382] : [-(hAPP(c_List_Orotate1(_1738380), _1738382) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1738380), _1738380, c_List_Olist_ONil(_1738380), hAPP(hAPP(c_COMBB(tc_List_Olist(_1738380), tc_fun(tc_List_Olist(_1738380), tc_List_Olist(_1738380)), _1738380), hAPP(c_COMBC(tc_List_Olist(_1738380), tc_List_Olist(_1738380), tc_List_Olist(_1738380)), c_List_Oappend(_1738380))), hAPP(hAPP(c_COMBC(_1738380, tc_List_Olist(_1738380), tc_List_Olist(_1738380)), c_List_Olist_OCons(_1738380)), c_List_Olist_ONil(_1738380)))), _1738382))], (26995 ^ _774244) ^ [_1248755, _1248757] : [26997 ^ _774244 : [(27000 ^ _774244) ^ [] : [hBOOL(hAPP(_1248757, 26996 ^ [_1248755, _1248757]))], (26998 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26996 ^ [_1248755, _1248757]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248755))))]], 27001 ^ _774244 : [(27002 ^ _774244) ^ [_1248908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1248908), _1248755)), -(hBOOL(hAPP(_1248757, _1248908)))]]], (22907 ^ _774244) ^ [_1170010, _1170012] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1170010), _1170012)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1170010), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1170012)))], (9784 ^ _774244) ^ [_935382, _935384, _935386] : [class_Rings_Oring__1(_935382), -(hAPP(c_Int_Oring__1__class_Oof__int(_935382), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _935384), _935386)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935382), hAPP(c_Int_Oring__1__class_Oof__int(_935382), _935384)), hAPP(c_Int_Oring__1__class_Oof__int(_935382), _935386)))], (23915 ^ _774244) ^ [_1189249, _1189251] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1189249), _1189251) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1189249, _1189251)))], (50669 ^ _774244) ^ [_1790766, _1790768] : [-(hAPP(c_List_Oset(_1790766), c_List_Oremdups(_1790766, _1790768)) = hAPP(c_List_Oset(_1790766), _1790768))], (48771 ^ _774244) ^ [_1748946, _1748948, _1748950, _1748952, _1748954] : [c_Finite__Set_Ofun__left__comm__idem(_1748946, _1748948, _1748950), -(hAPP(hAPP(c_Finite__Set_Ofold(_1748946, _1748948, _1748950), _1748952), hAPP(c_List_Oset(_1748946), _1748954)) = hAPP(c_List_Ofoldl(_1748948, _1748946, hAPP(c_COMBC(_1748946, _1748948, _1748948), _1748950), _1748952), _1748954))], (18435 ^ _774244) ^ [_1088808, _1088810] : [class_Int_Onumber__ring(_1088808), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088808), c_Groups_Oone__class_Oone(_1088808)), hAPP(c_Int_Onumber__class_Onumber__of(_1088808), _1088810)) = hAPP(c_Int_Onumber__class_Onumber__of(_1088808), 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), _1088810))))], (48542 ^ _774244) ^ [_1744592, _1744594, _1744596] : [_1744592 = c_List_Olist_ONil(_1744594), -(hAPP(c_List_Ohd(_1744594), hAPP(hAPP(c_List_Oappend(_1744594), _1744592), _1744596)) = hAPP(c_List_Ohd(_1744594), _1744596))], (46988 ^ _774244) ^ [_1705069, _1705071, _1705073] : [-(hAPP(c_Map_Omap__of(_1705069, _1705071, c_List_Olist_ONil(tc_prod(_1705069, _1705071))), _1705073) = c_Option_Ooption_ONone(_1705071))], (23013 ^ _774244) ^ [_1172356, _1172358, _1172360, _1172362, _1172364, _1172366] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1172356, _1172358), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1172360), _1172362))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1172356, _1172358), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1172364), _1172366))), -(_1172358 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1172360 = _1172364)], (9790 ^ _774244) ^ [_935517, _935519] : [class_Rings_Oring__1(_935517), -(hAPP(c_Int_Oring__1__class_Oof__int(_935517), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _935519)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_935517), _935519))], (29258 ^ _774244) ^ [_1294934, _1294936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1294934, tc_HOL_Obool)), _1294936), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1294934, tc_HOL_Obool)), _1294936))), -(_1294936 = c_Orderings_Obot__class_Obot(tc_fun(_1294934, tc_HOL_Obool)))], (47816 ^ _774244) ^ [_1725006, _1725008, _1725010, _1725012] : [-(c_List_Osublist(_1725006, hAPP(hAPP(c_List_Oappend(_1725006), _1725008), _1725010), _1725012) = hAPP(hAPP(c_List_Oappend(_1725006), c_List_Osublist(_1725006, _1725008, _1725012)), c_List_Osublist(_1725006, _1725010, 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(_1725006)), _1725008)))), _1725012)))))], (13662 ^ _774244) ^ [_1002118, _1002120] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1002118, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1002120)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1002118, _1002120) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (9708 ^ _774244) ^ [] : [-(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))))], (33848 ^ _774244) ^ [_1388957, _1388959, _1388961, _1388963, _1388965, _1388967] : [-(_1388957 = _1388959), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388961, _1388963), _1388965), _1388959), _1388967), _1388957) = hAPP(_1388965, _1388957))], (29586 ^ _774244) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39411 ^ _774244) ^ [_1513633, _1513635, _1513637, _1513639, _1513641, _1513643, _1513645] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1513633, _1513635, _1513637, _1513639, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1513633, tc_HOL_Obool)), _1513641), hAPP(hAPP(c_Set_Oinsert(_1513633), _1513643), c_Orderings_Obot__class_Obot(tc_fun(_1513633, tc_HOL_Obool))))), _1513645)), hBOOL(hAPP(hAPP(c_member(_1513633), _1513643), _1513641)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1513633, _1513635, _1513637, _1513639, _1513641), hAPP(hAPP(_1513637, _1513643), _1513645))))], (28807 ^ _774244) ^ [_1285950, _1285952] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1285950, tc_HOL_Obool)), _1285952) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285950, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1285950, tc_HOL_Obool))), _1285952))], (12812 ^ _774244) ^ [_986991, _986993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _986991), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _986993), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _986991), _986993)))], (8518 ^ _774244) ^ [_913128] : [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)), _913128)), _913128)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _913128), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41240 ^ _774244) ^ [_1564103, _1564105, _1564107, _1564109] : [hAPP(hAPP(c_Relation_Orel__comp(_1564103, _1564103, _1564103), _1564105), _1564107) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564103, _1564103), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1564103, _1564103, _1564103), _1564105), _1564109) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564103, _1564103), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1564103, _1564103, _1564103), _1564105), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564103, _1564103), tc_HOL_Obool)), _1564107), _1564109)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564103, _1564103), tc_HOL_Obool)))], (31743 ^ _774244) ^ [_1347362, _1347364, _1347366] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1347362), _1347364)), -(hBOOL(hAPP(hAPP(c_member(_1347362), _1347366), _1347364))), -(hAPP(c_Finite__Set_Ocard(_1347362), hAPP(hAPP(c_Set_Oinsert(_1347362), _1347366), _1347364)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1347362), _1347364)))], (47925 ^ _774244) ^ [_1728095, _1728097, _1728099, _1728101] : [-(hAPP(hAPP(c_List_Otake(_1728095), _1728097), hAPP(hAPP(c_List_Otake(_1728095), _1728099), _1728101)) = hAPP(hAPP(c_List_Otake(_1728095), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1728097), _1728099)), _1728101))], (50609 ^ _774244) ^ [_1789471, _1789473, _1789475, _1789477, _1789479] : [hBOOL(hAPP(hAPP(c_member(_1789471), _1789473), hAPP(c_List_Oset(_1789471), _1789475))), -(hBOOL(hAPP(_1789477, _1789473))), -(c_List_OtakeWhile(_1789471, _1789477, hAPP(hAPP(c_List_Oappend(_1789471), _1789475), _1789479)) = c_List_OtakeWhile(_1789471, _1789477, _1789475))], (6882 ^ _774244) ^ [_885612, _885614] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_885612, _885614))), -(hBOOL(hAPP(c_Com_OWT, _885614)))], (19347 ^ _774244) ^ [_1104479] : [class_Rings_Osemiring__1(_1104479), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1104479), c_Groups_Oone__class_Oone(_1104479)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1104479))], (4976 ^ _774244) ^ [_851134, _851136] : [_851136 = _851134, -(c_Groups_Ominus__class_Ominus(_851136) = c_Groups_Ominus__class_Ominus(_851134))], (18483 ^ _774244) ^ [_1089737, _1089739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1089737), _1089739)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1089737)), c_Int_OBit1(_1089739))))], (5814 ^ _774244) ^ [_866994, _866996, _866998, _867000, _867002, _867004, _867006, _867008, _867010, _867012, _867014] : [-(c_Com_Ocom_Ocom__case(_866994, _866996, _866998, _867000, _867002, _867004, _867006, _867008, _867010, c_Com_Ocom_OSemi(_867012, _867014)) = hAPP(hAPP(_867002, _867012), _867014))], (28563 ^ _774244) ^ [_1279983, _1279985, _1279987, _1279989, _1279991] : [28565 ^ _774244 : [(28568 ^ _774244) ^ [] : [hBOOL(hAPP(_1279991, 28564 ^ [_1279983, _1279985, _1279987, _1279989, _1279991]))], (28566 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1279983), 28564 ^ [_1279983, _1279985, _1279987, _1279989, _1279991]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279985, tc_fun(_1279983, tc_HOL_Obool)), _1279987), _1279989))))]], 28569 ^ _774244 : [(28570 ^ _774244) ^ [_1280205] : [hBOOL(hAPP(hAPP(c_member(_1279985), _1280205), _1279987)), 28573 ^ _774244 : [(28574 ^ _774244) ^ [_1280302] : [hBOOL(hAPP(hAPP(c_member(_1279983), _1280302), hAPP(_1279989, _1280205))), -(hBOOL(hAPP(_1279991, _1280302)))]]]]], (31521 ^ _774244) ^ [_1341410, _1341412, _1341414, _1341416, _1341418] : [hBOOL(hAPP(hAPP(c_member(_1341410), _1341412), _1341414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341416, tc_HOL_Obool)), hAPP(_1341418, _1341412)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1341410, tc_fun(_1341416, tc_HOL_Obool)), _1341414), _1341418))))], (12287 ^ _774244) ^ [_977596, _977598] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _977596)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _977598)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977596), _977598)))], (50256 ^ _774244) ^ [_1780679, _1780681] : [c_List_Olist_ONil(_1780679) = hAPP(c_List_Orev(_1780679), _1780681), -(_1780681 = c_List_Olist_ONil(_1780679))], (47094 ^ _774244) ^ [_1708333, _1708335, _1708337, _1708339] : [hBOOL(hAPP(c_List_Odistinct(_1708333), _1708335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708337), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708333)), _1708335))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708339), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708333)), _1708335))), 47105 ^ _774244 : [(47112 ^ _774244) ^ [] : [_1708337 = _1708339, -(hAPP(hAPP(c_List_Onth(_1708333), _1708335), _1708337) = hAPP(hAPP(c_List_Onth(_1708333), _1708335), _1708339))], (47106 ^ _774244) ^ [] : [hAPP(hAPP(c_List_Onth(_1708333), _1708335), _1708337) = hAPP(hAPP(c_List_Onth(_1708333), _1708335), _1708339), -(_1708337 = _1708339)]]], (30434 ^ _774244) ^ [_1317065, _1317067, _1317069, _1317071, _1317073] : [class_Groups_Ocomm__monoid__add(_1317065), class_Groups_Oordered__ab__semigroup__add(_1317065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317067), _1317069)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317067, tc_HOL_Obool)), _1317071), _1317069)), 30452 ^ _774244 : [(30455 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317065), c_Groups_Ozero__class_Ozero(_1317065)), hAPP(_1317073, 30451 ^ [_1317065, _1317067, _1317069, _1317071, _1317073])))], (30453 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1317067), 30451 ^ [_1317065, _1317067, _1317069, _1317071, _1317073]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1317067, tc_HOL_Obool)), _1317069), _1317071))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317065), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1317067, _1317065), _1317073), _1317071)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1317067, _1317065), _1317073), _1317069))))], (28737 ^ _774244) ^ [_1284609, _1284611] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284609, tc_HOL_Obool)), _1284611), c_Orderings_Otop__class_Otop(tc_fun(_1284609, tc_HOL_Obool)))))], (45884 ^ _774244) ^ [_1676702, _1676704] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1676702, _1676704) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1676702), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1676704)))], (14704 ^ _774244) ^ [_1020618, _1020620, _1020622] : [class_Divides_Osemiring__div(_1020618), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020618), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020618), _1020620), _1020622)), _1020622)), c_Divides_Odiv__class_Omod(_1020618, _1020620, _1020622)) = _1020620)], (20471 ^ _774244) ^ [_1124355, _1124357, _1124359] : [class_Fields_Olinordered__field(_1124355), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124355), c_Groups_Ozero__class_Ozero(_1124355)), _1124357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124355), _1124359), c_Groups_Ozero__class_Ozero(_1124355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124355), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124355), _1124357), _1124359)), c_Groups_Ozero__class_Ozero(_1124355))))], (27666 ^ _774244) ^ [_1261998, _1262000, _1262002] : [class_Orderings_Olinorder(_1261998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261998), _1262000), _1262002)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261998, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1261998), _1262000)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1261998, _1262000, _1262002)) = hAPP(c_SetInterval_Oord__class_OatMost(_1261998), _1262002))], (45746 ^ _774244) ^ [_1673595, _1673597, _1673599, _1673601] : [-(hBOOL(hAPP(hAPP(c_member(_1673595), _1673601), hAPP(c_Set_Oimage(tc_prod(_1673595, _1673597), _1673595, c_Product__Type_Ofst(_1673595, _1673597)), hAPP(c_List_Oset(tc_prod(_1673595, _1673597)), _1673599))))), -(hAPP(c_Map_Omap__of(_1673595, _1673597, _1673599), _1673601) = c_Option_Ooption_ONone(_1673597))], (36481 ^ _774244) ^ [_1448393, _1448395, _1448397] : [class_Lattices_Oboolean__algebra(_1448393), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1448393), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1448393), _1448395), _1448397)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1448393), hAPP(c_Groups_Ouminus__class_Ouminus(_1448393), _1448395)), hAPP(c_Groups_Ouminus__class_Ouminus(_1448393), _1448397)))], (49037 ^ _774244) ^ [_1755283, _1755285, _1755287] : [-(_1755283 = c_List_Olist_ONil(_1755285)), -(c_List_Olast(_1755285, hAPP(hAPP(c_List_Oappend(_1755285), _1755287), _1755283)) = c_List_Olast(_1755285, _1755283))], (26528 ^ _774244) ^ [_1239049, _1239051, _1239053] : [class_Orderings_Olinorder(_1239049), 26531 ^ _774244 : [(26538 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239049), _1239051), _1239053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239049, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239049), _1239051)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239049), _1239053))))], (26532 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239049, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239049), _1239051)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239049), _1239053))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239049), _1239051), _1239053)))]]], (17857 ^ _774244) ^ [_1080020] : [class_Int_Onumber__ring(_1080020), c_Int_Oiszero(_1080020, hAPP(c_Int_Onumber__class_Onumber__of(_1080020), c_Int_OMin))], (19207 ^ _774244) ^ [_1102039, _1102041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102039), _1102041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1102039)), c_Int_OBit0(_1102041))))], (24589 ^ _774244) ^ [_1202407, _1202409, _1202411] : [-(c_Nitpick_Oplus__frac(_1202407, _1202409, _1202411) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1202407), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1202407), _1202409), hAPP(c_Nitpick_Odenom(_1202407), _1202411))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1202407), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1202407), tc_Int_Oint), c_Nitpick_Ofrac(_1202407)), 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(_1202407), _1202409))), 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(_1202407), _1202409))))), 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(_1202407), _1202411))), 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(_1202407), _1202411)))))), c_COMBI(tc_Int_Oint))))], (22602 ^ _774244) ^ [_1164358, _1164360, _1164362, _1164364] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1164358, _1164360), _1164362)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1164358, _1164360), _1164364)), -(_1164362 = _1164364)], (38832 ^ _774244) ^ [_1500234, _1500236, _1500238, _1500240, _1500242, _1500244] : [-(hAPP(c_Set_Ovimage(_1500234, _1500236, hAPP(c_Fun_Ocomp(_1500238, _1500236, _1500234, _1500240), _1500242)), _1500244) = hAPP(c_Set_Ovimage(_1500234, _1500238, _1500242), hAPP(c_Set_Ovimage(_1500238, _1500236, _1500240), _1500244)))], (22368 ^ _774244) ^ [_1159830, _1159832] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159830), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 22371 ^ _774244 : [(22380 ^ _774244) ^ [] : [-(c_Nitpick_Onorm__frac(_1159832, _1159830) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1159832), _1159830)), 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), _1159832))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1159830)))), -(_1159832 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1159830 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22372 ^ _774244) ^ [] : [22373 ^ _774244 : [(22376 ^ _774244) ^ [] : [_1159830 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (22374 ^ _774244) ^ [] : [_1159832 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1159832, _1159830) = 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)))]]], (24401 ^ _774244) ^ [_1198581] : [class_Orderings_Oord(_1198581), -(c_Orderings_Oord__class_Omax(_1198581) = c_Orderings_Oord_Omax(_1198581, c_Orderings_Oord__class_Oless__eq(_1198581)))], (18711 ^ _774244) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (33284 ^ _774244) ^ [_1377673, _1377675, _1377677, _1377679, _1377681, _1377683, _1377685, _1377687] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1377673, _1377675), tc_prod(_1377673, _1377675))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1377673, _1377675), tc_prod(_1377673, _1377675)), hAPP(hAPP(c_Product__Type_OPair(_1377673, _1377675), _1377677), _1377679)), hAPP(hAPP(c_Product__Type_OPair(_1377673, _1377675), _1377681), _1377683))), c_Wellfounded_Olex__prod(_1377673, _1377675, _1377685, _1377687)))), 33285 ^ _774244 : [(33288 ^ _774244) ^ [] : [_1377677 = _1377681, hBOOL(hAPP(hAPP(c_member(tc_prod(_1377675, _1377675)), hAPP(hAPP(c_Product__Type_OPair(_1377675, _1377675), _1377679), _1377683)), _1377687))], (33286 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1377673, _1377673)), hAPP(hAPP(c_Product__Type_OPair(_1377673, _1377673), _1377677), _1377681)), _1377685))]]], (19645 ^ _774244) ^ [_1109948] : [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, _1109948, 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, _1109948, 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))], (7501 ^ _774244) ^ [_896022, _896024, _896026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _896022), _896024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _896022), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _896026), _896024))))], (30884 ^ _774244) ^ [_1328124, _1328126] : [-(hBOOL(hAPP(hAPP(c_member(_1328124), 30885 ^ [_1328124, _1328126]), _1328126))), -(_1328126 = c_Orderings_Obot__class_Obot(tc_fun(_1328124, tc_HOL_Obool)))], (9064 ^ _774244) ^ [_922611, _922613, _922615] : [class_Rings_Ono__zero__divisors(_922611), -(_922613 = c_Groups_Ozero__class_Ozero(_922611)), -(_922615 = c_Groups_Ozero__class_Ozero(_922611)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922611), _922613), _922615) = c_Groups_Ozero__class_Ozero(_922611)], (43542 ^ _774244) ^ [_1619302, _1619304, _1619306, _1619308, _1619310] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1619302, tc_fun(_1619304, tc_HOL_Obool)), _1619306), hAPP(hAPP(c_COMBS(_1619302, tc_fun(_1619304, tc_HOL_Obool), tc_fun(_1619304, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1619304, tc_HOL_Obool), tc_fun(tc_fun(_1619304, tc_HOL_Obool), tc_fun(_1619304, tc_HOL_Obool)), _1619302), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1619304, tc_HOL_Obool))), _1619308)), _1619310)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1619304, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1619302, tc_fun(_1619304, tc_HOL_Obool)), _1619306), _1619308)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1619302, tc_fun(_1619304, tc_HOL_Obool)), _1619306), _1619310)))], (39263 ^ _774244) ^ [_1509983, _1509985] : [-(c_Map_Odom(_1509983, _1509985, hAPP(c_COMBK(tc_Option_Ooption(_1509985), _1509983), c_Option_Ooption_ONone(_1509985))) = c_Orderings_Obot__class_Obot(tc_fun(_1509983, tc_HOL_Obool)))], (36871 ^ _774244) ^ [_1457563, _1457565, _1457567, _1457569, _1457571] : [class_Groups_Ocomm__monoid__add(_1457563), hBOOL(hAPP(c_Finite__Set_Ofinite(_1457565), _1457567)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457565, _1457563), _1457569), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457565, tc_HOL_Obool)), _1457567), _1457571)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457565, _1457563), hAPP(hAPP(c_COMBC(_1457565, _1457563, _1457563), hAPP(hAPP(c_COMBS(_1457565, _1457563, tc_fun(_1457563, _1457563)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1457563, tc_fun(_1457563, _1457563)), _1457565), c_If(_1457563)), hAPP(hAPP(c_COMBC(_1457565, tc_fun(_1457565, tc_HOL_Obool), tc_HOL_Obool), c_member(_1457565)), _1457571))), _1457569)), c_Groups_Ozero__class_Ozero(_1457563))), _1457567))], (36557 ^ _774244) ^ [_1450206, _1450208, _1450210] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450206, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1450206, tc_HOL_Obool)), _1450208), _1450210)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450206, tc_HOL_Obool)), _1450208), _1450210)) = _1450208)], (50825 ^ _774244) ^ [_1793744, _1793746, _1793748] : [-(c_List_OdropWhile(_1793744, _1793746, _1793748) = c_List_Olist_ONil(_1793744)), hBOOL(hAPP(_1793746, hAPP(c_List_Ohd(_1793744), c_List_OdropWhile(_1793744, _1793746, _1793748))))], (50947 ^ _774244) ^ [_1796369, _1796371] : [class_Lattices_Olattice(_1796369), -(class_Lattices_Osemilattice__sup(tc_fun(_1796371, _1796369)))], (13874 ^ _774244) ^ [_1005888, _1005890] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005888))), -(c_SMT_Oz3mod(_1005890, _1005888) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005890, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1005888)))], (29985 ^ _774244) ^ [_1308445, _1308447, _1308449] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308445), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308445, tc_HOL_Obool)), _1308447), _1308449)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308445), _1308447)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308445), _1308449))], (41318 ^ _774244) ^ [_1567485, _1567487, _1567489, _1567491] : [c_Wellfounded_Owf(_1567485, _1567487), -(c_Wellfounded_Owf(_1567489, hAPP(hAPP(c_Relation_Oinv__image(_1567485, _1567489), _1567487), _1567491)))], (27450 ^ _774244) ^ [_1258371, _1258373, _1258375] : [class_Groups_Ocomm__monoid__add(_1258371), class_Groups_Ocomm__monoid__mult(_1258371), c_Nat__Transfer_Onat__set(_1258373), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1258371), _1258375), _1258373) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1258371), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1258371, tc_Nat_Onat), _1258375), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258373)))], (46769 ^ _774244) ^ [_1701084, _1701086, _1701088] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1701084), tc_List_Olist(_1701084))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1701084), tc_List_Olist(_1701084)), _1701086), c_List_Olist_ONil(_1701084))), c_List_Olistrel(_1701084, _1701088))), -(_1701086 = c_List_Olist_ONil(_1701084))], (15220 ^ _774244) ^ [_1030225, _1030227] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030225), _1030227)), _1030227) = _1030225)], (49031 ^ _774244) ^ [_1755178, _1755180, _1755182] : [_1755178 = c_List_Olist_ONil(_1755180), -(c_List_Olast(_1755180, hAPP(hAPP(c_List_Oappend(_1755180), _1755182), _1755178)) = c_List_Olast(_1755180, _1755182))], (48879 ^ _774244) ^ [_1751707, _1751709] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1751707)), c_List_Olist_ONil(_1751707)), c_List_Olists(_1751707, _1751709))))], (41440 ^ _774244) ^ [_1569579, _1569581, _1569583] : [c_Wellfounded_Owf(_1569579, _1569581), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569579, _1569579)), hAPP(hAPP(c_Product__Type_OPair(_1569579, _1569579), _1569583), _1569583)), _1569581))], (44960 ^ _774244) ^ [_1654578, _1654580, _1654582, _1654584, _1654586] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1654578, _1654578)), hAPP(hAPP(c_Product__Type_OPair(_1654578, _1654578), _1654580), _1654582)), c_Transitive__Closure_Ortrancl(_1654578, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1654578, _1654578), tc_HOL_Obool)), _1654584), _1654586)))), 44966 ^ _774244 : [(44972 ^ _774244) ^ [] : [44965 ^ [_1654578, _1654580, _1654582, _1654584, _1654586] = 44968 ^ [_1654578, _1654580, _1654582, _1654584, _1654586]], (44970 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654578, _1654578)), hAPP(hAPP(c_Product__Type_OPair(_1654578, _1654578), 44965 ^ [_1654578, _1654580, _1654582, _1654584, _1654586]), 44968 ^ [_1654578, _1654580, _1654582, _1654584, _1654586])), _1654586)))], (44967 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654578, _1654578)), hAPP(hAPP(c_Product__Type_OPair(_1654578, _1654578), _1654580), 44965 ^ [_1654578, _1654580, _1654582, _1654584, _1654586])), c_Transitive__Closure_Ortrancl(_1654578, _1654584))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654578, _1654578)), hAPP(hAPP(c_Product__Type_OPair(_1654578, _1654578), _1654580), _1654582)), c_Transitive__Closure_Ortrancl(_1654578, _1654584))))], (47752 ^ _774244) ^ [_1723554, _1723556, _1723558, _1723560, _1723562] : [-(hAPP(hAPP(c_List_Olist__update(_1723554, hAPP(hAPP(c_List_Oappend(_1723554), _1723556), hAPP(hAPP(c_List_Olist_OCons(_1723554), _1723558), _1723560))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723554)), _1723556)), _1723562) = hAPP(hAPP(c_List_Oappend(_1723554), _1723556), hAPP(hAPP(c_List_Olist_OCons(_1723554), _1723562), _1723560)))], (36487 ^ _774244) ^ [_1448532, _1448534, _1448536, _1448538] : [hBOOL(hAPP(hAPP(c_member(_1448532), _1448534), _1448536)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448532, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1448532), _1448534), _1448538)), _1448536) = hAPP(hAPP(c_Set_Oinsert(_1448532), _1448534), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448532, tc_HOL_Obool)), _1448538), _1448536)))], (51231 ^ _774244) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (42014 ^ _774244) ^ [_1583966, _1583968, _1583970] : [hBOOL(hAPP(c_Predicate_OPowp(_1583966, _1583968), _1583970)), 42017 ^ _774244 : [(42018 ^ _774244) ^ [_1584050] : [hBOOL(hAPP(hAPP(c_member(_1583966), _1584050), _1583970)), -(hBOOL(hAPP(_1583968, _1584050)))]]], (43769 ^ _774244) ^ [_1625420, _1625422] : [c_Wellfounded_Oacyclic(_1625420, _1625422), -(c_Wellfounded_Oacyclic(_1625420, hAPP(c_Relation_Oconverse(_1625420, _1625420), _1625422)))], (22084 ^ _774244) ^ [_1153662] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1153662) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1153662)))], (15612 ^ _774244) ^ [_1037824, _1037826, _1037828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037824), _1037826)), 15615 ^ _774244 : [(15622 ^ _774244) ^ [] : [_1037826 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037828), _1037824), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037826), _1037824) = _1037828)], (15616 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037826), _1037824) = _1037828, -(_1037826 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037828), _1037824))]]], (41847 ^ _774244) ^ [_1579659, _1579661, _1579663, _1579665] : [hBOOL(hAPP(c_Predicate_ODomainP(_1579659, _1579661, hAPP(hAPP(c_COMBC(_1579659, tc_fun(tc_prod(_1579659, _1579661), tc_HOL_Obool), tc_fun(_1579661, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1579661, tc_fun(tc_fun(tc_prod(_1579659, _1579661), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1579659, _1579661), tc_HOL_Obool), tc_fun(_1579661, tc_HOL_Obool)), _1579659), c_COMBC(_1579661, tc_fun(tc_prod(_1579659, _1579661), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1579661, tc_prod(_1579659, _1579661)), tc_fun(_1579661, tc_fun(tc_fun(tc_prod(_1579659, _1579661), tc_HOL_Obool), tc_HOL_Obool)), _1579659), hAPP(c_COMBB(tc_prod(_1579659, _1579661), tc_fun(tc_fun(tc_prod(_1579659, _1579661), tc_HOL_Obool), tc_HOL_Obool), _1579661), c_member(tc_prod(_1579659, _1579661)))), c_Product__Type_OPair(_1579659, _1579661)))), _1579663)), _1579665)), -(hBOOL(hAPP(hAPP(c_member(_1579659), _1579665), hAPP(c_Relation_ODomain(_1579659, _1579661), _1579663))))], (15304 ^ _774244) ^ [_1031818, _1031820, _1031822] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031818), _1031820)), _1031822) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031818), _1031822)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031820), _1031822)))], (43221 ^ _774244) ^ [_1610580, _1610582, _1610584, _1610586] : [-(hBOOL(hAPP(hAPP(c_member(_1610580), _1610582), hAPP(c_Relation_ODomain(_1610580, _1610580), _1610584)))), 43224 ^ _774244 : [(43231 ^ _774244) ^ [] : [_1610582 = _1610586, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610580, _1610580)), hAPP(hAPP(c_Product__Type_OPair(_1610580, _1610580), _1610582), _1610586)), c_Transitive__Closure_Ortrancl(_1610580, _1610584))))], (43225 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1610580, _1610580)), hAPP(hAPP(c_Product__Type_OPair(_1610580, _1610580), _1610582), _1610586)), c_Transitive__Closure_Ortrancl(_1610580, _1610584))), -(_1610582 = _1610586)]]], (48887 ^ _774244) ^ [_1751845] : [-(c_List_Olists(_1751845, c_Orderings_Otop__class_Otop(tc_fun(_1751845, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1751845), tc_HOL_Obool)))], (46579 ^ _774244) ^ [_1696324, _1696326, _1696328, _1696330, _1696332] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1696324), tc_List_Olist(_1696324))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1696324), tc_List_Olist(_1696324)), _1696326), hAPP(hAPP(c_List_Olist_OCons(_1696324), _1696328), _1696330))), c_List_Olistrel(_1696324, _1696332))), 46584 ^ _774244 : [(46589 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1696324), tc_List_Olist(_1696324))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1696324), tc_List_Olist(_1696324)), 46583 ^ [_1696324, _1696326, _1696328, _1696330, _1696332]), _1696330)), c_List_Olistrel(_1696324, _1696332))))], (46587 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1696324, _1696324)), hAPP(hAPP(c_Product__Type_OPair(_1696324, _1696324), 46582 ^ [_1696324, _1696326, _1696328, _1696330, _1696332]), _1696328)), _1696332)))], (46585 ^ _774244) ^ [] : [-(_1696326 = hAPP(hAPP(c_List_Olist_OCons(_1696324), 46582 ^ [_1696324, _1696326, _1696328, _1696330, _1696332]), 46583 ^ [_1696324, _1696326, _1696328, _1696330, _1696332]))]]], (30733 ^ _774244) ^ [_1323066, _1323068] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1323066, tc_HOL_Obool)), _1323068)), -(hBOOL(hAPP(hAPP(c_member(_1323066), _1323068), c_Orderings_Obot__class_Obot(tc_fun(_1323066, tc_HOL_Obool)))))], (3314 ^ _774244) ^ [_825133, _825135, _825137, _825139, _825141, _825143, _825145, _825147] : [-(c_Sum__Type_OPlus(_825147, _825143, _825139, _825135) = c_Sum__Type_OPlus(_825145, _825141, _825137, _825133)), _825147 = _825145, _825143 = _825141, _825139 = _825137, _825135 = _825133], (18233 ^ _774244) ^ [_1085496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085496), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085496))], (29770 ^ _774244) ^ [_1304467, _1304469, _1304471] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1304467), _1304469)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1304467), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304467, tc_HOL_Obool)), _1304469), _1304471))))], (30605 ^ _774244) ^ [_1320596, _1320598, _1320600, _1320602] : [30606 ^ _774244 : [(30609 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1320596), _1320598), _1320602))], (30607 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1320596), _1320598), _1320600))]], -(hBOOL(hAPP(hAPP(c_member(_1320596), _1320598), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320596, tc_HOL_Obool)), _1320602), _1320600))))], (30573 ^ _774244) ^ [_1320041, _1320043, _1320045, _1320047] : [hBOOL(hAPP(hAPP(c_member(_1320041), _1320043), hAPP(hAPP(c_Set_Oinsert(_1320041), _1320045), _1320047))), -(_1320043 = _1320045), -(hBOOL(hAPP(hAPP(c_member(_1320041), _1320043), _1320047)))], (1922 ^ _774244) ^ [_802235, _802237, _802239, _802241] : [-(c_Com_Ocom_OWhile(_802241, _802237) = c_Com_Ocom_OWhile(_802239, _802235)), _802241 = _802239, _802237 = _802235], (29504 ^ _774244) ^ [_1299575] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1299575)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1299575)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1299575), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (23345 ^ _774244) ^ [_1178218, _1178220] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1178218, _1178220) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1178218, _1178220)))], (20485 ^ _774244) ^ [_1124610, _1124612, _1124614, _1124616, _1124618] : [class_Fields_Olinordered__field(_1124610), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124610), c_Groups_Ozero__class_Ozero(_1124610)), _1124612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124610), _1124612), _1124614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124610), c_Groups_Ozero__class_Ozero(_1124610)), _1124616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124610), _1124616), _1124618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124610), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124610), _1124612), _1124618)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124610), _1124614), _1124616))))], (41446 ^ _774244) ^ [_1569697, _1569699, _1569701, _1569703] : [c_Wellfounded_Owf(_1569697, _1569699), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569697, _1569697)), hAPP(hAPP(c_Product__Type_OPair(_1569697, _1569697), _1569701), _1569703)), _1569699)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569697, _1569697)), hAPP(hAPP(c_Product__Type_OPair(_1569697, _1569697), _1569703), _1569701)), _1569699))], (17013 ^ _774244) ^ [_1065210, _1065212] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065210)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065212)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1065210), _1065212)))], (15382 ^ _774244) ^ [_1033310, _1033312, _1033314, _1033316, _1033318, _1033320] : [class_Rings_Oring(_1033310), 15385 ^ _774244 : [(15392 ^ _774244) ^ [] : [_1033316 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033310), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033310), _1033318), _1033312)), _1033314)), _1033320), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033310), _1033312), _1033314)), _1033316) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033310), _1033318), _1033314)), _1033320))], (15386 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033310), _1033312), _1033314)), _1033316) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033310), _1033318), _1033314)), _1033320), -(_1033316 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033310), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033310), _1033318), _1033312)), _1033314)), _1033320))]]], (50324 ^ _774244) ^ [_1782184, _1782186] : [-(hAPP(c_List_Orev(_1782184), hAPP(c_List_Orev(_1782184), _1782186)) = _1782186)], (15188 ^ _774244) ^ [_1029718, _1029720, _1029722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029718), _1029720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029718), _1029722)), _1029720)))], (46832 ^ _774244) ^ [_1702311, _1702313] : [-(c_List_Olistrelp(_1702311, _1702313, c_List_Olist_ONil(_1702311), c_List_Olist_ONil(_1702311)))], (25591 ^ _774244) ^ [_1220573, _1220575, _1220577, _1220579, _1220581] : [class_Divides_Osemiring__div(_1220573), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220573), _1220575), _1220577)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220573), _1220579), _1220581)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220573), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1220573), _1220577), _1220575)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1220573), _1220581), _1220579)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1220573), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220573), _1220577), _1220581)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220573), _1220575), _1220579)))], (35953 ^ _774244) ^ [_1436869, _1436871, _1436873] : [class_Lattices_Osemilattice__inf(_1436869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436869), _1436871), _1436873)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1436869), _1436871), _1436873) = _1436871)], (14436 ^ _774244) ^ [_1016057, _1016059, _1016061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1016057), _1016059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1016061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016057), _1016061)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016059), _1016061))))], (3660 ^ _774244) ^ [_830662, _830664, _830666, _830668] : [-(c_New__DSequence_Opos__single(_830668, _830664) = c_New__DSequence_Opos__single(_830666, _830662)), _830668 = _830666, _830664 = _830662], (27794 ^ _774244) ^ [_1264782, _1264784, _1264786, _1264788] : [class_Lattices_Osemilattice__sup(_1264782), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264782), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264782), _1264784), _1264786)), _1264788) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264782), _1264784), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264782), _1264786), _1264788)))], (49846 ^ _774244) ^ [_1772005, _1772007] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1772005, _1772007))))], (1054 ^ _774244) ^ [_790143, _790145] : [-(class_Rings_Olinordered__ring(_790143)), _790145 = _790143, class_Rings_Olinordered__ring(_790145)], (11174 ^ _774244) ^ [_957937, _957939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957937), _957939)), 11177 ^ _774244 : [(11180 ^ _774244) ^ [] : [_957937 = _957939], (11178 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957937), _957939)))]]], (5170 ^ _774244) ^ [_854203, _854205, _854207, _854209] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_854209, _854205) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_854207, _854203)), _854209 = _854207, _854205 = _854203], (27532 ^ _774244) ^ [_1259615, _1259617] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1259615), _1259617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1259617), _1259615))], (8054 ^ _774244) ^ [_906146, _906148] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _906146)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _906148)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _906146), _906148)))], (12075 ^ _774244) ^ [_974132, _974134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974132), _974134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974132), hAPP(c_Nat_OSuc, _974134))))], (42532 ^ _774244) ^ [_1595551, _1595553, _1595555, _1595557, _1595559, _1595561] : [c_Finite__Set_Ofun__left__comm__idem(_1595551, _1595553, _1595555), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595551), _1595557)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1595551, _1595553, _1595555), _1595559), hAPP(hAPP(c_Set_Oinsert(_1595551), _1595561), _1595557)) = hAPP(hAPP(c_Finite__Set_Ofold(_1595551, _1595553, _1595555), hAPP(hAPP(_1595555, _1595561), _1595559)), _1595557))], (32108 ^ _774244) ^ [_1355449, _1355451, _1355453, _1355455] : [hBOOL(hAPP(hAPP(c_member(_1355449), _1355451), c_SetInterval_Oord_OlessThan(_1355449, _1355453, _1355455))), -(hBOOL(hAPP(hAPP(_1355453, _1355451), _1355455)))], (43459 ^ _774244) ^ [_1617066, _1617068, _1617070, _1617072, _1617074] : [hBOOL(hAPP(hAPP(c_member(_1617066), _1617068), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1617070, tc_fun(_1617066, tc_HOL_Obool)), _1617072), _1617074))), 43462 ^ _774244 : [(43463 ^ _774244) ^ [_1617190] : [hBOOL(hAPP(hAPP(c_member(_1617070), _1617190), _1617072)), -(hBOOL(hAPP(hAPP(c_member(_1617066), _1617068), hAPP(_1617074, _1617190))))]]], (9106 ^ _774244) ^ [_923228, _923230] : [class_Rings_Omult__zero(_923228), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923228), c_Groups_Ozero__class_Ozero(_923228)), _923230) = c_Groups_Ozero__class_Ozero(_923228))], (44675 ^ _774244) ^ [_1648043, _1648045] : [-(hAPP(c_Relation_OField(_1648043), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1648043, _1648043), tc_HOL_Obool), _1648045)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1648043, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1648043, _1648043), tc_HOL_Obool), tc_fun(_1648043, tc_HOL_Obool), c_Relation_OField(_1648043)), _1648045)))], (10382 ^ _774244) ^ [_945194, _945196, _945198] : [class_Rings_Olinordered__semidom(_945194), 10385 ^ _774244 : [(10392 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945196), _945198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945194), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_945194), _945196)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_945194), _945198))))], (10386 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945194), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_945194), _945196)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_945194), _945198))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945196), _945198)))]]], (5862 ^ _774244) ^ [_867962] : [-(c_Natural_Oevalc(c_Com_Ocom_OSKIP, _867962, _867962))], (41294 ^ _774244) ^ [_1567032, _1567034, _1567036] : [c_Wellfounded_Owf(_1567032, _1567034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1567032, _1567032), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1567032, _1567032, _1567032), _1567034), _1567036)), _1567034)), -(c_FunDef_Oreduction__pair(_1567032, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1567032, _1567032), tc_HOL_Obool), tc_fun(tc_prod(_1567032, _1567032), tc_HOL_Obool)), _1567034), _1567036)))], (29402 ^ _774244) ^ [_1297386, _1297388, _1297390, _1297392, _1297394] : [_1297386 = c_Orderings_Obot__class_Obot(tc_fun(_1297388, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297390, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297388, tc_fun(_1297390, tc_HOL_Obool)), _1297386), _1297392)), _1297394) = _1297394)], (28272 ^ _774244) ^ [_1274077, _1274079, _1274081] : [class_Orderings_Olinorder(_1274077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274077), _1274079), _1274081)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274077, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1274077), _1274079)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1274077, _1274079), _1274081)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1274077), _1274081))], (44860 ^ _774244) ^ [_1651958, _1651960, _1651962] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1651958, tc_HOL_Obool)), _1651960), _1651962))), 44866 ^ _774244 : [(44870 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1651958, tc_HOL_Obool)), 44868 ^ [_1651958, _1651960, _1651962]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1651958, tc_HOL_Obool)), _1651960), _1651962))))], (44872 ^ _774244) ^ [] : [44865 ^ [_1651958, _1651960, _1651962] = 44868 ^ [_1651958, _1651960, _1651962]], (44874 ^ _774244) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1651958, tc_HOL_Obool)), 44865 ^ [_1651958, _1651960, _1651962]), 44868 ^ [_1651958, _1651960, _1651962]) = c_Orderings_Obot__class_Obot(tc_fun(_1651958, tc_HOL_Obool))], (44867 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1651958, tc_HOL_Obool)), 44865 ^ [_1651958, _1651960, _1651962]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1651958, tc_HOL_Obool)), _1651960), _1651962))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1651958, tc_HOL_Obool)), _1651960), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1651958, tc_HOL_Obool), _1651962)) = c_Orderings_Obot__class_Obot(tc_fun(_1651958, tc_HOL_Obool)))], (24805 ^ _774244) ^ [_1207424, _1207426] : [class_Rings_Ocomm__semiring__1(_1207424), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207424), _1207426), c_Groups_Ozero__class_Ozero(_1207424))))], (26832 ^ _774244) ^ [_1245395, _1245397, _1245399] : [class_Groups_Ocomm__monoid__add(_1245395), hAPP(_1245397, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1245395), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245395), _1245397), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1245399)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245395), _1245397), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1245399)))], (49908 ^ _774244) ^ [_1772961, _1772963, _1772965, _1772967, _1772969] : [class_Orderings_Olinorder(_1772961), c_List_Olinorder__class_Osorted(_1772961, hAPP(hAPP(c_List_Omap(_1772963, _1772961), _1772965), _1772967)), -(c_List_Olinorder__class_Osorted(_1772961, hAPP(hAPP(c_List_Omap(_1772963, _1772961), _1772965), c_List_Oremove1(_1772963, _1772969, _1772967))))], (31827 ^ _774244) ^ [_1349229, _1349231, _1349233, _1349235, _1349237] : [class_Groups_Ocomm__monoid__add(_1349229), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349231), _1349233)), hBOOL(hAPP(hAPP(c_member(_1349231), _1349235), _1349233)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349231, _1349229), _1349237), _1349233) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349229), hAPP(_1349237, _1349235)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349231, _1349229), _1349237), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349231, tc_HOL_Obool)), _1349233), hAPP(hAPP(c_Set_Oinsert(_1349231), _1349235), c_Orderings_Obot__class_Obot(tc_fun(_1349231, tc_HOL_Obool)))))))], (25915 ^ _774244) ^ [_1226943, _1226945, _1226947, _1226949, _1226951] : [class_Divides_Osemiring__div(_1226943), -(_1226945 = c_Groups_Ozero__class_Ozero(_1226943)), -(_1226947 = c_Groups_Ozero__class_Ozero(_1226943)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1226943), _1226945), _1226949)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1226943), _1226947), _1226951)), 25934 ^ _774244 : [(25941 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226943), _1226949), _1226947) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226943), _1226945), _1226951), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226943), _1226949), _1226945) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226943), _1226951), _1226947))], (25935 ^ _774244) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226943), _1226949), _1226945) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226943), _1226951), _1226947), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226943), _1226949), _1226947) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226943), _1226945), _1226951))]]], (49918 ^ _774244) ^ [_1773144, _1773146] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1773144, _1773146)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1773144), hAPP(c_Nat_OSuc, _1773146)))], (33866 ^ _774244) ^ [_1389262, _1389264, _1389266, _1389268, _1389270, _1389272] : [-(_1389262 = _1389264), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1389266, _1389268), _1389270), _1389264), _1389272), _1389262) = hAPP(_1389270, _1389262))], (27890 ^ _774244) ^ [_1266865, _1266867] : [class_Lattices_Olattice(_1266865), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266865), _1266867), _1266867) = _1266867)], (2550 ^ _774244) ^ [_812815, _812817, _812819, _812821, _812823, _812825, _812827, _812829, _812831, _812833] : [-(c_Product__Type_Oprod_Oprod__rec(_812833, _812829, _812825, _812821, _812817) = c_Product__Type_Oprod_Oprod__rec(_812831, _812827, _812823, _812819, _812815)), _812833 = _812831, _812829 = _812827, _812825 = _812823, _812821 = _812819, _812817 = _812815], (22720 ^ _774244) ^ [_1166433, _1166435] : [-(_1166433 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22723 ^ _774244 : [(22730 ^ _774244) ^ [] : [-(_1166435 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1166433, _1166435) = 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, _1166435))), 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)), _1166435)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1166433))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1166435), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1166433), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1166433, _1166435)), 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), _1166435))))), c_Divides_Opdivmod(_1166433, _1166435)))))], (22724 ^ _774244) ^ [] : [_1166435 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1166433, _1166435) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1166433))]]], (26754 ^ _774244) ^ [_1243862, _1243864, _1243866] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1243862, tc_Nat_Onat), _1243864), _1243866)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1243862, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1243862), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1243864)), _1243866))], (39255 ^ _774244) ^ [_1509799, _1509801, _1509803, _1509805, _1509807] : [hAPP(_1509799, _1509801) = hAPP(c_Option_Ooption_OSome(_1509803), _1509805), -(hAPP(hAPP(c_Set_Oinsert(_1509807), _1509801), c_Map_Odom(_1509807, _1509803, _1509799)) = c_Map_Odom(_1509807, _1509803, _1509799))], (32974 ^ _774244) ^ [_1371476, _1371478, _1371480] : [class_Lattices_Olattice(_1371476), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371476), _1371478)), -(_1371478 = c_Orderings_Obot__class_Obot(tc_fun(_1371476, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371476), _1371480)), -(_1371480 = c_Orderings_Obot__class_Obot(tc_fun(_1371476, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1371476, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1371476, tc_HOL_Obool)), _1371478), _1371480)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1371476), c_Big__Operators_Olattice__class_OSup__fin(_1371476, _1371478)), c_Big__Operators_Olattice__class_OSup__fin(_1371476, _1371480)))], (25891 ^ _774244) ^ [_1226545, _1226547, _1226549, _1226551] : [class_Divides_Osemiring__div(_1226545), -(_1226547 = c_Groups_Ozero__class_Ozero(_1226545)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1226545), _1226547), _1226549)), 25902 ^ _774244 : [(25909 ^ _774244) ^ [] : [_1226549 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226545), _1226551), _1226547), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226545), _1226549), _1226547) = _1226551)], (25903 ^ _774244) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226545), _1226549), _1226547) = _1226551, -(_1226549 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226545), _1226551), _1226547))]]], (11204 ^ _774244) ^ [_958440, _958442, _958444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958440), _958442)), _958444)), 11207 ^ _774244 : [(11210 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _958442), _958444)))], (11208 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _958440), _958444)))]]], (31813 ^ _774244) ^ [_1348904, _1348906, _1348908, _1348910, _1348912] : [class_Groups_Ocomm__monoid__add(_1348904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348906), _1348908)), hBOOL(hAPP(hAPP(c_member(_1348906), _1348910), _1348908)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348906, _1348904), _1348912), _1348908) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348904), hAPP(_1348912, _1348910)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348906, _1348904), _1348912), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1348906, tc_HOL_Obool)), _1348908), hAPP(hAPP(c_Set_Oinsert(_1348906), _1348910), c_Orderings_Obot__class_Obot(tc_fun(_1348906, tc_HOL_Obool)))))))], (30805 ^ _774244) ^ [_1326660, _1326662, _1326664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326660, tc_HOL_Obool)), _1326662), _1326664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326660, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1326660, tc_fun(_1326660, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326660)), _1326662)), hAPP(hAPP(c_COMBC(_1326660, tc_fun(_1326660, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326660)), _1326664))))], (33626 ^ _774244) ^ [_1384618, _1384620, _1384622] : [class_Orderings_Olinorder(_1384618), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384618), _1384620)), hBOOL(hAPP(hAPP(c_member(_1384618), _1384622), _1384620)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1384618), _1384622), c_Big__Operators_Olattice_OInf__fin(_1384618, c_Orderings_Oord__class_Omin(_1384618), _1384620)) = _1384622)], (50919 ^ _774244) ^ [_1795976, _1795978] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1795976), tc_fun(_1795976, tc_HOL_Obool), c_List_Oset(_1795976)), hAPP(c_List_Oset(tc_List_Olist(_1795976)), c_Enum_Osublists(_1795976, _1795978))) = hAPP(c_Set_OPow(_1795976), hAPP(c_List_Oset(_1795976), _1795978)))], (50743 ^ _774244) ^ [_1792005, _1792007] : [-(c_List_Oremdups(_1792005, c_List_Oremdups(_1792005, _1792007)) = c_List_Oremdups(_1792005, _1792007))], (24299 ^ _774244) ^ [_1196282, _1196284, _1196286] : [class_Orderings_Olinorder(_1196282), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196282), _1196284), _1196286) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196282), _1196286), _1196284))], (49369 ^ _774244) ^ [_1761983, _1761985, _1761987] : [hAPP(c_List_Ofilter(_1761983, _1761985), _1761987) = c_List_Olist_ONil(_1761983), 49372 ^ _774244 : [(49373 ^ _774244) ^ [_1762080] : [hBOOL(hAPP(hAPP(c_member(_1761983), _1762080), hAPP(c_List_Oset(_1761983), _1761987))), hBOOL(hAPP(_1761985, _1762080))]]], (34451 ^ _774244) ^ [_1401866, _1401868, _1401870, _1401872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1401866), _1401868)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1401870), _1401872)), -(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), _1401866), _1401870)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1401868), _1401872))), c_FunDef_Opair__less)))], (31637 ^ _774244) ^ [_1345226] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1345226), 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, _1345226)) = _1345226)], (23485 ^ _774244) ^ [_1181137, _1181139, _1181141, _1181143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1181137, tc_HOL_Obool)), _1181139), _1181141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1181137, tc_HOL_Obool)), _1181141), _1181143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1181137, tc_HOL_Obool)), _1181139), _1181143)))], (38313 ^ _774244) ^ [_1488605, _1488607] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1488605), c_Orderings_Otop__class_Otop(tc_fun(_1488605, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1488605, _1488605, _1488607), c_Orderings_Otop__class_Otop(tc_fun(_1488605, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1488605, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1488605, _1488605, _1488607, c_Orderings_Otop__class_Otop(tc_fun(_1488605, tc_HOL_Obool))))], (19735 ^ _774244) ^ [] : [-(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)))], (476 ^ _774244) ^ [_781542, _781544, _781546, _781548, _781550, _781552, _781554, _781556, _781558, _781560, _781562, _781564] : [-(c_Finite__Set_Ofolding__image__simple(_781562, _781558, _781554, _781550, _781546, _781542)), c_Finite__Set_Ofolding__image__simple(_781564, _781560, _781556, _781552, _781548, _781544), _781564 = _781562, _781560 = _781558, _781556 = _781554, _781552 = _781550, _781548 = _781546, _781544 = _781542], (12172 ^ _774244) ^ [_975762] : [12173 ^ _774244 : [(12174 ^ _774244) ^ [_975819] : [hBOOL(hAPP(_975762, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _975819)))]], 12176 ^ _774244 : [(12179 ^ _774244) ^ [] : [-(hBOOL(hAPP(_975762, 12175 ^ [_975762])))], (12177 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12175 ^ [_975762])))]]], (15088 ^ _774244) ^ [_1027806, _1027808, _1027810, _1027812, _1027814] : [class_Groups_Oordered__ab__group__add(_1027806), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1027806), _1027808), _1027810) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1027806), _1027812), _1027814), 15095 ^ _774244 : [(15102 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027806), _1027812), _1027814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027806), _1027808), _1027810)))], (15096 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027806), _1027808), _1027810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027806), _1027812), _1027814)))]]], (41260 ^ _774244) ^ [_1564649, _1564651, _1564653, _1564655, _1564657, _1564659, _1564661, _1564663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564649, _1564651), tc_HOL_Obool)), _1564653), hAPP(hAPP(c_Product__Type_OSigma(_1564649, _1564651), _1564655), hAPP(c_COMBK(tc_fun(_1564651, tc_HOL_Obool), _1564649), _1564657)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564651, _1564659), tc_HOL_Obool)), _1564661), hAPP(hAPP(c_Product__Type_OSigma(_1564651, _1564659), _1564657), hAPP(c_COMBK(tc_fun(_1564659, tc_HOL_Obool), _1564651), _1564663)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564649, _1564659), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1564649, _1564651, _1564659), _1564653), _1564661)), hAPP(hAPP(c_Product__Type_OSigma(_1564649, _1564659), _1564655), hAPP(c_COMBK(tc_fun(_1564659, tc_HOL_Obool), _1564649), _1564663)))))], (30583 ^ _774244) ^ [_1320181, _1320183, _1320185, _1320187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1320181, tc_HOL_Obool)), _1320183), _1320185)), hBOOL(hAPP(hAPP(c_member(_1320181), _1320187), _1320183)), -(hBOOL(hAPP(hAPP(c_member(_1320181), _1320187), _1320185)))], (40864 ^ _774244) ^ [_1549383, _1549385, _1549387, _1549389] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1549383, _1549385), _1549387), _1549389) = hAPP(c_Set_OCollect(tc_prod(_1549385, _1549385)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549385, _1549385, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1549385, tc_fun(tc_prod(_1549383, _1549383), tc_HOL_Obool), tc_fun(_1549385, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549385, tc_fun(tc_fun(tc_prod(_1549383, _1549383), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1549383, _1549383), tc_HOL_Obool), tc_fun(_1549385, tc_HOL_Obool)), _1549385), c_COMBC(_1549385, tc_fun(tc_prod(_1549383, _1549383), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549385, tc_prod(_1549383, _1549383)), tc_fun(_1549385, tc_fun(tc_fun(tc_prod(_1549383, _1549383), tc_HOL_Obool), tc_HOL_Obool)), _1549385), hAPP(c_COMBB(tc_prod(_1549383, _1549383), tc_fun(tc_fun(tc_prod(_1549383, _1549383), tc_HOL_Obool), tc_HOL_Obool), _1549385), c_member(tc_prod(_1549383, _1549383)))), hAPP(hAPP(c_COMBC(_1549385, tc_fun(_1549385, _1549383), tc_fun(_1549385, tc_prod(_1549383, _1549383))), hAPP(hAPP(c_COMBB(tc_fun(_1549383, tc_prod(_1549383, _1549383)), tc_fun(tc_fun(_1549385, _1549383), tc_fun(_1549385, tc_prod(_1549383, _1549383))), _1549385), c_COMBB(_1549383, tc_prod(_1549383, _1549383), _1549385)), hAPP(hAPP(c_COMBB(_1549383, tc_fun(_1549383, tc_prod(_1549383, _1549383)), _1549385), c_Product__Type_OPair(_1549383, _1549383)), _1549389))), _1549389)))), _1549387))))], (16557 ^ _774244) ^ [_1056118, _1056120, _1056122, _1056124] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056118), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056118), _1056120), _1056122)), hAPP(c_Int_Onumber__class_Onumber__of(_1056118), _1056124)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056118), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056118), _1056120), hAPP(c_Int_Onumber__class_Onumber__of(_1056118), _1056124))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056118), _1056122), hAPP(c_Int_Onumber__class_Onumber__of(_1056118), _1056124)))), class_Int_Onumber(_1056118), class_Rings_Osemiring(_1056118)], (16699 ^ _774244) ^ [_1059127, _1059129] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1059127), _1059129)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1059127) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (46316 ^ _774244) ^ [_1687790, _1687792] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1687790), _1687792))), -(c_Nitpick_Ocard_H(_1687790, _1687792) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10930 ^ _774244) ^ [_954017, _954019, _954021] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954017), _954019) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954017), _954021), -(_954019 = _954021), -(_954017 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9830 ^ _774244) ^ [_936209, _936211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _936209), hAPP(c_Int_Onat, _936211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _936209)), _936211)))], (27008 ^ _774244) ^ [_1249009, _1249011] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1249009), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1249011), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1249009, _1249011))], (3496 ^ _774244) ^ [_828056, _828058] : [_828058 = _828056, -(c_Int_Oring__1__class_Oof__int(_828058) = c_Int_Oring__1__class_Oof__int(_828056))], (39926 ^ _774244) ^ [_1527920, _1527922, _1527924, _1527926, _1527928, _1527930, _1527932] : [-(hAPP(c_Product__Type_Osnd(_1527920, _1527922), hAPP(c_Product__Type_Omap__pair(_1527924, _1527920, _1527926, _1527922, _1527928, _1527930), _1527932)) = hAPP(_1527930, hAPP(c_Product__Type_Osnd(_1527924, _1527926), _1527932)))], (7074 ^ _774244) ^ [_889100, _889102, _889104, _889106, _889108, _889110, _889112, _889114, _889116, _889118, _889120] : [-(c_Com_Ocom_Ocom__rec(_889100, _889102, _889104, _889106, _889108, _889110, _889112, _889114, _889116, c_Com_Ocom_OWhile(_889118, _889120)) = hAPP(hAPP(hAPP(_889112, _889118), _889120), c_Com_Ocom_Ocom__rec(_889100, _889102, _889104, _889106, _889108, _889110, _889112, _889114, _889116, _889120)))], (6550 ^ _774244) ^ [_879806, _879808] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _879806), _879808) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _879806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _879808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2694 ^ _774244) ^ [_815061, _815063, _815065, _815067, _815069, _815071] : [-(c_Product__Type_Ointernal__split(_815071, _815067, _815063) = c_Product__Type_Ointernal__split(_815069, _815065, _815061)), _815071 = _815069, _815067 = _815065, _815063 = _815061], (8134 ^ _774244) ^ [_907430, _907432, _907434] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907430), _907432)), _907434) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907430), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907432), _907434)))], (23999 ^ _774244) ^ [_1190733, _1190735, _1190737, _1190739, _1190741, _1190743] : [-(c_Product__Type_Oprod_Oprod__rec(_1190733, _1190735, _1190737, _1190739, hAPP(hAPP(c_Product__Type_OPair(_1190733, _1190735), _1190741), _1190743)) = hAPP(hAPP(_1190739, _1190741), _1190743))], (28948 ^ _774244) ^ [_1289310, _1289312] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289310, tc_HOL_Obool)), _1289312), _1289312) = c_Orderings_Obot__class_Obot(tc_fun(_1289310, tc_HOL_Obool)))], (16405 ^ _774244) ^ [_1053169, _1053171] : [class_Groups_Oordered__ab__group__add__abs(_1053169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053169), c_Groups_Ozero__class_Ozero(_1053169)), _1053171)), -(hAPP(c_Groups_Oabs__class_Oabs(_1053169), _1053171) = _1053171)], (5320 ^ _774244) ^ [_856480, _856482, _856484, _856486, _856488, _856490] : [-(c_List_OdropWhile(_856490, _856486, _856482) = c_List_OdropWhile(_856488, _856484, _856480)), _856490 = _856488, _856486 = _856484, _856482 = _856480], (8002 ^ _774244) ^ [_905100, _905102, _905104] : [class_Rings_Olinordered__semidom(_905100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905100), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_905100), _905102)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_905100), _905104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905102), _905104)))], (36517 ^ _774244) ^ [_1449200, _1449202, _1449204, _1449206] : [-(hBOOL(hAPP(hAPP(c_member(_1449200), _1449202), _1449204))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449200, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1449200), _1449202), _1449206)), _1449204) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449200, tc_HOL_Obool)), _1449206), _1449204))], (40015 ^ _774244) ^ [_1530450, _1530452] : [-(c_Relation_Orefl__on(_1530450, _1530452, c_Relation_OId__on(_1530450, _1530452)))], (5690 ^ _774244) ^ [_864927, _864929, _864931, _864933] : [c_Natural_Oevalc(_864927, _864929, _864931), c_Natural_Oevalc(_864927, _864929, _864933), -(_864933 = _864931)], (43877 ^ _774244) ^ [_1628338, _1628340, _1628342, _1628344, _1628346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1628338, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1628340, _1628338, _1628342), _1628344)), _1628346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1628340, tc_HOL_Obool)), _1628344), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1628340, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1628338, _1628340, hAPP(c_Relation_Oconverse(_1628340, _1628338), _1628342)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1628338, tc_HOL_Obool)), _1628346))))))], (31545 ^ _774244) ^ [_1342213, _1342215, _1342217] : [hBOOL(hAPP(hAPP(c_member(_1342213), _1342215), c_Option_Oset(_1342213, _1342217))), -(_1342217 = hAPP(c_Option_Ooption_OSome(_1342213), _1342215))], (44568 ^ _774244) ^ [_1645442, _1645444] : [class_Complete__Lattice_Ocomplete__lattice(_1645442), hBOOL(hAPP(c_Finite__Set_Ofinite(_1645442), _1645444)), -(_1645444 = c_Orderings_Obot__class_Obot(tc_fun(_1645442, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1645442, _1645444) = c_Complete__Lattice_OInf__class_OInf(_1645442, _1645444))], (31591 ^ _774244) ^ [_1344029, _1344031, _1344033, _1344035, _1344037] : [class_Groups_Ocomm__monoid__add(_1344029), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344031), _1344033)), 31598 ^ _774244 : [(31605 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344031), _1344035), _1344033))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344031, _1344029), hAPP(hAPP(c_COMBC(_1344031, _1344029, _1344029), hAPP(hAPP(c_COMBS(_1344031, _1344029, tc_fun(_1344029, _1344029)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1344029, tc_fun(_1344029, _1344029)), _1344031), c_If(_1344029)), hAPP(hAPP(c_COMBC(_1344031, _1344031, tc_HOL_Obool), c_fequal), _1344035))), _1344037)), c_Groups_Ozero__class_Ozero(_1344029))), _1344033) = c_Groups_Ozero__class_Ozero(_1344029))], (31599 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1344031), _1344035), _1344033)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344031, _1344029), hAPP(hAPP(c_COMBC(_1344031, _1344029, _1344029), hAPP(hAPP(c_COMBS(_1344031, _1344029, tc_fun(_1344029, _1344029)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1344029, tc_fun(_1344029, _1344029)), _1344031), c_If(_1344029)), hAPP(hAPP(c_COMBC(_1344031, _1344031, tc_HOL_Obool), c_fequal), _1344035))), _1344037)), c_Groups_Ozero__class_Ozero(_1344029))), _1344033) = hAPP(_1344037, _1344035))]]], (7812 ^ _774244) ^ [_901831, _901833, _901835, _901837] : [_901835 = _901837, -(hAPP(c_Sum__Type_OInl(_901831, _901833), _901835) = hAPP(c_Sum__Type_OInl(_901831, _901833), _901837))], (17783 ^ _774244) ^ [_1078540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078540)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1078540) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1078540), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (12293 ^ _774244) ^ [_977749, _977751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _977749), _977751)), -(_977751 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _977749), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12296 ^ [_977749, _977751])))], (34000 ^ _774244) ^ [_1392366, _1392368, _1392370] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392366, tc_Nat_Onat), _1392368), _1392370) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392366, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1392366), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1392368)), _1392370)))], (5108 ^ _774244) ^ [_853234, _853236, _853238, _853240, _853242, _853244, _853246, _853248] : [-(c_Map_Omap__add(_853248, _853244, _853240, _853236) = c_Map_Omap__add(_853246, _853242, _853238, _853234)), _853248 = _853246, _853244 = _853242, _853240 = _853238, _853236 = _853234], (31009 ^ _774244) ^ [_1330385, _1330387, _1330389, _1330391] : [_1330385 = _1330387, 31012 ^ _774244 : [(31019 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1330389), _1330387), _1330391)), -(hBOOL(hAPP(hAPP(c_member(_1330389), _1330385), _1330391)))], (31013 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1330389), _1330385), _1330391)), -(hBOOL(hAPP(hAPP(c_member(_1330389), _1330387), _1330391)))]]], (23095 ^ _774244) ^ [_1173399, _1173401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1173399), 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)), _1173401)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1173399, _1173401) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1173399, _1173401)))], (26267 ^ _774244) ^ [_1233178, _1233180, _1233182] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1233180), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1233178), _1233182))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233178, _1233180) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233182, _1233180))], (40017 ^ _774244) ^ [_1530479, _1530481, _1530483, _1530485] : [_1530479 = c_Finite__Set_Ofold1(_1530481, _1530483), -(hAPP(_1530479, hAPP(hAPP(c_Set_Oinsert(_1530481), _1530485), c_Orderings_Obot__class_Obot(tc_fun(_1530481, tc_HOL_Obool)))) = _1530485)], (38804 ^ _774244) ^ [_1499603, _1499605, _1499607, _1499609, _1499611] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1499603, _1499605, _1499607), _1499609), _1499611)), -(hBOOL(hAPP(_1499609, hAPP(_1499607, _1499611))))], (38539 ^ _774244) ^ [_1493506, _1493508, _1493510, _1493512, _1493514] : [c_Fun_Oinj__on(_1493506, _1493508, _1493510, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1493506, tc_HOL_Obool)), _1493512), _1493514)), 38542 ^ _774244 : [(38547 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493508, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1493506, _1493508, _1493510), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493506, tc_HOL_Obool)), _1493512), _1493514))), hAPP(c_Set_Oimage(_1493506, _1493508, _1493510), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493506, tc_HOL_Obool)), _1493514), _1493512))) = c_Orderings_Obot__class_Obot(tc_fun(_1493508, tc_HOL_Obool)))], (38545 ^ _774244) ^ [] : [-(c_Fun_Oinj__on(_1493506, _1493508, _1493510, _1493514))], (38543 ^ _774244) ^ [] : [-(c_Fun_Oinj__on(_1493506, _1493508, _1493510, _1493512))]]], (15444 ^ _774244) ^ [_1034700, _1034702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1034700), _1034702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1034700), _1034702)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7467 ^ _774244) ^ [_895341, _895343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _895341)), _895343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _895341), _895343)))], (3904 ^ _774244) ^ [_834382, _834384] : [_834384 = _834382, -(c_Equiv__Relations_Oquotient(_834384) = c_Equiv__Relations_Oquotient(_834382))], (19033 ^ _774244) ^ [_1098997, _1098999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1098997)), c_Int_OBit1(_1098999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098997), _1098999)))], (13218 ^ _774244) ^ [_993974, _993976] : [_993974 = _993976, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993974), _993976)))], (34081 ^ _774244) ^ [_1394007, _1394009, _1394011] : [class_Groups_Ocomm__monoid__mult(_1394007), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1394009, _1394007), _1394011), c_Orderings_Obot__class_Obot(tc_fun(_1394009, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1394007))], (9434 ^ _774244) ^ [_929308, _929310, _929312, _929314] : [class_Rings_Olinordered__ring__strict(_929308), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929308), _929310), c_Groups_Ozero__class_Ozero(_929308))), 9441 ^ _774244 : [(9448 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929308), _929314), _929312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929308), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929308), _929310), _929312)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929308), _929310), _929314))))], (9442 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929308), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929308), _929310), _929312)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929308), _929310), _929314))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929308), _929314), _929312)))]]], (14398 ^ _774244) ^ [_1015370, _1015372, _1015374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1015370)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015370), _1015372)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015370), _1015374)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1015372), _1015374))], (36339 ^ _774244) ^ [_1445129, _1445131, _1445133, _1445135] : [class_Lattices_Osemilattice__inf(_1445129), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445129), _1445131), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445129), _1445133), _1445135)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445129), _1445133), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445129), _1445131), _1445135)))], (33878 ^ _774244) ^ [_1389523, _1389525, _1389527, _1389529, _1389531, _1389533] : [-(hBOOL(hAPP(hAPP(c_member(_1389523), _1389525), _1389527))), -(hAPP(c_Set_Oimage(_1389523, tc_Option_Ooption(_1389529), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1389523, tc_Option_Ooption(_1389529)), _1389531), _1389525), hAPP(c_Option_Ooption_OSome(_1389529), _1389533))), _1389527) = hAPP(c_Set_Oimage(_1389523, tc_Option_Ooption(_1389529), _1389531), _1389527))], (41364 ^ _774244) ^ [_1568244, _1568246] : [c_Wellfounded_Owf(_1568244, _1568246), 41367 ^ _774244 : [(41368 ^ _774244) ^ [_1568313] : [-(hBOOL(hAPP(hAPP(c_member(_1568244), _1568313), c_Wellfounded_Oacc(_1568244, _1568246))))]]], (15524 ^ _774244) ^ [_1036114, _1036116, _1036118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036114), _1036116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036118), _1036114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036114), _1036118)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036116), _1036118))))], (48700 ^ _774244) ^ [_1747427, _1747429, _1747431] : [class_Groups_Omonoid__add(_1747427), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1747427), _1747429), hAPP(c_List_Ofoldl(_1747427, _1747427, c_Groups_Oplus__class_Oplus(_1747427), c_Groups_Ozero__class_Ozero(_1747427)), _1747431)) = hAPP(c_List_Ofoldl(_1747427, _1747427, c_Groups_Oplus__class_Oplus(_1747427), _1747429), _1747431))], (29832 ^ _774244) ^ [_1305666, _1305668, _1305670, _1305672] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1305666), _1305668)), 29835 ^ _774244 : [(29836 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1305670), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1305666, tc_fun(_1305670, tc_HOL_Obool)), _1305668), _1305672))), 29839 ^ _774244 : [(29840 ^ _774244) ^ [_1305850] : [hBOOL(hAPP(hAPP(c_member(_1305666), _1305850), _1305668)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305670), hAPP(_1305672, _1305850))))]]], (29846 ^ _774244) ^ [] : [29848 ^ _774244 : [(29851 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1305670), hAPP(_1305672, 29847 ^ [_1305666, _1305668, _1305670, _1305672])))], (29849 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1305666), 29847 ^ [_1305666, _1305668, _1305670, _1305672]), _1305668)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305670), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1305666, tc_fun(_1305670, tc_HOL_Obool)), _1305668), _1305672))))]]], (19455 ^ _774244) ^ [_1106360, _1106362, _1106364] : [class_Rings_Olinordered__idom(_1106360), 19458 ^ _774244 : [(19467 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106360), hAPP(hAPP(c_Power_Opower__class_Opower(_1106360), _1106362), 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(_1106360), _1106364), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1106360)), _1106362 = c_Groups_Ozero__class_Ozero(_1106360), _1106364 = c_Groups_Ozero__class_Ozero(_1106360)], (19459 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106360), hAPP(hAPP(c_Power_Opower__class_Opower(_1106360), _1106362), 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(_1106360), _1106364), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1106360), 19462 ^ _774244 : [(19465 ^ _774244) ^ [] : [-(_1106364 = c_Groups_Ozero__class_Ozero(_1106360))], (19463 ^ _774244) ^ [] : [-(_1106362 = c_Groups_Ozero__class_Ozero(_1106360))]]]]], (33132 ^ _774244) ^ [_1374018, _1374020, _1374022] : [class_Orderings_Olinorder(_1374018), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374018), _1374020)), 33139 ^ _774244 : [(33146 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374018, tc_HOL_Obool)), _1374020), hAPP(hAPP(c_Set_Oinsert(_1374018), _1374022), c_Orderings_Obot__class_Obot(tc_fun(_1374018, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1374018, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1374018, hAPP(hAPP(c_Set_Oinsert(_1374018), _1374022), _1374020)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1374018), _1374022), c_Big__Operators_Olinorder__class_OMin(_1374018, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374018, tc_HOL_Obool)), _1374020), hAPP(hAPP(c_Set_Oinsert(_1374018), _1374022), c_Orderings_Obot__class_Obot(tc_fun(_1374018, tc_HOL_Obool)))))))], (33140 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374018, tc_HOL_Obool)), _1374020), hAPP(hAPP(c_Set_Oinsert(_1374018), _1374022), c_Orderings_Obot__class_Obot(tc_fun(_1374018, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1374018, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1374018, hAPP(hAPP(c_Set_Oinsert(_1374018), _1374022), _1374020)) = _1374022)]]], (31053 ^ _774244) ^ [_1331178, _1331180, _1331182] : [_1331180 = _1331182, -(hAPP(hAPP(c_COMBC(_1331178, tc_fun(_1331178, tc_HOL_Obool), tc_HOL_Obool), c_member(_1331178)), _1331180) = hAPP(hAPP(c_COMBC(_1331178, tc_fun(_1331178, tc_HOL_Obool), tc_HOL_Obool), c_member(_1331178)), _1331182))], (1064 ^ _774244) ^ [_790268, _790270] : [-(class_Rings_Olinordered__idom(_790268)), _790270 = _790268, class_Rings_Olinordered__idom(_790270)], (23065 ^ _774244) ^ [_1172984, _1172986, _1172988, _1172990] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1172984, _1172986), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1172988), _1172990))), -(_1172986 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1172984, _1172986) = _1172990)], (7539 ^ _774244) ^ [_896739, _896741] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_896739, _896741))))], (2364 ^ _774244) ^ [_809876, _809878, _809880, _809882, _809884, _809886, _809888, _809890] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_809890, _809886, _809882, _809878) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_809888, _809884, _809880, _809876)), _809890 = _809888, _809886 = _809884, _809882 = _809880, _809878 = _809876], (29098 ^ _774244) ^ [_1292258, _1292260] : [class_Lattices_Obounded__lattice__bot(_1292258), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292258), c_Orderings_Obot__class_Obot(_1292258)), _1292260) = _1292260)], (28916 ^ _774244) ^ [_1288637, _1288639, _1288641] : [hAPP(hAPP(c_Set_Oinsert(_1288637), _1288639), c_Orderings_Obot__class_Obot(tc_fun(_1288637, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_1288637), _1288641), c_Orderings_Obot__class_Obot(tc_fun(_1288637, tc_HOL_Obool))), -(_1288639 = _1288641)], (18739 ^ _774244) ^ [] : [-(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)))))], (10922 ^ _774244) ^ [_953856, _953858, _953860] : [10923 ^ _774244 : [(10926 ^ _774244) ^ [] : [_953858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10924 ^ _774244) ^ [] : [_953856 = _953860]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953856), _953858) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953860), _953858))], (29220 ^ _774244) ^ [_1294301, _1294303] : [class_Orderings_Oorder(_1294301), -(c_SetInterval_Oord__class_OatLeastAtMost(_1294301, _1294303, _1294303) = hAPP(hAPP(c_Set_Oinsert(_1294301), _1294303), c_Orderings_Obot__class_Obot(tc_fun(_1294301, tc_HOL_Obool))))], (36345 ^ _774244) ^ [_1445272, _1445274, _1445276] : [class_Lattices_Osemilattice__inf(_1445272), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445272), _1445274), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445272), _1445274), _1445276)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445272), _1445274), _1445276))], (9156 ^ _774244) ^ [_924109, _924111, _924113, _924115] : [class_Rings_Ocomm__semiring__1(_924109), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924109), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924109), _924111), _924113)), _924115) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924109), _924111), _924115)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924109), _924113), _924115)))], (8254 ^ _774244) ^ [_908855, _908857, _908859] : [class_Orderings_Oorder(_908855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908855), _908857), _908859)), _908857 = _908859], (5913 ^ _774244) ^ [_868877, _868879, _868881, _868883, _868885] : [hBOOL(hAPP(_868877, _868879)), c_Natural_Oevalc(_868881, _868879, _868883), -(c_Natural_Oevalc(c_Com_Ocom_OCond(_868877, _868881, _868885), _868879, _868883))], (29606 ^ _774244) ^ [_1301443] : [-(hAPP(c_Int_Onat, _1301443) = 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, _1301443)), 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)))))))], (12888 ^ _774244) ^ [_988411, _988413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _988411)), 12891 ^ _774244 : [(12898 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _988411), _988413)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _988411)), hAPP(c_Int_Onat, _988413))))], (12892 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _988411)), hAPP(c_Int_Onat, _988413))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _988411), _988413)))]]], (41170 ^ _774244) ^ [_1561830, _1561832, _1561834, _1561836] : [class_Groups_Ocomm__monoid__add(_1561830), c_Fun_Oinj__on(_1561832, _1561830, _1561834, _1561836), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561832, _1561830), _1561834), _1561836) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561830, _1561830), c_Fun_Oid(_1561830)), hAPP(c_Set_Oimage(_1561832, _1561830, _1561834), _1561836)))], (11859 ^ _774244) ^ [_970298] : [class_Rings_Olinordered__semidom(_970298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970298), c_Groups_Oone__class_Oone(_970298)), c_Groups_Ozero__class_Ozero(_970298)))], (10994 ^ _774244) ^ [_954995] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _954995)))], (36441 ^ _774244) ^ [_1447380, _1447382, _1447384, _1447386, _1447388] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447380, tc_fun(_1447382, tc_HOL_Obool)), _1447384), hAPP(hAPP(c_COMBC(_1447380, tc_fun(_1447382, tc_HOL_Obool), tc_fun(_1447382, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447382, tc_HOL_Obool), tc_fun(tc_fun(_1447382, tc_HOL_Obool), tc_fun(_1447382, tc_HOL_Obool)), _1447380), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447382, tc_HOL_Obool))), _1447386)), _1447388)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447382, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447380, tc_fun(_1447382, tc_HOL_Obool)), _1447384), _1447386)), _1447388))], (14123 ^ _774244) ^ [_1010744, _1010746, _1010748] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010744), _1010746)), _1010748) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010744), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1010746), _1010748))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010744), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1010746, _1010748))), _1010748)))], (19901 ^ _774244) ^ [_1114868, _1114870] : [c_Nat__Transfer_Ois__nat(_1114868), c_Nat__Transfer_Ois__nat(_1114870), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1114868, _1114870)))], (39421 ^ _774244) ^ [_1513888, _1513890, _1513892, _1513894, _1513896] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1513888, _1513888, _1513890, _1513892, _1513894), _1513896)), -(hBOOL(hAPP(hAPP(c_member(_1513888), _1513892), _1513894))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1513888, _1513890, hAPP(hAPP(c_Set_Oinsert(_1513888), _1513892), _1513894)), _1513896)))], (45081 ^ _774244) ^ [_1657897, _1657899, _1657901, _1657903] : [class_Lattices_Osemilattice__sup(_1657897), hBOOL(hAPP(c_Finite__Set_Ofinite(_1657897), _1657899)), 45091 ^ _774244 : [(45094 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1657897), 45090 ^ [_1657897, _1657899, _1657901, _1657903]), _1657901))], (45092 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1657897), 45090 ^ [_1657897, _1657899, _1657901, _1657903]), _1657899)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1657897), hAPP(hAPP(c_Finite__Set_Ofold(_1657897, _1657897, c_Lattices_Osemilattice__sup__class_Osup(_1657897)), _1657903), _1657899)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1657897), _1657901), _1657903))))], (40099 ^ _774244) ^ [_1531908, _1531910] : [class_Orderings_Olinorder(_1531908), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531908), _1531910)), -(c_Big__Operators_Olattice_OInf__fin(_1531908, c_Orderings_Oord__class_Omin(_1531908), _1531910) = hAPP(c_Finite__Set_Ofold1(_1531908, c_Orderings_Oord__class_Omin(_1531908)), _1531910))], (34640 ^ _774244) ^ [_1406229, _1406231, _1406233] : [class_Orderings_Olinorder(_1406229), hAPP(_1406231, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1406229), 34645 ^ [_1406229, _1406231, _1406233]), 34646 ^ [_1406229, _1406231, _1406233])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1406229), hAPP(_1406231, 34645 ^ [_1406229, _1406231, _1406233])), hAPP(_1406231, 34646 ^ [_1406229, _1406231, _1406233])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406229), _1406233)), -(_1406233 = c_Orderings_Obot__class_Obot(tc_fun(_1406229, tc_HOL_Obool))), -(hAPP(_1406231, c_Big__Operators_Olattice_OSup__fin(_1406229, c_Orderings_Oord__class_Omax(_1406229), _1406233)) = c_Big__Operators_Olattice_OSup__fin(_1406229, c_Orderings_Oord__class_Omax(_1406229), hAPP(c_Set_Oimage(_1406229, _1406229, _1406231), _1406233)))], (13716 ^ _774244) ^ [_1003001, _1003003] : [class_Lattices_Oab__semigroup__idem__mult(_1003001), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003001), _1003003), _1003003) = _1003003)], (48130 ^ _774244) ^ [_1733510, _1733512, _1733514, _1733516] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733510), tc_List_Olist(_1733510))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733510), tc_List_Olist(_1733510)), _1733512), _1733514)), c_List_Olistrel1(_1733510, _1733516))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733510)), _1733512) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733510)), _1733514))], (6337 ^ _774244) ^ [_876185, _876187, _876189, _876191, _876193, _876195, _876197, _876199, _876201, _876203, _876205, _876207] : [-(c_Com_Ocom_Ocom__rec(_876185, _876187, _876189, _876191, _876193, _876195, _876197, _876199, _876201, c_Com_Ocom_OCall(_876203, _876205, _876207)) = hAPP(hAPP(hAPP(_876201, _876203), _876205), _876207))], (22714 ^ _774244) ^ [_1166355, _1166357] : [_1166355 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1166355, _1166357) = 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)))], (11415 ^ _774244) ^ [_962196, _962198, _962200] : [class_Groups_Oordered__comm__monoid__add(_962196), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962196), _962198), c_Groups_Ozero__class_Ozero(_962196))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962196), _962200), c_Groups_Ozero__class_Ozero(_962196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962196), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962196), _962198), _962200)), c_Groups_Ozero__class_Ozero(_962196))))], (41698 ^ _774244) ^ [_1576121, _1576123, _1576125, _1576127] : [hBOOL(hAPP(c_Predicate_ORangeP(_1576121, _1576123, _1576125), _1576127)), -(hBOOL(hAPP(hAPP(_1576125, 41701 ^ [_1576121, _1576123, _1576125, _1576127]), _1576127)))], (23261 ^ _774244) ^ [_1176482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1176482)), 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), _1176482)) = 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), _1176482))))))], (5354 ^ _774244) ^ [_857007, _857009] : [_857009 = _857007, -(c_member(_857009) = c_member(_857007))], (16693 ^ _774244) ^ [_1058958, _1058960, _1058962, _1058964] : [class_Int_Onumber__ring(_1058958), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058958), hAPP(c_Int_Onumber__class_Onumber__of(_1058958), _1058960)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058958), hAPP(c_Int_Onumber__class_Onumber__of(_1058958), _1058962)), _1058964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058958), hAPP(c_Int_Onumber__class_Onumber__of(_1058958), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1058960), _1058962))), _1058964))], (24177 ^ _774244) ^ [_1194144, _1194146, _1194148, _1194150] : [class_Orderings_Olinorder(_1194144), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194144), _1194146), _1194148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194144), _1194150), _1194148)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194144), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194144), _1194146), _1194150)), _1194148)))], (12994 ^ _774244) ^ [_990026, _990028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990028)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _990026), _990028)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _990026)), hAPP(c_Int_Onat, _990028)))], (3442 ^ _774244) ^ [_827145, _827147, _827149, _827151, _827153, _827155] : [-(c_Finite__Set_Ofold1Set(_827155, _827151, _827147) = c_Finite__Set_Ofold1Set(_827153, _827149, _827145)), _827155 = _827153, _827151 = _827149, _827147 = _827145], (42200 ^ _774244) ^ [_1588298, _1588300, _1588302, _1588304, _1588306, _1588308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1588298, tc_HOL_Obool)), _1588300), _1588302)), 42206 ^ _774244 : [(42209 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1588304, tc_HOL_Obool)), hAPP(_1588306, 42205 ^ [_1588298, _1588300, _1588302, _1588304, _1588306, _1588308])), hAPP(_1588308, 42205 ^ [_1588298, _1588300, _1588302, _1588304, _1588306, _1588308])))], (42207 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588298), 42205 ^ [_1588298, _1588300, _1588302, _1588304, _1588306, _1588308]), _1588300)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588298, _1588304), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1588298, _1588304), _1588300), _1588306)), hAPP(hAPP(c_Product__Type_OSigma(_1588298, _1588304), _1588302), _1588308))))], (47642 ^ _774244) ^ [_1721383, _1721385, _1721387, _1721389] : [-(c_Map_Omap__of(_1721383, _1721385, hAPP(hAPP(c_List_Oappend(tc_prod(_1721383, _1721385)), _1721387), _1721389)) = c_Map_Omap__add(_1721383, _1721385, c_Map_Omap__of(_1721383, _1721385, _1721389), c_Map_Omap__of(_1721383, _1721385, _1721387)))], (37969 ^ _774244) ^ [_1482080, _1482082, _1482084, _1482086] : [c_Equiv__Relations_Oequivp(_1482080, _1482082), hBOOL(hAPP(hAPP(_1482082, _1482084), _1482086)), -(hBOOL(hAPP(hAPP(_1482082, _1482086), _1482084)))], (47439 ^ _774244) ^ [_1716473, _1716475, _1716477, _1716479, _1716481, _1716483] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1716473), tc_List_Olist(_1716473))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716473), tc_List_Olist(_1716473)), hAPP(hAPP(c_List_Olist_OCons(_1716473), _1716475), _1716477)), hAPP(hAPP(c_List_Olist_OCons(_1716473), _1716479), _1716481))), c_List_Olexord(_1716473, _1716483)))), 47440 ^ _774244 : [(47443 ^ _774244) ^ [] : [_1716475 = _1716479, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1716473), tc_List_Olist(_1716473))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716473), tc_List_Olist(_1716473)), _1716477), _1716481)), c_List_Olexord(_1716473, _1716483)))], (47441 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1716473, _1716473)), hAPP(hAPP(c_Product__Type_OPair(_1716473, _1716473), _1716475), _1716479)), _1716483))]]], (14147 ^ _774244) ^ [_1011254, _1011256] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1011254, _1011256)), _1011254)))], (11539 ^ _774244) ^ [_964358, _964360, _964362] : [class_Rings_Olinordered__ring__strict(_964358), 11542 ^ _774244 : [(11557 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964358), c_Groups_Ozero__class_Ozero(_964358)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964358), _964360), _964362)))), 11558 ^ _774244 : [(11565 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964358), _964360), c_Groups_Ozero__class_Ozero(_964358))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964358), _964362), c_Groups_Ozero__class_Ozero(_964358)))], (11559 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964358), c_Groups_Ozero__class_Ozero(_964358)), _964360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964358), c_Groups_Ozero__class_Ozero(_964358)), _964362))]]], (11543 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964358), c_Groups_Ozero__class_Ozero(_964358)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964358), _964360), _964362))), 11548 ^ _774244 : [(11551 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964358), c_Groups_Ozero__class_Ozero(_964358)), _964362)))], (11549 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964358), c_Groups_Ozero__class_Ozero(_964358)), _964360)))]], 11552 ^ _774244 : [(11555 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964358), _964362), c_Groups_Ozero__class_Ozero(_964358))))], (11553 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964358), _964360), c_Groups_Ozero__class_Ozero(_964358))))]]]]], (47245 ^ _774244) ^ [_1712283, _1712285, _1712287, _1712289, _1712291] : [class_Orderings_Olinorder(_1712283), -(hBOOL(hAPP(hAPP(c_member(_1712283), hAPP(_1712285, _1712287)), hAPP(c_Set_Oimage(_1712289, _1712283, _1712285), hAPP(c_List_Oset(_1712289), _1712291))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1712289, _1712283, _1712285, _1712287, _1712291) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712289, _1712283, _1712285), _1712287), _1712291))], (23403 ^ _774244) ^ [_1179649, _1179651, _1179653] : [-(_1179649 = _1179651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179653, tc_HOL_Obool)), _1179649), _1179651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179653, tc_HOL_Obool)), _1179651), _1179649))], (1214 ^ _774244) ^ [_792143, _792145] : [-(class_Orderings_Owellorder(_792143)), _792145 = _792143, class_Orderings_Owellorder(_792145)], (34566 ^ _774244) ^ [_1404085] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1404085)), -(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))), _1404085)), c_FunDef_Omax__weak)))], (47453 ^ _774244) ^ [_1716906, _1716908, _1716910, _1716912] : [-(hAPP(hAPP(c_List_Onth(_1716906), hAPP(hAPP(c_List_Oappend(_1716906), _1716908), _1716910)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716906)), _1716908)), _1716912)) = hAPP(hAPP(c_List_Onth(_1716906), _1716910), _1716912))], (22164 ^ _774244) ^ [_1155311, _1155313] : [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(_1155313))), 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)), _1155311))))), -(hAPP(c_Nat_OSuc, _1155311) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155313))], (39590 ^ _774244) ^ [_1518141, _1518143, _1518145, _1518147, _1518149] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518141, _1518143), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1518141, tc_HOL_Obool)), _1518145), _1518147)), hAPP(c_COMBK(tc_fun(_1518143, tc_HOL_Obool), _1518141), _1518149)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1518141, _1518143), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518141, _1518143), _1518145), hAPP(c_COMBK(tc_fun(_1518143, tc_HOL_Obool), _1518141), _1518149))), hAPP(hAPP(c_Product__Type_OSigma(_1518141, _1518143), _1518147), hAPP(c_COMBK(tc_fun(_1518143, tc_HOL_Obool), _1518141), _1518149))))], (8114 ^ _774244) ^ [_907111, _907113] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _907111) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _907113), -(_907111 = _907113)], (30673 ^ _774244) ^ [_1321921, _1321923, _1321925, _1321927, _1321929, _1321931, _1321933] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1321921, _1321923)), hAPP(hAPP(c_Product__Type_OPair(_1321921, _1321923), _1321925), _1321927)), _1321929)), -(hBOOL(hAPP(hAPP(c_member(_1321931), hAPP(hAPP(_1321933, _1321925), _1321927)), hAPP(c_Set_Oimage(tc_prod(_1321921, _1321923), _1321931, hAPP(c_Product__Type_Oprod_Oprod__case(_1321921, _1321923, _1321931), _1321933)), _1321929))))], (7930 ^ _774244) ^ [_903806, _903808] : [7931 ^ _774244 : [(7932 ^ _774244) ^ [_903862] : [_903808 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _903806), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _903862)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _903806), _903808)))], (48867 ^ _774244) ^ [_1751319, _1751321, _1751323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1751319, _1751319), tc_HOL_Obool)), _1751321), hAPP(hAPP(c_Product__Type_OSigma(_1751319, _1751319), _1751323), hAPP(c_COMBK(tc_fun(_1751319, tc_HOL_Obool), _1751319), _1751323)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1751319), tc_List_Olist(_1751319)), tc_HOL_Obool)), c_List_Olistrel(_1751319, _1751321)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1751319), tc_List_Olist(_1751319)), c_List_Olists(_1751319, _1751323)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1751319), tc_HOL_Obool), tc_List_Olist(_1751319)), c_List_Olists(_1751319, _1751323))))))], (6756 ^ _774244) ^ [_883219, _883221, _883223, _883225, _883227, _883229] : [c_Com_Ocom_OCall(_883219, _883221, _883223) = c_Com_Ocom_OLocal(_883225, _883227, _883229)], (50380 ^ _774244) ^ [_1783237, _1783239, _1783241] : [-(hAPP(c_List_Orev(_1783237), hAPP(hAPP(c_List_Otake(_1783237), _1783239), _1783241)) = hAPP(hAPP(c_List_Odrop(_1783237), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783237)), _1783241)), _1783239)), hAPP(c_List_Orev(_1783237), _1783241)))], (31255 ^ _774244) ^ [_1335528, _1335530, _1335532, _1335534] : [-(hBOOL(hAPP(hAPP(c_member(_1335528), _1335530), _1335532))), 31258 ^ _774244 : [(31265 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1335528, tc_HOL_Obool)), _1335532), _1335534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1335528, tc_HOL_Obool)), _1335532), hAPP(hAPP(c_Set_Oinsert(_1335528), _1335530), _1335534))))], (31259 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1335528, tc_HOL_Obool)), _1335532), hAPP(hAPP(c_Set_Oinsert(_1335528), _1335530), _1335534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1335528, tc_HOL_Obool)), _1335532), _1335534)))]]], (48124 ^ _774244) ^ [_1733331, _1733333, _1733335, _1733337] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733331), tc_List_Olist(_1733331))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733331), tc_List_Olist(_1733331)), _1733333), _1733335)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1733331), c_List_Olistrel1(_1733331, _1733337)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733331)), _1733333) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733331)), _1733335))], (27257 ^ _774244) ^ [_1254344, _1254346] : [_1254344 = _1254346, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254344) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254346))], (34950 ^ _774244) ^ [_1413577] : [-(hAPP(c_Set_OPow(_1413577), c_Orderings_Obot__class_Obot(tc_fun(_1413577, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1413577, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1413577, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1413577, tc_HOL_Obool), tc_HOL_Obool))))], (17607 ^ _774244) ^ [_1075730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075730), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1075730)))], (36005 ^ _774244) ^ [_1437768, _1437770, _1437772] : [class_Lattices_Osemilattice__inf(_1437768), 36008 ^ _774244 : [(36015 ^ _774244) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1437768), _1437770), _1437772) = _1437770, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437768), _1437770), _1437772)))], (36009 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437768), _1437770), _1437772)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1437768), _1437770), _1437772) = _1437770)]]], (8220 ^ _774244) ^ [_908461, _908463, _908465] : [class_Orderings_Olinorder(_908461), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908461), _908463), _908465))), 8227 ^ _774244 : [(8234 ^ _774244) ^ [] : [_908465 = _908463, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908461), _908465), _908463))], (8228 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908461), _908465), _908463))), -(_908465 = _908463)]]], (8469 ^ _774244) ^ [_912273] : [-(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, _912273)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13692 ^ _774244) ^ [_1002590, _1002592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002590), 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, _1002592, _1002590)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (4982 ^ _774244) ^ [_851219, _851221] : [_851221 = _851219, -(c_Groups_Oone__class_Oone(_851221) = c_Groups_Oone__class_Oone(_851219))], (18103 ^ _774244) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (25793 ^ _774244) ^ [_1224397, _1224399, _1224401] : [class_Rings_Odvd(_1224397), class_Rings_Osemiring__0(_1224397), 25800 ^ _774244 : [(25810 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1224399, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224397), _1224401), 25817 ^ [_1224397, _1224399, _1224401])))), 25811 ^ _774244 : [(25812 ^ _774244) ^ [_1224726] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224397), _1224401), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224397), _1224726), c_Groups_Ozero__class_Ozero(_1224397)))), hBOOL(hAPP(_1224399, _1224726))]]], (25801 ^ _774244) ^ [] : [25802 ^ _774244 : [(25803 ^ _774244) ^ [_1224589] : [hBOOL(hAPP(_1224399, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224397), _1224401), _1224589)))]], 25805 ^ _774244 : [(25808 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1224399, 25804 ^ [_1224397, _1224399, _1224401])))], (25806 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224397), _1224401), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224397), 25804 ^ [_1224397, _1224399, _1224401]), c_Groups_Ozero__class_Ozero(_1224397)))))]]]]], (19269 ^ _774244) ^ [_1103142, _1103144] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1103142)), c_Int_OBit1(_1103144)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1103142), c_Int_Osucc(_1103144))))], (8418 ^ _774244) ^ [_911435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _911435)), 8422 ^ _774244 : [(8425 ^ _774244) ^ [] : [-(_911435 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8421 ^ [_911435]))], (8423 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8421 ^ [_911435])))]]], (15500 ^ _774244) ^ [_1035676, _1035678] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035676), _1035678))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035678), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035676), _1035678)) = _1035676)], (17405 ^ _774244) ^ [_1072163, _1072165, _1072167] : [class_Rings_Olinordered__semidom(_1072163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072163), c_Groups_Oone__class_Oone(_1072163)), _1072165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072163), c_Groups_Oone__class_Oone(_1072163)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072163), _1072165), hAPP(c_Nat_OSuc, _1072167)))))], (24755 ^ _774244) ^ [_1206602, _1206604, _1206606] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1206602), _1206604)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1206602), _1206606))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1206602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206604), _1206606)))], (45098 ^ _774244) ^ [_1658261, _1658263] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1658261, _1658261)), _1658263), c_Relation_OId(_1658261))), -(_1658263 = hAPP(hAPP(c_Product__Type_OPair(_1658261, _1658261), 45101 ^ [_1658261, _1658263]), 45101 ^ [_1658261, _1658263]))], (40637 ^ _774244) ^ [_1542232, _1542234, _1542236] : [hBOOL(hAPP(hAPP(c_member(_1542232), _1542234), hAPP(c_Set_OCollect(_1542232), _1542236))), -(hBOOL(hAPP(_1542236, _1542234)))], (23755 ^ _774244) ^ [_1186399, _1186401, _1186403, _1186405] : [class_Orderings_Olinorder(_1186399), 23758 ^ _774244 : [(23767 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186399), _1186401), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186399), _1186403), _1186405)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186399), _1186401), _1186403)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186399), _1186401), _1186405))], (23759 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186399), _1186401), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186399), _1186403), _1186405))), 23762 ^ _774244 : [(23765 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186399), _1186401), _1186405)))], (23763 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186399), _1186401), _1186403)))]]]]], (45229 ^ _774244) ^ [_1661309, _1661311, _1661313] : [hBOOL(hAPP(hAPP(c_member(_1661309), _1661311), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1661309, tc_HOL_Obool), _1661313))), 45233 ^ _774244 : [(45236 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1661309, tc_HOL_Obool)), 45232 ^ [_1661309, _1661311, _1661313]), _1661313)))], (45234 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1661309), _1661311), 45232 ^ [_1661309, _1661311, _1661313])))]]], (34087 ^ _774244) ^ [_1394116, _1394118, _1394120, _1394122] : [class_Groups_Ocomm__monoid__mult(_1394116), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1394118), _1394120))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1394118, _1394116), _1394122), _1394120) = c_Groups_Oone__class_Oone(_1394116))], (8730 ^ _774244) ^ [_916728] : [class_Rings_Oring__1(_916728), -(hAPP(c_Int_Oring__1__class_Oof__int(_916728), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_916728))], (23893 ^ _774244) ^ [_1188800, _1188802, _1188804] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1188800), _1188802)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1188804), _1188802)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1188800), _1188804)), _1188802))], (17937 ^ _774244) ^ [_1081156] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1081156, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47614 ^ _774244) ^ [_1720814, _1720816, _1720818, _1720820] : [_1720818 = _1720820, -(hAPP(hAPP(c_List_Oappend(_1720814), _1720816), _1720818) = hAPP(hAPP(c_List_Oappend(_1720814), _1720816), _1720820))], (38728 ^ _774244) ^ [_1497683, _1497685, _1497687, _1497689, _1497691] : [-(hAPP(c_Fun_Othe__inv__into(_1497683, _1497685, _1497687, _1497689), _1497691) = c_HOL_OThe(_1497683, hAPP(hAPP(c_COMBS(_1497683, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497683), c_fconj), hAPP(hAPP(c_COMBC(_1497683, tc_fun(_1497683, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497683)), _1497687))), hAPP(hAPP(c_COMBC(_1497683, _1497685, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1497685, tc_fun(_1497685, tc_HOL_Obool), _1497683), c_fequal), _1497689)), _1497691))))], (44735 ^ _774244) ^ [_1649484, _1649486, _1649488, _1649490] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1649484, tc_fun(_1649486, tc_HOL_Obool)), _1649488), _1649490) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649486, tc_HOL_Obool), hAPP(c_Set_Oimage(_1649484, tc_fun(_1649486, tc_HOL_Obool), _1649490), _1649488)))], (48346 ^ _774244) ^ [_1739772, _1739774] : [-(hAPP(hAPP(c_List_Odrop(_1739772), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1739774) = _1739774)], (40799 ^ _774244) ^ [_1547428, _1547430] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1547428)), -(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)), _1547428))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1547430))))) = 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)), _1547428))), 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, _1547430))))))], (66 ^ _774244) ^ [_775159, _775161] : [-(class_Rings_Odivision__ring__inverse__zero(_775159)), _775161 = _775159, class_Rings_Odivision__ring__inverse__zero(_775161)], (28446 ^ _774244) ^ [_1277422, _1277424, _1277426, _1277428, _1277430] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1277422, tc_fun(_1277424, tc_HOL_Obool)), _1277426), _1277428), _1277430)), 28450 ^ _774244 : [(28453 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1277428, 28449 ^ [_1277422, _1277424, _1277426, _1277428, _1277430]), _1277430)))], (28451 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277422), 28449 ^ [_1277422, _1277424, _1277426, _1277428, _1277430]), _1277426)))]]], (32391 ^ _774244) ^ [_1361144, _1361146, _1361148, _1361150, _1361152] : [class_Groups_Oordered__ab__semigroup__add(_1361144), class_Rings_Osemiring__1(_1361144), 32401 ^ _774244 : [(32404 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361144), hAPP(_1361150, 32400 ^ [_1361144, _1361146, _1361148, _1361150, _1361152])), _1361152))], (32402 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1361146), 32400 ^ [_1361144, _1361146, _1361148, _1361150, _1361152]), _1361148)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361144), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361146, _1361144), _1361150), _1361148)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361144), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1361144), hAPP(c_Finite__Set_Ocard(_1361146), _1361148))), _1361152))))], (48606 ^ _774244) ^ [_1745524, _1745526, _1745528] : [-(hAPP(c_List_Oset(_1745524), hAPP(c_List_Orotate(_1745524, _1745526), _1745528)) = hAPP(c_List_Oset(_1745524), _1745528))], (47987 ^ _774244) ^ [_1729611, _1729613, _1729615, _1729617, _1729619, _1729621, _1729623] : [-(c_Map_Omap__upds(_1729611, _1729613, _1729615, hAPP(hAPP(c_List_Olist_OCons(_1729611), _1729617), _1729619), hAPP(hAPP(c_List_Olist_OCons(_1729613), _1729621), _1729623)) = c_Map_Omap__upds(_1729611, _1729613, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1729611, tc_Option_Ooption(_1729613)), _1729615), _1729617), hAPP(c_Option_Ooption_OSome(_1729613), _1729621)), _1729619, _1729623))], (36117 ^ _774244) ^ [_1439812, _1439814] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439812, tc_HOL_Obool)), _1439814), c_Orderings_Otop__class_Otop(tc_fun(_1439812, tc_HOL_Obool))) = _1439814)], (49866 ^ _774244) ^ [_1772293] : [class_Orderings_Olinorder(_1772293), -(c_List_Olinorder__class_Osorted(_1772293, c_List_Olist_ONil(_1772293)))], (8080 ^ _774244) ^ [_906623, _906625, _906627, _906629, _906631] : [c_Natural_Oevaln(c_Com_Ocom_OAss(_906623, _906625), _906627, _906629, _906631), -(_906631 = c_Natural_Oupdate(_906627, _906623, hAPP(_906625, _906627)))], (13581 ^ _774244) ^ [_1000705, _1000707] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1000705), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1000707)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1000705, _1000707)))], (6672 ^ _774244) ^ [_881673, _881675] : [class_Groups_Olinordered__ab__group__add(_881673), 6675 ^ _774244 : [(6682 ^ _774244) ^ [] : [_881675 = c_Groups_Ozero__class_Ozero(_881673), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881673), _881675), _881675) = c_Groups_Ozero__class_Ozero(_881673))], (6676 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881673), _881675), _881675) = c_Groups_Ozero__class_Ozero(_881673), -(_881675 = c_Groups_Ozero__class_Ozero(_881673))]]], (15216 ^ _774244) ^ [_1030137, _1030139, _1030141] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030137), _1030139)), _1030141) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030137), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030139), _1030141)))], (43835 ^ _774244) ^ [_1627180, _1627182, _1627184, _1627186, _1627188] : [-(_1627180 = c_Orderings_Obot__class_Obot(tc_fun(_1627182, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1627182, tc_fun(_1627184, tc_HOL_Obool)), _1627180), hAPP(hAPP(c_COMBC(_1627182, tc_fun(_1627184, tc_HOL_Obool), tc_fun(_1627184, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1627184, tc_HOL_Obool), tc_fun(tc_fun(_1627184, tc_HOL_Obool), tc_fun(_1627184, tc_HOL_Obool)), _1627182), c_Groups_Ominus__class_Ominus(tc_fun(_1627184, tc_HOL_Obool))), _1627186)), _1627188)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1627184, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1627182, tc_fun(_1627184, tc_HOL_Obool)), _1627180), _1627186)), _1627188))], (36579 ^ _774244) ^ [_1450870, _1450872, _1450874] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450870, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450870, tc_HOL_Obool)), _1450872), _1450874)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450870, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450870, tc_HOL_Obool)), _1450872)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450870, tc_HOL_Obool)), _1450874)))], (6394 ^ _774244) ^ [_877112, _877114, _877116] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_877112, _877114, _877116)) = 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), _877114)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _877116))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20447 ^ _774244) ^ [_1123971, _1123973] : [c_Nat__Transfer_Ois__nat(_1123971), c_Nat__Transfer_Ois__nat(_1123973), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1123971, _1123973)))], (18105 ^ _774244) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43883 ^ _774244) ^ [_1628529, _1628531, _1628533, _1628535, _1628537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1628531, tc_HOL_Obool)), _1628535), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1628531, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1628529, _1628531, hAPP(c_Relation_Oconverse(_1628531, _1628529), _1628533)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1628529, tc_HOL_Obool)), _1628537))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1628529, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1628531, _1628529, _1628533), _1628535)), _1628537)))], (45934 ^ _774244) ^ [_1677594, _1677596, _1677598, _1677600] : [-(c_List_Oremove1(_1677594, _1677596, c_List_Oremove1(_1677594, _1677598, _1677600)) = c_List_Oremove1(_1677594, _1677598, c_List_Oremove1(_1677594, _1677596, _1677600)))], (36405 ^ _774244) ^ [_1446384, _1446386, _1446388, _1446390] : [class_Lattices_Osemilattice__inf(_1446384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446384), _1446386), _1446388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446384), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1446384), _1446386), _1446390)), _1446388)))], (6566 ^ _774244) ^ [_880047, _880049] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _880047)), _880049) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _880047), _880049)))], (27288 ^ _774244) ^ [_1254993, _1254995, _1254997, _1254999, _1255001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254993, tc_HOL_Obool)), _1254995), _1254997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254999, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1254993, _1254999, _1255001), _1254995)), hAPP(c_Set_Oimage(_1254993, _1254999, _1255001), _1254997))))], (50280 ^ _774244) ^ [_1781164, _1781166, _1781168, _1781170] : [_1781166 = hAPP(hAPP(c_List_Oappend(_1781164), hAPP(c_List_Orev(_1781164), _1781170)), hAPP(hAPP(c_List_Olist_OCons(_1781164), _1781168), c_List_Olist_ONil(_1781164))), -(hAPP(c_List_Orev(_1781164), _1781166) = hAPP(hAPP(c_List_Olist_OCons(_1781164), _1781168), _1781170))], (8443 ^ _774244) ^ [_911827, _911829] : [class_Rings_Olinordered__idom(_911827), 8446 ^ _774244 : [(8453 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _911829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911827), c_Groups_Ozero__class_Ozero(_911827)), hAPP(c_Int_Oring__1__class_Oof__int(_911827), _911829))))], (8447 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911827), c_Groups_Ozero__class_Ozero(_911827)), hAPP(c_Int_Oring__1__class_Oof__int(_911827), _911829))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _911829)))]]], (43964 ^ _774244) ^ [_1630845, _1630847, _1630849, _1630851] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630845, _1630845)), hAPP(hAPP(c_Product__Type_OPair(_1630845, _1630845), _1630849), _1630851)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1630845, _1630845), tc_HOL_Obool)), _1630847), c_Relation_OId(_1630845)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1630845, tc_fun(_1630845, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1630845, tc_fun(tc_prod(_1630845, _1630845), tc_HOL_Obool), tc_fun(_1630845, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1630845, tc_fun(tc_fun(tc_prod(_1630845, _1630845), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1630845, _1630845), tc_HOL_Obool), tc_fun(_1630845, tc_HOL_Obool)), _1630845), c_COMBC(_1630845, tc_fun(tc_prod(_1630845, _1630845), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1630845, tc_prod(_1630845, _1630845)), tc_fun(_1630845, tc_fun(tc_fun(tc_prod(_1630845, _1630845), tc_HOL_Obool), tc_HOL_Obool)), _1630845), hAPP(c_COMBB(tc_prod(_1630845, _1630845), tc_fun(tc_fun(tc_prod(_1630845, _1630845), tc_HOL_Obool), tc_HOL_Obool), _1630845), c_member(tc_prod(_1630845, _1630845)))), c_Product__Type_OPair(_1630845, _1630845)))), _1630847)), c_fequal), _1630849), _1630851)))], (6037 ^ _774244) ^ [_870929] : [hAPP(c_Nat_OSuc, _870929) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (40057 ^ _774244) ^ [_1531240, _1531242, _1531244] : [-(hAPP(c_Finite__Set_Ofold1(_1531240, _1531242), _1531244) = c_HOL_OThe(_1531240, c_Finite__Set_Ofold1Set(_1531240, _1531242, _1531244)))], (50987 ^ _774244) ^ [_1796893, _1796895] : [class_Lattices_Olattice(_1796893), -(class_Lattices_Olattice(tc_fun(_1796895, _1796893)))], (26101 ^ _774244) ^ [_1230219, _1230221] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230219)), _1230221)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230219), _1230221)))], (46936 ^ _774244) ^ [_1704215, _1704217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1704215), _1704217)), -(c_List_Oupto(_1704215, _1704217) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1704215), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1704215), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1704217)))], (51079 ^ _774244) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (44626 ^ _774244) ^ [_1647088, _1647090, _1647092, _1647094] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1647088, tc_HOL_Obool), tc_fun(_1647090, tc_HOL_Obool)), _1647092), hAPP(hAPP(c_COMBC(tc_fun(_1647088, tc_HOL_Obool), tc_fun(_1647088, tc_fun(_1647090, tc_HOL_Obool)), tc_fun(_1647090, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647088, tc_fun(_1647090, tc_HOL_Obool))), _1647094)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647088, tc_fun(_1647090, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1647088, tc_HOL_Obool), _1647092)), _1647094))], (13591 ^ _774244) ^ [_1000895, _1000897, _1000899] : [class_Divides_Osemiring__div(_1000895), -(c_Divides_Odiv__class_Omod(_1000895, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000895), _1000897), _1000899), _1000899) = c_Groups_Ozero__class_Ozero(_1000895))], (36667 ^ _774244) ^ [_1452777, _1452779, _1452781] : [class_Orderings_Oorder(_1452777), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452777, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1452777), _1452779)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1452777, _1452779), _1452781)) = c_Orderings_Obot__class_Obot(tc_fun(_1452777, tc_HOL_Obool)))], (25339 ^ _774244) ^ [_1216182, _1216184, _1216186, _1216188] : [class_Rings_Ocomm__semiring__1(_1216182), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216182), _1216184), _1216186)), _1216188)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1216182), _1216184), _1216188)))], (45773 ^ _774244) ^ [_1673967, _1673969, _1673971, _1673973] : [-(c_Map_Omap__of(_1673967, _1673969, hAPP(hAPP(c_List_Omap(_1673967, tc_prod(_1673967, _1673969)), hAPP(hAPP(c_COMBS(_1673967, _1673969, tc_prod(_1673967, _1673969)), c_Product__Type_OPair(_1673967, _1673969)), _1673971)), _1673973)) = c_Map_Orestrict__map(_1673967, _1673969, hAPP(c_Fun_Ocomp(_1673969, tc_Option_Ooption(_1673969), _1673967, c_Option_Ooption_OSome(_1673969)), _1673971), hAPP(c_List_Oset(_1673967), _1673973)))], (5766 ^ _774244) ^ [_866154, _866156, _866158, _866160, _866162] : [c_Natural_Oevalc(_866154, _866156, _866158), c_Natural_Oevalc(_866160, _866158, _866162), -(c_Natural_Oevalc(c_Com_Ocom_OSemi(_866154, _866160), _866156, _866162))], (44243 ^ _774244) ^ [_1637805, _1637807, _1637809, _1637811] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1637805, _1637805), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1637807), _1637809)), _1637811) = hAPP(hAPP(c_Relation_Orel__comp(_1637805, _1637805, _1637805), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1637805, _1637805), tc_HOL_Obool), _1637807), _1637811)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1637805, _1637805), tc_HOL_Obool), _1637809), _1637811)))], (26930 ^ _774244) ^ [_1247499, _1247501] : [26932 ^ _774244 : [(26935 ^ _774244) ^ [] : [hBOOL(hAPP(_1247501, 26931 ^ [_1247499, _1247501]))], (26933 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26931 ^ [_1247499, _1247501]), _1247499)))]], 26936 ^ _774244 : [(26937 ^ _774244) ^ [_1247650] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1247650), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1247499))), -(hBOOL(hAPP(_1247501, _1247650)))]]], (40761 ^ _774244) ^ [_1546007, _1546009, _1546011, _1546013] : [_1546007 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1546009, _1546011), 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)), _1546013))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1546009), _1546007)))], (16843 ^ _774244) ^ [_1061967] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1061967), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1061967) = _1061967)], (36327 ^ _774244) ^ [_1444843, _1444845, _1444847, _1444849] : [class_Lattices_Osemilattice__inf(_1444843), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444843), _1444845), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444843), _1444847), _1444849)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444843), _1444847), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444843), _1444845), _1444849)))], (22868 ^ _774244) ^ [_1169216, _1169218, _1169220, _1169222, _1169224, _1169226] : [hAPP(hAPP(c_Product__Type_OPair(_1169216, _1169218), _1169220), _1169222) = hAPP(hAPP(c_Product__Type_OPair(_1169216, _1169218), _1169224), _1169226), 22871 ^ _774244 : [(22874 ^ _774244) ^ [] : [-(_1169222 = _1169226)], (22872 ^ _774244) ^ [] : [-(_1169220 = _1169224)]]], (7315 ^ _774244) ^ [_893082, _893084, _893086, _893088] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_893082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893082), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893082), _893084), _893086)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893082), _893088), _893086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893082), _893084), _893088)))], (5150 ^ _774244) ^ [_853905, _853907, _853909, _853911] : [-(c_List_Olast(_853911, _853907) = c_List_Olast(_853909, _853905)), _853911 = _853909, _853907 = _853905], (28362 ^ _774244) ^ [_1275846, _1275848, _1275850] : [class_Orderings_Olinorder(_1275846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275846), _1275848), _1275850)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275846, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1275846, _1275848, _1275850)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1275846), _1275850)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1275846), _1275848))], (51417 ^ _774244) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (28801 ^ _774244) ^ [_1285814, _1285816] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285814, tc_HOL_Obool)), _1285816), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1285814, tc_HOL_Obool)), _1285816)) = c_Orderings_Otop__class_Otop(tc_fun(_1285814, tc_HOL_Obool)))], (32942 ^ _774244) ^ [_1370954, _1370956, _1370958] : [class_Orderings_Olinorder(_1370954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370954), _1370956)), -(_1370956 = c_Orderings_Obot__class_Obot(tc_fun(_1370954, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1370954, hAPP(hAPP(c_Set_Oinsert(_1370954), _1370958), _1370956)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1370954), _1370958), c_Big__Operators_Olinorder__class_OMax(_1370954, _1370956)))], (51173 ^ _774244) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (12704 ^ _774244) ^ [_985351, _985353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _985351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _985353)), -(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), _985353), _985351))))], (20441 ^ _774244) ^ [_1123822, _1123824, _1123826] : [class_Fields_Ofield__inverse__zero(_1123822), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123822), c_Groups_Oone__class_Oone(_1123822)), hAPP(hAPP(c_Power_Opower__class_Opower(_1123822), _1123824), _1123826)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1123822), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123822), c_Groups_Oone__class_Oone(_1123822)), _1123824)), _1123826))], (28992 ^ _774244) ^ [_1290184, _1290186, _1290188] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290184, tc_HOL_Obool)), _1290186), _1290188) = c_Orderings_Obot__class_Obot(tc_fun(_1290184, tc_HOL_Obool))), _1290186 = c_Orderings_Obot__class_Obot(tc_fun(_1290184, tc_HOL_Obool)), _1290188 = c_Orderings_Obot__class_Obot(tc_fun(_1290184, tc_HOL_Obool))], (34564 ^ _774244) ^ [_1404051] : [-(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)), _1404051), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (24645 ^ _774244) ^ [_1203473, _1203475, _1203477, _1203479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203473, tc_HOL_Obool)), _1203475), _1203477)), hBOOL(hAPP(_1203475, _1203479)), -(hBOOL(hAPP(_1203477, _1203479)))], (41776 ^ _774244) ^ [_1577562, _1577564, _1577566] : [hAPP(c_Relation_ODomain(_1577562, _1577564), _1577566) = c_Orderings_Obot__class_Obot(tc_fun(_1577562, tc_HOL_Obool)), -(_1577566 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1577562, _1577564), tc_HOL_Obool)))], (29274 ^ _774244) ^ [_1295260] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1295260), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34731 ^ _774244) ^ [_1408712, _1408714] : [-(c_Relation_OId__on(_1408712, _1408714) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408712, tc_fun(tc_prod(_1408712, _1408712), tc_HOL_Obool)), _1408714), hAPP(hAPP(c_COMBC(_1408712, tc_fun(tc_prod(_1408712, _1408712), tc_HOL_Obool), tc_fun(tc_prod(_1408712, _1408712), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1408712, _1408712), tc_fun(tc_fun(tc_prod(_1408712, _1408712), tc_HOL_Obool), tc_fun(tc_prod(_1408712, _1408712), tc_HOL_Obool)), _1408712), c_Set_Oinsert(tc_prod(_1408712, _1408712))), hAPP(hAPP(c_COMBS(_1408712, _1408712, tc_prod(_1408712, _1408712)), c_Product__Type_OPair(_1408712, _1408712)), c_COMBI(_1408712)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1408712, _1408712), tc_HOL_Obool)))))], (43121 ^ _774244) ^ [_1608146, _1608148, _1608150, _1608152] : [43122 ^ _774244 : [(43125 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608146, _1608146)), _1608148), c_Transitive__Closure_Ortrancl(_1608146, _1608152)))], (43123 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608146, _1608146)), _1608148), c_Transitive__Closure_Ortrancl(_1608146, _1608150)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608146, _1608146)), _1608148), c_Transitive__Closure_Ortrancl(_1608146, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1608146, _1608146), tc_HOL_Obool)), _1608150), _1608152)))))], (28769 ^ _774244) ^ [_1285202, _1285204, _1285206, _1285208, _1285210] : [-(hAPP(c_Set_Oimage(_1285202, _1285204, hAPP(hAPP(c_COMBB(_1285206, _1285204, _1285202), _1285208), _1285210)), c_Orderings_Otop__class_Otop(tc_fun(_1285202, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1285206, _1285204, _1285208), hAPP(c_Set_Oimage(_1285202, _1285206, _1285210), c_Orderings_Otop__class_Otop(tc_fun(_1285202, tc_HOL_Obool)))))], (36205 ^ _774244) ^ [_1442121, _1442123, _1442125, _1442127] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442121, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442121, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442121, tc_HOL_Obool)), _1442123), _1442125)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442121, tc_HOL_Obool)), _1442125), _1442127))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442121, tc_HOL_Obool)), _1442127), _1442123)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442121, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442121, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442121, tc_HOL_Obool)), _1442123), _1442125)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442121, tc_HOL_Obool)), _1442125), _1442127))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442121, tc_HOL_Obool)), _1442127), _1442123)))], (45633 ^ _774244) ^ [_1670871, _1670873, _1670875, _1670877, _1670879, _1670881, _1670883] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1670871), tc_Option_Ooption(_1670873), tc_sum(_1670875, _1670877), hAPP(c_Option_Omap(_1670871, _1670873), _1670879)), c_Sum__Type_Osum_Osum__case(_1670875, tc_Option_Ooption(_1670871), _1670877, _1670881, _1670883)) = c_Sum__Type_Osum_Osum__case(_1670875, tc_Option_Ooption(_1670873), _1670877, hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1670871), tc_Option_Ooption(_1670873), _1670875, hAPP(c_Option_Omap(_1670871, _1670873), _1670879)), _1670881), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1670871), tc_Option_Ooption(_1670873), _1670877, hAPP(c_Option_Omap(_1670871, _1670873), _1670879)), _1670883)))], (30091 ^ _774244) ^ [_1310207, _1310209] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1310207), _1310209))), -(hAPP(c_Finite__Set_Ocard(_1310207), _1310209) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23739 ^ _774244) ^ [_1186143, _1186145, _1186147] : [class_Orderings_Olinorder(_1186143), 23742 ^ _774244 : [(23749 ^ _774244) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186143), _1186145), _1186147) = _1186145, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186143), _1186145), _1186147)))], (23743 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186143), _1186145), _1186147)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186143), _1186145), _1186147) = _1186145)]]], (26522 ^ _774244) ^ [_1238876, _1238878, _1238880, _1238882] : [class_Groups_Oordered__ab__group__add__abs(_1238876), -(hAPP(c_Groups_Oabs__class_Oabs(_1238876), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238878, _1238876), hAPP(hAPP(c_COMBB(_1238876, _1238876, _1238878), c_Groups_Oabs__class_Oabs(_1238876)), _1238880)), _1238882)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238878, _1238876), hAPP(hAPP(c_COMBB(_1238876, _1238876, _1238878), c_Groups_Oabs__class_Oabs(_1238876)), _1238880)), _1238882))], (1704 ^ _774244) ^ [_798268, _798270] : [-(class_Groups_Ominus(_798268)), _798270 = _798268, class_Groups_Ominus(_798270)], (39706 ^ _774244) ^ [_1521751, _1521753, _1521755, _1521757, _1521759, _1521761] : [hBOOL(hAPP(hAPP(c_member(_1521751), _1521753), _1521755)), 39709 ^ _774244 : [(39716 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521757, tc_HOL_Obool)), _1521759), _1521761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521757, _1521751), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1521757, _1521751), _1521759), hAPP(c_COMBK(tc_fun(_1521751, tc_HOL_Obool), _1521757), _1521755))), hAPP(hAPP(c_Product__Type_OSigma(_1521757, _1521751), _1521761), hAPP(c_COMBK(tc_fun(_1521751, tc_HOL_Obool), _1521757), _1521755)))))], (39710 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521757, _1521751), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1521757, _1521751), _1521759), hAPP(c_COMBK(tc_fun(_1521751, tc_HOL_Obool), _1521757), _1521755))), hAPP(hAPP(c_Product__Type_OSigma(_1521757, _1521751), _1521761), hAPP(c_COMBK(tc_fun(_1521751, tc_HOL_Obool), _1521757), _1521755)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521757, tc_HOL_Obool)), _1521759), _1521761)))]]], (46892 ^ _774244) ^ [_1703350, _1703352] : [hAPP(c_List_Oset(_1703350), _1703352) = c_Orderings_Obot__class_Obot(tc_fun(_1703350, tc_HOL_Obool)), -(_1703352 = c_List_Olist_ONil(_1703350))], (27306 ^ _774244) ^ [_1255414, _1255416, _1255418, _1255420, _1255422] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1255414, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1255414, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1255416, _1255414, _1255418), _1255420)), hAPP(c_Set_Oimage(_1255416, _1255414, _1255418), _1255422))), hAPP(c_Set_Oimage(_1255416, _1255414, _1255418), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1255416, tc_HOL_Obool)), _1255420), _1255422)))))], (47295 ^ _774244) ^ [_1713326, _1713328, _1713330, _1713332, _1713334, _1713336] : [-(_1713326 = _1713328), -(hAPP(hAPP(c_List_Olist__update(_1713330, hAPP(hAPP(c_List_Olist__update(_1713330, _1713332), _1713326), _1713334)), _1713328), _1713336) = hAPP(hAPP(c_List_Olist__update(_1713330, hAPP(hAPP(c_List_Olist__update(_1713330, _1713332), _1713328), _1713336)), _1713326), _1713334))], (35340 ^ _774244) ^ [_1422928, _1422930, _1422932, _1422934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1422928), _1422934)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1422932), _1422930))), -(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), _1422928), _1422930)), 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), _1422932), _1422934)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (39658 ^ _774244) ^ [_1520351, _1520353, _1520355, _1520357, _1520359] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1520351, _1520353), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520351, tc_HOL_Obool)), _1520355), _1520357)), hAPP(c_COMBK(tc_fun(_1520353, tc_HOL_Obool), _1520351), _1520359)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1520351, _1520353), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1520351, _1520353), _1520355), hAPP(c_COMBK(tc_fun(_1520353, tc_HOL_Obool), _1520351), _1520359))), hAPP(hAPP(c_Product__Type_OSigma(_1520351, _1520353), _1520357), hAPP(c_COMBK(tc_fun(_1520353, tc_HOL_Obool), _1520351), _1520359))))], (18593 ^ _774244) ^ [_1091566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1091566))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1091566)))], (50172 ^ _774244) ^ [_1778754, _1778756] : [-(c_List_Oconcat(_1778754, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1778754), tc_List_Olist(_1778754)), c_List_Olist_Olist__case(tc_List_Olist(_1778754), _1778754, c_List_Olist_ONil(_1778754), hAPP(hAPP(c_COMBB(tc_List_Olist(_1778754), tc_fun(tc_List_Olist(_1778754), tc_List_Olist(_1778754)), _1778754), c_COMBK(tc_List_Olist(_1778754), tc_List_Olist(_1778754))), hAPP(hAPP(c_COMBC(_1778754, tc_List_Olist(_1778754), tc_List_Olist(_1778754)), c_List_Olist_OCons(_1778754)), c_List_Olist_ONil(_1778754))))), _1778756)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1778754), _1778754), c_List_Ohd(_1778754)), hAPP(c_List_Ofilter(tc_List_Olist(_1778754), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1778754)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1778754), tc_List_Olist(_1778754), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1778754)))), _1778756)))], (49438 ^ _774244) ^ [_1763950, _1763952, _1763954] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763950)), hAPP(c_List_Ofilter(_1763950, _1763952), _1763954)) = 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(_1763950)), _1763954)))), hAPP(hAPP(c_COMBB(_1763950, tc_HOL_Obool, tc_Nat_Onat), _1763952), hAPP(c_List_Onth(_1763950), _1763954))))))], (20737 ^ _774244) ^ [_1129326, _1129328, _1129330, _1129332] : [class_Fields_Olinordered__field(_1129326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129326), c_Groups_Ozero__class_Ozero(_1129326)), _1129328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129326), _1129330), _1129328)), _1129332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129326), _1129330), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129326), _1129332), _1129328))))], (12289 ^ _774244) ^ [_977642, _977644] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977642), _977644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _977642)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _977644)))], (18599 ^ _774244) ^ [_1091649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1091649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1091649))))], (5706 ^ _774244) ^ [_865173, _865175, _865177] : [c_Natural_Oevalc(_865173, _865175, _865177), -(c_Natural_Oevaln(_865173, _865175, 5709 ^ [_865173, _865175, _865177], _865177))], (33702 ^ _774244) ^ [_1385836, _1385838, _1385840] : [class_Orderings_Olinorder(_1385836), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385836), _1385838)), -(hBOOL(hAPP(hAPP(c_member(_1385836), _1385840), _1385838))), -(_1385838 = c_Orderings_Obot__class_Obot(tc_fun(_1385836, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1385836, c_Orderings_Oord__class_Omax(_1385836), hAPP(hAPP(c_Set_Oinsert(_1385836), _1385840), _1385838)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1385836), _1385840), c_Big__Operators_Olattice_OSup__fin(_1385836, c_Orderings_Oord__class_Omax(_1385836), _1385838)))], (24597 ^ _774244) ^ [_1202653, _1202655, _1202657, _1202659, _1202661] : [-(_1202653 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1202655, _1202657, _1202659, _1202661), _1202653) = c_Lazy__Sequence_Obind(_1202655, _1202657, hAPP(_1202659, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1202653), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1202655, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1202657)), _1202661), _1202653)))], (44976 ^ _774244) ^ [_1655137, _1655139, _1655141, _1655143, _1655145] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1655137, _1655137)), hAPP(hAPP(c_Product__Type_OPair(_1655137, _1655137), _1655139), _1655141)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1655137, _1655137), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1655143)), _1655145))), 44980 ^ _774244 : [(44983 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655137, _1655137)), hAPP(hAPP(c_Product__Type_OPair(_1655137, _1655137), 44979 ^ [_1655137, _1655139, _1655141, _1655143, _1655145]), _1655141)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1655137, _1655137), tc_HOL_Obool), _1655143), _1655145))))], (44981 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655137, _1655137)), hAPP(hAPP(c_Product__Type_OPair(_1655137, _1655137), _1655139), 44979 ^ [_1655137, _1655139, _1655141, _1655143, _1655145])), _1655145)))]]], (40651 ^ _774244) ^ [_1542489, _1542491, _1542493, _1542495] : [-(hAPP(c_Set_Ovimage(_1542489, _1542491, _1542493), hAPP(c_Set_OCollect(_1542491), _1542495)) = hAPP(c_Set_OCollect(_1542489), hAPP(hAPP(c_COMBB(_1542491, tc_HOL_Obool, _1542489), _1542495), _1542493)))], (46467 ^ _774244) ^ [_1692856, _1692858, _1692860, _1692862] : [-(_1692856 = _1692858), -(c_List_Oremove1(_1692860, _1692856, hAPP(hAPP(c_List_Olist_OCons(_1692860), _1692858), _1692862)) = hAPP(hAPP(c_List_Olist_OCons(_1692860), _1692858), c_List_Oremove1(_1692860, _1692856, _1692862)))], (37963 ^ _774244) ^ [_1481991, _1481993, _1481995] : [c_Equiv__Relations_Oequivp(_1481991, _1481993), -(hBOOL(hAPP(hAPP(_1481993, _1481995), _1481995)))], (51145 ^ _774244) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (22506 ^ _774244) ^ [_1162609, _1162611, _1162613, _1162615, _1162617] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1162609, _1162611), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1162613), _1162615))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162617)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1162609, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162611), _1162617)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1162613), _1162617)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162611), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1162613, _1162617))), _1162615)))))], (49756 ^ _774244) ^ [_1770625, _1770627, _1770629] : [class_Orderings_Olinorder(_1770625), c_List_Olinorder__class_Osorted(_1770625, _1770627), -(c_List_Olinorder__class_Osorted(_1770625, hAPP(hAPP(c_List_Odrop(_1770625), _1770629), _1770627)))], (13182 ^ _774244) ^ [_993379, _993381, _993383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993379)), 13185 ^ _774244 : [(13192 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993381), _993383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993379), _993381)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993379), _993383))))], (13186 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993379), _993381)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993379), _993383))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993381), _993383)))]]], (38255 ^ _774244) ^ [_1487526, _1487528, _1487530, _1487532] : [-(_1487526 = c_Orderings_Obot__class_Obot(tc_fun(_1487528, tc_HOL_Obool))), 38258 ^ _774244 : [(38259 ^ _774244) ^ [] : [-(hAPP(c_Set_Oimage(_1487530, _1487528, 38266 ^ [_1487526, _1487528, _1487530, _1487532]), _1487532) = _1487526), 38260 ^ _774244 : [(38261 ^ _774244) ^ [_1487667] : [c_Fun_Oinj__on(_1487528, _1487530, _1487667, _1487526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1487530, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1487528, _1487530, _1487667), _1487526)), _1487532))]]], (38270 ^ _774244) ^ [] : [38271 ^ _774244 : [(38272 ^ _774244) ^ [_1487859] : [hAPP(c_Set_Oimage(_1487530, _1487528, _1487859), _1487532) = _1487526]], 38274 ^ _774244 : [(38277 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1487530, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1487528, _1487530, 38273 ^ [_1487526, _1487528, _1487530, _1487532]), _1487526)), _1487532)))], (38275 ^ _774244) ^ [] : [-(c_Fun_Oinj__on(_1487528, _1487530, 38273 ^ [_1487526, _1487528, _1487530, _1487532], _1487526))]]]]], (48240 ^ _774244) ^ [_1736812, _1736814, _1736816, _1736818, _1736820, _1736822] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1736812, _1736812)), hAPP(hAPP(c_Product__Type_OPair(_1736812, _1736812), _1736814), _1736816)), c_Transitive__Closure_Ortrancl(_1736812, _1736818))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1736812), tc_List_Olist(_1736812))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1736812), tc_List_Olist(_1736812)), _1736820), _1736822)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1736812), c_List_Olistrel1(_1736812, _1736818)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1736812), tc_List_Olist(_1736812))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1736812), tc_List_Olist(_1736812)), hAPP(hAPP(c_List_Olist_OCons(_1736812), _1736814), _1736820)), hAPP(hAPP(c_List_Olist_OCons(_1736812), _1736816), _1736822))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1736812), c_List_Olistrel1(_1736812, _1736818)))))], (30647 ^ _774244) ^ [_1321336, _1321338, _1321340, _1321342, _1321344, _1321346] : [hBOOL(hAPP(hAPP(c_member(_1321336), _1321338), _1321340)), hBOOL(hAPP(hAPP(_1321342, _1321338), _1321344)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1321336, tc_fun(_1321346, tc_HOL_Obool)), _1321340), _1321342), _1321344)))], (31841 ^ _774244) ^ [_1349554, _1349556, _1349558, _1349560, _1349562] : [class_Groups_Oab__group__add(_1349554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349556), _1349558)), 31848 ^ _774244 : [(31855 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1349556), _1349560), _1349558))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349556, _1349554), _1349562), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349556, tc_HOL_Obool)), _1349558), hAPP(hAPP(c_Set_Oinsert(_1349556), _1349560), c_Orderings_Obot__class_Obot(tc_fun(_1349556, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349556, _1349554), _1349562), _1349558))], (31849 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1349556), _1349560), _1349558)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349556, _1349554), _1349562), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349556, tc_HOL_Obool)), _1349558), hAPP(hAPP(c_Set_Oinsert(_1349556), _1349560), c_Orderings_Obot__class_Obot(tc_fun(_1349556, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1349554), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349556, _1349554), _1349562), _1349558)), hAPP(_1349562, _1349560)))]]], (7948 ^ _774244) ^ [_904163, _904165] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _904163)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _904165)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _904163), _904165)))], (43847 ^ _774244) ^ [_1627458, _1627460, _1627462, _1627464, _1627466] : [-(_1627458 = c_Orderings_Obot__class_Obot(tc_fun(_1627460, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1627462, tc_HOL_Obool)), _1627464), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1627460, tc_fun(_1627462, tc_HOL_Obool)), _1627458), _1627466)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1627460, tc_fun(_1627462, tc_HOL_Obool)), _1627458), hAPP(hAPP(c_COMBB(tc_fun(_1627462, tc_HOL_Obool), tc_fun(_1627462, tc_HOL_Obool), _1627460), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1627462, tc_HOL_Obool)), _1627464)), _1627466)))], (4710 ^ _774244) ^ [_847025, _847027, _847029, _847031] : [-(c_Random_Opick(_847031, _847027) = c_Random_Opick(_847029, _847025)), _847031 = _847029, _847027 = _847025], (30963 ^ _774244) ^ [_1329604, _1329606, _1329608] : [-(hBOOL(hAPP(hAPP(c_member(_1329604), _1329606), _1329608))), -(hBOOL(hAPP(hAPP(c_member(_1329604), _1329606), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1329604, tc_HOL_Obool)), _1329608))))], (582 ^ _774244) ^ [_783319, _783321] : [-(c_Nitpick_Ounknown(_783319)), _783321 = _783319, c_Nitpick_Ounknown(_783321)], (45190 ^ _774244) ^ [_1660411, _1660413, _1660415, _1660417, _1660419, _1660421, _1660423, _1660425] : [c_Finite__Set_Ofolding__image__simple__idem(_1660411, _1660413, _1660415, _1660417, _1660419, _1660421), hBOOL(hAPP(c_Finite__Set_Ofinite(_1660413), _1660423)), -(hAPP(_1660421, hAPP(hAPP(c_Set_Oinsert(_1660413), _1660425), _1660423)) = hAPP(hAPP(_1660415, hAPP(_1660419, _1660425)), hAPP(_1660421, _1660423)))], (15168 ^ _774244) ^ [_1029347] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029347), _1029347) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18973 ^ _774244) ^ [_1097960] : [_1097960 = c_Int_OPls, -(c_Int_OBit0(_1097960) = c_Int_OPls)], (48364 ^ _774244) ^ [_1740139, _1740141, _1740143] : [hAPP(hAPP(c_List_Odrop(_1740139), _1740141), _1740143) = c_List_Olist_ONil(_1740139), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740139)), _1740143)), _1740141)))], (19955 ^ _774244) ^ [_1115757, _1115759, _1115761] : [class_Fields_Olinordered__field__inverse__zero(_1115757), 19958 ^ _774244 : [(19973 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115757), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115757), _1115759), _1115761)), c_Groups_Ozero__class_Ozero(_1115757)))), 19974 ^ _774244 : [(19981 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115757), _1115759), c_Groups_Ozero__class_Ozero(_1115757))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115757), c_Groups_Ozero__class_Ozero(_1115757)), _1115761))], (19975 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115757), c_Groups_Ozero__class_Ozero(_1115757)), _1115759)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115757), _1115761), c_Groups_Ozero__class_Ozero(_1115757)))]]], (19959 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115757), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115757), _1115759), _1115761)), c_Groups_Ozero__class_Ozero(_1115757))), 19964 ^ _774244 : [(19967 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115757), _1115761), c_Groups_Ozero__class_Ozero(_1115757))))], (19965 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115757), c_Groups_Ozero__class_Ozero(_1115757)), _1115759)))]], 19968 ^ _774244 : [(19971 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115757), c_Groups_Ozero__class_Ozero(_1115757)), _1115761)))], (19969 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115757), _1115759), c_Groups_Ozero__class_Ozero(_1115757))))]]]]], (38604 ^ _774244) ^ [_1494914, _1494916, _1494918, _1494920] : [c_Fun_Oinj__on(_1494914, tc_fun(tc_fun(_1494914, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1494914, tc_fun(tc_prod(_1494914, _1494914), tc_HOL_Obool), tc_fun(tc_fun(_1494914, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494914, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1494914, _1494914), tc_HOL_Obool), tc_fun(tc_fun(_1494914, tc_HOL_Obool), tc_HOL_Obool)), _1494914), c_Equiv__Relations_Oquotient(_1494914)), hAPP(hAPP(c_COMBC(_1494914, tc_fun(_1494914, tc_HOL_Obool), tc_fun(_1494914, tc_HOL_Obool)), c_Set_Oinsert(_1494914)), c_Orderings_Obot__class_Obot(tc_fun(_1494914, tc_HOL_Obool))))), _1494916), _1494918), hBOOL(hAPP(hAPP(c_member(_1494914), _1494920), _1494918)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1494914), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494914, tc_HOL_Obool)), _1494918), hAPP(hAPP(c_Set_Oinsert(_1494914), _1494920), c_Orderings_Obot__class_Obot(tc_fun(_1494914, tc_HOL_Obool))))), _1494916) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1494914, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1494914), _1494918), _1494916)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1494914), hAPP(hAPP(c_Set_Oinsert(_1494914), _1494920), c_Orderings_Obot__class_Obot(tc_fun(_1494914, tc_HOL_Obool)))), _1494916)))], (42994 ^ _774244) ^ [_1605021, _1605023, _1605025, _1605027, _1605029, _1605031] : [c_Finite__Set_Ofun__left__comm(_1605021, _1605023, _1605025), hBOOL(hAPP(c_Finite__Set_Ofinite(_1605021), _1605027)), -(hBOOL(hAPP(hAPP(c_member(_1605021), _1605029), _1605027))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1605021, _1605023, _1605025), _1605031), hAPP(hAPP(c_Set_Oinsert(_1605021), _1605029), _1605027)) = hAPP(hAPP(_1605025, _1605029), hAPP(hAPP(c_Finite__Set_Ofold(_1605021, _1605023, _1605025), _1605031), _1605027)))], (28555 ^ _774244) ^ [_1279699, _1279701, _1279703, _1279705, _1279707] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279699, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279701, tc_fun(_1279699, tc_HOL_Obool)), _1279703), _1279705)), _1279707) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279701, tc_fun(_1279699, tc_HOL_Obool)), _1279703), hAPP(hAPP(c_COMBC(_1279701, tc_fun(_1279699, tc_HOL_Obool), tc_fun(_1279699, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1279699, tc_HOL_Obool), tc_fun(tc_fun(_1279699, tc_HOL_Obool), tc_fun(_1279699, tc_HOL_Obool)), _1279701), c_Groups_Ominus__class_Ominus(tc_fun(_1279699, tc_HOL_Obool))), _1279705)), _1279707)))], (40874 ^ _774244) ^ [_1549880] : [-(c_Int_Oint__ge__less__than2(_1549880) = 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), _1549880)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (37494 ^ _774244) ^ [_1472305, _1472307, _1472309, _1472311, _1472313, _1472315] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472305, tc_fun(_1472307, tc_HOL_Obool))), _1472309), _1472311), _1472313), _1472315)), 37497 ^ _774244 : [(37500 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1472311, _1472313), _1472315)))], (37498 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1472309, _1472313), _1472315)))]]], (24737 ^ _774244) ^ [_1206111, _1206113] : [-(c_HOL_OThe(_1206111, hAPP(hAPP(c_COMBC(_1206111, _1206111, tc_HOL_Obool), c_fequal), _1206113)) = _1206113)], (48548 ^ _774244) ^ [_1744705, _1744707, _1744709] : [-(_1744705 = c_List_Olist_ONil(_1744707)), -(hAPP(c_List_Ohd(_1744707), hAPP(hAPP(c_List_Oappend(_1744707), _1744705), _1744709)) = hAPP(c_List_Ohd(_1744707), _1744705))], (2650 ^ _774244) ^ [_814377, _814379, _814381, _814383, _814385, _814387, _814389, _814391] : [-(c_Random_Oiterate(_814391, _814387, _814383, _814379) = c_Random_Oiterate(_814389, _814385, _814381, _814377)), _814391 = _814389, _814387 = _814385, _814383 = _814381, _814379 = _814377], (50661 ^ _774244) ^ [_1790603, _1790605] : [-(hBOOL(hAPP(c_List_Odistinct(_1790603), c_List_Oremdups(_1790603, _1790605))))], (5684 ^ _774244) ^ [_864828, _864830, _864832] : [c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _864828)), _864830, _864832), -(c_Natural_Oevalc(c_Com_Ocom_OBODY(_864828), _864830, _864832))], (51075 ^ _774244) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (29186 ^ _774244) ^ [_1293805, _1293807, _1293809] : [class_Orderings_Oorder(_1293805), 29189 ^ _774244 : [(29196 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293805), _1293807), _1293809))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293805, _1293807), _1293809) = c_Orderings_Obot__class_Obot(tc_fun(_1293805, tc_HOL_Obool)))], (29190 ^ _774244) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293805, _1293807), _1293809) = c_Orderings_Obot__class_Obot(tc_fun(_1293805, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293805), _1293807), _1293809))]]], (22929 ^ _774244) ^ [_1170596, _1170598] : [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), _1170596), _1170598))), 22932 ^ _774244 : [(22939 ^ _774244) ^ [] : [-(_1170598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1170596, _1170598) = c_Nitpick_Onat__gcd(_1170598, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1170596, _1170598)))], (22933 ^ _774244) ^ [] : [_1170598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1170596, _1170598) = _1170596)]]], (49462 ^ _774244) ^ [_1764705, _1764707] : [c_List_Otranspose(_1764705, _1764707) = c_List_Olist_ONil(tc_List_Olist(_1764705)), 49465 ^ _774244 : [(49466 ^ _774244) ^ [_1764800] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1764705)), _1764800), hAPP(c_List_Oset(tc_List_Olist(_1764705)), _1764707))), -(_1764800 = c_List_Olist_ONil(_1764705))]]], (17037 ^ _774244) ^ [_1065574, _1065576] : [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), _1065574), _1065576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1065574))), -(_1065576 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6490 ^ _774244) ^ [_878831, _878833, _878835] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878831), _878833)), _878835) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878831), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878833), _878835)))], (16777 ^ _774244) ^ [_1060826, _1060828] : [class_Groups_Oordered__ab__group__add__abs(_1060826), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060826), hAPP(c_Groups_Ouminus__class_Ouminus(_1060826), hAPP(c_Groups_Oabs__class_Oabs(_1060826), _1060828))), c_Groups_Ozero__class_Ozero(_1060826))))], (24569 ^ _774244) ^ [_1201964, _1201966, _1201968, _1201970, _1201972, _1201974, _1201976] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1201964, _1201966, _1201968, _1201970), _1201972), _1201974), _1201976) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1201966, _1201968, _1201970), _1201974), hAPP(_1201972, _1201976)))], (13306 ^ _774244) ^ [] : [-(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))))], (18981 ^ _774244) ^ [_1098094, _1098096] : [c_Int_OBit1(_1098094) = c_Int_OBit0(_1098096)], (24409 ^ _774244) ^ [_1198746, _1198748, _1198750, _1198752, _1198754, _1198756, _1198758] : [-(hAPP(c_Product__Type_Oapsnd(_1198746, _1198748, _1198750, _1198752), hAPP(c_Product__Type_Oapfst(_1198754, _1198750, _1198746, _1198756), _1198758)) = hAPP(hAPP(c_Product__Type_OPair(_1198750, _1198748), hAPP(_1198756, hAPP(c_Product__Type_Ofst(_1198754, _1198746), _1198758))), hAPP(_1198752, hAPP(c_Product__Type_Osnd(_1198754, _1198746), _1198758))))], (51477 ^ _774244) ^ [_1801914, _1801916] : [hBOOL(hAPP(hAPP(c_fconj, _1801914), _1801916)), -(hBOOL(_1801916))], (5846 ^ _774244) ^ [_867671, _867673, _867675, _867677] : [-(c_Natural_Oevalc(c_Com_Ocom_OSemi(_867671, _867673), _867675, _867677)), 5847 ^ _774244 : [(5848 ^ _774244) ^ [_867721] : [c_Natural_Oevalc(_867671, _867675, _867721), c_Natural_Oevalc(_867673, _867721, _867677)]]], (6171 ^ _774244) ^ [_873177, _873179, _873181, _873183, _873185] : [c_Natural_Oevalc(c_Com_Ocom_OCond(_873177, _873179, _873181), _873183, _873185), 6176 ^ _774244 : [(6179 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_873179, _873183, _873185))], (6177 ^ _774244) ^ [] : [-(hBOOL(hAPP(_873177, _873183)))]], 6180 ^ _774244 : [(6183 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_873181, _873183, _873185))], (6181 ^ _774244) ^ [] : [hBOOL(hAPP(_873177, _873183))]]], (28747 ^ _774244) ^ [_1284797, _1284799, _1284801, _1284803] : [-(hAPP(hAPP(c_Set_Oinsert(_1284797), _1284799), hAPP(hAPP(c_Set_Oinsert(_1284797), _1284801), _1284803)) = hAPP(hAPP(c_Set_Oinsert(_1284797), _1284801), hAPP(hAPP(c_Set_Oinsert(_1284797), _1284799), _1284803)))], (51157 ^ _774244) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (2498 ^ _774244) ^ [_811979, _811981, _811983, _811985] : [-(c_Divides_Odivmod__int(_811985, _811981) = c_Divides_Odivmod__int(_811983, _811979)), _811985 = _811983, _811981 = _811979], (29738 ^ _774244) ^ [_1303938, _1303940] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1303938, _1303940))))], (5810 ^ _774244) ^ [_866894, _866896, _866898, _866900, _866902, _866904, _866906, _866908, _866910] : [-(c_Com_Ocom_Ocom__rec(_866894, _866896, _866898, _866900, _866902, _866904, _866906, _866908, _866910, c_Com_Ocom_OSKIP) = _866896)], (6408 ^ _774244) ^ [_877380, _877382, _877384, _877386] : [class_Groups_Ocancel__ab__semigroup__add(_877380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877380), _877382), _877384) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_877380), _877382), _877386), -(_877384 = _877386)], (29957 ^ _774244) ^ [_1307932, _1307934, _1307936] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307932), _1307934)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307932, tc_HOL_Obool)), _1307936), _1307934)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307932), _1307936)))], (23435 ^ _774244) ^ [_1180219, _1180221, _1180223] : [_1180219 = _1180221, 23438 ^ _774244 : [(23441 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1180223, tc_HOL_Obool)), _1180221), _1180219)))], (23439 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1180223, tc_HOL_Obool)), _1180219), _1180221)))]]], (10323 ^ _774244) ^ [_944258, _944260, _944262] : [class_Orderings_Opreorder(_944258), _944260 = _944262, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944258), _944260), _944262)))], (41230 ^ _774244) ^ [_1563666, _1563668, _1563670, _1563672, _1563674, _1563676] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1563666, _1563668, _1563670), _1563672), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563668, _1563670), tc_HOL_Obool)), _1563674), _1563676)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563666, _1563670), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1563666, _1563668, _1563670), _1563672), _1563674)), hAPP(hAPP(c_Relation_Orel__comp(_1563666, _1563668, _1563670), _1563672), _1563676)))], (11409 ^ _774244) ^ [_962055, _962057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _962055), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _962055), _962057)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _962055))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _962057))))], (26434 ^ _774244) ^ [_1236377, _1236379, _1236381] : [class_Orderings_Olinorder(_1236377), 26437 ^ _774244 : [(26444 ^ _774244) ^ [] : [_1236379 = _1236381, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1236377), _1236379) = hAPP(c_SetInterval_Oord__class_OlessThan(_1236377), _1236381))], (26438 ^ _774244) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1236377), _1236379) = hAPP(c_SetInterval_Oord__class_OlessThan(_1236377), _1236381), -(_1236379 = _1236381)]]], (51205 ^ _774244) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (14698 ^ _774244) ^ [_1020485, _1020487, _1020489] : [class_Divides_Osemiring__div(_1020485), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020485), _1020487), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020485), _1020489), _1020487))), c_Divides_Odiv__class_Omod(_1020485, _1020489, _1020487)) = _1020489)], (7563 ^ _774244) ^ [_897371, _897373, _897375, _897377] : [c_Com_Ocom_OAss(_897371, _897373) = c_Com_Ocom_OSemi(_897375, _897377)], (39754 ^ _774244) ^ [_1522854, _1522856, _1522858, _1522860] : [-(_1522854 = c_Orderings_Obot__class_Obot(tc_fun(_1522856, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1522858, _1522856), _1522858, c_Product__Type_Ofst(_1522858, _1522856)), hAPP(hAPP(c_Product__Type_OSigma(_1522858, _1522856), _1522860), hAPP(c_COMBK(tc_fun(_1522856, tc_HOL_Obool), _1522858), _1522854))) = _1522860)], (9612 ^ _774244) ^ [_932557, _932559] : [class_Rings_Olinordered__ring(_932557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932557), _932559), _932559)), c_Groups_Ozero__class_Ozero(_932557)))], (13650 ^ _774244) ^ [_1001917, _1001919] : [13651 ^ _774244 : [(13652 ^ _774244) ^ [_1001966] : [_1001917 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1001919), _1001966)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1001917, _1001919) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14662 ^ _774244) ^ [_1019846, _1019848, _1019850, _1019852] : [class_Divides_Osemiring__div(_1019846), -(_1019848 = c_Groups_Ozero__class_Ozero(_1019846)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019846), _1019850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019846), _1019848), _1019852))), _1019848) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019846), _1019852), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019846), _1019850), _1019848)))], (19363 ^ _774244) ^ [_1104760, _1104762, _1104764] : [class_Groups_Omonoid__mult(_1104760), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1104760), _1104762), 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)))), _1104764)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1104760), hAPP(hAPP(c_Power_Opower__class_Opower(_1104760), _1104762), _1104764)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (17085 ^ _774244) ^ [_1066375, _1066377] : [_1066375 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1066377), _1066375) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (36751 ^ _774244) ^ [_1454695, _1454697, _1454699, _1454701] : [class_Orderings_Oorder(_1454695), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454695, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1454695, _1454697, _1454699)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1454695, _1454699, _1454701)) = c_Orderings_Obot__class_Obot(tc_fun(_1454695, tc_HOL_Obool)))], (6642 ^ _774244) ^ [_881197, _881199, _881201] : [-(c_Option_Ooption_Ooption__size(_881197, _881199, hAPP(c_Option_Ooption_OSome(_881197), _881201)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_881199, _881201)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48156 ^ _774244) ^ [_1734296, _1734298, _1734300, _1734302] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1734296), tc_List_Olist(_1734296))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1734296), tc_List_Olist(_1734296)), _1734298), _1734300)), c_List_Olistrel1(_1734296, hAPP(c_Relation_Oconverse(_1734296, _1734296), _1734302)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1734296), tc_List_Olist(_1734296))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1734296), tc_List_Olist(_1734296)), _1734298), _1734300)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1734296), tc_List_Olist(_1734296)), c_List_Olistrel1(_1734296, _1734302)))))], (36763 ^ _774244) ^ [_1454949, _1454951, _1454953] : [class_Orderings_Oorder(_1454949), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454949, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1454949, _1454951, _1454953)), hAPP(c_SetInterval_Oord__class_OatLeast(_1454949), _1454953)) = c_Orderings_Obot__class_Obot(tc_fun(_1454949, tc_HOL_Obool)))], (16765 ^ _774244) ^ [_1060452, _1060454, _1060456, _1060458, _1060460] : [class_Groups_Oordered__ab__group__add__abs(_1060452), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060452), hAPP(c_Groups_Oabs__class_Oabs(_1060452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060452), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060452), _1060454), _1060456)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060452), _1060458), _1060460)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060452), hAPP(c_Groups_Oabs__class_Oabs(_1060452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060452), _1060454), _1060458))), hAPP(c_Groups_Oabs__class_Oabs(_1060452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060452), _1060456), _1060460))))))], (29822 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (28739 ^ _774244) ^ [_1284649, _1284651, _1284653] : [class_Orderings_Otop(_1284649), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1284651, _1284649)), _1284653) = c_Orderings_Otop__class_Otop(_1284649))], (45998 ^ _774244) ^ [_1679329, _1679331, _1679333, _1679335, _1679337, _1679339] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1679329, _1679331)), hAPP(hAPP(c_Product__Type_OPair(_1679329, _1679331), _1679333), _1679335)), hAPP(c_List_Oset(tc_prod(_1679329, _1679331)), hAPP(hAPP(c_List_Ozip(_1679329, _1679331), _1679337), _1679339)))), -(hBOOL(hAPP(hAPP(c_member(_1679329), _1679333), hAPP(c_List_Oset(_1679329), _1679337))))], (46004 ^ _774244) ^ [_1679531, _1679533, _1679535, _1679537] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1679531, _1679531)), hAPP(hAPP(c_Product__Type_OPair(_1679531, _1679531), _1679533), _1679535)), hAPP(c_List_Oset(tc_prod(_1679531, _1679531)), hAPP(hAPP(c_List_Ozip(_1679531, _1679531), _1679537), _1679537)))), 46007 ^ _774244 : [(46010 ^ _774244) ^ [] : [-(_1679533 = _1679535)], (46008 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1679531), _1679533), hAPP(c_List_Oset(_1679531), _1679537))))]]], (36673 ^ _774244) ^ [_1452908, _1452910, _1452912, _1452914] : [class_Orderings_Oorder(_1452908), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452908, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1452908, _1452910, _1452912)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1452908, _1452912, _1452914)) = c_Orderings_Obot__class_Obot(tc_fun(_1452908, tc_HOL_Obool)))], (24363 ^ _774244) ^ [_1197651, _1197653, _1197655, _1197657] : [class_Orderings_Olinorder(_1197651), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197651), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197651), _1197653), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197651), _1197655), _1197657))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197651), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197651), _1197653), _1197655)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197651), _1197653), _1197657)))))], (50687 ^ _774244) ^ [_1791039, _1791041] : [_1791041 = c_List_Olist_ONil(_1791039), -(c_List_Oremdups(_1791039, _1791041) = c_List_Olist_ONil(_1791039))], (44048 ^ _774244) ^ [_1633068, _1633070] : [-(c_Transitive__Closure_Otrancl(_1633068, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1633068, _1633068), tc_HOL_Obool)), _1633070), c_Relation_OId(_1633068))) = c_Transitive__Closure_Ortrancl(_1633068, _1633070))], (22186 ^ _774244) ^ [_1155940, _1155942] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1155940)), hAPP(c_Code__Numeral_Oof__nat, _1155942)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1155940), _1155942)))], (47979 ^ _774244) ^ [_1729417, _1729419, _1729421] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729417)), hAPP(hAPP(c_List_Otake(_1729417), _1729419), _1729421)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729417)), _1729421)), _1729419))], (19719 ^ _774244) ^ [_1111390] : [-(_1111390 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 19722 ^ _774244 : [(19729 ^ _774244) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1111390, 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, _1111390) = 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), _1111390), 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)))], (19723 ^ _774244) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1111390, 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, _1111390) = 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), _1111390), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (12830 ^ _774244) ^ [_987327, _987329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987327), _987329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987327), c_Groups_Oone__class_Oone(tc_Int_Oint))), _987329)))], (51353 ^ _774244) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (45497 ^ _774244) ^ [_1667518, _1667520, _1667522, _1667524, _1667526, _1667528, _1667530] : [-(c_Map_Omap__comp(_1667518, _1667520, _1667522, _1667524, _1667526, _1667528) = hAPP(c_Option_Ooption_OSome(_1667520), _1667530)), 45498 ^ _774244 : [(45499 ^ _774244) ^ [_1667596] : [hAPP(_1667526, _1667528) = hAPP(c_Option_Ooption_OSome(_1667518), _1667596), hAPP(_1667524, _1667596) = hAPP(c_Option_Ooption_OSome(_1667520), _1667530)]]], (34733 ^ _774244) ^ [_1408836, _1408838] : [-(c_Relation_OId__on(_1408836, _1408838) = hAPP(c_Product__Type_Oprod_Oprod__case(_1408836, _1408836, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1408836, tc_HOL_Obool, tc_fun(_1408836, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408836, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1408836, tc_HOL_Obool)), _1408836), c_COMBC(_1408836, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408836, tc_HOL_Obool), tc_fun(_1408836, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1408836), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1408836), c_fconj)), c_fequal))), _1408838)))], (17137 ^ _774244) ^ [_1067226, _1067228, _1067230, _1067232] : [class_Groups_Ocomm__monoid__mult(_1067226), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1067226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067226), _1067228), _1067230)), _1067232) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067226), hAPP(hAPP(c_Power_Opower__class_Opower(_1067226), _1067228), _1067232)), hAPP(hAPP(c_Power_Opower__class_Opower(_1067226), _1067230), _1067232)))], (43805 ^ _774244) ^ [_1626311, _1626313, _1626315, _1626317, _1626319] : [_1626311 = c_Orderings_Obot__class_Obot(tc_fun(_1626313, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626313, tc_fun(_1626315, tc_HOL_Obool)), _1626311), hAPP(hAPP(c_COMBC(_1626313, tc_fun(_1626315, tc_HOL_Obool), tc_fun(_1626315, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1626315, tc_HOL_Obool), tc_fun(tc_fun(_1626315, tc_HOL_Obool), tc_fun(_1626315, tc_HOL_Obool)), _1626313), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1626315, tc_HOL_Obool))), _1626317)), _1626319)) = c_Orderings_Otop__class_Otop(tc_fun(_1626315, tc_HOL_Obool)))], (9814 ^ _774244) ^ [_935935, _935937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935935)), 9817 ^ _774244 : [(9824 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _935937), _935935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _935937)), hAPP(c_Int_Onat, _935935))))], (9818 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _935937)), hAPP(c_Int_Onat, _935935))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _935937), _935935)))]]], (42130 ^ _774244) ^ [_1586761, _1586763, _1586765, _1586767, _1586769, _1586771] : [42133 ^ _774244 : [(42136 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1586767), _1586769), hAPP(hAPP(_1586771, 42131 ^ [_1586761, _1586763, _1586765, _1586767, _1586769, _1586771]), 42132 ^ [_1586761, _1586763, _1586765, _1586767, _1586769, _1586771])))], (42134 ^ _774244) ^ [] : [-(_1586761 = hAPP(hAPP(c_Product__Type_OPair(_1586763, _1586765), 42131 ^ [_1586761, _1586763, _1586765, _1586767, _1586769, _1586771]), 42132 ^ [_1586761, _1586763, _1586765, _1586767, _1586769, _1586771]))]], -(hBOOL(hAPP(hAPP(c_member(_1586767), _1586769), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1586763, _1586765, tc_fun(_1586767, tc_HOL_Obool)), _1586771), _1586761))))], (29542 ^ _774244) ^ [_1300320, _1300322, _1300324] : [class_Orderings_Olinorder(_1300320), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300320), _1300322), _1300324)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1300320, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1300320), _1300322), c_Orderings_Obot__class_Obot(tc_fun(_1300320, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1300320, _1300322, _1300324)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300320, _1300322, _1300324))], (51183 ^ _774244) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (45299 ^ _774244) ^ [_1662793, _1662795, _1662797, _1662799, _1662801] : [-(hBOOL(hAPP(hAPP(c_member(_1662793), _1662795), c_Map_Odom(_1662793, _1662797, _1662799)))), -(hAPP(c_Map_Omap__add(_1662793, _1662797, _1662801, _1662799), _1662795) = hAPP(_1662801, _1662795))], (24473 ^ _774244) ^ [_1200025, _1200027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1200025)), hAPP(c_Code__Numeral_Onat__of, _1200027))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1200025), _1200027)))], (6339 ^ _774244) ^ [_876254, _876256, _876258, _876260, _876262, _876264, _876266, _876268, _876270, _876272, _876274, _876276] : [-(c_Com_Ocom_Ocom__case(_876254, _876256, _876258, _876260, _876262, _876264, _876266, _876268, _876270, c_Com_Ocom_OCall(_876272, _876274, _876276)) = hAPP(hAPP(hAPP(_876270, _876272), _876274), _876276))], (48670 ^ _774244) ^ [_1746844, _1746846, _1746848] : [-(hAPP(c_List_Otl(_1746844), hAPP(hAPP(c_List_Otake(_1746844), _1746846), _1746848)) = hAPP(hAPP(c_List_Otake(_1746844), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1746846), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1746844), _1746848)))], (17583 ^ _774244) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20879 ^ _774244) ^ [_1131951, _1131953, _1131955, _1131957, _1131959] : [class_Fields_Ofield(_1131951), -(_1131953 = c_Groups_Ozero__class_Ozero(_1131951)), -(_1131955 = c_Groups_Ozero__class_Ozero(_1131951)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131951), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131951), _1131957), _1131953)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131951), _1131959), _1131955)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131951), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131951), _1131957), _1131955)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131951), _1131959), _1131953))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131951), _1131953), _1131955)))], (1674 ^ _774244) ^ [_797893, _797895] : [-(class_Orderings_Oorder(_797893)), _797895 = _797893, class_Orderings_Oorder(_797895)], (35358 ^ _774244) ^ [_1423540] : [-(c_Nitpick_Odenom(_1423540) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1423540, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1423540)))], (51103 ^ _774244) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (41276 ^ _774244) ^ [_1565379, _1565381, _1565383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565379, _1565379), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1565379, _1565379, _1565379), _1565381), _1565383)), _1565381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1565379, tc_HOL_Obool), tc_fun(_1565379, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1565379, tc_HOL_Obool), tc_fun(_1565379, tc_HOL_Obool), tc_fun(_1565379, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1565379, _1565381)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1565379, tc_HOL_Obool), tc_fun(_1565379, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1565379, _1565383)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1565379, tc_HOL_Obool), tc_fun(_1565379, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1565379, tc_HOL_Obool), tc_fun(_1565379, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1565379, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1565379, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1565379, tc_HOL_Obool), tc_fun(_1565379, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1565379, _1565381))))], (48420 ^ _774244) ^ [_1741483, _1741485, _1741487, _1741489] : [-(_1741483 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1741485), _1741483), hAPP(hAPP(c_List_Olist_OCons(_1741485), _1741487), _1741489)) = hAPP(hAPP(c_List_Odrop(_1741485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1741483), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1741489))], (11871 ^ _774244) ^ [_970489, _970491] : [class_Groups_Olinordered__ab__group__add(_970489), 11874 ^ _774244 : [(11881 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970489), c_Groups_Ozero__class_Ozero(_970489)), _970491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970489), hAPP(c_Groups_Ouminus__class_Ouminus(_970489), _970491)), _970491)))], (11875 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970489), hAPP(c_Groups_Ouminus__class_Ouminus(_970489), _970491)), _970491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970489), c_Groups_Ozero__class_Ozero(_970489)), _970491)))]]], (47790 ^ _774244) ^ [_1724404, _1724406, _1724408, _1724410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724404), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724406)), _1724408))), -(hAPP(hAPP(c_List_Onth(_1724406), hAPP(hAPP(c_List_Oappend(_1724406), _1724408), _1724410)), _1724404) = hAPP(hAPP(c_List_Onth(_1724406), _1724408), _1724404))], (15884 ^ _774244) ^ [_1043936, _1043938, _1043940, _1043942, _1043944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043936), _1043938)), -(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), _1043938), _1043940)), _1043942)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043936), _1043940)), _1043944)) = 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), _1043938), _1043936)), _1043940)), _1043942)), _1043944))], (50731 ^ _774244) ^ [_1791773, _1791775] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791773)), c_List_Oremdups(_1791773, _1791775)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791773)), _1791775), -(c_List_Oremdups(_1791773, _1791775) = _1791775)], (17595 ^ _774244) ^ [_1075547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1075547)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1075547))], (17585 ^ _774244) ^ [_1075455] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1075455)))], (10071 ^ _774244) ^ [_940206, _940208] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940206), _940208) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _940206 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _940208 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5744 ^ _774244) ^ [_865792, _865794, _865796, _865798] : [-(c_Nat_Onat_Onat__case(_865792, _865794, _865796, hAPP(c_Nat_OSuc, _865798)) = hAPP(_865796, _865798))], (38852 ^ _774244) ^ [_1500709, _1500711, _1500713, _1500715, _1500717] : [hBOOL(hAPP(hAPP(c_member(_1500713), hAPP(_1500715, _1500711)), _1500717)), -(hBOOL(hAPP(hAPP(c_member(_1500709), _1500711), hAPP(c_Set_Ovimage(_1500709, _1500713, _1500715), _1500717))))], (15200 ^ _774244) ^ [_1029889, _1029891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029889), _1029891)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029889, _1029891) = _1029889)], (32043 ^ _774244) ^ [_1354088, _1354090, _1354092, _1354094, _1354096, _1354098, _1354100] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1354088, tc_fun(_1354090, tc_fun(_1354092, tc_HOL_Obool))), _1354094), _1354096), _1354098), _1354100))), 32044 ^ _774244 : [(32045 ^ _774244) ^ [_1354173] : [hBOOL(hAPP(hAPP(c_member(_1354088), _1354173), _1354094)), hBOOL(hAPP(hAPP(hAPP(_1354096, _1354173), _1354098), _1354100))]]], (37993 ^ _774244) ^ [_1482487, _1482489, _1482491, _1482493] : [c_Fun_Oinj__on(_1482487, _1482489, _1482491, _1482493), 37996 ^ _774244 : [(37997 ^ _774244) ^ [_1482595] : [hBOOL(hAPP(hAPP(c_member(_1482487), _1482595), _1482493)), 38000 ^ _774244 : [(38001 ^ _774244) ^ [_1482697] : [hBOOL(hAPP(hAPP(c_member(_1482487), _1482697), _1482493)), hAPP(_1482491, _1482595) = hAPP(_1482491, _1482697), -(_1482595 = _1482697)]]]]], (35645 ^ _774244) ^ [_1430265, _1430267, _1430269, _1430271] : [c_Equiv__Relations_Oequiv(_1430265, _1430267, _1430269), hBOOL(hAPP(hAPP(c_member(_1430265), _1430271), _1430267)), -(hBOOL(hAPP(hAPP(c_member(_1430265), _1430271), hAPP(c_Relation_OImage(_1430265, _1430265, _1430269), hAPP(hAPP(c_Set_Oinsert(_1430265), _1430271), c_Orderings_Obot__class_Obot(tc_fun(_1430265, tc_HOL_Obool)))))))], (24429 ^ _774244) ^ [_1199077, _1199079] : [hAPP(c_Code__Numeral_Onat__of, _1199077) = hAPP(c_Code__Numeral_Onat__of, _1199079), -(_1199077 = _1199079)], (45325 ^ _774244) ^ [_1663227, _1663229, _1663231, _1663233, _1663235] : [-(hAPP(c_Map_Omap__add(_1663227, _1663229, _1663231, _1663233), _1663235) = c_Option_Ooption_ONone(_1663229)), hAPP(_1663233, _1663235) = c_Option_Ooption_ONone(_1663229), hAPP(_1663231, _1663235) = c_Option_Ooption_ONone(_1663229)], (46026 ^ _774244) ^ [_1680240, _1680242, _1680244, _1680246, _1680248, _1680250] : [-(hAPP(hAPP(c_List_Ozip(_1680240, _1680242), _1680244), hAPP(hAPP(c_List_Omap(_1680246, _1680242), _1680248), _1680250)) = hAPP(hAPP(c_List_Omap(tc_prod(_1680240, _1680246), tc_prod(_1680240, _1680242)), hAPP(c_Product__Type_Oprod_Oprod__case(_1680240, _1680246, tc_prod(_1680240, _1680242)), hAPP(hAPP(c_COMBC(_1680240, tc_fun(_1680246, _1680242), tc_fun(_1680246, tc_prod(_1680240, _1680242))), hAPP(hAPP(c_COMBB(tc_fun(_1680242, tc_prod(_1680240, _1680242)), tc_fun(tc_fun(_1680246, _1680242), tc_fun(_1680246, tc_prod(_1680240, _1680242))), _1680240), c_COMBB(_1680242, tc_prod(_1680240, _1680242), _1680246)), c_Product__Type_OPair(_1680240, _1680242))), _1680248))), hAPP(hAPP(c_List_Ozip(_1680240, _1680246), _1680244), _1680250)))], (40587 ^ _774244) ^ [_1541301, _1541303, _1541305] : [-(hAPP(c_Set_OCollect(_1541301), hAPP(hAPP(c_COMBS(_1541301, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541301), c_fconj), _1541303)), _1541305)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1541301, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1541301), _1541303)), hAPP(c_Set_OCollect(_1541301), _1541305)))], (41628 ^ _774244) ^ [_1573969, _1573971] : [-(hAPP(c_Relation_ORange(_1573969, _1573969), c_Relation_OId__on(_1573969, _1573971)) = _1573971)], (16267 ^ _774244) ^ [_1050883, _1050885] : [class_Rings_Olinordered__idom(_1050883), -(hAPP(c_Groups_Oabs__class_Oabs(_1050883), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1050883), _1050885)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1050883), _1050885))], (7495 ^ _774244) ^ [_895911, _895913, _895915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _895911), _895913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _895911), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _895913), _895915))))], (28557 ^ _774244) ^ [_1279808, _1279810, _1279812, _1279814, _1279816, _1279818] : [class_Complete__Lattice_Ocomplete__lattice(_1279808), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279810, tc_fun(_1279812, _1279808)), _1279814), _1279816), _1279818) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279810, _1279808), _1279814), hAPP(hAPP(c_COMBC(_1279810, _1279812, _1279808), _1279816), _1279818)))], (39626 ^ _774244) ^ [_1519268, _1519270, _1519272, _1519274, _1519276, _1519278] : [class_Groups_Ocomm__monoid__mult(_1519268), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1519270, _1519268), hAPP(hAPP(c_COMBC(_1519270, tc_fun(_1519272, tc_HOL_Obool), _1519268), hAPP(hAPP(c_COMBB(tc_fun(_1519272, _1519268), tc_fun(tc_fun(_1519272, tc_HOL_Obool), _1519268), _1519270), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1519272, _1519268)), _1519274)), _1519276)), _1519278) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1519270, _1519272), _1519268), hAPP(c_Product__Type_Oprod_Oprod__case(_1519270, _1519272, _1519268), _1519274)), hAPP(hAPP(c_Product__Type_OSigma(_1519270, _1519272), _1519278), hAPP(c_COMBK(tc_fun(_1519272, tc_HOL_Obool), _1519270), _1519276))))], (29925 ^ _774244) ^ [_1307372, _1307374, _1307376] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307372), _1307374)), 29928 ^ _774244 : [(29935 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307372), _1307376)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307372), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307372, tc_HOL_Obool)), _1307376), _1307374))))], (29929 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307372), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307372, tc_HOL_Obool)), _1307376), _1307374))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307372), _1307376)))]]], (16185 ^ _774244) ^ [_1049347, _1049349] : [-(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), _1049347)), _1049349))))], (46192 ^ _774244) ^ [_1684062, _1684064, _1684066, _1684068, _1684070] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684062)), _1684064) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684066)), _1684068), 46195 ^ _774244 : [(46204 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1684062, _1684066), _1684064), _1684068) = _1684070), hAPP(hAPP(c_List_Omap(tc_prod(_1684062, _1684066), _1684062), c_Product__Type_Ofst(_1684062, _1684066)), _1684070) = _1684064, hAPP(hAPP(c_List_Omap(tc_prod(_1684062, _1684066), _1684066), c_Product__Type_Osnd(_1684062, _1684066)), _1684070) = _1684068], (46196 ^ _774244) ^ [] : [hAPP(hAPP(c_List_Ozip(_1684062, _1684066), _1684064), _1684068) = _1684070, 46199 ^ _774244 : [(46202 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1684062, _1684066), _1684066), c_Product__Type_Osnd(_1684062, _1684066)), _1684070) = _1684068)], (46200 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1684062, _1684066), _1684062), c_Product__Type_Ofst(_1684062, _1684066)), _1684070) = _1684064)]]]]], (34851 ^ _774244) ^ [_1411361, _1411363, _1411365, _1411367, _1411369] : [class_Groups_Ocomm__monoid__mult(_1411361), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411363), _1411365)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1411363, tc_HOL_Obool)), _1411367), _1411365)), 34865 ^ _774244 : [(34868 ^ _774244) ^ [] : [hAPP(_1411369, 34864 ^ [_1411361, _1411363, _1411365, _1411367, _1411369]) = c_Groups_Oone__class_Oone(_1411361)], (34866 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411363), 34864 ^ [_1411361, _1411363, _1411365, _1411367, _1411369]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1411363, tc_HOL_Obool)), _1411365), _1411367))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411363, _1411361), _1411369), _1411365) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411363, _1411361), _1411369), _1411367))], (36757 ^ _774244) ^ [_1454822, _1454824, _1454826] : [class_Orderings_Oorder(_1454822), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454822, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1454822), _1454824)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1454822, _1454824, _1454826)) = c_Orderings_Obot__class_Obot(tc_fun(_1454822, tc_HOL_Obool)))], (21952 ^ _774244) ^ [_1151483, _1151485] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1151483), _1151485) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1151483), _1151485))], (32818 ^ _774244) ^ [_1368907, _1368909, _1368911] : [class_Lattices_Olattice(_1368907), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368907), _1368909)), hBOOL(hAPP(hAPP(c_member(_1368907), _1368911), _1368909)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1368907), _1368911), c_Big__Operators_Olattice__class_OSup__fin(_1368907, _1368909)) = c_Big__Operators_Olattice__class_OSup__fin(_1368907, _1368909))], (7964 ^ _774244) ^ [_904457, _904459] : [class_Rings_Olinordered__semidom(_904457), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904457), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904457), _904459)), c_Groups_Ozero__class_Ozero(_904457)))], (51199 ^ _774244) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (33780 ^ _774244) ^ [_1387511, _1387513] : [class_Orderings_Olinorder(_1387511), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387511), _1387513)), -(_1387513 = c_Orderings_Obot__class_Obot(tc_fun(_1387511, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1387511), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1387511), 33793 ^ [_1387511, _1387513]), 33794 ^ [_1387511, _1387513])), hAPP(hAPP(c_Set_Oinsert(_1387511), 33793 ^ [_1387511, _1387513]), hAPP(hAPP(c_Set_Oinsert(_1387511), 33794 ^ [_1387511, _1387513]), c_Orderings_Obot__class_Obot(tc_fun(_1387511, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1387511), c_Big__Operators_Olattice_OInf__fin(_1387511, c_Orderings_Oord__class_Omin(_1387511), _1387513)), _1387513)))], (50310 ^ _774244) ^ [_1781867, _1781869, _1781871] : [-(c_List_Oconcat(_1781867, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1781867)), _1781869), _1781871)) = hAPP(hAPP(c_List_Oappend(_1781867), c_List_Oconcat(_1781867, _1781869)), c_List_Oconcat(_1781867, _1781871)))], (10860 ^ _774244) ^ [_952722, _952724, _952726, _952728] : [class_Groups_Oordered__ab__semigroup__add(_952722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952722), _952724), _952726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952722), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952722), _952728), _952724)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952722), _952728), _952726))))], (48795 ^ _774244) ^ [_1749450, _1749452, _1749454] : [class_Lattices_Olattice(_1749450), -(c_Big__Operators_Olattice__class_OInf__fin(_1749450, hAPP(c_List_Oset(_1749450), hAPP(hAPP(c_List_Olist_OCons(_1749450), _1749452), _1749454))) = hAPP(c_List_Ofoldl(_1749450, _1749450, c_Lattices_Osemilattice__inf__class_Oinf(_1749450), _1749452), _1749454))], (39176 ^ _774244) ^ [_1508108, _1508110, _1508112, _1508114, _1508116, _1508118, _1508120, _1508122] : [class_Groups_Ocomm__monoid__mult(_1508108), c_Fun_Oinj__on(_1508110, _1508112, _1508114, _1508116), _1508118 = hAPP(c_Set_Oimage(_1508110, _1508112, _1508114), _1508116), 39190 ^ _774244 : [(39193 ^ _774244) ^ [] : [hAPP(_1508120, 39189 ^ [_1508108, _1508110, _1508112, _1508114, _1508116, _1508118, _1508120, _1508122]) = hAPP(hAPP(c_Fun_Ocomp(_1508112, _1508108, _1508110, _1508122), _1508114), 39189 ^ [_1508108, _1508110, _1508112, _1508114, _1508116, _1508118, _1508120, _1508122])], (39191 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508110), 39189 ^ [_1508108, _1508110, _1508112, _1508114, _1508116, _1508118, _1508120, _1508122]), _1508116)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1508112, _1508108), _1508122), _1508118) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1508110, _1508108), _1508120), _1508116))], (39790 ^ _774244) ^ [_1523916, _1523918, _1523920, _1523922] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1523916, _1523918), _1523920), _1523922) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523916, tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool)), _1523920), hAPP(hAPP(c_COMBS(_1523916, tc_fun(_1523918, tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool)), tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523918, tc_HOL_Obool), tc_fun(tc_fun(_1523918, tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool)), tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool)), _1523916), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523918, tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool))), _1523922)), hAPP(hAPP(c_COMBC(_1523916, tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool), tc_fun(_1523918, tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523918, tc_fun(tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool), tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool), tc_fun(_1523918, tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool))), _1523916), c_COMBC(_1523918, tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool), tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523918, tc_prod(_1523916, _1523918)), tc_fun(_1523918, tc_fun(tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool), tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool))), _1523916), hAPP(c_COMBB(tc_prod(_1523916, _1523918), tc_fun(tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool), tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool)), _1523918), c_Set_Oinsert(tc_prod(_1523916, _1523918)))), c_Product__Type_OPair(_1523916, _1523918)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523916, _1523918), tc_HOL_Obool))))))], (33936 ^ _774244) ^ [_1390858, _1390860, _1390862, _1390864, _1390866] : [hBOOL(hAPP(hAPP(c_member(_1390858), _1390860), _1390862)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1390858, tc_Option_Ooption(_1390864)), c_Map_Orestrict__map(_1390858, _1390864, _1390866, _1390862)), _1390860), c_Option_Ooption_ONone(_1390864)) = c_Map_Orestrict__map(_1390858, _1390864, _1390866, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1390858, tc_HOL_Obool)), _1390862), hAPP(hAPP(c_Set_Oinsert(_1390858), _1390860), c_Orderings_Obot__class_Obot(tc_fun(_1390858, tc_HOL_Obool))))))], (38081 ^ _774244) ^ [_1484266, _1484268, _1484270, _1484272, _1484274, _1484276] : [c_Fun_Oinj__on(_1484266, _1484268, _1484270, _1484272), c_Fun_Oinj__on(_1484268, _1484274, _1484276, hAPP(c_Set_Oimage(_1484266, _1484268, _1484270), _1484272)), -(c_Fun_Oinj__on(_1484266, _1484274, hAPP(c_Fun_Ocomp(_1484268, _1484274, _1484266, _1484276), _1484270), _1484272))], (17741 ^ _774244) ^ [_1077945, _1077947] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077945)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077945)), _1077947) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077945)), _1077947)))], (912 ^ _774244) ^ [_788306, _788308] : [-(c_List_Onat__list(_788306)), _788308 = _788306, c_List_Onat__list(_788308)], (46906 ^ _774244) ^ [_1703617, _1703619, _1703621] : [c_List_Olist_ONil(_1703617) = hAPP(hAPP(c_List_Olist_OCons(_1703617), _1703619), _1703621)], (11429 ^ _774244) ^ [_962451, _962453, _962455, _962457] : [class_Groups_Oordered__comm__monoid__add(_962451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962451), c_Groups_Ozero__class_Ozero(_962451)), _962453)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962451), _962455), _962457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962451), _962455), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962451), _962457), _962453))))], (18079 ^ _774244) ^ [_1083269, _1083271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083269), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083269)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083271)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15590 ^ _774244) ^ [_1037424, _1037426, _1037428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037424), _1037426)), 15593 ^ _774244 : [(15600 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037428), _1037424)), _1037426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037426), _1037424))))], (15594 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037426), _1037424))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037428), _1037424)), _1037426)))]]], (14267 ^ _774244) ^ [_1013255, _1013257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013255)), 14270 ^ _774244 : [(14277 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013257), 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), _1013257), _1013255)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14271 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1013257), _1013255)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013257), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (20703 ^ _774244) ^ [_1128676, _1128678, _1128680, _1128682] : [class_Fields_Olinordered__field(_1128676), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128676), c_Groups_Ozero__class_Ozero(_1128676)), _1128678)), 20710 ^ _774244 : [(20717 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128676), _1128680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128676), _1128682), _1128678))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128676), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128676), _1128680), _1128678)), _1128682)))], (20711 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128676), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128676), _1128680), _1128678)), _1128682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128676), _1128680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128676), _1128682), _1128678))))]]], (45305 ^ _774244) ^ [_1662853, _1662855, _1662857, _1662859, _1662861] : [-(hBOOL(hAPP(hAPP(c_member(_1662853), _1662855), c_Map_Odom(_1662853, _1662857, _1662859)))), -(hAPP(c_Map_Omap__add(_1662853, _1662857, _1662859, _1662861), _1662855) = hAPP(_1662861, _1662855))], (28465 ^ _774244) ^ [_1277834] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1277834)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1277834))], (42049 ^ _774244) ^ [_1584833, _1584835, _1584837, _1584839] : [42051 ^ _774244 : [(42054 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1584833, _1584833, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1584833, tc_fun(_1584833, _1584835), tc_fun(_1584833, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584835, tc_HOL_Obool), tc_fun(tc_fun(_1584833, _1584835), tc_fun(_1584833, tc_HOL_Obool)), _1584833), c_COMBB(_1584835, tc_HOL_Obool, _1584833)), hAPP(hAPP(c_COMBB(_1584835, tc_fun(_1584835, tc_HOL_Obool), _1584833), c_fequal), _1584839))), _1584839)), 42050 ^ [_1584833, _1584835, _1584837, _1584839]))], (42052 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584833, _1584833)), 42050 ^ [_1584833, _1584835, _1584837, _1584839]), _1584837)))]], -(c_Equiv__Relations_Ocongruent(_1584833, _1584835, _1584837, _1584839))], (51189 ^ _774244) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (14568 ^ _774244) ^ [_1018202, _1018204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018202)), 14571 ^ _774244 : [(14578 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018204)), -(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), _1018204), _1018202))))], (14572 ^ _774244) ^ [] : [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), _1018204), _1018202))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018204)))]]], (3954 ^ _774244) ^ [_835175, _835177, _835179, _835181, _835183, _835185] : [-(c_Relation_Orel__comp(_835185, _835181, _835177) = c_Relation_Orel__comp(_835183, _835179, _835175)), _835185 = _835183, _835181 = _835179, _835177 = _835175], (15578 ^ _774244) ^ [_1037176, _1037178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037176), _1037178)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037176), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037178), _1037176)) = _1037178)], (3618 ^ _774244) ^ [_829975, _829977, _829979, _829981, _829983, _829985, _829987, _829989] : [-(c_New__Random__Sequence_Opos__map(_829989, _829985, _829981, _829977) = c_New__Random__Sequence_Opos__map(_829987, _829983, _829979, _829975)), _829989 = _829987, _829985 = _829983, _829981 = _829979, _829977 = _829975], (35014 ^ _774244) ^ [_1415188, _1415190, _1415192] : [hBOOL(hAPP(c_Predicate_OPowp(_1415188, hAPP(hAPP(c_COMBC(_1415188, tc_fun(_1415188, tc_HOL_Obool), tc_HOL_Obool), c_member(_1415188)), _1415190)), _1415192)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1415188, tc_HOL_Obool)), _1415192), hAPP(c_Set_OPow(_1415188), _1415190))))], (8982 ^ _774244) ^ [_921159, _921161, _921163] : [class_Groups_Oordered__ab__group__add(_921159), 8985 ^ _774244 : [(8992 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921159), hAPP(c_Groups_Ouminus__class_Ouminus(_921159), _921163)), _921161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921159), hAPP(c_Groups_Ouminus__class_Ouminus(_921159), _921161)), _921163)))], (8986 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921159), hAPP(c_Groups_Ouminus__class_Ouminus(_921159), _921161)), _921163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921159), hAPP(c_Groups_Ouminus__class_Ouminus(_921159), _921163)), _921161)))]]], (21041 ^ _774244) ^ [_1134601, _1134603, _1134605, _1134607] : [class_Fields_Ofield__inverse__zero(_1134601), class_Int_Onumber(_1134601), 21048 ^ _774244 : [(21049 ^ _774244) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134601), _1134603), hAPP(c_Int_Onumber__class_Onumber__of(_1134601), _1134605)) = _1134607, 21052 ^ _774244 : [(21059 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1134601), _1134605) = c_Groups_Ozero__class_Ozero(_1134601), -(_1134607 = c_Groups_Ozero__class_Ozero(_1134601))], (21053 ^ _774244) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1134601), _1134605) = c_Groups_Ozero__class_Ozero(_1134601)), -(_1134603 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134601), _1134607), hAPP(c_Int_Onumber__class_Onumber__of(_1134601), _1134605)))]]], (21065 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134601), _1134603), hAPP(c_Int_Onumber__class_Onumber__of(_1134601), _1134605)) = _1134607), 21068 ^ _774244 : [(21071 ^ _774244) ^ [] : [_1134603 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134601), _1134607), hAPP(c_Int_Onumber__class_Onumber__of(_1134601), _1134605))], (21069 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1134601), _1134605) = c_Groups_Ozero__class_Ozero(_1134601)]], 21072 ^ _774244 : [(21075 ^ _774244) ^ [] : [_1134607 = c_Groups_Ozero__class_Ozero(_1134601)], (21073 ^ _774244) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1134601), _1134605) = c_Groups_Ozero__class_Ozero(_1134601))]]]]], (42213 ^ _774244) ^ [_1588688, _1588690, _1588692] : [-(hBOOL(hAPP(hAPP(c_member(_1588688), _1588690), c_Wellfounded_Oacc(_1588688, _1588692)))), 42217 ^ _774244 : [(42220 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1588688), 42216 ^ [_1588688, _1588690, _1588692]), c_Wellfounded_Oacc(_1588688, _1588692)))], (42218 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588688, _1588688)), hAPP(hAPP(c_Product__Type_OPair(_1588688, _1588688), 42216 ^ [_1588688, _1588690, _1588692]), _1588690)), _1588692)))]]], (31047 ^ _774244) ^ [_1331043, _1331045, _1331047] : [hAPP(hAPP(c_COMBC(_1331043, tc_fun(_1331043, tc_HOL_Obool), tc_HOL_Obool), c_member(_1331043)), _1331045) = hAPP(hAPP(c_COMBC(_1331043, tc_fun(_1331043, tc_HOL_Obool), tc_HOL_Obool), c_member(_1331043)), _1331047), -(_1331045 = _1331047)], (22134 ^ _774244) ^ [_1154699, _1154701] : [class_Rings_Osemiring__1(_1154699), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1154699), _1154701) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1154699, hAPP(hAPP(c_COMBC(_1154699, _1154699, _1154699), c_Groups_Oplus__class_Oplus(_1154699)), c_Groups_Oone__class_Oone(_1154699)), _1154701, c_Groups_Ozero__class_Ozero(_1154699)))], (14139 ^ _774244) ^ [_1011108, _1011110, _1011112] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1011108), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011110), _1011112)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1011108), _1011110)), _1011112))], (8574 ^ _774244) ^ [_914286, _914288, _914290] : [class_Rings_Oring(_914286), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914286), hAPP(c_Groups_Ouminus__class_Ouminus(_914286), _914288)), _914290) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914286), _914288), hAPP(c_Groups_Ouminus__class_Ouminus(_914286), _914290)))], (14153 ^ _774244) ^ [_1011394, _1011396] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1011394)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1011396)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1011394), _1011396))], (23387 ^ _774244) ^ [_1179304, _1179306, _1179308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179304, tc_HOL_Obool)), _1179306), _1179308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179304, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1179304, tc_HOL_Obool)), _1179308)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1179304, tc_HOL_Obool)), _1179306))))], (14306 ^ _774244) ^ [_1013841] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1013841, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1013841)], (40868 ^ _774244) ^ [_1549665] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1549665) = 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), _1549665), c_Int_Onat)))))], (30276 ^ _774244) ^ [_1313739, _1313741, _1313743] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1313739), _1313741)), 30279 ^ _774244 : [(30299 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1313739, tc_Nat_Onat), _1313743), _1313741) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 30300 ^ _774244 : [(30301 ^ _774244) ^ [_1314220] : [hBOOL(hAPP(hAPP(c_member(_1313739), _1314220), _1313741)), hAPP(_1313743, _1314220) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 30309 ^ _774244 : [(30314 ^ _774244) ^ [] : [hAPP(_1313743, 30308 ^ [_1313739, _1313741, _1313743, _1314220]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30312 ^ _774244) ^ [] : [_1314220 = 30308 ^ [_1313739, _1313741, _1313743, _1314220]], (30310 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1313739), 30308 ^ [_1313739, _1313741, _1313743, _1314220]), _1313741)))]]]]], (30280 ^ _774244) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1313739, tc_Nat_Onat), _1313743), _1313741) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 30284 ^ _774244 : [(30289 ^ _774244) ^ [_1314059] : [hBOOL(hAPP(hAPP(c_member(_1313739), _1314059), _1313741)), -(30283 ^ [_1313739, _1313741, _1313743] = _1314059), -(hAPP(_1313743, _1314059) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30287 ^ _774244) ^ [] : [-(hAPP(_1313743, 30283 ^ [_1313739, _1313741, _1313743]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (30285 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1313739), 30283 ^ [_1313739, _1313741, _1313743]), _1313741)))]]]]], (22020 ^ _774244) ^ [_1152620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1152620)), _1152620 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8960 ^ _774244) ^ [_920785] : [class_Groups_Ogroup__add(_920785), -(hAPP(c_Groups_Ouminus__class_Ouminus(_920785), c_Groups_Ozero__class_Ozero(_920785)) = c_Groups_Ozero__class_Ozero(_920785))], (1124 ^ _774244) ^ [_791018, _791020] : [-(class_Rings_Ocomm__ring(_791018)), _791020 = _791018, class_Rings_Ocomm__ring(_791020)], (5788 ^ _774244) ^ [_866539, _866541] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_866539, _866541)], (41859 ^ _774244) ^ [_1580367, _1580369, _1580371, _1580373] : [hBOOL(hAPP(hAPP(c_member(_1580367), _1580369), hAPP(c_Relation_ODomain(_1580367, _1580371), _1580373))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580367, _1580371)), hAPP(hAPP(c_Product__Type_OPair(_1580367, _1580371), _1580369), 41862 ^ [_1580367, _1580369, _1580371, _1580373])), _1580373)))], (7349 ^ _774244) ^ [_893638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893638), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9919 ^ _774244) ^ [_937745, _937747] : [class_Rings_Olinordered__idom(_937745), 9922 ^ _774244 : [(9929 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937745), _937747), c_Groups_Ozero__class_Ozero(_937745))), -(c_Groups_Osgn__class_Osgn(_937745, _937747) = hAPP(c_Groups_Ouminus__class_Ouminus(_937745), c_Groups_Oone__class_Oone(_937745)))], (9923 ^ _774244) ^ [] : [c_Groups_Osgn__class_Osgn(_937745, _937747) = hAPP(c_Groups_Ouminus__class_Ouminus(_937745), c_Groups_Oone__class_Oone(_937745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937745), _937747), c_Groups_Ozero__class_Ozero(_937745))))]]], (28864 ^ _774244) ^ [_1287337, _1287339, _1287341, _1287343] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1287337, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28865 ^ [_1287337, _1287339, _1287341, _1287343])), _1287339) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1287337, 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), 28865 ^ [_1287337, _1287339, _1287341, _1287343]), _1287341))), _1287343), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1287337, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1287339) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1287337, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1287343))], (37773 ^ _774244) ^ [_1477712, _1477714, _1477716] : [class_Lattices_Olattice(_1477712), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477712), _1477714)), 37780 ^ _774244 : [(37787 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1477712, tc_HOL_Obool)), _1477714), hAPP(hAPP(c_Set_Oinsert(_1477712), _1477716), c_Orderings_Obot__class_Obot(tc_fun(_1477712, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1477712, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1477712, hAPP(hAPP(c_Set_Oinsert(_1477712), _1477716), _1477714)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1477712), _1477716), c_Big__Operators_Olattice__class_OInf__fin(_1477712, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1477712, tc_HOL_Obool)), _1477714), hAPP(hAPP(c_Set_Oinsert(_1477712), _1477716), c_Orderings_Obot__class_Obot(tc_fun(_1477712, tc_HOL_Obool)))))))], (37781 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1477712, tc_HOL_Obool)), _1477714), hAPP(hAPP(c_Set_Oinsert(_1477712), _1477716), c_Orderings_Obot__class_Obot(tc_fun(_1477712, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1477712, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1477712, hAPP(hAPP(c_Set_Oinsert(_1477712), _1477716), _1477714)) = _1477716)]]], (23471 ^ _774244) ^ [_1180859, _1180861, _1180863] : [23472 ^ _774244 : [(23475 ^ _774244) ^ [] : [_1180861 = _1180863], (23473 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1180859, tc_HOL_Obool)), _1180861), _1180863))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1180859, tc_HOL_Obool)), _1180861), _1180863)))], (24825 ^ _774244) ^ [_1207773, _1207775, _1207777] : [class_Rings_Olinordered__idom(_1207773), 24828 ^ _774244 : [(24835 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207773), _1207775), _1207777)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207773), _1207775), hAPP(c_Groups_Oabs__class_Oabs(_1207773), _1207777))))], (24829 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207773), _1207775), hAPP(c_Groups_Oabs__class_Oabs(_1207773), _1207777))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207773), _1207775), _1207777)))]]], (37512 ^ _774244) ^ [_1472681, _1472683, _1472685, _1472687, _1472689, _1472691] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472681, tc_fun(_1472683, tc_HOL_Obool))), _1472685), _1472687), _1472689), _1472691)), -(hBOOL(hAPP(hAPP(_1472687, _1472689), _1472691)))], (43991 ^ _774244) ^ [_1631879, _1631881, _1631883, _1631885, _1631887] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631879, tc_fun(_1631881, tc_HOL_Obool)), _1631883), _1631885), _1631887)), 43994 ^ _774244 : [(43995 ^ _774244) ^ [_1631988] : [hBOOL(hAPP(hAPP(c_member(_1631879), _1631988), _1631883)), -(hBOOL(hAPP(hAPP(_1631885, _1631988), _1631887)))]]], (49167 ^ _774244) ^ [_1757794, _1757796, _1757798, _1757800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1757794), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757796)), _1757798))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1757794), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757796)), _1757800))), 49177 ^ _774244 : [(49180 ^ _774244) ^ [] : [hAPP(hAPP(c_List_Onth(_1757796), _1757798), 49176 ^ [_1757794, _1757796, _1757798, _1757800]) = hAPP(hAPP(c_List_Onth(_1757796), _1757800), 49176 ^ [_1757794, _1757796, _1757798, _1757800])], (49178 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49176 ^ [_1757794, _1757796, _1757798, _1757800]), _1757794)))]], -(hAPP(hAPP(c_List_Otake(_1757796), _1757794), _1757798) = hAPP(hAPP(c_List_Otake(_1757796), _1757794), _1757800))], (38740 ^ _774244) ^ [_1497978, _1497980, _1497982, _1497984, _1497986] : [class_Groups_Ocomm__monoid__mult(_1497978), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497980), _1497982)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497980), _1497984)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1497980, tc_HOL_Obool)), _1497982), _1497984) = c_Orderings_Obot__class_Obot(tc_fun(_1497980, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1497978, _1497980, c_Groups_Otimes__class_Otimes(_1497978)), _1497986), c_Groups_Oone__class_Oone(_1497978)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1497980, tc_HOL_Obool)), _1497982), _1497984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1497978), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1497978, _1497980, c_Groups_Otimes__class_Otimes(_1497978)), _1497986), c_Groups_Oone__class_Oone(_1497978)), _1497982)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1497978, _1497980, c_Groups_Otimes__class_Otimes(_1497978)), _1497986), c_Groups_Oone__class_Oone(_1497978)), _1497984)))], (24547 ^ _774244) ^ [_1201424, _1201426, _1201428, _1201430, _1201432] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1201424, _1201426, _1201428, hAPP(c_COMBK(_1201426, _1201424), _1201430), hAPP(c_COMBK(_1201426, _1201428), _1201430)), _1201432) = _1201430)], (29588 ^ _774244) ^ [] : [-(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))], (35619 ^ _774244) ^ [_1429693, _1429695, _1429697, _1429699, _1429701] : [c_Equiv__Relations_Oequiv(_1429693, _1429695, _1429697), hBOOL(hAPP(hAPP(c_member(_1429693), _1429699), _1429695)), hBOOL(hAPP(hAPP(c_member(_1429693), _1429701), _1429695)), 35630 ^ _774244 : [(35637 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1429693, _1429693)), hAPP(hAPP(c_Product__Type_OPair(_1429693, _1429693), _1429699), _1429701)), _1429697)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1429693), hAPP(hAPP(c_Set_Oinsert(_1429693), _1429699), c_Orderings_Obot__class_Obot(tc_fun(_1429693, tc_HOL_Obool)))), _1429697) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1429693), hAPP(hAPP(c_Set_Oinsert(_1429693), _1429701), c_Orderings_Obot__class_Obot(tc_fun(_1429693, tc_HOL_Obool)))), _1429697))], (35631 ^ _774244) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1429693), hAPP(hAPP(c_Set_Oinsert(_1429693), _1429699), c_Orderings_Obot__class_Obot(tc_fun(_1429693, tc_HOL_Obool)))), _1429697) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1429693), hAPP(hAPP(c_Set_Oinsert(_1429693), _1429701), c_Orderings_Obot__class_Obot(tc_fun(_1429693, tc_HOL_Obool)))), _1429697), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1429693, _1429693)), hAPP(hAPP(c_Product__Type_OPair(_1429693, _1429693), _1429699), _1429701)), _1429697)))]]], (10035 ^ _774244) ^ [_939645] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _939645), _939645))))], (30342 ^ _774244) ^ [_1315012, _1315014, _1315016, _1315018, _1315020] : [class_Groups_Oab__group__add(_1315012), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315014), _1315016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315014, tc_HOL_Obool)), _1315018), _1315016)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1315014, _1315012), _1315020), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1315014, tc_HOL_Obool)), _1315016), _1315018)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1315012), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1315014, _1315012), _1315020), _1315016)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1315014, _1315012), _1315020), _1315018)))], (38449 ^ _774244) ^ [_1491496, _1491498, _1491500, _1491502, _1491504, _1491506] : [class_Groups_Ocomm__monoid__mult(_1491496), c_Fun_Oinj__on(_1491498, _1491500, _1491502, _1491504), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1491500, _1491496), _1491506), hAPP(c_Set_Oimage(_1491498, _1491500, _1491502), _1491504)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1491498, _1491496), hAPP(c_Fun_Ocomp(_1491500, _1491496, _1491498, _1491506), _1491502)), _1491504))], (51261 ^ _774244) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (49198 ^ _774244) ^ [_1758444, _1758446, _1758448] : [hBOOL(hAPP(hAPP(c_member(_1758444), _1758446), hAPP(c_List_Oset(_1758444), c_List_Obutlast(_1758444, _1758448)))), -(hBOOL(hAPP(hAPP(c_member(_1758444), _1758446), hAPP(c_List_Oset(_1758444), _1758448))))], (7197 ^ _774244) ^ [_890936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890936), _890936))], (9762 ^ _774244) ^ [_935018] : [class_Rings_Oring__1(_935018), -(hAPP(c_Int_Oring__1__class_Oof__int(_935018), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_935018))], (24565 ^ _774244) ^ [_1201867, _1201869, _1201871, _1201873] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1201867, _1201869, _1201871, tc_prod(_1201869, _1201871)), _1201873), c_Product__Type_OPair(_1201869, _1201871)) = _1201873)], (38658 ^ _774244) ^ [_1496350, _1496352, _1496354] : [-(c_Fun_Oinj__on(_1496350, tc_sum(_1496352, _1496350), c_Sum__Type_OInr(_1496350, _1496352), _1496354))], (9686 ^ _774244) ^ [_933844, _933846] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _933844)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _933846)), _933844 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _933846 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4186 ^ _774244) ^ [_838991, _838993] : [_838993 = _838991, -(c_Groups_Oabs__class_Oabs(_838993) = c_Groups_Oabs__class_Oabs(_838991))], (51311 ^ _774244) ^ [_1800023] : [class_Finite__Set_Ofinite(_1800023), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1800023)))], (10912 ^ _774244) ^ [_953744, _953746, _953748] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953744), _953746) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953748), _953746), -(_953744 = _953748), -(_953746 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45608 ^ _774244) ^ [_1670163, _1670165, _1670167, _1670169, _1670171] : [hAPP(hAPP(c_List_Omap(_1670163, _1670165), _1670167), _1670169) = hAPP(hAPP(c_List_Omap(_1670163, _1670165), _1670171), _1670169), 45611 ^ _774244 : [(45612 ^ _774244) ^ [_1670286] : [hBOOL(hAPP(hAPP(c_member(_1670163), _1670286), hAPP(c_List_Oset(_1670163), _1670169))), -(hAPP(_1670167, _1670286) = hAPP(_1670171, _1670286))]]], (22302 ^ _774244) ^ [_1158601, _1158603] : [-(c_Divides_OnegDivAlg(_1158601, _1158603) = hAPP(c_Divides_Oadjust(_1158603), c_Divides_OnegDivAlg(_1158601, 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)))), _1158603)))), -(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), _1158601), _1158603)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158603), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39197 ^ _774244) ^ [_1508616, _1508618, _1508620, _1508622, _1508624] : [class_Groups_Ocomm__monoid__add(_1508616), class_Groups_Ocomm__monoid__mult(_1508616), _1508618 = _1508620, c_Nat__Transfer_Onat__set(_1508620), 39215 ^ _774244 : [(39218 ^ _774244) ^ [] : [hAPP(_1508622, 39214 ^ [_1508616, _1508618, _1508620, _1508622, _1508624]) = hAPP(_1508624, 39214 ^ [_1508616, _1508618, _1508620, _1508622, _1508624])], (39216 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 39214 ^ [_1508616, _1508618, _1508620, _1508622, _1508624])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1508616), _1508622), _1508618) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1508616), _1508624), _1508620))], (3332 ^ _774244) ^ [_825434, _825436] : [_825436 = _825434, -(c_Nitpick_Odenom(_825436) = c_Nitpick_Odenom(_825434))], (7976 ^ _774244) ^ [_904648, _904650, _904652] : [class_Rings_Olinordered__semidom(_904648), 7979 ^ _774244 : [(7986 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _904650), _904652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904648), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904648), _904650)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904648), _904652))))], (7980 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904648), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904648), _904650)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_904648), _904652))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _904650), _904652)))]]], (28306 ^ _774244) ^ [_1274736, _1274738] : [class_Orderings_Olinorder(_1274736), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1274736, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1274736), _1274738)) = hAPP(c_SetInterval_Oord__class_OatMost(_1274736), _1274738))], (21637 ^ _774244) ^ [_1145814, _1145816] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145814), hAPP(c_Int_Onumber__class_Onumber__of(_1145814), c_Int_OMin)), _1145816) = hAPP(c_Groups_Ouminus__class_Ouminus(_1145814), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145814), c_Groups_Oone__class_Oone(_1145814)), _1145816))), class_Fields_Ofield__inverse__zero(_1145814), class_Int_Onumber__ring(_1145814)], (15952 ^ _774244) ^ [_1045195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1045195)), -(_1045195 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045195), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (12850 ^ _774244) ^ [_987689, _987691] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _987689)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _987691))))), _987689 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _987691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13437 ^ _774244) ^ [_997720, _997722] : [class_Divides_Osemiring__div(_997720), -(c_Divides_Odiv__class_Omod(_997720, _997722, c_Groups_Ozero__class_Ozero(_997720)) = _997722)], (48807 ^ _774244) ^ [_1749708, _1749710, _1749712] : [class_Orderings_Olinorder(_1749708), -(c_Big__Operators_Olinorder__class_OMax(_1749708, hAPP(c_List_Oset(_1749708), hAPP(hAPP(c_List_Olist_OCons(_1749708), _1749710), _1749712))) = hAPP(c_List_Ofoldl(_1749708, _1749708, c_Orderings_Oord__class_Omax(_1749708), _1749710), _1749712))], (30372 ^ _774244) ^ [_1315715, _1315717, _1315719] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1315715), _1315717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315715, tc_HOL_Obool)), _1315719), _1315717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1315715), _1315719)), hAPP(c_Finite__Set_Ocard(_1315715), _1315717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1315715, tc_HOL_Obool)), _1315719), _1315717)))], (7072 ^ _774244) ^ [_889072, _889074] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_889072, _889074)], (34920 ^ _774244) ^ [_1412841, _1412843, _1412845] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1412841), _1412843)), hBOOL(hAPP(_1412845, _1412843)), 34931 ^ _774244 : [(34934 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1412841), 34929 ^ [_1412841, _1412843, _1412845]), 34930 ^ [_1412841, _1412843, _1412845])))], (34936 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1412845, 34930 ^ [_1412841, _1412843, _1412845])))], (34938 ^ _774244) ^ [] : [hBOOL(hAPP(_1412845, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1412841, tc_HOL_Obool)), 34930 ^ [_1412841, _1412843, _1412845]), hAPP(hAPP(c_Set_Oinsert(_1412841), 34929 ^ [_1412841, _1412843, _1412845]), c_Orderings_Obot__class_Obot(tc_fun(_1412841, tc_HOL_Obool))))))], (34932 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1412841), 34930 ^ [_1412841, _1412843, _1412845])))]], -(hBOOL(hAPP(_1412845, c_Orderings_Obot__class_Obot(tc_fun(_1412841, tc_HOL_Obool)))))], (38123 ^ _774244) ^ [_1485068, _1485070, _1485072, _1485074, _1485076] : [c_Fun_Oinj__on(_1485068, _1485070, _1485072, c_Orderings_Otop__class_Otop(tc_fun(_1485068, tc_HOL_Obool))), 38126 ^ _774244 : [(38133 ^ _774244) ^ [] : [_1485074 = _1485076, -(hAPP(c_Set_Oimage(_1485068, _1485070, _1485072), _1485074) = hAPP(c_Set_Oimage(_1485068, _1485070, _1485072), _1485076))], (38127 ^ _774244) ^ [] : [hAPP(c_Set_Oimage(_1485068, _1485070, _1485072), _1485074) = hAPP(c_Set_Oimage(_1485068, _1485070, _1485072), _1485076), -(_1485074 = _1485076)]]], (31527 ^ _774244) ^ [_1341578, _1341580, _1341582, _1341584] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1341578, tc_fun(_1341580, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1341578, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1341580, tc_HOL_Obool), tc_fun(_1341580, tc_HOL_Obool), _1341578), hAPP(c_COMBC(_1341580, tc_fun(_1341580, tc_HOL_Obool), tc_HOL_Obool), c_member(_1341580))), _1341582)), _1341584)), -(hBOOL(hAPP(hAPP(c_member(_1341580), _1341584), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1341578, tc_fun(_1341580, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1341578, tc_HOL_Obool))), _1341582))))], (51049 ^ _774244) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (23921 ^ _774244) ^ [_1189394, _1189396, _1189398] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1189394, _1189396), _1189398)), 23924 ^ _774244 : [(23933 ^ _774244) ^ [] : [-(_1189396 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 23936 ^ _774244 : [(23945 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1189396))), 23948 ^ _774244 : [(23951 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1189398)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23949 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189396), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1189398))))]]], (23937 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1189396)), 23940 ^ _774244 : [(23943 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1189398)), _1189396)))], (23941 ^ _774244) ^ [] : [-(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), _1189398))))]]]]], (23927 ^ _774244) ^ [] : [_1189396 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1189398) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23925 ^ _774244) ^ [] : [-(_1189394 = 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), _1189398)), _1189396)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1189398)))]]], (16225 ^ _774244) ^ [_1049974, _1049976, _1049978] : [class_Groups_Oordered__ab__group__add__abs(_1049974), -(hAPP(c_Groups_Oabs__class_Oabs(_1049974), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049974), hAPP(c_Groups_Oabs__class_Oabs(_1049974), _1049976)), hAPP(c_Groups_Oabs__class_Oabs(_1049974), _1049978))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049974), hAPP(c_Groups_Oabs__class_Oabs(_1049974), _1049976)), hAPP(c_Groups_Oabs__class_Oabs(_1049974), _1049978)))], (25323 ^ _774244) ^ [_1215910, _1215912] : [class_Rings_Ocomm__semiring__1(_1215910), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215910), c_Groups_Oone__class_Oone(_1215910)), _1215912)))], (47879 ^ _774244) ^ [_1727117, _1727119, _1727121, _1727123] : [-(hAPP(hAPP(c_List_Otake(_1727117), _1727119), hAPP(hAPP(c_List_Oappend(_1727117), _1727121), _1727123)) = hAPP(hAPP(c_List_Oappend(_1727117), hAPP(hAPP(c_List_Otake(_1727117), _1727119), _1727121)), hAPP(hAPP(c_List_Otake(_1727117), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1727119), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727117)), _1727121))), _1727123)))], (25429 ^ _774244) ^ [_1217816, _1217818, _1217820, _1217822] : [class_Rings_Ocomm__semiring__1(_1217816), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1217816), _1217818), _1217820)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1217816), hAPP(hAPP(c_Power_Opower__class_Opower(_1217816), _1217818), _1217822)), hAPP(hAPP(c_Power_Opower__class_Opower(_1217816), _1217820), _1217822))))], (48586 ^ _774244) ^ [_1745103, _1745105, _1745107] : [-(hAPP(hAPP(c_List_Odrop(_1745103), _1745105), hAPP(c_List_Otl(_1745103), _1745107)) = hAPP(c_List_Otl(_1745103), hAPP(hAPP(c_List_Odrop(_1745103), _1745105), _1745107)))], (38674 ^ _774244) ^ [_1496575, _1496577, _1496579] : [-(c_Fun_Oinj__on(tc_prod(_1496575, _1496577), tc_prod(_1496577, _1496575), hAPP(c_Product__Type_Oprod_Oprod__case(_1496575, _1496577, tc_prod(_1496577, _1496575)), hAPP(c_COMBC(_1496577, _1496575, tc_prod(_1496577, _1496575)), c_Product__Type_OPair(_1496577, _1496575))), _1496579))], (24003 ^ _774244) ^ [_1190825, _1190827] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1190825)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1190827)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1190827))), 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, _1190825))), 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), _1190825)), c_Int_Onat)))))], (20381 ^ _774244) ^ [_1122888, _1122890, _1122892] : [class_Rings_Odivision__ring(_1122888), -(_1122890 = c_Groups_Ozero__class_Ozero(_1122888)), 20388 ^ _774244 : [(20395 ^ _774244) ^ [] : [_1122892 = _1122890, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122888), _1122892), _1122890) = c_Groups_Oone__class_Oone(_1122888))], (20389 ^ _774244) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122888), _1122892), _1122890) = c_Groups_Oone__class_Oone(_1122888), -(_1122892 = _1122890)]]], (39546 ^ _774244) ^ [_1516799, _1516801, _1516803, _1516805, _1516807] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1516799, _1516801, hAPP(hAPP(c_Set_Oinsert(_1516799), _1516803), _1516805)), _1516807)), 39551 ^ _774244 : [(39556 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1516799), 39549 ^ [_1516799, _1516801, _1516803, _1516805, _1516807]), 39550 ^ [_1516799, _1516801, _1516803, _1516805, _1516807]))], (39554 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1516799, _1516799, _1516801, 39549 ^ [_1516799, _1516801, _1516803, _1516805, _1516807], 39550 ^ [_1516799, _1516801, _1516803, _1516805, _1516807]), _1516807)))], (39552 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1516799), _1516803), _1516805) = hAPP(hAPP(c_Set_Oinsert(_1516799), 39549 ^ [_1516799, _1516801, _1516803, _1516805, _1516807]), 39550 ^ [_1516799, _1516801, _1516803, _1516805, _1516807]))]]], (2926 ^ _774244) ^ [_818941, _818943] : [_818943 = _818941, -(c_Lazy__Sequence_Oempty(_818943) = c_Lazy__Sequence_Oempty(_818941))], (14516 ^ _774244) ^ [_1017385, _1017387, _1017389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017385)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017387)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1017387), _1017389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1017385), _1017389)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1017385), _1017387))))], (7958 ^ _774244) ^ [_904366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _904366)), -(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), _904366))))], (46349 ^ _774244) ^ [_1689383, _1689385, _1689387, _1689389] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1689383), tc_List_Olist(_1689383))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689383), tc_List_Olist(_1689383)), _1689385), _1689387)), c_List_Olistrel(_1689383, _1689389))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689383)), _1689385) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689383)), _1689387))], (39728 ^ _774244) ^ [_1522354, _1522356, _1522358, _1522360] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1522354, _1522356)), hAPP(hAPP(c_Product__Type_OSigma(_1522354, _1522356), _1522358), hAPP(c_COMBK(tc_fun(_1522356, tc_HOL_Obool), _1522354), _1522360)))), -(_1522360 = c_Orderings_Obot__class_Obot(tc_fun(_1522356, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1522354), _1522358)))], (29742 ^ _774244) ^ [_1304000] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1304000))))], (3910 ^ _774244) ^ [_834467, _834469] : [_834469 = _834467, -(c_Relation_OField(_834469) = c_Relation_OField(_834467))], (26428 ^ _774244) ^ [_1236238, _1236240, _1236242, _1236244] : [class_Groups_Oordered__ab__group__add__abs(_1236238), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236238), c_Groups_Ozero__class_Ozero(_1236238)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236240, _1236238), hAPP(hAPP(c_COMBB(_1236238, _1236238, _1236240), c_Groups_Oabs__class_Oabs(_1236238)), _1236242)), _1236244))))], (36545 ^ _774244) ^ [_1449830, _1449832, _1449834, _1449836] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1449830, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449830, tc_HOL_Obool)), _1449832), _1449834)), _1449836) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449830, tc_HOL_Obool)), _1449832), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1449830, tc_HOL_Obool)), _1449834), _1449836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1449830, tc_HOL_Obool)), _1449836), _1449832)))], (48180 ^ _774244) ^ [_1735205, _1735207, _1735209, _1735211, _1735213, _1735215] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1735205), tc_List_Olist(_1735205))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1735205), tc_List_Olist(_1735205)), hAPP(hAPP(c_List_Olist_OCons(_1735205), _1735207), _1735209)), hAPP(hAPP(c_List_Olist_OCons(_1735205), _1735211), _1735213))), c_List_Olistrel1(_1735205, _1735215))), 48185 ^ _774244 : [(48188 ^ _774244) ^ [] : [-(_1735209 = _1735213)], (48186 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1735205, _1735205)), hAPP(hAPP(c_Product__Type_OPair(_1735205, _1735205), _1735207), _1735211)), _1735215)))]], 48189 ^ _774244 : [(48192 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1735205), tc_List_Olist(_1735205))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1735205), tc_List_Olist(_1735205)), _1735209), _1735213)), c_List_Olistrel1(_1735205, _1735215))))], (48190 ^ _774244) ^ [] : [-(_1735207 = _1735211)]]], (26560 ^ _774244) ^ [_1239633, _1239635, _1239637, _1239639] : [class_Rings_Ocomm__semiring__1(_1239633), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239633), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1239633), c_Groups_Oone__class_Oone(_1239633)), c_Groups_Oone__class_Oone(_1239633))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1239633), hAPP(hAPP(c_COMBB(_1239633, _1239633, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1239633), _1239635)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1239633, _1239633), hAPP(hAPP(c_COMBB(_1239633, tc_fun(_1239633, _1239633), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1239633)), c_Nat_Osemiring__1__class_Oof__nat(_1239633))), _1239637))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1239639))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239633), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1239633), _1239639)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1239633), _1239635), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1239633), _1239635), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239633), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1239633), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1239639), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1239637)))))], (51167 ^ _774244) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (27906 ^ _774244) ^ [_1267085, _1267087, _1267089] : [class_Orderings_Olinorder(_1267085), 27909 ^ _774244 : [(27916 ^ _774244) ^ [] : [_1267087 = _1267089, -(hAPP(c_SetInterval_Oord__class_OatMost(_1267085), _1267087) = hAPP(c_SetInterval_Oord__class_OatMost(_1267085), _1267089))], (27910 ^ _774244) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1267085), _1267087) = hAPP(c_SetInterval_Oord__class_OatMost(_1267085), _1267089), -(_1267087 = _1267089)]]], (40787 ^ _774244) ^ [_1546942, _1546944, _1546946, _1546948] : [-(hAPP(c_Relation_OImage(_1546942, _1546944, _1546946), hAPP(hAPP(c_Set_Oinsert(_1546942), _1546948), c_Orderings_Obot__class_Obot(tc_fun(_1546942, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1546944), hAPP(hAPP(c_COMBC(_1546944, tc_fun(tc_prod(_1546942, _1546944), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1546942, _1546944), tc_fun(tc_fun(tc_prod(_1546942, _1546944), tc_HOL_Obool), tc_HOL_Obool), _1546944), c_member(tc_prod(_1546942, _1546944))), hAPP(c_Product__Type_OPair(_1546942, _1546944), _1546948))), _1546946)))], (10049 ^ _774244) ^ [_939871, _939873] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _939871), _939873)), _939871 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _939873 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (39636 ^ _774244) ^ [_1519738, _1519740, _1519742, _1519744, _1519746] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519738, _1519740), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1519738, tc_HOL_Obool)), _1519742), _1519744)), _1519746) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1519738, _1519740), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519738, _1519740), _1519742), _1519746)), hAPP(hAPP(c_Product__Type_OSigma(_1519738, _1519740), _1519744), _1519746)))], (42854 ^ _774244) ^ [_1601841, _1601843, _1601845, _1601847, _1601849] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601841, _1601841)), hAPP(hAPP(c_Product__Type_OPair(_1601841, _1601841), _1601843), _1601845)), _1601847)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1601841, _1601841)), hAPP(hAPP(c_Product__Type_OPair(_1601841, _1601841), _1601845), _1601849)), c_Transitive__Closure_Otrancl(_1601841, _1601847))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601841, _1601841)), hAPP(hAPP(c_Product__Type_OPair(_1601841, _1601841), _1601843), _1601849)), c_Transitive__Closure_Otrancl(_1601841, _1601847))))], (41673 ^ _774244) ^ [_1575122, _1575124, _1575126, _1575128] : [hBOOL(hAPP(c_Predicate_ORangeP(_1575122, _1575124, hAPP(hAPP(c_COMBC(_1575122, tc_fun(tc_prod(_1575122, _1575124), tc_HOL_Obool), tc_fun(_1575124, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575124, tc_fun(tc_fun(tc_prod(_1575122, _1575124), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1575122, _1575124), tc_HOL_Obool), tc_fun(_1575124, tc_HOL_Obool)), _1575122), c_COMBC(_1575124, tc_fun(tc_prod(_1575122, _1575124), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575124, tc_prod(_1575122, _1575124)), tc_fun(_1575124, tc_fun(tc_fun(tc_prod(_1575122, _1575124), tc_HOL_Obool), tc_HOL_Obool)), _1575122), hAPP(c_COMBB(tc_prod(_1575122, _1575124), tc_fun(tc_fun(tc_prod(_1575122, _1575124), tc_HOL_Obool), tc_HOL_Obool), _1575124), c_member(tc_prod(_1575122, _1575124)))), c_Product__Type_OPair(_1575122, _1575124)))), _1575126)), _1575128)), -(hBOOL(hAPP(hAPP(c_member(_1575124), _1575128), hAPP(c_Relation_ORange(_1575122, _1575124), _1575126))))], (19303 ^ _774244) ^ [_1103806, _1103808] : [class_Rings_Oring__1__no__zero__divisors(_1103806), 19306 ^ _774244 : [(19313 ^ _774244) ^ [] : [_1103808 = c_Groups_Ozero__class_Ozero(_1103806), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1103806), _1103808), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1103806))], (19307 ^ _774244) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1103806), _1103808), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1103806), -(_1103808 = c_Groups_Ozero__class_Ozero(_1103806))]]], (7062 ^ _774244) ^ [_888805, _888807, _888809, _888811, _888813] : [c_Com_Ocom_OCall(_888805, _888807, _888809) = c_Com_Ocom_OWhile(_888811, _888813)], (42305 ^ _774244) ^ [_1590854, _1590856, _1590858, _1590860, _1590862, _1590864] : [class_Groups_Oab__semigroup__mult(_1590854), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590856), _1590858)), 42315 ^ _774244 : [(42318 ^ _774244) ^ [] : [hAPP(_1590860, 42314 ^ [_1590854, _1590856, _1590858, _1590860, _1590862, _1590864]) = hAPP(_1590862, 42314 ^ [_1590854, _1590856, _1590858, _1590860, _1590862, _1590864])], (42316 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590856), 42314 ^ [_1590854, _1590856, _1590858, _1590860, _1590862, _1590864]), _1590858)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1590854, _1590856, c_Groups_Otimes__class_Otimes(_1590854)), _1590860), _1590864), _1590858) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1590854, _1590856, c_Groups_Otimes__class_Otimes(_1590854)), _1590862), _1590864), _1590858))], (40023 ^ _774244) ^ [_1530598, _1530600, _1530602] : [-(hAPP(c_Finite__Set_Ofold1(_1530598, _1530600), hAPP(hAPP(c_Set_Oinsert(_1530598), _1530602), c_Orderings_Obot__class_Obot(tc_fun(_1530598, tc_HOL_Obool)))) = _1530602)], (16657 ^ _774244) ^ [_1058152, _1058154, _1058156, _1058158] : [class_Int_Onumber__ring(_1058152), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058152), hAPP(c_Int_Onumber__class_Onumber__of(_1058152), _1058154)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058152), hAPP(c_Int_Onumber__class_Onumber__of(_1058152), _1058156)), _1058158)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058152), hAPP(c_Int_Onumber__class_Onumber__of(_1058152), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1058154), _1058156))), _1058158))], (19213 ^ _774244) ^ [_1102161, _1102163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1102161)), c_Int_OBit1(_1102163))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102161), _1102163)))], (6047 ^ _774244) ^ [_871104] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _871104)], (51219 ^ _774244) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (32924 ^ _774244) ^ [_1370640, _1370642, _1370644] : [class_Lattices_Olattice(_1370640), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370640), _1370642)), -(_1370644 = c_Orderings_Obot__class_Obot(tc_fun(_1370640, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1370640, tc_HOL_Obool)), _1370644), _1370642)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1370640), c_Big__Operators_Olattice__class_OSup__fin(_1370640, _1370644)), c_Big__Operators_Olattice__class_OSup__fin(_1370640, _1370642)) = c_Big__Operators_Olattice__class_OSup__fin(_1370640, _1370642))], (19139 ^ _774244) ^ [_1100863, _1100865] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1100863))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1100865))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1100863)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1100865)))], (29830 ^ _774244) ^ [_1305634] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305634), c_Orderings_Obot__class_Obot(tc_fun(_1305634, tc_HOL_Obool)))))], (6341 ^ _774244) ^ [_876323, _876325] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _876323) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _876325), -(hBOOL(hAPP(c_Com_OWT, _876325)))], (19695 ^ _774244) ^ [_1110967, _1110969] : [class_Int_Onumber__ring(_1110967), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1110967), hAPP(c_Int_Onumber__class_Onumber__of(_1110967), 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)))), _1110969)) = c_Groups_Oone__class_Oone(_1110967))], (28230 ^ _774244) ^ [_1273244, _1273246] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1273244, _1273246)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1273246), hAPP(c_Nat_OSuc, _1273244)))], (40577 ^ _774244) ^ [_1541072, _1541074, _1541076] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1541072), hAPP(c_Set_OCollect(_1541072), hAPP(hAPP(c_COMBS(_1541072, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541072), c_fdisj), _1541074)), _1541076))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1541072), hAPP(c_Set_OCollect(_1541072), _1541074))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1541072), hAPP(c_Set_OCollect(_1541072), _1541076)))], (41909 ^ _774244) ^ [_1581297, _1581299] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1581297, _1581297)), _1581299)), 41912 ^ _774244 : [(41919 ^ _774244) ^ [] : [c_Wellfounded_Oacyclic(_1581297, _1581299), -(c_Wellfounded_Owf(_1581297, _1581299))], (41913 ^ _774244) ^ [] : [c_Wellfounded_Owf(_1581297, _1581299), -(c_Wellfounded_Oacyclic(_1581297, _1581299))]]], (22573 ^ _774244) ^ [_1163819, _1163821, _1163823] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1163819, _1163821), _1163823)), 22576 ^ _774244 : [(22577 ^ _774244) ^ [_1163904] : [hBOOL(hAPP(hAPP(_1163821, _1163904), _1163823)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1163819, _1163821), _1163904)))]]], (14223 ^ _774244) ^ [_1012555] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1012555, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15072 ^ _774244) ^ [_1027565, _1027567, _1027569] : [class_Groups_Ogroup__add(_1027565), 15075 ^ _774244 : [(15082 ^ _774244) ^ [] : [_1027567 = _1027569, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1027565), _1027567), _1027569) = c_Groups_Ozero__class_Ozero(_1027565))], (15076 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1027565), _1027567), _1027569) = c_Groups_Ozero__class_Ozero(_1027565), -(_1027567 = _1027569)]]], (8142 ^ _774244) ^ [_907600, _907602] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _907600), _907602))), -(_907600 = _907602), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _907602), _907600)))], (46791 ^ _774244) ^ [_1701558] : [46793 ^ _774244 : [(46796 ^ _774244) ^ [] : [46792 ^ [_1701558] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46794 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 46792 ^ [_1701558]), hAPP(c_List_Oset(tc_Nat_Onat), _1701558))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1701558) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37440 ^ _774244) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (18465 ^ _774244) ^ [_1089413, _1089415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1089413)), c_Int_OBit1(_1089415))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1089413), _1089415)))], (23349 ^ _774244) ^ [_1178354, _1178356, _1178358, _1178360, _1178362] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1178354, _1178356, _1178358), _1178360), _1178362) = hAPP(hAPP(_1178360, hAPP(c_Product__Type_Ofst(_1178354, _1178356), _1178362)), hAPP(c_Product__Type_Osnd(_1178354, _1178356), _1178362)))], (6327 ^ _774244) ^ [_875934, _875936, _875938, _875940, _875942, _875944] : [c_Com_Ocom_OCond(_875934, _875936, _875938) = c_Com_Ocom_OCall(_875940, _875942, _875944)], (7559 ^ _774244) ^ [_897256, _897258, _897260, _897262, _897264] : [c_Com_Ocom_OAss(_897256, _897258) = c_Com_Ocom_OCall(_897260, _897262, _897264)], (27231 ^ _774244) ^ [_1253803, _1253805, _1253807, _1253809, _1253811, _1253813] : [-(hAPP(c_Set_Oimage(_1253803, _1253805, _1253807), hAPP(c_Set_Oimage(_1253809, _1253803, _1253811), _1253813)) = hAPP(c_Set_Oimage(_1253809, _1253805, hAPP(hAPP(c_COMBB(_1253803, _1253805, _1253809), _1253807), _1253811)), _1253813))], (43041 ^ _774244) ^ [_1606156, _1606158, _1606160] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606156, _1606156)), _1606158), _1606160)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606156, _1606156)), _1606158), c_Transitive__Closure_Ortrancl(_1606156, _1606160))))], (26139 ^ _774244) ^ [_1230885, _1230887] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230885), _1230887)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230887), _1230885)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1230885) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1230887))], (16094 ^ _774244) ^ [_1047869, _1047871, _1047873] : [16096 ^ _774244 : [(16101 ^ _774244) ^ [] : [hBOOL(hAPP(_1047871, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 16095 ^ [_1047869, _1047871, _1047873]), _1047869)))], (16099 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1047871, 16095 ^ [_1047869, _1047871, _1047873])))], (16097 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16095 ^ [_1047869, _1047871, _1047873]), _1047869)))]], hBOOL(hAPP(_1047871, _1047873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047873), _1047869)), -(hBOOL(hAPP(_1047871, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45311 ^ _774244) ^ [_1662917, _1662919, _1662921, _1662923, _1662925] : [-(hAPP(c_Map_Omap__add(_1662917, _1662919, _1662921, _1662923), _1662925) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1662919), _1662919, hAPP(_1662921, _1662925), c_Option_Ooption_OSome(_1662919)), hAPP(_1662923, _1662925)))], (24573 ^ _774244) ^ [_1202077, _1202079, _1202081, _1202083, _1202085, _1202087] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1202077, _1202079, _1202081, _1202083, _1202085), hAPP(c_Sum__Type_OInl(_1202077, _1202081), _1202087)) = hAPP(_1202083, _1202087))], (25235 ^ _774244) ^ [_1214441, _1214443] : [-(_1214441 = _1214443), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214441), _1214443)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214443), _1214441))], (6207 ^ _774244) ^ [_873815, _873817, _873819, _873821, _873823] : [c_Com_Ocom_OCond(_873815, _873817, _873819) = c_Com_Ocom_OSemi(_873821, _873823)], (47325 ^ _774244) ^ [_1713948, _1713950, _1713952, _1713954, _1713956] : [-(hAPP(hAPP(c_List_Olist__update(_1713948, hAPP(hAPP(c_List_Olist_OCons(_1713948), _1713950), _1713952)), _1713954), _1713956) = c_Nat_Onat_Onat__case(tc_List_Olist(_1713948), hAPP(hAPP(c_List_Olist_OCons(_1713948), _1713956), _1713952), hAPP(hAPP(c_COMBB(tc_List_Olist(_1713948), tc_List_Olist(_1713948), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1713948), _1713950)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1713948, tc_List_Olist(_1713948)), c_List_Olist__update(_1713948, _1713952)), _1713956)), _1713954))], (44147 ^ _774244) ^ [_1635443, _1635445, _1635447] : [44150 ^ _774244 : [(44156 ^ _774244) ^ [] : [44149 ^ [_1635443, _1635445, _1635447] = 44152 ^ [_1635443, _1635445, _1635447]], (44154 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635443, _1635445)), hAPP(hAPP(c_Product__Type_OPair(_1635443, _1635445), 44148 ^ [_1635443, _1635445, _1635447]), 44152 ^ [_1635443, _1635445, _1635447])), _1635447)))], (44151 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635443, _1635445)), hAPP(hAPP(c_Product__Type_OPair(_1635443, _1635445), 44148 ^ [_1635443, _1635445, _1635447]), 44149 ^ [_1635443, _1635445, _1635447])), _1635447)))]], -(c_Relation_Osingle__valued(_1635443, _1635445, _1635447))], (45964 ^ _774244) ^ [_1678217, _1678219, _1678221, _1678223] : [hBOOL(hAPP(c_List_Odistinct(_1678217), _1678219)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1678217, _1678221)), hAPP(hAPP(c_List_Ozip(_1678217, _1678221), _1678219), _1678223))))], (39738 ^ _774244) ^ [_1522518, _1522520, _1522522, _1522524] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1522518, _1522520)), hAPP(hAPP(c_Product__Type_OSigma(_1522518, _1522520), _1522522), hAPP(c_COMBK(tc_fun(_1522520, tc_HOL_Obool), _1522518), _1522524)))), -(_1522522 = c_Orderings_Obot__class_Obot(tc_fun(_1522518, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1522520), _1522524)))], (35346 ^ _774244) ^ [_1423148, _1423150, _1423152, _1423154] : [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), _1423148), _1423150)), 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), _1423152), _1423154)), 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), _1423148), _1423154)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1423152), _1423150))))], (8630 ^ _774244) ^ [_915170, _915172] : [class_Groups_Ogroup__add(_915170), -(hAPP(c_Groups_Ouminus__class_Ouminus(_915170), hAPP(c_Groups_Ouminus__class_Ouminus(_915170), _915172)) = _915172)], (19021 ^ _774244) ^ [_1098786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1098786)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098786), c_Int_OPls)))], (3842 ^ _774244) ^ [_833459, _833461] : [_833461 = _833459, -(c_SetInterval_Oord__class_OgreaterThan(_833461) = c_SetInterval_Oord__class_OgreaterThan(_833459))], (39954 ^ _774244) ^ [_1528926, _1528928, _1528930, _1528932, _1528934, _1528936, _1528938, _1528940] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528926, _1528928)), _1528930), hAPP(c_Set_Oimage(tc_prod(_1528932, _1528934), tc_prod(_1528926, _1528928), c_Product__Type_Omap__pair(_1528932, _1528926, _1528934, _1528928, _1528936, _1528938)), _1528940))), 39959 ^ _774244 : [(39962 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1528932, _1528934)), hAPP(hAPP(c_Product__Type_OPair(_1528932, _1528934), 39957 ^ [_1528926, _1528928, _1528930, _1528932, _1528934, _1528936, _1528938, _1528940]), 39958 ^ [_1528926, _1528928, _1528930, _1528932, _1528934, _1528936, _1528938, _1528940])), _1528940)))], (39960 ^ _774244) ^ [] : [-(_1528930 = hAPP(hAPP(c_Product__Type_OPair(_1528926, _1528928), hAPP(_1528936, 39957 ^ [_1528926, _1528928, _1528930, _1528932, _1528934, _1528936, _1528938, _1528940])), hAPP(_1528938, 39958 ^ [_1528926, _1528928, _1528930, _1528932, _1528934, _1528936, _1528938, _1528940])))]]], (964 ^ _774244) ^ [_789018, _789020] : [-(class_Rings_Olinordered__semiring__1__strict(_789018)), _789020 = _789018, class_Rings_Olinordered__semiring__1__strict(_789020)], (15478 ^ _774244) ^ [_1035294, _1035296] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035294), _1035296)), hAPP(c_Nat_OSuc, _1035294))))], (29368 ^ _774244) ^ [_1296896, _1296898] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1296898, _1296896) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1296896), _1296898)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1296898), _1296896)))], (6268 ^ _774244) ^ [_874802, _874804, _874806, _874808] : [hAPP(_874802, 6269 ^ [_874802, _874804, _874806, _874808]) = hAPP(c_Nat_Onat_Onat__rec(_874804, _874806, _874808), 6269 ^ [_874802, _874804, _874806, _874808]), -(hAPP(_874802, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _874806)], (29126 ^ _774244) ^ [_1292745, _1292747, _1292749] : [-(hAPP(hAPP(c_Set_Oinsert(_1292745), _1292747), _1292749) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292745, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1292745), _1292747), c_Orderings_Obot__class_Obot(tc_fun(_1292745, tc_HOL_Obool)))), _1292749))], (19757 ^ _774244) ^ [_1112018, _1112020] : [class_Fields_Olinordered__field__inverse__zero(_1112018), class_Int_Onumber__ring(_1112018), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112018), c_Groups_Ozero__class_Ozero(_1112018)), _1112020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112018), c_Groups_Ozero__class_Ozero(_1112018)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112018), _1112020), hAPP(c_Int_Onumber__class_Onumber__of(_1112018), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35382 ^ _774244) ^ [_1424086, _1424088, _1424090, _1424092, _1424094, _1424096] : [c_Finite__Set_Ofolding(_1424086, _1424088, _1424090, _1424092), -(hAPP(c_Fun_Ocomp(_1424088, _1424088, _1424088, hAPP(_1424090, _1424094)), hAPP(_1424090, _1424096)) = hAPP(c_Fun_Ocomp(_1424088, _1424088, _1424088, hAPP(_1424090, _1424096)), hAPP(_1424090, _1424094)))], (22242 ^ _774244) ^ [_1157113, _1157115] : [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(_1157115))), 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), _1157113)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1157113)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157115))))], (29562 ^ _774244) ^ [_1300742, _1300744, _1300746] : [class_Orderings_Olinorder(_1300742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300742), _1300744), _1300746)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1300742, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1300742, _1300744, _1300746)), hAPP(hAPP(c_Set_Oinsert(_1300742), _1300746), c_Orderings_Obot__class_Obot(tc_fun(_1300742, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1300742, _1300744, _1300746))], (44291 ^ _774244) ^ [_1639085, _1639087, _1639089] : [-(hAPP(hAPP(c_Nat_Ocompow(_1639085, _1639085), hAPP(c_Nat_OSuc, _1639087)), _1639089) = hAPP(c_Fun_Ocomp(_1639085, _1639085, _1639085, _1639089), hAPP(hAPP(c_Nat_Ocompow(_1639085, _1639085), _1639087), _1639089)))], (17169 ^ _774244) ^ [_1067927, _1067929, _1067931] : [class_Rings_Olinordered__idom(_1067927), -(hAPP(c_Groups_Oabs__class_Oabs(_1067927), hAPP(hAPP(c_Power_Opower__class_Opower(_1067927), _1067929), _1067931)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1067927), hAPP(c_Groups_Oabs__class_Oabs(_1067927), _1067929)), _1067931))], (43453 ^ _774244) ^ [_1616553, _1616555, _1616557, _1616559, _1616561, _1616563] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616555, _1616557)), hAPP(hAPP(c_Product__Type_OPair(_1616555, _1616557), _1616561), _1616563)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616553, tc_fun(tc_prod(_1616555, _1616557), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1616553, tc_HOL_Obool))), _1616559))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616553, tc_fun(_1616555, tc_fun(_1616557, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1616553, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1616555, _1616557), tc_HOL_Obool), tc_fun(_1616555, tc_fun(_1616557, tc_HOL_Obool)), _1616553), hAPP(c_COMBC(_1616555, tc_fun(tc_prod(_1616555, _1616557), tc_HOL_Obool), tc_fun(_1616557, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616557, tc_fun(tc_fun(tc_prod(_1616555, _1616557), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1616555, _1616557), tc_HOL_Obool), tc_fun(_1616557, tc_HOL_Obool)), _1616555), c_COMBC(_1616557, tc_fun(tc_prod(_1616555, _1616557), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616557, tc_prod(_1616555, _1616557)), tc_fun(_1616557, tc_fun(tc_fun(tc_prod(_1616555, _1616557), tc_HOL_Obool), tc_HOL_Obool)), _1616555), hAPP(c_COMBB(tc_prod(_1616555, _1616557), tc_fun(tc_fun(tc_prod(_1616555, _1616557), tc_HOL_Obool), tc_HOL_Obool), _1616557), c_member(tc_prod(_1616555, _1616557)))), c_Product__Type_OPair(_1616555, _1616557))))), _1616559)), _1616561), _1616563)))], (27436 ^ _774244) ^ [_1258070, _1258072] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1258070, _1258072) = 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), _1258070), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258072))))], (28036 ^ _774244) ^ [_1269356, _1269358, _1269360, _1269362] : [class_Lattices_Osemilattice__sup(_1269356), 28039 ^ _774244 : [(28048 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269356), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269356), _1269358), _1269360)), _1269362))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269356), _1269358), _1269362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269356), _1269360), _1269362))], (28040 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269356), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269356), _1269358), _1269360)), _1269362)), 28043 ^ _774244 : [(28046 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269356), _1269360), _1269362)))], (28044 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269356), _1269358), _1269362)))]]]]], (30717 ^ _774244) ^ [_1322763, _1322765, _1322767, _1322769, _1322771, _1322773] : [c_Typedef_Otype__definition(_1322763, _1322765, _1322767, _1322769, _1322771), hBOOL(hAPP(hAPP(c_member(_1322765), _1322773), _1322771)), -(hAPP(_1322767, hAPP(_1322769, _1322773)) = _1322773)], (20219 ^ _774244) ^ [_1120448, _1120450, _1120452, _1120454] : [class_Fields_Ofield__inverse__zero(_1120448), 20222 ^ _774244 : [(20223 ^ _774244) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120448), _1120450), _1120452) = _1120454, 20226 ^ _774244 : [(20233 ^ _774244) ^ [] : [_1120452 = c_Groups_Ozero__class_Ozero(_1120448), -(_1120454 = c_Groups_Ozero__class_Ozero(_1120448))], (20227 ^ _774244) ^ [] : [-(_1120452 = c_Groups_Ozero__class_Ozero(_1120448)), -(_1120450 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120448), _1120454), _1120452))]]], (20239 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120448), _1120450), _1120452) = _1120454), 20242 ^ _774244 : [(20245 ^ _774244) ^ [] : [_1120450 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120448), _1120454), _1120452)], (20243 ^ _774244) ^ [] : [_1120452 = c_Groups_Ozero__class_Ozero(_1120448)]], 20246 ^ _774244 : [(20249 ^ _774244) ^ [] : [_1120454 = c_Groups_Ozero__class_Ozero(_1120448)], (20247 ^ _774244) ^ [] : [-(_1120452 = c_Groups_Ozero__class_Ozero(_1120448))]]]]], (12340 ^ _774244) ^ [_978546, _978548, _978550, _978552] : [class_Groups_Oordered__comm__monoid__add(_978546), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978546), c_Groups_Ozero__class_Ozero(_978546)), _978548)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978546), _978550), _978552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978546), _978550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978546), _978548), _978552))))], (1444 ^ _774244) ^ [_795018, _795020] : [-(class_Rings_Oordered__comm__semiring(_795018)), _795020 = _795018, class_Rings_Oordered__comm__semiring(_795020)], (24797 ^ _774244) ^ [_1207271, _1207273, _1207275, _1207277, _1207279] : [hBOOL(hAPP(_1207271, hAPP(hAPP(c_Product__Type_OPair(_1207273, _1207275), _1207277), _1207279))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1207273, _1207275, tc_HOL_Obool, _1207271), _1207277), _1207279)))], (5582 ^ _774244) ^ [_860409, _860411] : [_860411 = _860409, -(c_Option_Othe(_860411) = c_Option_Othe(_860409))], (32762 ^ _774244) ^ [_1368093, _1368095, _1368097] : [class_Orderings_Olinorder(_1368093), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368093), _1368095)), hBOOL(hAPP(hAPP(c_member(_1368093), _1368097), _1368095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368093), _1368097), c_Big__Operators_Olinorder__class_OMax(_1368093, _1368095))))], (46633 ^ _774244) ^ [_1697683, _1697685, _1697687] : [class_Groups_Omonoid__add(_1697683), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1697683), hAPP(hAPP(c_List_Olist_OCons(_1697683), _1697685), _1697687)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1697683), _1697685), hAPP(c_List_Omonoid__add__class_Olistsum(_1697683), _1697687)))], (46371 ^ _774244) ^ [_1690063, _1690065, _1690067, _1690069] : [c_List_Olistrelp(_1690063, hAPP(hAPP(c_COMBC(_1690063, tc_fun(tc_prod(_1690063, _1690063), tc_HOL_Obool), tc_fun(_1690063, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1690063, tc_fun(tc_fun(tc_prod(_1690063, _1690063), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1690063, _1690063), tc_HOL_Obool), tc_fun(_1690063, tc_HOL_Obool)), _1690063), c_COMBC(_1690063, tc_fun(tc_prod(_1690063, _1690063), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1690063, tc_prod(_1690063, _1690063)), tc_fun(_1690063, tc_fun(tc_fun(tc_prod(_1690063, _1690063), tc_HOL_Obool), tc_HOL_Obool)), _1690063), hAPP(c_COMBB(tc_prod(_1690063, _1690063), tc_fun(tc_fun(tc_prod(_1690063, _1690063), tc_HOL_Obool), tc_HOL_Obool), _1690063), c_member(tc_prod(_1690063, _1690063)))), c_Product__Type_OPair(_1690063, _1690063)))), _1690065), _1690067, _1690069), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1690063), tc_List_Olist(_1690063))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1690063), tc_List_Olist(_1690063)), _1690067), _1690069)), c_List_Olistrel(_1690063, _1690065))))], (48960 ^ _774244) ^ [_1753568, _1753570, _1753572] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1753568)), _1753570), c_List_Olists(_1753568, c_Wellfounded_Oacc(_1753568, _1753572)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1753568)), _1753570), c_Wellfounded_Oacc(tc_List_Olist(_1753568), c_List_Olistrel1(_1753568, _1753572)))))], (29672 ^ _774244) ^ [_1302606, _1302608] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1302606), _1302608)), -(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)))), _1302608, _1302606) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (7066 ^ _774244) ^ [_888923, _888925, _888927, _888929, _888931] : [c_Com_Ocom_OLocal(_888923, _888925, _888927) = c_Com_Ocom_OWhile(_888929, _888931)], (14994 ^ _774244) ^ [_1026128, _1026130, _1026132] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026128), _1026130)), _1026132) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026128), _1026132)), _1026130))], (28100 ^ _774244) ^ [_1270468, _1270470, _1270472] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270468, tc_HOL_Obool)), _1270470), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270468, tc_HOL_Obool)), _1270472), _1270470))))], (42864 ^ _774244) ^ [_1602108, _1602110, _1602112, _1602114, _1602116] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602108, _1602108)), hAPP(hAPP(c_Product__Type_OPair(_1602108, _1602108), _1602110), _1602112)), _1602114)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602108, _1602108)), hAPP(hAPP(c_Product__Type_OPair(_1602108, _1602108), _1602112), _1602116)), _1602114)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602108, _1602108)), hAPP(hAPP(c_Product__Type_OPair(_1602108, _1602108), _1602110), _1602116)), c_Transitive__Closure_Otrancl(_1602108, _1602114))))], (46974 ^ _774244) ^ [_1704876, _1704878] : [-(c_List_Oset__Cons(_1704876, _1704878, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1704876)), c_List_Olist_ONil(_1704876)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1704876), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1704876, tc_List_Olist(_1704876), hAPP(hAPP(c_COMBC(_1704876, tc_List_Olist(_1704876), tc_List_Olist(_1704876)), c_List_Olist_OCons(_1704876)), c_List_Olist_ONil(_1704876))), _1704878))], (24211 ^ _774244) ^ [_1194715, _1194717, _1194719, _1194721] : [class_Orderings_Olinorder(_1194715), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194715), _1194717), _1194719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194715), _1194717), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194715), _1194721), _1194719))))], (50314 ^ _774244) ^ [_1781979, _1781981] : [-(hAPP(c_List_Oset(_1781979), c_List_Oconcat(_1781979, _1781981)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1781979), tc_fun(_1781979, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1781979)), _1781981)), c_List_Oset(_1781979)))], (44548 ^ _774244) ^ [_1644907, _1644909, _1644911, _1644913, _1644915] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644907, tc_fun(_1644909, tc_HOL_Obool)), _1644911), hAPP(hAPP(c_COMBS(_1644907, tc_fun(_1644909, tc_HOL_Obool), tc_fun(_1644909, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1644909, tc_HOL_Obool), tc_fun(tc_fun(_1644909, tc_HOL_Obool), tc_fun(_1644909, tc_HOL_Obool)), _1644907), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1644909, tc_HOL_Obool))), _1644913)), _1644915)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1644909, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1644909, tc_HOL_Obool), hAPP(c_Set_Oimage(_1644907, tc_fun(_1644909, tc_HOL_Obool), _1644913), _1644911))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1644909, tc_HOL_Obool), hAPP(c_Set_Oimage(_1644907, tc_fun(_1644909, tc_HOL_Obool), _1644915), _1644911))))], (2718 ^ _774244) ^ [_815431, _815433, _815435, _815437] : [-(c_Nitpick_Oint__lcm(_815437, _815433) = c_Nitpick_Oint__lcm(_815435, _815431)), _815437 = _815435, _815433 = _815431], (7054 ^ _774244) ^ [_888581, _888583, _888585, _888587, _888589] : [c_Com_Ocom_OCond(_888581, _888583, _888585) = c_Com_Ocom_OWhile(_888587, _888589)], (6524 ^ _774244) ^ [_879401, _879403] : [class_Groups_Omonoid__add(_879401), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879401), _879403), c_Groups_Ozero__class_Ozero(_879401)) = _879403)], (48484 ^ _774244) ^ [_1743140, _1743142, _1743144, _1743146] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1743140) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1743142), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1743140)), hAPP(hAPP(c_List_Olist_OCons(_1743142), _1743144), _1743146)) = hAPP(hAPP(c_List_Olist_OCons(_1743142), _1743144), _1743146))], (40404 ^ _774244) ^ [_1537397, _1537399, _1537401, _1537403] : [c_Big__Operators_Osemilattice__big(_1537397, _1537399, _1537401), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537397), _1537403)), -(hAPP(_1537401, _1537403) = hAPP(c_Finite__Set_Ofold1(_1537397, _1537399), _1537403))], (5877 ^ _774244) ^ [_868204, _868206, _868208, _868210, _868212] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_868204, _868206), _868208, _868210, _868212), 5881 ^ _774244 : [(5884 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_868206, 5880 ^ [_868204, _868206, _868208, _868210, _868212], _868210, _868212))], (5882 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_868204, _868208, _868210, 5880 ^ [_868204, _868206, _868208, _868210, _868212]))]]], (13577 ^ _774244) ^ [_1000612, _1000614, _1000616] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1000612), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1000614, _1000616)), _1000616) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1000612), _1000614), _1000616))], (15716 ^ _774244) ^ [_1040258, _1040260, _1040262, _1040264, _1040266, _1040268] : [class_Rings_Oordered__ring(_1040258), 15719 ^ _774244 : [(15726 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040258), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040258), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1040258), _1040260), _1040266)), _1040262)), _1040264)), _1040268)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040258), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040258), _1040260), _1040262)), _1040264)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040258), _1040266), _1040262)), _1040268))))], (15720 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040258), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040258), _1040260), _1040262)), _1040264)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040258), _1040266), _1040262)), _1040268))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040258), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040258), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1040258), _1040260), _1040266)), _1040262)), _1040264)), _1040268)))]]], (39788 ^ _774244) ^ [_1523642, _1523644, _1523646, _1523648, _1523650, _1523652, _1523654, _1523656] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1523642, _1523644), tc_fun(tc_prod(_1523646, _1523648), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1523642, _1523644), _1523650), hAPP(c_COMBK(tc_fun(_1523644, tc_HOL_Obool), _1523642), _1523652))), hAPP(c_Product__Type_Oprod_Oprod__case(_1523642, _1523644, tc_fun(tc_prod(_1523646, _1523648), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1523642, tc_fun(_1523644, tc_fun(_1523646, tc_fun(_1523648, tc_HOL_Obool))), tc_fun(_1523644, tc_fun(tc_prod(_1523646, _1523648), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1523646, tc_fun(_1523648, tc_HOL_Obool)), tc_fun(tc_prod(_1523646, _1523648), tc_HOL_Obool)), tc_fun(tc_fun(_1523644, tc_fun(_1523646, tc_fun(_1523648, tc_HOL_Obool))), tc_fun(_1523644, tc_fun(tc_prod(_1523646, _1523648), tc_HOL_Obool))), _1523642), c_COMBB(tc_fun(_1523646, tc_fun(_1523648, tc_HOL_Obool)), tc_fun(tc_prod(_1523646, _1523648), tc_HOL_Obool), _1523644)), hAPP(hAPP(c_COMBB(tc_fun(_1523646, tc_HOL_Obool), tc_fun(tc_fun(_1523646, tc_fun(_1523648, tc_HOL_Obool)), tc_fun(tc_prod(_1523646, _1523648), tc_HOL_Obool)), _1523642), c_Product__Type_OSigma(_1523646, _1523648)), _1523654))), hAPP(hAPP(c_COMBB(tc_fun(_1523648, tc_HOL_Obool), tc_fun(_1523646, tc_fun(_1523648, tc_HOL_Obool)), _1523644), c_COMBK(tc_fun(_1523648, tc_HOL_Obool), _1523646)), _1523656)))) = hAPP(hAPP(c_Product__Type_OSigma(_1523646, _1523648), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523642, tc_fun(_1523646, tc_HOL_Obool)), _1523650), _1523654)), hAPP(c_COMBK(tc_fun(_1523648, tc_HOL_Obool), _1523646), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523644, tc_fun(_1523648, tc_HOL_Obool)), _1523652), _1523656))))], (10422 ^ _774244) ^ [_945933, _945935, _945937] : [class_Rings_Olinordered__idom(_945933), 10425 ^ _774244 : [(10432 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _945935), _945937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945933), hAPP(c_Int_Oring__1__class_Oof__int(_945933), _945935)), hAPP(c_Int_Oring__1__class_Oof__int(_945933), _945937))))], (10426 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945933), hAPP(c_Int_Oring__1__class_Oof__int(_945933), _945935)), hAPP(c_Int_Oring__1__class_Oof__int(_945933), _945937))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _945935), _945937)))]]], (23993 ^ _774244) ^ [_1190646] : [class_Orderings_Oord(_1190646), -(c_Orderings_Oord__class_Omin(_1190646) = c_Orderings_Oord_Omin(_1190646, c_Orderings_Oord__class_Oless__eq(_1190646)))], (23353 ^ _774244) ^ [_1178472, _1178474, _1178476] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1178472, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1178472, tc_HOL_Obool)), _1178474), _1178476)), _1178474)))], (11092 ^ _774244) ^ [_956738, _956740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956738), hAPP(c_Nat_OSuc, _956740))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956738), _956740))), -(_956738 = hAPP(c_Nat_OSuc, _956740))], (2850 ^ _774244) ^ [_817601, _817603, _817605, _817607] : [-(c_Nitpick_Ouminus__frac(_817607, _817603) = c_Nitpick_Ouminus__frac(_817605, _817601)), _817607 = _817605, _817603 = _817601], (50713 ^ _774244) ^ [_1791487, _1791489] : [c_List_Oremdups(_1791487, _1791489) = _1791489, -(hBOOL(hAPP(c_List_Odistinct(_1791487), _1791489)))], (23351 ^ _774244) ^ [_1178413, _1178415, _1178417, _1178419, _1178421] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1178413, _1178415, _1178417), _1178419), _1178421) = hAPP(hAPP(_1178419, hAPP(c_Product__Type_Ofst(_1178413, _1178415), _1178421)), hAPP(c_Product__Type_Osnd(_1178413, _1178415), _1178421)))], (7555 ^ _774244) ^ [_897138, _897140, _897142, _897144, _897146] : [c_Com_Ocom_OAss(_897138, _897140) = c_Com_Ocom_OLocal(_897142, _897144, _897146)], (29008 ^ _774244) ^ [_1290464, _1290466, _1290468, _1290470] : [class_Complete__Lattice_Ocomplete__lattice(_1290464), -(_1290466 = c_Orderings_Obot__class_Obot(tc_fun(_1290468, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1290468, _1290464), _1290466), hAPP(c_COMBK(_1290464, _1290468), _1290470)) = _1290470)], (49079 ^ _774244) ^ [_1755766, _1755768, _1755770] : [-(c_List_Olast(_1755766, hAPP(hAPP(c_List_Oappend(_1755766), _1755768), hAPP(hAPP(c_List_Olist_OCons(_1755766), _1755770), c_List_Olist_ONil(_1755766)))) = _1755770)], (14410 ^ _774244) ^ [_1015606, _1015608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1015606)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015608), _1015606)), _1015606) = _1015608)], (46377 ^ _774244) ^ [_1690440, _1690442, _1690444, _1690446] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1690440), tc_List_Olist(_1690440))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1690440), tc_List_Olist(_1690440)), _1690444), _1690446)), c_List_Olistrel(_1690440, _1690442))), -(c_List_Olistrelp(_1690440, hAPP(hAPP(c_COMBC(_1690440, tc_fun(tc_prod(_1690440, _1690440), tc_HOL_Obool), tc_fun(_1690440, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1690440, tc_fun(tc_fun(tc_prod(_1690440, _1690440), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1690440, _1690440), tc_HOL_Obool), tc_fun(_1690440, tc_HOL_Obool)), _1690440), c_COMBC(_1690440, tc_fun(tc_prod(_1690440, _1690440), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1690440, tc_prod(_1690440, _1690440)), tc_fun(_1690440, tc_fun(tc_fun(tc_prod(_1690440, _1690440), tc_HOL_Obool), tc_HOL_Obool)), _1690440), hAPP(c_COMBB(tc_prod(_1690440, _1690440), tc_fun(tc_fun(tc_prod(_1690440, _1690440), tc_HOL_Obool), tc_HOL_Obool), _1690440), c_member(tc_prod(_1690440, _1690440)))), c_Product__Type_OPair(_1690440, _1690440)))), _1690442), _1690444, _1690446))], (38399 ^ _774244) ^ [_1490461, _1490463, _1490465, _1490467, _1490469] : [c_Fun_Oinj__on(_1490461, _1490463, _1490465, c_Orderings_Otop__class_Otop(tc_fun(_1490461, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1490461, _1490463, _1490465), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1490461, tc_HOL_Obool)), _1490467), _1490469)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1490463, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1490461, _1490463, _1490465), _1490467)), hAPP(c_Set_Oimage(_1490461, _1490463, _1490465), _1490469)))], (2728 ^ _774244) ^ [_815580, _815582] : [_815582 = _815580, -(c_Lazy__Sequence_Ohit__bound(_815582) = c_Lazy__Sequence_Ohit__bound(_815580))], (44160 ^ _774244) ^ [_1635813, _1635815, _1635817, _1635819, _1635821] : [c_Relation_Osingle__valued(_1635813, _1635813, _1635815), hBOOL(hAPP(hAPP(c_member(tc_prod(_1635813, _1635813)), hAPP(hAPP(c_Product__Type_OPair(_1635813, _1635813), _1635817), _1635819)), c_Transitive__Closure_Ortrancl(_1635813, _1635815))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1635813, _1635813)), hAPP(hAPP(c_Product__Type_OPair(_1635813, _1635813), _1635817), _1635821)), c_Transitive__Closure_Ortrancl(_1635813, _1635815))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635813, _1635813)), hAPP(hAPP(c_Product__Type_OPair(_1635813, _1635813), _1635819), _1635821)), c_Transitive__Closure_Ortrancl(_1635813, _1635815)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635813, _1635813)), hAPP(hAPP(c_Product__Type_OPair(_1635813, _1635813), _1635821), _1635819)), c_Transitive__Closure_Ortrancl(_1635813, _1635815))))], (16149 ^ _774244) ^ [_1048811, _1048813, _1048815] : [class_Int_Onumber(_1048811), 16152 ^ _774244 : [(16159 ^ _774244) ^ [] : [_1048815 = hAPP(c_Int_Onumber__class_Onumber__of(_1048811), _1048813), -(hAPP(c_Int_Onumber__class_Onumber__of(_1048811), _1048813) = _1048815)], (16153 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1048811), _1048813) = _1048815, -(_1048815 = hAPP(c_Int_Onumber__class_Onumber__of(_1048811), _1048813))]]], (45511 ^ _774244) ^ [_1667828, _1667830] : [-(hAPP(hAPP(c_List_Omap(_1667828, _1667828), c_COMBI(_1667828)), _1667830) = _1667830)], (29748 ^ _774244) ^ [_1304089, _1304091] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1304089, _1304091))))], (3698 ^ _774244) ^ [_831261, _831263, _831265, _831267, _831269, _831271, _831273, _831275] : [-(c_New__Random__Sequence_Oneg__bind(_831275, _831271, _831267, _831263) = c_New__Random__Sequence_Oneg__bind(_831273, _831269, _831265, _831261)), _831275 = _831273, _831271 = _831269, _831267 = _831265, _831263 = _831261], (50288 ^ _774244) ^ [_1781382, _1781384, _1781386, _1781388] : [-(hAPP(c_List_Orev(_1781382), hAPP(hAPP(c_List_Omap(_1781384, _1781382), _1781386), _1781388)) = hAPP(hAPP(c_List_Omap(_1781384, _1781382), _1781386), hAPP(c_List_Orev(_1781384), _1781388)))], (14119 ^ _774244) ^ [_1010652, _1010654] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1010652), _1010654)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1010652)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1010654)))], (23131 ^ _774244) ^ [_1173925] : [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), _1173925))), -(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), _1173925)) = 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), _1173925))))], (15700 ^ _774244) ^ [_1039819, _1039821, _1039823, _1039825, _1039827, _1039829] : [class_Rings_Oordered__ring(_1039819), 15703 ^ _774244 : [(15710 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039819), _1039825), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039819), _1039827), _1039821)), _1039823)), _1039829))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039819), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039819), _1039821), _1039823)), _1039825)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039819), _1039827), _1039823)), _1039829))))], (15704 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039819), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039819), _1039821), _1039823)), _1039825)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039819), _1039827), _1039823)), _1039829))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039819), _1039825), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039819), _1039827), _1039821)), _1039823)), _1039829))))]]], (49537 ^ _774244) ^ [_1766621, _1766623, _1766625, _1766627, _1766629] : [class_Orderings_Olinorder(_1766621), -(c_List_Olinorder__class_Osorted(_1766621, hAPP(hAPP(c_List_Omap(_1766623, _1766621), _1766625), hAPP(c_List_Ofilter(_1766623, hAPP(hAPP(c_COMBC(_1766623, _1766621, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1766621, tc_fun(_1766621, tc_HOL_Obool), _1766623), c_fequal), _1766625)), hAPP(_1766627, _1766629))), _1766629))))], (16249 ^ _774244) ^ [_1050528] : [class_Rings_Olinordered__idom(_1050528), -(hAPP(c_Groups_Oabs__class_Oabs(_1050528), c_Groups_Oone__class_Oone(_1050528)) = c_Groups_Oone__class_Oone(_1050528))], (47062 ^ _774244) ^ [_1707441, _1707443] : [hBOOL(hAPP(c_List_Odistinct(_1707441), _1707443)), 47065 ^ _774244 : [(47066 ^ _774244) ^ [_1707573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707573), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707441)), _1707443))), 47069 ^ _774244 : [(47070 ^ _774244) ^ [_1707700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707700), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707441)), _1707443))), -(_1707573 = _1707700), hAPP(hAPP(c_List_Onth(_1707441), _1707443), _1707573) = hAPP(hAPP(c_List_Onth(_1707441), _1707443), _1707700)]]]]], (10031 ^ _774244) ^ [_939581] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _939581)))], (45012 ^ _774244) ^ [_1656329, _1656331, _1656333, _1656335] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656329, _1656329)), hAPP(hAPP(c_Product__Type_OPair(_1656329, _1656329), _1656331), _1656333)), c_Transitive__Closure_Otrancl(_1656329, _1656335))), 45016 ^ _774244 : [(45019 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1656329, _1656329)), hAPP(hAPP(c_Product__Type_OPair(_1656329, _1656329), 45015 ^ [_1656329, _1656331, _1656333, _1656335]), _1656333)), _1656335)))], (45017 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1656329, _1656329)), hAPP(hAPP(c_Product__Type_OPair(_1656329, _1656329), _1656331), 45015 ^ [_1656329, _1656331, _1656333, _1656335])), c_Transitive__Closure_Ortrancl(_1656329, _1656335))))]]], (36569 ^ _774244) ^ [_1450569, _1450571] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1450569), _1450571) = 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)), _1450569)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1450571))))], (36221 ^ _774244) ^ [_1442592, _1442594, _1442596] : [36223 ^ _774244 : [(36229 ^ _774244) ^ [] : [-(36222 ^ [_1442592, _1442594, _1442596] = 36225 ^ [_1442592, _1442594, _1442596])], (36227 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1442592), 36225 ^ [_1442592, _1442594, _1442596]), _1442596)))], (36224 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1442592), 36222 ^ [_1442592, _1442594, _1442596]), _1442594)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442592, tc_HOL_Obool)), _1442594), _1442596) = c_Orderings_Obot__class_Obot(tc_fun(_1442592, tc_HOL_Obool)))], (43498 ^ _774244) ^ [_1618146, _1618148, _1618150] : [-(hAPP(c_Relation_Oconverse(_1618146, _1618148), hAPP(c_Relation_Oconverse(_1618148, _1618146), _1618150)) = _1618150)], (45764 ^ _774244) ^ [] : [45766 ^ _774244 : [(45769 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), 45765 ^ []))], (45767 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 45765 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))]], -(c_Com_OWT__bodies)], (30811 ^ _774244) ^ [_1326841, _1326843, _1326845] : [-(hBOOL(hAPP(hAPP(c_member(_1326841), _1326843), hAPP(hAPP(c_Set_Oinsert(_1326841), _1326843), _1326845))))], (39392 ^ _774244) ^ [_1513140, _1513142, _1513144] : [hBOOL(hAPP(hAPP(c_member(_1513140), _1513142), c_Wellfounded_Oacc(_1513140, _1513144))), 39395 ^ _774244 : [(39396 ^ _774244) ^ [_1513254] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1513140, _1513140)), hAPP(hAPP(c_Product__Type_OPair(_1513140, _1513140), _1513254), _1513142)), _1513144)), -(hBOOL(hAPP(hAPP(c_member(_1513140), _1513254), c_Wellfounded_Oacc(_1513140, _1513144))))]]], (30679 ^ _774244) ^ [_1322106, _1322108, _1322110, _1322112, _1322114, _1322116, _1322118, _1322120] : [c_Finite__Set_Ofolding__image__simple(_1322106, _1322108, _1322110, _1322112, _1322114, _1322116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322108), _1322118)), -(hBOOL(hAPP(hAPP(c_member(_1322108), _1322120), _1322118))), -(hAPP(_1322116, hAPP(hAPP(c_Set_Oinsert(_1322108), _1322120), _1322118)) = hAPP(hAPP(_1322110, hAPP(_1322114, _1322120)), hAPP(_1322116, _1322118)))], (15488 ^ _774244) ^ [_1035480, _1035482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035480), _1035482)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035480), _1035482) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48534 ^ _774244) ^ [_1744476, _1744478, _1744480, _1744482] : [-(_1744476 = c_List_Olist_ONil(_1744478)), -(hAPP(c_List_Ohd(_1744480), hAPP(hAPP(c_List_Omap(_1744478, _1744480), _1744482), _1744476)) = hAPP(_1744482, hAPP(c_List_Ohd(_1744478), _1744476)))], (42177 ^ _774244) ^ [_1587805, _1587807] : [hBOOL(hAPP(_1587805, c_Hilbert__Choice_OEps(_1587807, _1587805))), -(hBOOL(hAPP(_1587805, 42180 ^ [_1587805, _1587807])))], (17819 ^ _774244) ^ [_1079256, _1079258, _1079260] : [17821 ^ _774244 : [(17824 ^ _774244) ^ [] : [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(_1079258, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 17820 ^ [_1079256, _1079258, _1079260]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1079258, 17820 ^ [_1079256, _1079258, _1079260])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (17822 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17820 ^ [_1079256, _1079258, _1079260]), _1079256)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1079258, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1079260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079260), hAPP(_1079258, _1079256))), 17834 ^ _774244 : [(17837 ^ _774244) ^ [] : [-(hAPP(_1079258, 17833 ^ [_1079256, _1079258, _1079260]) = _1079260)], (17835 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 17833 ^ [_1079256, _1079258, _1079260]), _1079256)))]]], (19113 ^ _774244) ^ [_1100428, _1100430] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1100428)), c_Int_OBit1(_1100430)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1100428), _1100430)))], (6614 ^ _774244) ^ [_880757, _880759] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _880757), _880759) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 6615 ^ _774244 : [(6622 ^ _774244) ^ [] : [_880757 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _880759 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6616 ^ _774244) ^ [] : [_880757 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _880759 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (17489 ^ _774244) ^ [_1073808, _1073810, _1073812] : [class_Rings_Olinordered__semidom(_1073808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073808), c_Groups_Ozero__class_Ozero(_1073808)), _1073810)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073808), _1073810), c_Groups_Oone__class_Oone(_1073808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073808), _1073810), hAPP(hAPP(c_Power_Opower__class_Opower(_1073808), _1073810), _1073812))), hAPP(hAPP(c_Power_Opower__class_Opower(_1073808), _1073810), _1073812))))], (22248 ^ _774244) ^ [_1157279, _1157281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157279)), hAPP(c_Nat_OSuc, _1157281))), -(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(_1157279))), 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)), _1157281)))))], (50569 ^ _774244) ^ [_1788832, _1788834, _1788836] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788832)), c_List_OtakeWhile(_1788832, _1788834, _1788836))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788832)), _1788836))))], (39222 ^ _774244) ^ [_1509100, _1509102, _1509104, _1509106] : [c_Map_Odom(_1509100, _1509102, _1509104) = hAPP(hAPP(c_Set_Oinsert(_1509100), _1509106), c_Orderings_Obot__class_Obot(tc_fun(_1509100, tc_HOL_Obool))), -(_1509104 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1509100, tc_Option_Ooption(_1509102)), hAPP(c_COMBK(tc_Option_Ooption(_1509102), _1509100), c_Option_Ooption_ONone(_1509102))), _1509106), hAPP(c_Option_Ooption_OSome(_1509102), 39225 ^ [_1509100, _1509102, _1509104, _1509106])))], (17863 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (6802 ^ _774244) ^ [_884436, _884438, _884440] : [class_Rings_Ocomm__semiring__1(_884436), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884436), _884438), _884440) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884436), _884440), _884438))], (41236 ^ _774244) ^ [_1563867, _1563869, _1563871, _1563873, _1563875, _1563877, _1563879] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1563867, _1563869, _1563871), _1563873), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1563875, tc_fun(tc_prod(_1563869, _1563871), tc_HOL_Obool)), _1563877), _1563879)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1563875, tc_fun(tc_prod(_1563867, _1563871), tc_HOL_Obool)), _1563877), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1563869, _1563871), tc_HOL_Obool), tc_fun(tc_prod(_1563867, _1563871), tc_HOL_Obool), _1563875), hAPP(c_Relation_Orel__comp(_1563867, _1563869, _1563871), _1563873)), _1563879)))], (48168 ^ _774244) ^ [_1734760, _1734762, _1734764, _1734766] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1734760), tc_List_Olist(_1734760))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1734760), tc_List_Olist(_1734760)), _1734762), _1734764)), c_List_Olistrel(_1734760, _1734766))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1734760), tc_List_Olist(_1734760))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1734760), tc_List_Olist(_1734760)), _1734762), _1734764)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1734760), c_List_Olistrel1(_1734760, _1734766)))))], (25781 ^ _774244) ^ [_1224147, _1224149, _1224151, _1224153, _1224155] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1224147, _1224149, tc_HOL_Obool, _1224151), _1224153), _1224155)), -(hBOOL(hAPP(_1224151, hAPP(hAPP(c_Product__Type_OPair(_1224147, _1224149), _1224153), _1224155))))], (50162 ^ _774244) ^ [_1778427, _1778429, _1778431] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1778427), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1778427))), _1778429))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1778431), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1778427))), _1778429))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1778427), _1778427), hAPP(hAPP(c_COMBC(tc_List_Olist(_1778427), tc_Nat_Onat, _1778427), c_List_Onth(_1778427)), _1778431)), hAPP(c_List_Ofilter(tc_List_Olist(_1778427), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1778427)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1778431)), c_Nat_Osize__class_Osize(tc_List_Olist(_1778427)))), c_List_Otranspose(_1778427, _1778429))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1778427)), _1778429), _1778431))], (19111 ^ _774244) ^ [_1100385, _1100387] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1100385)), c_Int_OBit0(_1100387)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1100385), _1100387)))], (6360 ^ _774244) ^ [_876615, _876617] : [-(_876615 = c_Option_Ooption_ONone(_876617)), -(_876615 = hAPP(c_Option_Ooption_OSome(_876617), 6363 ^ [_876615, _876617]))], (42142 ^ _774244) ^ [_1587167, _1587169] : [42144 ^ _774244 : [(42147 ^ _774244) ^ [] : [42143 ^ [_1587167, _1587169] = c_Orderings_Obot__class_Obot(tc_fun(_1587167, tc_HOL_Obool))], (42145 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1587167, tc_HOL_Obool)), 42143 ^ [_1587167, _1587169]), hAPP(c_Relation_OImage(_1587167, _1587167, _1587169), 42143 ^ [_1587167, _1587169]))))]], -(c_Wellfounded_Owf(_1587167, _1587169))], (42059 ^ _774244) ^ [_1585206] : [-(_1585206 = hAPP(c_Int_OAbs__Integ, 42057 ^ [_1585206]))], (36955 ^ _774244) ^ [_1459415, _1459417, _1459419, _1459421, _1459423] : [c_Finite__Set_Ofolding__one(_1459415, _1459417, _1459419), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459415), _1459421)), -(_1459421 = c_Orderings_Obot__class_Obot(tc_fun(_1459415, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459415), _1459423)), -(_1459423 = c_Orderings_Obot__class_Obot(tc_fun(_1459415, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459415, tc_HOL_Obool)), _1459421), _1459423) = c_Orderings_Obot__class_Obot(tc_fun(_1459415, tc_HOL_Obool)), -(hAPP(_1459419, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459415, tc_HOL_Obool)), _1459421), _1459423)) = hAPP(hAPP(_1459417, hAPP(_1459419, _1459421)), hAPP(_1459419, _1459423)))], (7874 ^ _774244) ^ [_902940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _902940)), -(_902940 = hAPP(c_Nat_OSuc, 7877 ^ [_902940]))], (8132 ^ _774244) ^ [_907379, _907381, _907383] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907379), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907381), _907383)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907381), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907379), _907383)))], (17903 ^ _774244) ^ [_1080595, _1080597] : [class_Int_Onumber__ring(_1080595), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080595), hAPP(c_Int_Onumber__class_Onumber__of(_1080595), c_Int_OMin)), _1080597) = hAPP(c_Groups_Ouminus__class_Ouminus(_1080595), _1080597))], (22116 ^ _774244) ^ [_1154419, _1154421] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1154419))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1154421)), hAPP(c_Int_Onat, _1154419)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1154421), _1154419)), 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)))], (29875 ^ _774244) ^ [_1306531] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1306531)), 29879 ^ _774244 : [(29880 ^ _774244) ^ [_1306611] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1306611), _1306531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1306611), 29878 ^ [_1306531])))]]], (16971 ^ _774244) ^ [_1064415, _1064417, _1064419] : [class_Rings_Olinordered__semidom(_1064415), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064415), c_Groups_Ozero__class_Ozero(_1064415)), _1064417)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064415), _1064417), c_Groups_Oone__class_Oone(_1064415))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064415), hAPP(hAPP(c_Power_Opower__class_Opower(_1064415), _1064417), hAPP(c_Nat_OSuc, _1064419))), c_Groups_Oone__class_Oone(_1064415))))], (39249 ^ _774244) ^ [_1509678, _1509680, _1509682, _1509684, _1509686] : [hAPP(_1509678, _1509680) = hAPP(c_Option_Ooption_OSome(_1509682), _1509684), -(hBOOL(hAPP(hAPP(c_member(_1509686), _1509680), c_Map_Odom(_1509686, _1509682, _1509678))))], (40888 ^ _774244) ^ [_1550177, _1550179, _1550181] : [c_Predicate_Oreflp(_1550177, _1550179), -(hBOOL(hAPP(hAPP(_1550179, _1550181), _1550181)))], (47842 ^ _774244) ^ [_1725916, _1725918, _1725920, _1725922] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1725916), tc_List_Olist(_1725916))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1725916), tc_List_Olist(_1725916)), _1725918), _1725920)), c_List_Olexord(_1725916, _1725922))), 47847 ^ _774244 : [(47850 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1725916), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725916)), _1725918)), _1725920) = _1725918)], (47848 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725916)), _1725918)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725916)), _1725920))))]], 47852 ^ _774244 : [(47857 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1725916, _1725916)), hAPP(hAPP(c_Product__Type_OPair(_1725916, _1725916), hAPP(hAPP(c_List_Onth(_1725916), _1725918), 47851 ^ [_1725916, _1725918, _1725920, _1725922])), hAPP(hAPP(c_List_Onth(_1725916), _1725920), 47851 ^ [_1725916, _1725918, _1725920, _1725922]))), _1725922)))], (47855 ^ _774244) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1725916), 47851 ^ [_1725916, _1725918, _1725920, _1725922]), _1725918) = hAPP(hAPP(c_List_Otake(_1725916), 47851 ^ [_1725916, _1725918, _1725920, _1725922]), _1725920))], (47853 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47851 ^ [_1725916, _1725918, _1725920, _1725922]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725916)), _1725918)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725916)), _1725920)))))]]], (36179 ^ _774244) ^ [_1441308, _1441310, _1441312, _1441314] : [class_Lattices_Odistrib__lattice(_1441308), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441308), _1441310), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441308), _1441312), _1441314)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441308), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441308), _1441310), _1441312)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441308), _1441310), _1441314)))], (24575 ^ _774244) ^ [_1202128, _1202130, _1202132, _1202134, _1202136, _1202138, _1202140] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1202128, _1202130, _1202132, _1202134), _1202136), _1202138), _1202140) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1202130, _1202132, _1202134), _1202138), hAPP(_1202136, _1202140)))], (44269 ^ _774244) ^ [_1638401, _1638403, _1638405] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638401, _1638401)), hAPP(hAPP(c_Product__Type_OPair(_1638401, _1638401), _1638403), _1638403)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638401, _1638401), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1638405))))], (6233 ^ _774244) ^ [_874263, _874265, _874267] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_874263, _874265, _874267))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OBODY(_874265))))], (2442 ^ _774244) ^ [_811149, _811151] : [_811151 = _811149, -(c_Divides_Oadjust(_811151) = c_Divides_Oadjust(_811149))], (25655 ^ _774244) ^ [_1221871, _1221873, _1221875] : [class_Divides_Oring__div(_1221871), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221871), _1221873), _1221875)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1221871), _1221875), hAPP(c_Groups_Ouminus__class_Ouminus(_1221871), _1221873)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1221871), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1221871), _1221875), _1221873)))], (34355 ^ _774244) ^ [_1399596, _1399598, _1399600, _1399602, _1399604] : [class_Fields_Ofield(_1399596), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399598), _1399600)), -(hAPP(_1399602, _1399604) = c_Groups_Ozero__class_Ozero(_1399596)), 34366 ^ _774244 : [(34373 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399598), _1399604), _1399600))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399598, _1399596), _1399602), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399598, tc_HOL_Obool)), _1399600), hAPP(hAPP(c_Set_Oinsert(_1399598), _1399604), c_Orderings_Obot__class_Obot(tc_fun(_1399598, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399598, _1399596), _1399602), _1399600))], (34367 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1399598), _1399604), _1399600)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399598, _1399596), _1399602), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399598, tc_HOL_Obool)), _1399600), hAPP(hAPP(c_Set_Oinsert(_1399598), _1399604), c_Orderings_Obot__class_Obot(tc_fun(_1399598, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1399596), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399598, _1399596), _1399602), _1399600)), hAPP(_1399602, _1399604)))]]], (4640 ^ _774244) ^ [_845950, _845952] : [_845952 = _845950, -(c_Set_Oinsert(_845952) = c_Set_Oinsert(_845950))], (6005 ^ _774244) ^ [_870403, _870405, _870407, _870409, _870411, _870413] : [-(c_Com_Ocom_OCond(_870403, _870405, _870407) = c_Com_Ocom_OCond(_870409, _870411, _870413)), _870403 = _870409, _870405 = _870411, _870407 = _870413], (12129 ^ _774244) ^ [_975035] : [-(hAPP(c_Nat_OSuc, _975035) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _975035), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47265 ^ _774244) ^ [_1712673, _1712675, _1712677] : [-(hAPP(hAPP(c_List_Olist__update(_1712673, _1712675), _1712677), hAPP(hAPP(c_List_Onth(_1712673), _1712675), _1712677)) = _1712675)], (38225 ^ _774244) ^ [_1486896, _1486898, _1486900, _1486902] : [c_Fun_Oinj__on(_1486896, _1486898, _1486900, c_Orderings_Otop__class_Otop(tc_fun(_1486896, tc_HOL_Obool))), 38228 ^ _774244 : [(38242 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486898), _1486902), hAPP(c_Set_Oimage(_1486896, _1486898, _1486900), c_Orderings_Otop__class_Otop(tc_fun(_1486896, tc_HOL_Obool)))))), 38243 ^ _774244 : [(38244 ^ _774244) ^ [_1487299] : [_1486902 = hAPP(_1486900, _1487299), 38248 ^ _774244 : [(38251 ^ _774244) ^ [] : [38247 ^ [_1486896, _1486898, _1486900, _1486902, _1487299] = _1487299], (38249 ^ _774244) ^ [] : [-(_1486902 = hAPP(_1486900, 38247 ^ [_1486896, _1486898, _1486900, _1486902, _1487299]))]]]]], (38229 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1486898), _1486902), hAPP(c_Set_Oimage(_1486896, _1486898, _1486900), c_Orderings_Otop__class_Otop(tc_fun(_1486896, tc_HOL_Obool))))), 38233 ^ _774244 : [(38236 ^ _774244) ^ [_1487161] : [_1486902 = hAPP(_1486900, _1487161), -(_1487161 = 38232 ^ [_1486896, _1486898, _1486900, _1486902])], (38234 ^ _774244) ^ [] : [-(_1486902 = hAPP(_1486900, 38232 ^ [_1486896, _1486898, _1486900, _1486902]))]]]]], (6842 ^ _774244) ^ [_885075, _885077, _885079, _885081, _885083, _885085] : [hBOOL(hAPP(_885075, _885077)), c_Natural_Oevaln(_885079, _885077, _885081, _885083), c_Natural_Oevaln(c_Com_Ocom_OWhile(_885075, _885079), _885083, _885081, _885085), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_885075, _885079), _885077, _885081, _885085))], (51367 ^ _774244) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (47327 ^ _774244) ^ [_1714045, _1714047, _1714049, _1714051, _1714053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1714045, tc_HOL_Obool)), hAPP(c_List_Oset(_1714045), _1714047)), _1714049)), hBOOL(hAPP(hAPP(c_member(_1714045), _1714051), _1714049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1714045, tc_HOL_Obool)), hAPP(c_List_Oset(_1714045), hAPP(hAPP(c_List_Olist__update(_1714045, _1714047), _1714053), _1714051))), _1714049)))], (40655 ^ _774244) ^ [_1542598, _1542600, _1542602, _1542604] : [-(hAPP(c_Set_OCollect(tc_prod(_1542598, _1542600)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542598, _1542600, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1542598, tc_fun(_1542600, tc_HOL_Obool), tc_fun(_1542600, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1542600, tc_HOL_Obool), tc_fun(_1542600, tc_HOL_Obool)), _1542598), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1542600)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542598), c_fconj), _1542602))), _1542604))) = hAPP(hAPP(c_Product__Type_OSigma(_1542598, _1542600), hAPP(c_Set_OCollect(_1542598), _1542602)), hAPP(c_COMBK(tc_fun(_1542600, tc_HOL_Obool), _1542598), hAPP(c_Set_OCollect(_1542600), _1542604))))], (40741 ^ _774244) ^ [_1544969, _1544971] : [-(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), _1544969)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1544971))))))], (8786 ^ _774244) ^ [_917739, _917741, _917743, _917745] : [class_Rings_Ocomm__semiring__1(_917739), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917739), _917741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917739), _917743), _917745)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917739), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917739), _917741), _917743)), _917745))], (40846 ^ _774244) ^ [_1548872, _1548874] : [-(c_Fun_Oinj__on(tc_fun(_1548872, _1548874), tc_fun(tc_prod(_1548872, _1548874), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1548872, _1548874), tc_HOL_Obool), tc_fun(tc_prod(_1548872, _1548874), tc_HOL_Obool), tc_fun(_1548872, _1548874)), c_Set_OCollect(tc_prod(_1548872, _1548874))), hAPP(hAPP(c_COMBB(tc_fun(_1548872, tc_fun(_1548874, tc_HOL_Obool)), tc_fun(tc_prod(_1548872, _1548874), tc_HOL_Obool), tc_fun(_1548872, _1548874)), c_Product__Type_Oprod_Oprod__case(_1548872, _1548874, tc_HOL_Obool)), hAPP(c_COMBB(_1548874, tc_fun(_1548874, tc_HOL_Obool), _1548872), hAPP(c_COMBC(_1548874, _1548874, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1548872, _1548874), tc_HOL_Obool))))], (5672 ^ _774244) ^ [_864640, _864642] : [hAPP(c_Nat_OSuc, _864640) = hAPP(c_Nat_OSuc, _864642), -(_864640 = _864642)], (39634 ^ _774244) ^ [_1519628, _1519630, _1519632, _1519634, _1519636] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519628, _1519630), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1519628, tc_HOL_Obool)), _1519632), _1519634)), hAPP(c_COMBK(tc_fun(_1519630, tc_HOL_Obool), _1519628), _1519636)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1519628, _1519630), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519628, _1519630), _1519632), hAPP(c_COMBK(tc_fun(_1519630, tc_HOL_Obool), _1519628), _1519636))), hAPP(hAPP(c_Product__Type_OSigma(_1519628, _1519630), _1519634), hAPP(c_COMBK(tc_fun(_1519630, tc_HOL_Obool), _1519628), _1519636))))], (27404 ^ _774244) ^ [_1257427, _1257429, _1257431] : [-(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)), _1257427)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1257429, _1257431)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1257429), _1257427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1257431), _1257427)))], (26333 ^ _774244) ^ [_1234315, _1234317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234315)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234317)), 26340 ^ _774244 : [(26347 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234315), _1234317)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1234315)), hAPP(c_Int_Onat, _1234317))))], (26341 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1234315)), hAPP(c_Int_Onat, _1234317))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234315), _1234317)))]]], (15146 ^ _774244) ^ [_1028924, _1028926, _1028928, _1028930] : [class_Divides_Oring__div(_1028924), -(c_Divides_Odiv__class_Omod(_1028924, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1028924), _1028926), _1028928), _1028930) = c_Divides_Odiv__class_Omod(_1028924, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1028924), c_Divides_Odiv__class_Omod(_1028924, _1028926, _1028930)), _1028928), _1028930))], (40757 ^ _774244) ^ [_1545704, _1545706, _1545708, _1545710, _1545712, _1545714] : [-(hAPP(c_Set_Oimage(_1545704, _1545706, hAPP(hAPP(c_COMBS(_1545704, _1545706, _1545706), hAPP(hAPP(c_COMBS(_1545704, _1545706, tc_fun(_1545706, _1545706)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1545706, tc_fun(_1545706, _1545706)), _1545704), c_If(_1545706)), _1545708)), _1545710)), _1545712)), _1545714) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1545706, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1545704, _1545706, _1545710), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545704, tc_HOL_Obool)), _1545714), hAPP(c_Set_OCollect(_1545704), _1545708)))), hAPP(c_Set_Oimage(_1545704, _1545706, _1545712), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545704, tc_HOL_Obool)), _1545714), hAPP(c_Set_OCollect(_1545704), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1545704), c_fNot), _1545708))))))], (51387 ^ _774244) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (45468 ^ _774244) ^ [_1666862, _1666864, _1666866, _1666868, _1666870, _1666872] : [-(c_Map_Omap__comp(_1666862, _1666864, _1666866, _1666868, _1666870, _1666872) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1666864), _1666862, c_Option_Ooption_ONone(_1666864), _1666868), hAPP(_1666870, _1666872)))], (614 ^ _774244) ^ [_783797, _783799, _783801, _783803] : [-(c_Wellfounded_OwfP(_783801, _783797)), c_Wellfounded_OwfP(_783803, _783799), _783803 = _783801, _783799 = _783797], (50705 ^ _774244) ^ [_1791327] : [-(c_List_Oremdups(_1791327, c_List_Olist_ONil(_1791327)) = c_List_Olist_ONil(_1791327))], (6508 ^ _774244) ^ [_879160, _879162] : [class_Groups_Olinordered__ab__group__add(_879160), 6511 ^ _774244 : [(6518 ^ _774244) ^ [] : [_879162 = c_Groups_Ozero__class_Ozero(_879160), -(c_Groups_Ozero__class_Ozero(_879160) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879160), _879162), _879162))], (6512 ^ _774244) ^ [] : [c_Groups_Ozero__class_Ozero(_879160) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879160), _879162), _879162), -(_879162 = c_Groups_Ozero__class_Ozero(_879160))]]], (45431 ^ _774244) ^ [_1665800, _1665802, _1665804, _1665806] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1665800), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1665802), _1665804)))), -(hBOOL(hAPP(hAPP(hAPP(_1665806, _1665800), _1665802), _1665804))), 45439 ^ _774244 : [(45442 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 45437 ^ [_1665800, _1665802, _1665804, _1665806]), 45438 ^ [_1665800, _1665802, _1665804, _1665806]))), hAPP(45436 ^ [_1665800, _1665802, _1665804, _1665806], 45438 ^ [_1665800, _1665802, _1665804, _1665806]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1665806, 45436 ^ [_1665800, _1665802, _1665804, _1665806]), 45437 ^ [_1665800, _1665802, _1665804, _1665806]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 45438 ^ [_1665800, _1665802, _1665804, _1665806]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (45452 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1665806, 45436 ^ [_1665800, _1665802, _1665804, _1665806]), 45437 ^ [_1665800, _1665802, _1665804, _1665806]), 45438 ^ [_1665800, _1665802, _1665804, _1665806]))], (45440 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), 45436 ^ [_1665800, _1665802, _1665804, _1665806]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 45437 ^ [_1665800, _1665802, _1665804, _1665806]), 45438 ^ [_1665800, _1665802, _1665804, _1665806])))))]]], (15974 ^ _774244) ^ [_1045683, _1045685, _1045687, _1045689, _1045691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045683), _1045685)), 15977 ^ _774244 : [(15984 ^ _774244) ^ [] : [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), _1045685), _1045683)), _1045687)), _1045689)), _1045691)), -(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), _1045685), _1045687)), _1045689)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045683), _1045687)), _1045691))))], (15978 ^ _774244) ^ [] : [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), _1045685), _1045687)), _1045689)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045683), _1045687)), _1045691))), -(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), _1045685), _1045683)), _1045687)), _1045689)), _1045691)))]]], (41055 ^ _774244) ^ [_1556787, _1556789, _1556791] : [class_Orderings_Olinorder(_1556787), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556787), _1556789)), -(_1556789 = c_Orderings_Obot__class_Obot(tc_fun(_1556787, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556787), _1556791)), -(_1556791 = c_Orderings_Obot__class_Obot(tc_fun(_1556787, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1556787), c_Big__Operators_Olattice_OSup__fin(_1556787, c_Orderings_Oord__class_Omax(_1556787), _1556789)), c_Big__Operators_Olattice_OSup__fin(_1556787, c_Orderings_Oord__class_Omax(_1556787), _1556791)) = c_Big__Operators_Olattice_OSup__fin(_1556787, c_Orderings_Oord__class_Omax(_1556787), hAPP(c_Set_OCollect(_1556787), hAPP(hAPP(c_COMBB(tc_fun(_1556787, tc_HOL_Obool), tc_HOL_Obool, _1556787), c_HOL_OEx(_1556787)), hAPP(hAPP(c_COMBB(tc_fun(_1556787, tc_fun(_1556787, tc_HOL_Obool)), tc_fun(_1556787, tc_HOL_Obool), _1556787), hAPP(c_COMBB(tc_fun(_1556787, tc_HOL_Obool), tc_HOL_Obool, _1556787), c_HOL_OEx(_1556787))), hAPP(hAPP(c_COMBC(_1556787, tc_fun(_1556787, tc_fun(_1556787, tc_HOL_Obool)), tc_fun(_1556787, tc_fun(_1556787, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1556787, tc_fun(tc_fun(_1556787, tc_HOL_Obool), tc_fun(_1556787, tc_HOL_Obool))), tc_fun(tc_fun(_1556787, tc_fun(_1556787, tc_HOL_Obool)), tc_fun(_1556787, tc_fun(_1556787, tc_HOL_Obool))), _1556787), c_COMBS(_1556787, tc_fun(_1556787, tc_HOL_Obool), tc_fun(_1556787, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1556787, tc_fun(_1556787, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1556787, tc_fun(tc_fun(_1556787, tc_HOL_Obool), tc_fun(_1556787, tc_HOL_Obool))), _1556787), hAPP(c_COMBB(tc_fun(_1556787, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1556787, tc_HOL_Obool), tc_fun(_1556787, tc_HOL_Obool)), _1556787), c_COMBS(_1556787, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1556787, tc_fun(_1556787, tc_HOL_Obool)), tc_fun(_1556787, tc_fun(_1556787, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1556787), hAPP(c_COMBB(tc_fun(_1556787, tc_HOL_Obool), tc_fun(_1556787, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1556787), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1556787), c_fconj))), hAPP(hAPP(c_COMBC(_1556787, tc_fun(_1556787, tc_fun(_1556787, _1556787)), tc_fun(_1556787, tc_fun(_1556787, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1556787, _1556787), tc_fun(_1556787, tc_HOL_Obool)), tc_fun(tc_fun(_1556787, tc_fun(_1556787, _1556787)), tc_fun(_1556787, tc_fun(_1556787, tc_HOL_Obool))), _1556787), c_COMBB(tc_fun(_1556787, _1556787), tc_fun(_1556787, tc_HOL_Obool), _1556787)), hAPP(hAPP(c_COMBB(tc_fun(_1556787, tc_HOL_Obool), tc_fun(tc_fun(_1556787, _1556787), tc_fun(_1556787, tc_HOL_Obool)), _1556787), c_COMBB(_1556787, tc_HOL_Obool, _1556787)), c_fequal))), c_Orderings_Oord__class_Omin(_1556787)))))), hAPP(hAPP(c_COMBC(_1556787, tc_fun(_1556787, tc_HOL_Obool), tc_fun(_1556787, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1556787, tc_HOL_Obool), tc_fun(_1556787, tc_HOL_Obool)), _1556787), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1556787)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1556787), c_fconj), hAPP(hAPP(c_COMBC(_1556787, tc_fun(_1556787, tc_HOL_Obool), tc_HOL_Obool), c_member(_1556787)), _1556789)))), hAPP(hAPP(c_COMBC(_1556787, tc_fun(_1556787, tc_HOL_Obool), tc_HOL_Obool), c_member(_1556787)), _1556791))))))))], (29272 ^ _774244) ^ [_1295219] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1295219, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1295219, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1295219, tc_HOL_Obool)))], (46547 ^ _774244) ^ [_1694821, _1694823, _1694825, _1694827, _1694829, _1694831] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694821), tc_List_Olist(_1694821))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694821), tc_List_Olist(_1694821)), hAPP(hAPP(c_List_Olist_OCons(_1694821), _1694823), _1694825)), hAPP(hAPP(c_List_Olist_OCons(_1694821), _1694827), _1694829))), c_List_Olex(_1694821, _1694831)))), 46548 ^ _774244 : [(46555 ^ _774244) ^ [] : [_1694823 = _1694827, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694821), tc_List_Olist(_1694821))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694821), tc_List_Olist(_1694821)), _1694825), _1694829)), c_List_Olex(_1694821, _1694831)))], (46549 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1694821, _1694821)), hAPP(hAPP(c_Product__Type_OPair(_1694821, _1694821), _1694823), _1694827)), _1694831)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694821)), _1694825) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694821)), _1694829)]]], (38822 ^ _774244) ^ [_1499965, _1499967, _1499969] : [-(hAPP(c_Set_Ovimage(_1499965, _1499967, _1499969), c_Orderings_Obot__class_Obot(tc_fun(_1499967, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1499965, tc_HOL_Obool)))], (13549 ^ _774244) ^ [_1000064, _1000066, _1000068, _1000070] : [class_Divides_Osemiring__div(_1000064), -(c_Divides_Odiv__class_Omod(_1000064, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000064), _1000066), _1000068), _1000070) = c_Divides_Odiv__class_Omod(_1000064, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000064), _1000066), c_Divides_Odiv__class_Omod(_1000064, _1000068, _1000070)), _1000070))], (48956 ^ _774244) ^ [_1753440, _1753442] : [-(c_List_Olists(_1753440, _1753442) = hAPP(c_Set_OCollect(tc_List_Olist(_1753440)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1753440), tc_fun(_1753440, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1753440, tc_HOL_Obool), tc_fun(tc_fun(_1753440, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1753440)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1753440, tc_HOL_Obool))), c_List_Oset(_1753440))), _1753442)))], (14716 ^ _774244) ^ [_1020918, _1020920, _1020922, _1020924] : [class_Divides_Osemiring__div(_1020918), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020918), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020918), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020918), _1020920), _1020922)), _1020922)), c_Divides_Odiv__class_Omod(_1020918, _1020920, _1020922))), _1020924) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020918), _1020920), _1020924))], (36457 ^ _774244) ^ [_1447925, _1447927] : [class_Lattices_Oboolean__algebra(_1447925), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1447925), hAPP(c_Groups_Ouminus__class_Ouminus(_1447925), _1447927)), _1447927) = c_Orderings_Obot__class_Obot(_1447925))], (5933 ^ _774244) ^ [_869185, _869187, _869189, _869191, _869193, _869195] : [-(hBOOL(hAPP(_869185, _869187))), c_Natural_Oevaln(_869189, _869187, _869191, _869193), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_869185, _869195, _869189), _869187, _869191, _869193))], (21891 ^ _774244) ^ [_1150595, _1150597] : [21892 ^ _774244 : [(21895 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1150597), _1150595))], (21893 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1150595), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1150595, _1150597) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (31345 ^ _774244) ^ [_1337411, _1337413, _1337415, _1337417, _1337419] : [-(hBOOL(hAPP(hAPP(c_member(_1337411), _1337413), c_SetInterval_Oord_OgreaterThanLessThan(_1337411, _1337415, _1337417, _1337419)))), hBOOL(hAPP(hAPP(_1337415, _1337417), _1337413)), hBOOL(hAPP(hAPP(_1337415, _1337413), _1337419))], (51235 ^ _774244) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (15172 ^ _774244) ^ [_1029405] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1029405) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27336 ^ _774244) ^ [_1256015, _1256017, _1256019, _1256021] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1256015, tc_Nat_Onat), _1256017), _1256019) = hAPP(c_Nat_OSuc, _1256021), 27340 ^ _774244 : [(27343 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1256017, 27339 ^ [_1256015, _1256017, _1256019, _1256021]))))], (27341 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1256015), 27339 ^ [_1256015, _1256017, _1256019, _1256021]), _1256019)))]]], (41134 ^ _774244) ^ [_1561153, _1561155] : [-(hAPP(c_Fun_Oid(_1561153), _1561155) = _1561155)], (22254 ^ _774244) ^ [_1157406, _1157408] : [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(_1157406))), 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)), _1157408)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157406)), hAPP(c_Nat_OSuc, _1157408))))], (9190 ^ _774244) ^ [_924845, _924847, _924849, _924851, _924853] : [class_Rings_Osemiring(_924845), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924845), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924845), _924847), _924849)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924845), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924845), _924851), _924849)), _924853)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924845), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924845), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924845), _924847), _924851)), _924849)), _924853))], (8162 ^ _774244) ^ [_907822, _907824, _907826] : [class_Orderings_Olinorder(_907822), 8165 ^ _774244 : [(8166 ^ _774244) ^ [] : [-(_907824 = _907826), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907822), _907824), _907826))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907822), _907826), _907824)))], (8176 ^ _774244) ^ [] : [8177 ^ _774244 : [(8180 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907822), _907826), _907824))], (8178 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907822), _907824), _907826))]], _907824 = _907826]]], (33820 ^ _774244) ^ [_1388447, _1388449, _1388451, _1388453, _1388455] : [hAPP(_1388451, _1388453) = _1388455, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388447, _1388449), _1388451), _1388453), _1388455) = _1388451)], (28228 ^ _774244) ^ [_1273214] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1273214) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1273214))], (38359 ^ _774244) ^ [_1489659, _1489661, _1489663, _1489665] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1489659), _1489661)), hAPP(c_Finite__Set_Ocard(_1489663), hAPP(c_Set_Oimage(_1489659, _1489663, _1489665), _1489661)) = hAPP(c_Finite__Set_Ocard(_1489659), _1489661), -(c_Fun_Oinj__on(_1489659, _1489663, _1489665, _1489661))], (37929 ^ _774244) ^ [_1481326] : [-(c_Equiv__Relations_Oequivp(_1481326, c_fequal))], (1932 ^ _774244) ^ [_802384, _802386, _802388, _802390, _802392, _802394] : [-(c_Com_Ocom_OCond(_802394, _802390, _802386) = c_Com_Ocom_OCond(_802392, _802388, _802384)), _802394 = _802392, _802390 = _802388, _802386 = _802384], (24335 ^ _774244) ^ [_1197070, _1197072, _1197074, _1197076] : [class_Orderings_Olinorder(_1197070), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197070), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197070), _1197072), _1197074)), _1197076) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197070), _1197072), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197070), _1197074), _1197076)))], (46886 ^ _774244) ^ [_1703232, _1703234] : [_1703234 = c_List_Olist_ONil(_1703232), -(c_Orderings_Obot__class_Obot(tc_fun(_1703232, tc_HOL_Obool)) = hAPP(c_List_Oset(_1703232), _1703234))], (35388 ^ _774244) ^ [_1424231, _1424233, _1424235, _1424237, _1424239, _1424241, _1424243, _1424245] : [c_Finite__Set_Ofolding(_1424231, _1424233, _1424235, _1424237), -(hAPP(c_Fun_Ocomp(_1424233, _1424233, _1424239, hAPP(_1424235, _1424241)), hAPP(c_Fun_Ocomp(_1424233, _1424233, _1424239, hAPP(_1424235, _1424243)), _1424245)) = hAPP(c_Fun_Ocomp(_1424233, _1424233, _1424239, hAPP(_1424235, _1424243)), hAPP(c_Fun_Ocomp(_1424233, _1424233, _1424239, hAPP(_1424235, _1424241)), _1424245)))], (51483 ^ _774244) ^ [_1802001, _1802003] : [hBOOL(_1802001), -(hBOOL(hAPP(hAPP(c_fdisj, _1802001), _1802003)))], (18573 ^ _774244) ^ [_1091211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091211), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1091211)), c_Int_OPls)))], (44706 ^ _774244) ^ [_1648689, _1648691, _1648693] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648689, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1648689, tc_HOL_Obool), _1648691)), _1648693) = c_Orderings_Obot__class_Obot(tc_fun(_1648689, tc_HOL_Obool)), 44709 ^ _774244 : [(44710 ^ _774244) ^ [_1648824] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1648689, tc_HOL_Obool)), _1648824), _1648691)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648689, tc_HOL_Obool)), _1648824), _1648693) = c_Orderings_Obot__class_Obot(tc_fun(_1648689, tc_HOL_Obool)))]]], (26510 ^ _774244) ^ [_1238544, _1238546, _1238548, _1238550] : [class_Groups_Oab__group__add(_1238544), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238546, _1238544), hAPP(hAPP(c_COMBB(_1238544, _1238544, _1238546), c_Groups_Ouminus__class_Ouminus(_1238544)), _1238548)), _1238550) = hAPP(c_Groups_Ouminus__class_Ouminus(_1238544), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238546, _1238544), _1238548), _1238550)))], (15230 ^ _774244) ^ [_1030421, _1030423, _1030425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030421), _1030423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030421), _1030425)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030423), _1030425))))], (10996 ^ _774244) ^ [_955020, _955022, _955024] : [class_Groups_Oordered__ab__group__add(_955020), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955020), _955022), _955024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955020), hAPP(c_Groups_Ouminus__class_Ouminus(_955020), _955024)), hAPP(c_Groups_Ouminus__class_Ouminus(_955020), _955022))))], (24685 ^ _774244) ^ [_1204373, _1204375, _1204377] : [c_Nitpick_Oless__eq__frac(_1204373, _1204375, _1204377), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1204373), c_Nitpick_Oplus__frac(_1204373, _1204375, c_Nitpick_Ouminus__frac(_1204373, _1204377)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29744 ^ _774244) ^ [_1304028] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304028))))], (38896 ^ _774244) ^ [_1501691, _1501693, _1501695, _1501697, _1501699] : [-(hAPP(c_Set_Ovimage(_1501691, _1501693, _1501695), hAPP(hAPP(c_Set_Oinsert(_1501693), _1501697), _1501699)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1501691, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1501691, _1501693, _1501695), hAPP(hAPP(c_Set_Oinsert(_1501693), _1501697), c_Orderings_Obot__class_Obot(tc_fun(_1501693, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1501691, _1501693, _1501695), _1501699)))], (18363 ^ _774244) ^ [_1087591] : [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), _1087591))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1087591)))], (39330 ^ _774244) ^ [_1511668, _1511670, _1511672] : [hBOOL(hAPP(hAPP(c_member(_1511668), _1511672), c_Wellfounded_Oacc(_1511668, _1511670))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1511668, hAPP(hAPP(c_COMBC(_1511668, tc_fun(tc_prod(_1511668, _1511668), tc_HOL_Obool), tc_fun(_1511668, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511668, tc_fun(tc_fun(tc_prod(_1511668, _1511668), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511668, _1511668), tc_HOL_Obool), tc_fun(_1511668, tc_HOL_Obool)), _1511668), c_COMBC(_1511668, tc_fun(tc_prod(_1511668, _1511668), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511668, tc_prod(_1511668, _1511668)), tc_fun(_1511668, tc_fun(tc_fun(tc_prod(_1511668, _1511668), tc_HOL_Obool), tc_HOL_Obool)), _1511668), hAPP(c_COMBB(tc_prod(_1511668, _1511668), tc_fun(tc_fun(tc_prod(_1511668, _1511668), tc_HOL_Obool), tc_HOL_Obool), _1511668), c_member(tc_prod(_1511668, _1511668)))), c_Product__Type_OPair(_1511668, _1511668)))), _1511670)), _1511672)))], (48783 ^ _774244) ^ [_1749206, _1749208] : [class_Complete__Lattice_Ocomplete__lattice(_1749206), -(c_Complete__Lattice_OInf__class_OInf(_1749206, hAPP(c_List_Oset(_1749206), _1749208)) = hAPP(c_List_Ofoldl(_1749206, _1749206, c_Lattices_Osemilattice__inf__class_Oinf(_1749206), c_Orderings_Otop__class_Otop(_1749206)), _1749208))], (35973 ^ _774244) ^ [_1437209, _1437211, _1437213, _1437215] : [class_Lattices_Osemilattice__inf(_1437209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437209), _1437211), _1437213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437209), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1437209), _1437211), _1437215)), _1437213)))], (50803 ^ _774244) ^ [_1793416, _1793418, _1793420] : [class_Orderings_Olinorder(_1793416), c_List_Olinorder__class_Osorted(_1793416, _1793418), -(c_List_Olinorder__class_Osorted(_1793416, c_List_OdropWhile(_1793416, _1793420, _1793418)))], (30539 ^ _774244) ^ [_1319341, _1319343, _1319345, _1319347] : [_1319341 = _1319343, 30544 ^ _774244 : [(30547 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1319345), _1319347), _1319343)))], (30545 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1319345), _1319347), _1319341)))]], 30548 ^ _774244 : [(30551 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1319345), _1319347), _1319343))], (30549 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1319345), _1319347), _1319341))]]], (12458 ^ _774244) ^ [_980747, _980749, _980751, _980753, _980755] : [class_Rings_Olinordered__semiring__strict(_980747), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980747), _980749), _980751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980747), _980753), _980755)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980747), c_Groups_Ozero__class_Ozero(_980747)), _980749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980747), c_Groups_Ozero__class_Ozero(_980747)), _980753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980747), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980747), _980749), _980753)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980747), _980751), _980755))))], (36277 ^ _774244) ^ [_1443746, _1443748, _1443750, _1443752] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443746, tc_HOL_Obool)), _1443748), _1443750), _1443752)), -(hBOOL(hAPP(_1443748, _1443752)))], (28120 ^ _774244) ^ [_1270895, _1270897, _1270899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270895, tc_HOL_Obool)), _1270897), _1270899)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270895, tc_HOL_Obool)), _1270899), _1270897) = _1270899)], (42984 ^ _774244) ^ [_1604834, _1604836, _1604838, _1604840, _1604842] : [c_Finite__Set_Ofun__left__comm(_1604834, _1604836, _1604838), hBOOL(hAPP(c_Finite__Set_Ofinite(_1604834), _1604840)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1604834, _1604836, _1604838, _1604842, _1604840), hAPP(hAPP(c_Finite__Set_Ofold(_1604834, _1604836, _1604838), _1604842), _1604840))))], (5314 ^ _774244) ^ [_856395, _856397] : [_856397 = _856395, -(c_List_Odrop(_856397) = c_List_Odrop(_856395))], (24369 ^ _774244) ^ [_1197824, _1197826, _1197828, _1197830] : [class_Orderings_Olinorder(_1197824), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197824), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197824), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197824), _1197826), _1197828)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197824), _1197826), _1197830))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197824), _1197826), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197824), _1197828), _1197830)))))], (42618 ^ _774244) ^ [_1597266, _1597268, _1597270] : [class_Lattices_Oab__semigroup__idem__mult(_1597266), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597266), _1597268)), -(hAPP(c_Finite__Set_Ofold1(_1597266, c_Groups_Otimes__class_Otimes(_1597266)), hAPP(hAPP(c_Set_Oinsert(_1597266), _1597270), _1597268)) = hAPP(hAPP(c_Finite__Set_Ofold(_1597266, _1597266, c_Groups_Otimes__class_Otimes(_1597266)), _1597270), _1597268))], (18865 ^ _774244) ^ [_1096020, _1096022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096020)), -(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)))), _1096022))), 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)))), _1096020)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1096022), _1096020))], (49964 ^ _774244) ^ [_1774040, _1774042] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1774040, _1774042) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1774040, hAPP(c_Nat_OSuc, _1774042))))], (14362 ^ _774244) ^ [_1014808, _1014810, _1014812, _1014814] : [class_Divides_Osemiring__div(_1014808), -(_1014810 = c_Groups_Ozero__class_Ozero(_1014808)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1014808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014808), _1014810), _1014812)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014808), _1014810), _1014814)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1014808), _1014812), _1014814))], (49196 ^ _774244) ^ [_1758414] : [-(c_List_Obutlast(_1758414, c_List_Olist_ONil(_1758414)) = c_List_Olist_ONil(_1758414))], (35213 ^ _774244) ^ [_1419513, _1419515, _1419517, _1419519, _1419521, _1419523, _1419525] : [-(hAPP(c_Product__Type_Oapfst(_1419513, _1419515, _1419517, _1419519), hAPP(c_Product__Type_Oapfst(_1419521, _1419513, _1419517, _1419523), _1419525)) = hAPP(c_Product__Type_Oapfst(_1419521, _1419515, _1419517, hAPP(c_Fun_Ocomp(_1419513, _1419515, _1419521, _1419519), _1419523)), _1419525))], (28677 ^ _774244) ^ [_1282987, _1282989, _1282991, _1282993, _1282995, _1282997] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1282987, tc_fun(_1282989, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1282991, _1282987, _1282993), _1282995)), _1282997) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1282991, tc_fun(_1282989, tc_HOL_Obool)), _1282995), hAPP(hAPP(c_COMBB(_1282987, tc_fun(_1282989, tc_HOL_Obool), _1282991), _1282997), _1282993)))], (23375 ^ _774244) ^ [_1179004, _1179006, _1179008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179004, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1179004, tc_HOL_Obool)), _1179006)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1179004, tc_HOL_Obool)), _1179008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179004, tc_HOL_Obool)), _1179008), _1179006)))], (17415 ^ _774244) ^ [_1072352, _1072354, _1072356, _1072358] : [class_Rings_Olinordered__semidom(_1072352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072352), c_Groups_Oone__class_Oone(_1072352)), _1072354)), 17422 ^ _774244 : [(17429 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1072356), _1072358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072352), hAPP(hAPP(c_Power_Opower__class_Opower(_1072352), _1072354), _1072356)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072352), _1072354), _1072358))))], (17423 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072352), hAPP(hAPP(c_Power_Opower__class_Opower(_1072352), _1072354), _1072356)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072352), _1072354), _1072358))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1072356), _1072358)))]]], (18823 ^ _774244) ^ [_1095119, _1095121] : [class_Int_Onumber__ring(_1095119), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095119), hAPP(c_Int_Onumber__class_Onumber__of(_1095119), _1095121)), c_Groups_Oone__class_Oone(_1095119)) = hAPP(c_Int_Onumber__class_Onumber__of(_1095119), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1095121), c_Int_OBit1(c_Int_OPls))))], (50180 ^ _774244) ^ [_1779038, _1779040, _1779042] : [-(c_List_Oconcat(_1779038, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1779038)), _1779040), _1779042)) = hAPP(hAPP(c_List_Oappend(_1779038), _1779040), c_List_Oconcat(_1779038, _1779042)))], (9510 ^ _774244) ^ [_930709, _930711, _930713] : [class_Rings_Olinordered__semiring__strict(_930709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930709), c_Groups_Ozero__class_Ozero(_930709)), _930711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930709), c_Groups_Ozero__class_Ozero(_930709)), _930713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930709), c_Groups_Ozero__class_Ozero(_930709)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930709), _930711), _930713))))], (10015 ^ _774244) ^ [_939337, _939339] : [class_Rings_Olinordered__idom(_939337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939337), c_Groups_Ozero__class_Ozero(_939337)), _939339)), -(c_Groups_Osgn__class_Osgn(_939337, _939339) = c_Groups_Oone__class_Oone(_939337))], (43972 ^ _774244) ^ [_1631348, _1631350, _1631352, _1631354, _1631356, _1631358, _1631360] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631348, tc_fun(_1631350, tc_fun(_1631352, tc_HOL_Obool))), _1631354), _1631356), _1631358), _1631360)), 43975 ^ _774244 : [(43976 ^ _774244) ^ [_1631476] : [hBOOL(hAPP(hAPP(c_member(_1631348), _1631476), _1631354)), -(hBOOL(hAPP(hAPP(hAPP(_1631356, _1631476), _1631358), _1631360)))]]], (51011 ^ _774244) ^ [_1797209, _1797211] : [class_Orderings_Obot(_1797209), -(class_Orderings_Obot(tc_fun(_1797211, _1797209)))], (17115 ^ _774244) ^ [_1066833, _1066835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1066833)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1066833)), _1066835) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1066833), _1066835)))], (46976 ^ _774244) ^ [_1704947, _1704949] : [-(_1704947 = c_List_Olist_ONil(_1704949)), -(c_Random_Oselect__weight(_1704949, hAPP(hAPP(c_List_Omap(_1704949, tc_prod(tc_Code__Numeral_Ocode__numeral, _1704949)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1704949), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1704947)) = c_Random_Oselect(_1704949, _1704947))], (37419 ^ _774244) ^ [_1469571, _1469573, _1469575, _1469577, _1469579, _1469581, _1469583] : [c_Equiv__Relations_Oequiv(_1469571, _1469573, _1469575), c_Equiv__Relations_Ocongruent(_1469571, tc_fun(_1469577, tc_HOL_Obool), _1469575, _1469579), hBOOL(hAPP(hAPP(c_member(tc_fun(_1469571, tc_HOL_Obool)), _1469581), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1469571), _1469573), _1469575))), 37433 ^ _774244 : [(37436 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1469577, tc_HOL_Obool)), hAPP(_1469579, 37432 ^ [_1469571, _1469573, _1469575, _1469577, _1469579, _1469581, _1469583])), _1469583))], (37434 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1469571), 37432 ^ [_1469571, _1469573, _1469575, _1469577, _1469579, _1469581, _1469583]), _1469573)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1469577, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1469571, tc_fun(_1469577, tc_HOL_Obool)), _1469581), _1469579)), _1469583)))], (7903 ^ _774244) ^ [_903379, _903381, _903383, _903385, _903387] : [c_Sum__Type_OSuml(_903379, _903381, _903383, _903385) = c_Sum__Type_OSuml(_903379, _903381, _903383, _903387), -(_903385 = _903387)], (890 ^ _774244) ^ [_787953, _787955, _787957, _787959, _787961, _787963, _787965, _787967] : [-(c_Fun_Oinj__on(_787965, _787961, _787957, _787953)), c_Fun_Oinj__on(_787967, _787963, _787959, _787955), _787967 = _787965, _787963 = _787961, _787959 = _787957, _787955 = _787953], (50579 ^ _774244) ^ [_1789035, _1789037] : [-(c_List_OtakeWhile(_1789035, _1789037, c_List_Olist_ONil(_1789035)) = c_List_Olist_ONil(_1789035))], (27634 ^ _774244) ^ [_1261444, _1261446, _1261448, _1261450] : [class_Orderings_Olinorder(_1261444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261444), _1261446), _1261448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261444), _1261448), _1261450)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261444, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1261444, _1261446, _1261448)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1261444, _1261448, _1261450)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1261444, _1261446), _1261450))], (27398 ^ _774244) ^ [_1257278, _1257280] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1257278), _1257280)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1257278)), hAPP(c_Nat_OSuc, _1257280)))], (28952 ^ _774244) ^ [_1289392, _1289394] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289392, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1289392, tc_HOL_Obool))), _1289394) = c_Orderings_Obot__class_Obot(tc_fun(_1289392, tc_HOL_Obool)))], (4876 ^ _774244) ^ [_849620, _849622] : [_849622 = _849620, -(c_Finite__Set_Ofinite(_849622) = c_Finite__Set_Ofinite(_849620))], (10063 ^ _774244) ^ [_940095, _940097] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940095), _940097) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 10066 ^ _774244 : [(10069 ^ _774244) ^ [] : [-(_940097 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10067 ^ _774244) ^ [] : [-(_940095 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (33414 ^ _774244) ^ [_1380568, _1380570] : [-(c_Sum__Type_OPlus(_1380568, _1380570, c_Orderings_Otop__class_Otop(tc_fun(_1380568, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1380570, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1380568, _1380570), tc_HOL_Obool)))], (26422 ^ _774244) ^ [_1236075, _1236077, _1236079, _1236081] : [class_Groups_Oordered__ab__group__add__abs(_1236075), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236075), hAPP(c_Groups_Oabs__class_Oabs(_1236075), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236077, _1236075), _1236079), _1236081))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236077, _1236075), hAPP(hAPP(c_COMBB(_1236075, _1236075, _1236077), c_Groups_Oabs__class_Oabs(_1236075)), _1236079)), _1236081))))], (28080 ^ _774244) ^ [_1270099, _1270101, _1270103] : [class_Lattices_Olattice(_1270099), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270099), _1270101), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1270099), _1270103), _1270101))))], (26969 ^ _774244) ^ [_1248252, _1248254] : [26977 ^ _774244 : [(26980 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1248254, 26976 ^ [_1248252, _1248254])))], (26978 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26976 ^ [_1248252, _1248254]), _1248252)))]], 26970 ^ _774244 : [(26971 ^ _774244) ^ [_1248320] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1248320), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248252))), hBOOL(hAPP(_1248254, _1248320))]]], (44016 ^ _774244) ^ [_1632431, _1632433] : [-(hAPP(c_Relation_OImage(_1632431, _1632431, c_Relation_OId(_1632431)), _1632433) = _1632433)], (44032 ^ _774244) ^ [_1632759] : [-(c_Transitive__Closure_Ortrancl(_1632759, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1632759, _1632759), tc_HOL_Obool))) = c_Relation_OId(_1632759))], (36543 ^ _774244) ^ [_1449755, _1449757, _1449759] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449755, tc_HOL_Obool)), _1449757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1449755, tc_HOL_Obool)), _1449759), _1449757)) = c_Orderings_Obot__class_Obot(tc_fun(_1449755, tc_HOL_Obool)))], (17463 ^ _774244) ^ [_1073257, _1073259, _1073261] : [class_Rings_Olinordered__idom(_1073257), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073257), c_Groups_Ozero__class_Ozero(_1073257)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073257), hAPP(c_Groups_Oabs__class_Oabs(_1073257), _1073259)), _1073261))))], (27326 ^ _774244) ^ [_1255856, _1255858] : [c_Nat__Transfer_Ois__nat(_1255856), c_Nat__Transfer_Ois__nat(_1255858), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1255856, _1255858) = 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, _1255856), hAPP(c_Int_Onat, _1255858))))], (33548 ^ _774244) ^ [_1383279, _1383281, _1383283] : [class_Orderings_Olinorder(_1383279), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383279), _1383281)), -(_1383281 = c_Orderings_Obot__class_Obot(tc_fun(_1383279, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1383279, c_Orderings_Oord__class_Omin(_1383279), hAPP(hAPP(c_Set_Oinsert(_1383279), _1383283), _1383281)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1383279), _1383283), c_Big__Operators_Olattice_OInf__fin(_1383279, c_Orderings_Oord__class_Omin(_1383279), _1383281)))], (49754 ^ _774244) ^ [_1770580, _1770582, _1770584] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1770580), c_List_Oupt(_1770582, _1770584)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1770582), _1770580), _1770584))], (6824 ^ _774244) ^ [_884795, _884797] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_884795, _884797)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_884797)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49310 ^ _774244) ^ [_1760886, _1760888, _1760890, _1760892] : [hBOOL(hAPP(_1760886, _1760888)), -(hAPP(c_List_Ofilter(_1760890, _1760886), hAPP(hAPP(c_List_Olist_OCons(_1760890), _1760888), _1760892)) = hAPP(hAPP(c_List_Olist_OCons(_1760890), _1760888), hAPP(c_List_Ofilter(_1760890, _1760886), _1760892)))], (39261 ^ _774244) ^ [_1509930, _1509932, _1509934, _1509936] : [-(c_Map_Odom(_1509930, _1509932, c_Map_Orestrict__map(_1509930, _1509932, _1509934, _1509936)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509930, tc_HOL_Obool)), c_Map_Odom(_1509930, _1509932, _1509934)), _1509936))], (51415 ^ _774244) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (7760 ^ _774244) ^ [_900947, _900949, _900951, _900953] : [hAPP(c_Sum__Type_OInl(_900947, _900949), _900951) = hAPP(c_Sum__Type_OInr(_900949, _900947), _900953)], (13722 ^ _774244) ^ [_1003092, _1003094] : [class_Lattices_Oab__semigroup__idem__mult(_1003092), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003092), _1003094), _1003094) = _1003094)], (9210 ^ _774244) ^ [_925381] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _925381)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _925381))], (50073 ^ _774244) ^ [_1776119, _1776121] : [class_Orderings_Olinorder(_1776119), 50076 ^ _774244 : [(50077 ^ _774244) ^ [] : [c_List_Olinorder__class_Osorted(_1776119, _1776121), 50080 ^ _774244 : [(50081 ^ _774244) ^ [_1776290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1776290), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776119)), _1776121))), 50084 ^ _774244 : [(50085 ^ _774244) ^ [_1776407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1776407), _1776290)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1776119), hAPP(hAPP(c_List_Onth(_1776119), _1776121), _1776407)), hAPP(hAPP(c_List_Onth(_1776119), _1776121), _1776290))))]]]]], (50091 ^ _774244) ^ [] : [50093 ^ _774244 : [(50099 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1776119), hAPP(hAPP(c_List_Onth(_1776119), _1776121), 50095 ^ [_1776119, _1776121])), hAPP(hAPP(c_List_Onth(_1776119), _1776121), 50092 ^ [_1776119, _1776121])))], (50097 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50095 ^ [_1776119, _1776121]), 50092 ^ [_1776119, _1776121])))], (50094 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50092 ^ [_1776119, _1776121]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776119)), _1776121))))]], -(c_List_Olinorder__class_Osorted(_1776119, _1776121))]]], (1544 ^ _774244) ^ [_796268, _796270] : [-(class_Rings_Ocomm__semiring__1(_796268)), _796270 = _796268, class_Rings_Ocomm__semiring__1(_796270)], (22979 ^ _774244) ^ [_1171634, _1171636, _1171638, _1171640] : [-(hAPP(c_Product__Type_Osnd(_1171634, _1171636), hAPP(hAPP(c_Product__Type_OPair(_1171634, _1171636), _1171638), _1171640)) = _1171640)], (6812 ^ _774244) ^ [_884612] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _884612)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _884612)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (40129 ^ _774244) ^ [_1532429, _1532431, _1532433, _1532435, _1532437] : [c_Relation_Orefl__on(_1532429, _1532431, _1532433), hBOOL(hAPP(hAPP(c_member(tc_prod(_1532429, _1532429)), hAPP(hAPP(c_Product__Type_OPair(_1532429, _1532429), _1532435), _1532437)), _1532433)), -(hBOOL(hAPP(hAPP(c_member(_1532429), _1532435), _1532431)))], (49379 ^ _774244) ^ [_1762188, _1762190, _1762192] : [49381 ^ _774244 : [(49384 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1762190, 49380 ^ [_1762188, _1762190, _1762192])))], (49382 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1762188), 49380 ^ [_1762188, _1762190, _1762192]), hAPP(c_List_Oset(_1762188), _1762192))))]], -(hAPP(c_List_Ofilter(_1762188, _1762190), _1762192) = c_List_Olist_ONil(_1762188))], (11691 ^ _774244) ^ [_967082, _967084, _967086, _967088] : [class_Rings_Oordered__semiring(_967082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967082), _967084), _967086)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967082), c_Groups_Ozero__class_Ozero(_967082)), _967088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967082), _967088), _967084)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967082), _967088), _967086))))], (5460 ^ _774244) ^ [_858576, _858578] : [_858578 = _858576, -(tc_List_Olist(_858578) = tc_List_Olist(_858576))], (23299 ^ _774244) ^ [_1177272, _1177274, _1177276, _1177278, _1177280] : [hAPP(c_Product__Type_Ofst(_1177272, _1177274), hAPP(hAPP(c_Product__Type_OPair(_1177272, _1177274), _1177276), _1177278)) = _1177280, -(_1177276 = _1177280)], (49497 ^ _774244) ^ [_1765726, _1765728, _1765730, _1765732, _1765734] : [-(hAPP(hAPP(c_List_Omap(_1765726, _1765728), _1765730), hAPP(c_List_Ofilter(_1765726, _1765732), _1765734)) = c_List_Omap__filter(_1765726, _1765728, hAPP(hAPP(c_COMBC(_1765726, tc_Option_Ooption(_1765728), tc_Option_Ooption(_1765728)), hAPP(hAPP(c_COMBS(_1765726, tc_Option_Ooption(_1765728), tc_fun(tc_Option_Ooption(_1765728), tc_Option_Ooption(_1765728))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1765728), tc_fun(tc_Option_Ooption(_1765728), tc_Option_Ooption(_1765728))), _1765726), c_If(tc_Option_Ooption(_1765728))), _1765732)), hAPP(hAPP(c_COMBB(_1765728, tc_Option_Ooption(_1765728), _1765726), c_Option_Ooption_OSome(_1765728)), _1765730))), c_Option_Ooption_ONone(_1765728)), _1765734))], (29502 ^ _774244) ^ [_1299528] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1299528)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1299528)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1299528)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (23711 ^ _774244) ^ [_1185591, _1185593, _1185595, _1185597] : [class_Orderings_Olinorder(_1185591), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185591), _1185593), _1185595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185591), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1185591), _1185597), _1185593)), _1185595)))], (51383 ^ _774244) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (2644 ^ _774244) ^ [_814292, _814294] : [_814294 = _814292, -(c_New__DSequence_Opos__not__seq(_814294) = c_New__DSequence_Opos__not__seq(_814292))], (29420 ^ _774244) ^ [_1297797, _1297799, _1297801, _1297803, _1297805] : [-(_1297797 = c_Orderings_Obot__class_Obot(tc_fun(_1297799, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297801, tc_HOL_Obool)), _1297803), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297799, tc_fun(_1297801, tc_HOL_Obool)), _1297797), _1297805)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297799, tc_fun(_1297801, tc_HOL_Obool)), _1297797), hAPP(hAPP(c_COMBB(tc_fun(_1297801, tc_HOL_Obool), tc_fun(_1297801, tc_HOL_Obool), _1297799), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297801, tc_HOL_Obool)), _1297803)), _1297805)))], (6700 ^ _774244) ^ [_882166, _882168, _882170] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_882166, _882168, _882170))), -(hBOOL(hAPP(c_Com_OWT, _882170)))], (29051 ^ _774244) ^ [_1291377, _1291379, _1291381, _1291383] : [c_Orderings_Obot__class_Obot(tc_fun(_1291377, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291379, tc_fun(_1291377, tc_HOL_Obool)), _1291381), _1291383), 29054 ^ _774244 : [(29055 ^ _774244) ^ [_1291493] : [hBOOL(hAPP(hAPP(c_member(_1291379), _1291493), _1291381)), -(hAPP(_1291383, _1291493) = c_Orderings_Obot__class_Obot(tc_fun(_1291377, tc_HOL_Obool)))]]], (22742 ^ _774244) ^ [_1166880, _1166882] : [-(_1166880 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22745 ^ _774244 : [(22752 ^ _774244) ^ [] : [-(_1166882 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1166880, _1166882) = 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, _1166882))), 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, _1166880)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1166882))), c_Divides_Opdivmod(_1166880, _1166882)), 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), _1166882))))), c_Divides_Opdivmod(_1166880, _1166882)))))], (22746 ^ _774244) ^ [] : [_1166882 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1166880, _1166882) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1166880))]]], (23895 ^ _774244) ^ [_1188857, _1188859, _1188861] : [class_Int_Onumber(_1188857), class_Orderings_Oord(_1188857), 23902 ^ _774244 : [(23909 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188857), hAPP(c_Int_Onumber__class_Onumber__of(_1188857), _1188859)), hAPP(c_Int_Onumber__class_Onumber__of(_1188857), _1188861)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188857), hAPP(c_Int_Onumber__class_Onumber__of(_1188857), _1188859)), hAPP(c_Int_Onumber__class_Onumber__of(_1188857), _1188861)) = hAPP(c_Int_Onumber__class_Onumber__of(_1188857), _1188861))], (23903 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188857), hAPP(c_Int_Onumber__class_Onumber__of(_1188857), _1188859)), hAPP(c_Int_Onumber__class_Onumber__of(_1188857), _1188861))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188857), hAPP(c_Int_Onumber__class_Onumber__of(_1188857), _1188859)), hAPP(c_Int_Onumber__class_Onumber__of(_1188857), _1188861)) = hAPP(c_Int_Onumber__class_Onumber__of(_1188857), _1188859))]]], (40697 ^ _774244) ^ [_1543870, _1543872, _1543874] : [hBOOL(hAPP(_1543870, _1543872)), -(hAPP(c_Set_OCollect(_1543874), hAPP(hAPP(c_COMBS(_1543874, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543874), c_fconj), hAPP(c_fequal, _1543872))), _1543870)) = hAPP(hAPP(c_Set_Oinsert(_1543874), _1543872), c_Orderings_Obot__class_Obot(tc_fun(_1543874, tc_HOL_Obool))))], (24703 ^ _774244) ^ [_1204811, _1204813, _1204815, _1204817] : [-(c_New__Random__Sequence_Opos__empty(_1204811, _1204813, _1204815, _1204817) = c_New__DSequence_Opos__empty(_1204811))], (25259 ^ _774244) ^ [_1214825, _1214827] : [class_Rings_Ocomm__semiring__1(_1214825), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214825), _1214827), _1214827)))], (11769 ^ _774244) ^ [_968581, _968583, _968585, _968587, _968589] : [class_Rings_Oordered__semiring(_968581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968581), _968583), _968585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968581), _968587), _968589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968581), c_Groups_Ozero__class_Ozero(_968581)), _968585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968581), c_Groups_Ozero__class_Ozero(_968581)), _968587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968581), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968581), _968583), _968587)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968581), _968585), _968589))))], (20809 ^ _774244) ^ [_1130716, _1130718, _1130720, _1130722] : [class_Fields_Olinordered__field(_1130716), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130716), _1130718), _1130720)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130716), _1130722), c_Groups_Ozero__class_Ozero(_1130716))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130716), c_Groups_Ozero__class_Ozero(_1130716)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130716), _1130718), _1130720))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130716), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130716), _1130722), _1130718)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130716), _1130722), _1130720))))], (48474 ^ _774244) ^ [_1742857, _1742859, _1742861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1742857), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742859)), _1742861))), -(hAPP(hAPP(c_List_Olist_OCons(_1742859), hAPP(hAPP(c_List_Onth(_1742859), _1742861), _1742857)), hAPP(hAPP(c_List_Odrop(_1742859), hAPP(c_Nat_OSuc, _1742857)), _1742861)) = hAPP(hAPP(c_List_Odrop(_1742859), _1742857), _1742861))], (26255 ^ _774244) ^ [_1232936, _1232938] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1232936), _1232938)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232936), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232938), _1232936)) = _1232938)], (14129 ^ _774244) ^ [_1010916, _1010918, _1010920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1010916), _1010918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1010916), _1010920)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1010918), _1010920))))], (21187 ^ _774244) ^ [_1137196, _1137198, _1137200, _1137202] : [class_Fields_Olinordered__field(_1137196), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137196), _1137198), c_Groups_Ozero__class_Ozero(_1137196))), 21194 ^ _774244 : [(21201 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137196), _1137202), _1137198)), _1137200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137196), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137196), _1137200), _1137198)), _1137202)))], (21195 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137196), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137196), _1137200), _1137198)), _1137202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137196), _1137202), _1137198)), _1137200)))]]], (35209 ^ _774244) ^ [_1419379, _1419381, _1419383, _1419385, _1419387, _1419389, _1419391] : [-(hAPP(c_Fun_Ocomp(_1419379, _1419381, _1419383, _1419385), hAPP(c_Fun_Ocomp(_1419387, _1419379, _1419383, _1419389), _1419391)) = hAPP(c_Fun_Ocomp(_1419387, _1419381, _1419383, hAPP(c_Fun_Ocomp(_1419379, _1419381, _1419387, _1419385), _1419389)), _1419391))], (40595 ^ _774244) ^ [_1541528] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1541528, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1541528), hAPP(c_COMBK(tc_HOL_Obool, _1541528), c_fFalse)))], (21960 ^ _774244) ^ [_1151616, _1151618] : [_1151616 = _1151618, -(c_Code__Numeral_OSuc__code__numeral(_1151616) = c_Code__Numeral_OSuc__code__numeral(_1151618))], (2168 ^ _774244) ^ [_806764, _806766, _806768, _806770, _806772, _806774, _806776, _806778, _806780, _806782, _806784, _806786] : [-(c_Sum__Type_Osum_Osum__rec(_806786, _806782, _806778, _806774, _806770, _806766) = c_Sum__Type_Osum_Osum__rec(_806784, _806780, _806776, _806772, _806768, _806764)), _806786 = _806784, _806782 = _806780, _806778 = _806776, _806774 = _806772, _806770 = _806768, _806766 = _806764], (16953 ^ _774244) ^ [_1064076, _1064078, _1064080, _1064082] : [class_Rings_Olinordered__semidom(_1064076), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1064078), _1064080)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064076), c_Groups_Ozero__class_Ozero(_1064076)), _1064082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064076), _1064082), c_Groups_Oone__class_Oone(_1064076))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064076), hAPP(hAPP(c_Power_Opower__class_Opower(_1064076), _1064082), _1064080)), hAPP(hAPP(c_Power_Opower__class_Opower(_1064076), _1064082), _1064078))))], (39136 ^ _774244) ^ [_1507213, _1507215, _1507217, _1507219, _1507221] : [class_Groups_Ocomm__monoid__mult(_1507213), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507215), _1507217)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507215), _1507219)), 39150 ^ _774244 : [(39153 ^ _774244) ^ [] : [hAPP(_1507221, 39149 ^ [_1507213, _1507215, _1507217, _1507219, _1507221]) = c_Groups_Oone__class_Oone(_1507213)], (39151 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1507215), 39149 ^ [_1507213, _1507215, _1507217, _1507219, _1507221]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507215, tc_HOL_Obool)), _1507217), _1507219))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1507213, _1507215, c_Groups_Otimes__class_Otimes(_1507213)), _1507221), c_Groups_Oone__class_Oone(_1507213)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1507215, tc_HOL_Obool)), _1507217), _1507219)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1507213), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1507213, _1507215, c_Groups_Otimes__class_Otimes(_1507213)), _1507221), c_Groups_Oone__class_Oone(_1507213)), _1507217)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1507213, _1507215, c_Groups_Otimes__class_Otimes(_1507213)), _1507221), c_Groups_Oone__class_Oone(_1507213)), _1507219)))], (14217 ^ _774244) ^ [_1012496, _1012498] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1012496, _1012498)) = _1012498), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1012496), _1012498) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1012496, _1012498)))], (3110 ^ _774244) ^ [_821861, _821863] : [_821863 = _821861, -(c_Int_OBit1(_821863) = c_Int_OBit1(_821861))], (22044 ^ _774244) ^ [_1152944, _1152946] : [_1152944 = _1152946, -(hAPP(c_Code__Numeral_Oof__nat, _1152944) = hAPP(c_Code__Numeral_Oof__nat, _1152946))], (47230 ^ _774244) ^ [_1711614, _1711616, _1711618, _1711620] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711614), tc_List_Olist(_1711614))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711614), tc_List_Olist(_1711614)), _1711616), _1711618)), c_List_Olistrel(_1711614, _1711620)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711614)), _1711616) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711614)), _1711618), 47236 ^ _774244 : [(47239 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1711614, _1711614)), hAPP(hAPP(c_Product__Type_OPair(_1711614, _1711614), hAPP(hAPP(c_List_Onth(_1711614), _1711616), 47235 ^ [_1711614, _1711616, _1711618, _1711620])), hAPP(hAPP(c_List_Onth(_1711614), _1711618), 47235 ^ [_1711614, _1711616, _1711618, _1711620]))), _1711620))], (47237 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47235 ^ [_1711614, _1711616, _1711618, _1711620]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711614)), _1711616))))]]], (18629 ^ _774244) ^ [_1092142] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1092142)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092142))))], (8070 ^ _774244) ^ [_906441, _906443, _906445, _906447] : [c_Natural_Oevalc(c_Com_Ocom_OAss(_906441, _906443), _906445, _906447), -(_906447 = c_Natural_Oupdate(_906445, _906441, hAPP(_906443, _906445)))], (17979 ^ _774244) ^ [_1081710] : [class_Int_Onumber__ring(_1081710), -(hAPP(c_Int_Oring__1__class_Oof__int(_1081710), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1081710), c_Int_OMin))], (4078 ^ _774244) ^ [_837239, _837241, _837243, _837245] : [-(c_Option_Omap(_837245, _837241) = c_Option_Omap(_837243, _837239)), _837245 = _837243, _837241 = _837239], (6925 ^ _774244) ^ [_886325, _886327, _886329, _886331, _886333] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_886325, _886327), _886329, _886331, _886333)), 6926 ^ _774244 : [(6933 ^ _774244) ^ [] : [hBOOL(hAPP(_886325, _886329)), 6936 ^ _774244 : [(6937 ^ _774244) ^ [_886535] : [c_Natural_Oevaln(_886327, _886329, _886331, _886535), c_Natural_Oevaln(c_Com_Ocom_OWhile(_886325, _886327), _886535, _886331, _886333)]]], (6927 ^ _774244) ^ [] : [_886333 = _886329, -(hBOOL(hAPP(_886325, _886329)))]]], (40657 ^ _774244) ^ [_1542719, _1542721, _1542723, _1542725] : [-(hAPP(c_Set_OCollect(tc_prod(_1542719, _1542721)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542719, _1542721, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1542719, tc_fun(_1542721, tc_HOL_Obool), tc_fun(_1542721, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1542721, tc_HOL_Obool), tc_fun(_1542721, tc_HOL_Obool)), _1542719), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1542721)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542719), c_fconj), _1542723))), _1542725))) = hAPP(hAPP(c_Product__Type_OSigma(_1542719, _1542721), hAPP(c_Set_OCollect(_1542719), _1542723)), hAPP(hAPP(c_COMBB(tc_fun(_1542721, tc_HOL_Obool), tc_fun(_1542721, tc_HOL_Obool), _1542719), c_Set_OCollect(_1542721)), _1542725)))], (27269 ^ _774244) ^ [_1254544, _1254546, _1254548, _1254550, _1254552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254544, tc_HOL_Obool)), _1254546), hAPP(c_Set_Oimage(_1254548, _1254544, _1254550), _1254552))), 27273 ^ _774244 : [(27276 ^ _774244) ^ [] : [-(_1254546 = hAPP(c_Set_Oimage(_1254548, _1254544, _1254550), 27272 ^ [_1254544, _1254546, _1254548, _1254550, _1254552]))], (27274 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254548, tc_HOL_Obool)), 27272 ^ [_1254544, _1254546, _1254548, _1254550, _1254552]), _1254552)))]]], (37257 ^ _774244) ^ [_1465475, _1465477, _1465479] : [class_Orderings_Olinorder(_1465475), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465475), _1465477)), -(_1465477 = c_Orderings_Obot__class_Obot(tc_fun(_1465475, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465475), _1465479)), -(_1465479 = c_Orderings_Obot__class_Obot(tc_fun(_1465475, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465475, tc_HOL_Obool)), _1465477), _1465479) = c_Orderings_Obot__class_Obot(tc_fun(_1465475, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1465475, c_Orderings_Oord__class_Omax(_1465475), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1465475, tc_HOL_Obool)), _1465477), _1465479)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1465475), c_Big__Operators_Olattice_OSup__fin(_1465475, c_Orderings_Oord__class_Omax(_1465475), _1465477)), c_Big__Operators_Olattice_OSup__fin(_1465475, c_Orderings_Oord__class_Omax(_1465475), _1465479)))], (41180 ^ _774244) ^ [_1562023, _1562025, _1562027, _1562029] : [class_Groups_Ocomm__monoid__mult(_1562023), c_Fun_Oinj__on(_1562025, _1562023, _1562027, _1562029), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1562025, _1562023), _1562027), _1562029) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1562023, _1562023), c_Fun_Oid(_1562023)), hAPP(c_Set_Oimage(_1562025, _1562023, _1562027), _1562029)))], (33942 ^ _774244) ^ [_1391049, _1391051, _1391053, _1391055, _1391057] : [-(hBOOL(hAPP(hAPP(c_member(_1391049), _1391051), _1391053))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1391049, tc_Option_Ooption(_1391055)), c_Map_Orestrict__map(_1391049, _1391055, _1391057, _1391053)), _1391051), c_Option_Ooption_ONone(_1391055)) = c_Map_Orestrict__map(_1391049, _1391055, _1391057, _1391053))], (45732 ^ _774244) ^ [_1673207, _1673209, _1673211, _1673213, _1673215] : [hAPP(c_Map_Omap__of(_1673207, _1673209, _1673211), _1673213) = hAPP(c_Option_Ooption_OSome(_1673209), _1673215), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1673207, _1673209)), hAPP(hAPP(c_Product__Type_OPair(_1673207, _1673209), _1673213), _1673215)), hAPP(c_List_Oset(tc_prod(_1673207, _1673209)), _1673211))))], (27782 ^ _774244) ^ [_1264500, _1264502, _1264504] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264500, tc_HOL_Obool)), _1264502), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264500, tc_HOL_Obool)), _1264502), _1264504)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264500, tc_HOL_Obool)), _1264502), _1264504))], (6778 ^ _774244) ^ [_883864, _883866, _883868, _883870] : [class_Rings_Ocomm__semiring__1(_883864), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883864), _883866), _883868)), _883870) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883864), _883866), _883870)), _883868))], (7818 ^ _774244) ^ [_901938, _901940, _901942, _901944] : [hAPP(c_Sum__Type_OInl(_901938, _901940), _901942) = hAPP(c_Sum__Type_OInl(_901938, _901940), _901944), -(_901942 = _901944)], (50039 ^ _774244) ^ [_1775516] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1775516) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1775516))))], (48873 ^ _774244) ^ [_1751564, _1751566, _1751568] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1751564)), _1751566), c_Wellfounded_Oacc(tc_List_Olist(_1751564), c_List_Olistrel1(_1751564, _1751568)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1751564)), _1751566), c_List_Olists(_1751564, c_Wellfounded_Oacc(_1751564, _1751568)))))], (4780 ^ _774244) ^ [_848100, _848102, _848104, _848106] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_848106, _848102) = c_SetInterval_Oord__class_OatLeastLessThan(_848104, _848100)), _848106 = _848104, _848102 = _848100], (15482 ^ _774244) ^ [_1035385, _1035387] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035385), _1035387) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035385), _1035387)))], (7357 ^ _774244) ^ [_893750] : [-(_893750 = 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)), _893750)))], (764 ^ _774244) ^ [_785998, _786000, _786002, _786004, _786006, _786008, _786010, _786012, _786014, _786016, _786018, _786020] : [-(c_Finite__Set_Ofolding__image__simple__idem(_786018, _786014, _786010, _786006, _786002, _785998)), c_Finite__Set_Ofolding__image__simple__idem(_786020, _786016, _786012, _786008, _786004, _786000), _786020 = _786018, _786016 = _786014, _786012 = _786010, _786008 = _786006, _786004 = _786002, _786000 = _785998], (47279 ^ _774244) ^ [_1712904, _1712906, _1712908, _1712910] : [_1712906 = c_List_Olist_ONil(_1712904), -(hAPP(hAPP(c_List_Olist__update(_1712904, _1712906), _1712908), _1712910) = c_List_Olist_ONil(_1712904))], (48426 ^ _774244) ^ [_1741555, _1741557, _1741559, _1741561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1741555), _1741557)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741559)), _1741561))), -(hAPP(hAPP(c_List_Onth(_1741559), hAPP(hAPP(c_List_Odrop(_1741559), _1741555), _1741561)), _1741557) = hAPP(hAPP(c_List_Onth(_1741559), _1741561), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1741555), _1741557)))], (41804 ^ _774244) ^ [_1578174, _1578176, _1578178] : [-(hAPP(c_Set_Oimage(tc_prod(_1578174, _1578176), _1578174, c_Product__Type_Ofst(_1578174, _1578176)), _1578178) = hAPP(c_Relation_ODomain(_1578174, _1578176), _1578178))], (49332 ^ _774244) ^ [_1761303, _1761305, _1761307] : [49334 ^ _774244 : [(49337 ^ _774244) ^ [] : [hBOOL(hAPP(_1761305, 49333 ^ [_1761303, _1761305, _1761307]))], (49335 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1761303), 49333 ^ [_1761303, _1761305, _1761307]), hAPP(c_List_Oset(_1761303), _1761307))))]], -(hAPP(c_List_Ofilter(_1761303, _1761305), _1761307) = _1761307)], (48140 ^ _774244) ^ [_1733827, _1733829, _1733831, _1733833, _1733835, _1733837] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733827), tc_List_Olist(_1733827))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733827), tc_List_Olist(_1733827)), hAPP(hAPP(c_List_Oappend(_1733827), _1733829), _1733835)), hAPP(hAPP(c_List_Oappend(_1733827), _1733831), _1733837))), c_List_Olistrel1(_1733827, _1733833)))), 48141 ^ _774244 : [(48148 ^ _774244) ^ [] : [_1733829 = _1733831, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733827), tc_List_Olist(_1733827))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733827), tc_List_Olist(_1733827)), _1733835), _1733837)), c_List_Olistrel1(_1733827, _1733833)))], (48142 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733827), tc_List_Olist(_1733827))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733827), tc_List_Olist(_1733827)), _1733829), _1733831)), c_List_Olistrel1(_1733827, _1733833))), _1733835 = _1733837]]], (46593 ^ _774244) ^ [_1696794, _1696796, _1696798, _1696800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1696794), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1696796), _1696798))), -(hAPP(c_Random_Opick(_1696796, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1696796)), _1696798), _1696800)), _1696794) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1696796), _1696798))], (26468 ^ _774244) ^ [_1237069, _1237071, _1237073, _1237075, _1237077, _1237079] : [class_Groups_Ocomm__monoid__add(_1237069), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237071, _1237069), hAPP(hAPP(c_COMBC(_1237071, tc_fun(_1237073, tc_HOL_Obool), _1237069), hAPP(hAPP(c_COMBB(tc_fun(_1237073, _1237069), tc_fun(tc_fun(_1237073, tc_HOL_Obool), _1237069), _1237071), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237073, _1237069)), _1237075)), _1237077)), _1237079) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237073, _1237069), hAPP(hAPP(c_COMBC(_1237073, tc_fun(_1237071, tc_HOL_Obool), _1237069), hAPP(hAPP(c_COMBB(tc_fun(_1237071, _1237069), tc_fun(tc_fun(_1237071, tc_HOL_Obool), _1237069), _1237073), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237071, _1237069)), hAPP(c_COMBC(_1237071, _1237073, _1237069), _1237075))), _1237079)), _1237077))], (2358 ^ _774244) ^ [_809791, _809793] : [_809793 = _809791, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_809793) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_809791))], (164 ^ _774244) ^ [_776550, _776552, _776554, _776556, _776558, _776560, _776562, _776564] : [-(c_Orderings_Oorder_Ostrict__mono(_776562, _776558, _776554, _776550)), c_Orderings_Oorder_Ostrict__mono(_776564, _776560, _776556, _776552), _776564 = _776562, _776560 = _776558, _776556 = _776554, _776552 = _776550], (47547 ^ _774244) ^ [_1719087, _1719089, _1719091, _1719093, _1719095, _1719097, _1719099] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1719087, _1719087)), hAPP(hAPP(c_Product__Type_OPair(_1719087, _1719087), _1719089), _1719091)), _1719093)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1719087), tc_List_Olist(_1719087))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1719087), tc_List_Olist(_1719087)), hAPP(hAPP(c_List_Oappend(_1719087), _1719095), hAPP(hAPP(c_List_Olist_OCons(_1719087), _1719089), _1719097))), hAPP(hAPP(c_List_Oappend(_1719087), _1719095), hAPP(hAPP(c_List_Olist_OCons(_1719087), _1719091), _1719099)))), c_List_Olexord(_1719087, _1719093))))], (35026 ^ _774244) ^ [_1415484, _1415486, _1415488, _1415490, _1415492] : [c_Finite__Set_Ofolding__one__idem(_1415484, _1415486, _1415488), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415484), _1415490)), -(_1415490 = c_Orderings_Obot__class_Obot(tc_fun(_1415484, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415484), _1415492)), -(_1415492 = c_Orderings_Obot__class_Obot(tc_fun(_1415484, tc_HOL_Obool))), -(hAPP(_1415488, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415484, tc_HOL_Obool)), _1415490), _1415492)) = hAPP(hAPP(_1415486, hAPP(_1415488, _1415490)), hAPP(_1415488, _1415492)))], (28497 ^ _774244) ^ [_1278462, _1278464, _1278466] : [class_Orderings_Olinorder(_1278462), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278462), _1278464), _1278466)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278462, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1278462, _1278464), _1278466)), hAPP(c_SetInterval_Oord__class_OatLeast(_1278462), _1278466)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1278462), _1278464))], (6185 ^ _774244) ^ [_873399, _873401, _873403, _873405, _873407] : [-(c_Natural_Oevalc(c_Com_Ocom_OCond(_873399, _873401, _873403), _873405, _873407)), 6186 ^ _774244 : [(6193 ^ _774244) ^ [] : [-(hBOOL(hAPP(_873399, _873405))), c_Natural_Oevalc(_873403, _873405, _873407)], (6187 ^ _774244) ^ [] : [hBOOL(hAPP(_873399, _873405)), c_Natural_Oevalc(_873401, _873405, _873407)]]], (50953 ^ _774244) ^ [_1796448, _1796450] : [class_Lattices_Olattice(_1796448), -(class_Lattices_Osemilattice__inf(tc_fun(_1796450, _1796448)))], (43684 ^ _774244) ^ [_1623212, _1623214, _1623216, _1623218, _1623220] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623212, tc_HOL_Obool)), _1623214), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623216, tc_fun(_1623212, tc_HOL_Obool)), _1623218), _1623220)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623216, tc_fun(_1623212, tc_HOL_Obool)), _1623218), hAPP(hAPP(c_COMBB(tc_fun(_1623212, tc_HOL_Obool), tc_fun(_1623212, tc_HOL_Obool), _1623216), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623212, tc_HOL_Obool)), _1623214)), _1623220)))], (19821 ^ _774244) ^ [_1113278, _1113280, _1113282, _1113284, _1113286] : [class_Fields_Ofield__inverse__zero(_1113278), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113278), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113278), _1113280), _1113282)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113278), _1113284), _1113286)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113278), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113278), _1113280), _1113284)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113278), _1113282), _1113286)))], (22176 ^ _774244) ^ [_1155578, _1155580] : [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(_1155578))), 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)), _1155580))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155578) = hAPP(c_Nat_OSuc, _1155580))], (43645 ^ _774244) ^ [_1622056, _1622058, _1622060, _1622062, _1622064] : [class_Complete__Lattice_Ocomplete__lattice(_1622056), 43648 ^ _774244 : [(43649 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1622056), _1622058), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622060, _1622056), _1622062), _1622064))), 43652 ^ _774244 : [(43653 ^ _774244) ^ [_1622237] : [hBOOL(hAPP(hAPP(c_member(_1622060), _1622237), _1622062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1622056), _1622058), hAPP(_1622064, _1622237))))]]], (43659 ^ _774244) ^ [] : [43661 ^ _774244 : [(43664 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1622056), _1622058), hAPP(_1622064, 43660 ^ [_1622056, _1622058, _1622060, _1622062, _1622064])))], (43662 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622060), 43660 ^ [_1622056, _1622058, _1622060, _1622062, _1622064]), _1622062)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1622056), _1622058), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622060, _1622056), _1622062), _1622064))))]]], (31945 ^ _774244) ^ [_1351975, _1351977, _1351979] : [31947 ^ _774244 : [(31950 ^ _774244) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1351979, 31946 ^ [_1351975, _1351977, _1351979]))], (31948 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1351975), 31946 ^ [_1351975, _1351977, _1351979]), _1351977)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351975, tc_Int_Oint), _1351979), _1351977) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351975, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1351975), c_Int_Onat), _1351979)), _1351977)))], (19439 ^ _774244) ^ [_1106136, _1106138] : [class_Rings_Olinordered__idom(_1106136), 19442 ^ _774244 : [(19449 ^ _774244) ^ [] : [-(_1106138 = c_Groups_Ozero__class_Ozero(_1106136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106136), c_Groups_Ozero__class_Ozero(_1106136)), hAPP(hAPP(c_Power_Opower__class_Opower(_1106136), _1106138), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (19443 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106136), c_Groups_Ozero__class_Ozero(_1106136)), hAPP(hAPP(c_Power_Opower__class_Opower(_1106136), _1106138), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1106138 = c_Groups_Ozero__class_Ozero(_1106136)]]], (11663 ^ _774244) ^ [_966558, _966560, _966562] : [class_Rings_Oordered__ring(_966558), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966558), _966560), c_Groups_Ozero__class_Ozero(_966558))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966558), _966562), c_Groups_Ozero__class_Ozero(_966558))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966558), c_Groups_Ozero__class_Ozero(_966558)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966558), _966560), _966562))))], (48584 ^ _774244) ^ [_1745050, _1745052, _1745054] : [-(hAPP(c_List_Otl(_1745050), hAPP(hAPP(c_List_Odrop(_1745050), _1745052), _1745054)) = hAPP(hAPP(c_List_Odrop(_1745050), _1745052), hAPP(c_List_Otl(_1745050), _1745054)))], (40848 ^ _774244) ^ [_1548992] : [-(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)))), _1548992))))], (1024 ^ _774244) ^ [_789768, _789770] : [-(class_Rings_Olinordered__semiring__1(_789768)), _789770 = _789768, class_Rings_Olinordered__semiring__1(_789770)], (25055 ^ _774244) ^ [_1211572, _1211574, _1211576] : [_1211572 = _1211574, 25066 ^ _774244 : [(25069 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211576), _1211572))], (25067 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211572), _1211576)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211574), _1211576)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211576), _1211574)))], (15450 ^ _774244) ^ [_1034805, _1034807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1034805), _1034807)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1034805), _1034807)))], (34026 ^ _774244) ^ [_1393035, _1393037, _1393039, _1393041] : [class_Rings_Ocomm__semiring__1(_1393035), class_Rings_Ono__zero__divisors(_1393035), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393037), _1393039)), 34037 ^ _774244 : [(34047 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1393037, _1393035), _1393041), _1393039) = c_Groups_Ozero__class_Ozero(_1393035)), 34048 ^ _774244 : [(34049 ^ _774244) ^ [_1393413] : [hBOOL(hAPP(hAPP(c_member(_1393037), _1393413), _1393039)), hAPP(_1393041, _1393413) = c_Groups_Ozero__class_Ozero(_1393035)]]], (34038 ^ _774244) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1393037, _1393035), _1393041), _1393039) = c_Groups_Ozero__class_Ozero(_1393035), 34042 ^ _774244 : [(34045 ^ _774244) ^ [] : [-(hAPP(_1393041, 34041 ^ [_1393035, _1393037, _1393039, _1393041]) = c_Groups_Ozero__class_Ozero(_1393035))], (34043 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1393037), 34041 ^ [_1393035, _1393037, _1393039, _1393041]), _1393039)))]]]]], (34130 ^ _774244) ^ [_1394784, _1394786, _1394788, _1394790] : [-(hAPP(c_Map_Orestrict__map(_1394784, _1394786, hAPP(c_COMBK(tc_Option_Ooption(_1394786), _1394784), c_Option_Ooption_ONone(_1394786)), _1394788), _1394790) = c_Option_Ooption_ONone(_1394786))], (47018 ^ _774244) ^ [_1706288, _1706290, _1706292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706288), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706290)), _1706292))), -(hAPP(c_Random_Opick(_1706290, hAPP(hAPP(c_List_Omap(_1706290, tc_prod(tc_Code__Numeral_Ocode__numeral, _1706290)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1706290), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1706292)), hAPP(c_Code__Numeral_Oof__nat, _1706288)) = hAPP(hAPP(c_List_Onth(_1706290), _1706292), _1706288))], (42522 ^ _774244) ^ [_1595328, _1595330, _1595332, _1595334, _1595336, _1595338] : [c_Finite__Set_Ofun__left__comm__idem(_1595328, _1595330, _1595332), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595328), _1595334)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1595328, _1595330, _1595332), _1595336), hAPP(hAPP(c_Set_Oinsert(_1595328), _1595338), _1595334)) = hAPP(hAPP(_1595332, _1595338), hAPP(hAPP(c_Finite__Set_Ofold(_1595328, _1595330, _1595332), _1595336), _1595334)))], (35171 ^ _774244) ^ [_1418353, _1418355, _1418357, _1418359, _1418361, _1418363] : [class_Groups_Ocomm__monoid__add(_1418353), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418355), _1418357)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418359), _1418361)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(_1418355, _1418359), _1418353), _1418363), c_Sum__Type_OPlus(_1418355, _1418359, _1418357, _1418361)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1418353), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418355, _1418353), hAPP(c_Fun_Ocomp(tc_sum(_1418355, _1418359), _1418353, _1418355, _1418363), c_Sum__Type_OInl(_1418355, _1418359))), _1418357)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418359, _1418353), hAPP(c_Fun_Ocomp(tc_sum(_1418355, _1418359), _1418353, _1418359, _1418363), c_Sum__Type_OInr(_1418359, _1418355))), _1418361)))], (7545 ^ _774244) ^ [_896861, _896863, _896865] : [c_Com_Ocom_OAss(_896861, _896863) = c_Com_Ocom_OBODY(_896865)], (36261 ^ _774244) ^ [_1443500, _1443502] : [c_Nat__Transfer_Onat__set(_1443500), c_Nat__Transfer_Onat__set(_1443502), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1443500), _1443502)))], (13698 ^ _774244) ^ [_1002695, _1002697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002695), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13701 ^ _774244 : [(13704 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002695), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1002697, _1002695))))], (13702 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1002697, _1002695)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (28771 ^ _774244) ^ [_1285274, _1285276] : [class_Orderings_Otop(_1285274), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285274), _1285276), c_Orderings_Otop__class_Otop(_1285274))))], (7942 ^ _774244) ^ [_904052, _904054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _904052), _904054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _904052)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _904054))))], (1184 ^ _774244) ^ [_791768, _791770] : [-(class_Rings_Oring(_791768)), _791770 = _791768, class_Rings_Oring(_791770)], (36321 ^ _774244) ^ [_1444700, _1444702, _1444704, _1444706] : [class_Lattices_Osemilattice__inf(_1444700), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444700), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444700), _1444702), _1444704)), _1444706) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444700), _1444702), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444700), _1444704), _1444706)))], (19707 ^ _774244) ^ [_1111201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1111201)), -(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), _1111201), 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)))))))], (50831 ^ _774244) ^ [_1793868, _1793870, _1793872] : [c_List_OdropWhile(_1793868, _1793870, _1793872) = c_List_Olist_ONil(_1793868), 50834 ^ _774244 : [(50835 ^ _774244) ^ [_1793959] : [hBOOL(hAPP(hAPP(c_member(_1793868), _1793959), hAPP(c_List_Oset(_1793868), _1793872))), -(hBOOL(hAPP(_1793870, _1793959)))]]], (39807 ^ _774244) ^ [_1524595, _1524597, _1524599, _1524601] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524597, _1524595), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1524595, tc_prod(_1524597, _1524595), 39803 ^ [_1524595, _1524597, _1524599, _1524601]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524597, tc_fun(_1524595, tc_HOL_Obool)), _1524599), _1524601))), hAPP(hAPP(c_Product__Type_OSigma(_1524597, _1524595), _1524599), _1524601))))], (39096 ^ _774244) ^ [_1506390, _1506392, _1506394, _1506396] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506390), _1506392)), -(hAPP(c_Set_Oimage(_1506390, _1506394, _1506396), _1506392) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1506394, tc_HOL_Obool), _1506390, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1506394, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1506390, tc_fun(_1506394, tc_HOL_Obool), tc_fun(_1506394, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1506394, tc_fun(tc_fun(_1506394, tc_HOL_Obool), tc_fun(_1506394, tc_HOL_Obool)), _1506390), c_Set_Oinsert(_1506394)), _1506396)), c_Orderings_Obot__class_Obot(tc_fun(_1506394, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1506394, tc_HOL_Obool))), _1506392))], (44536 ^ _774244) ^ [_1644598, _1644600, _1644602] : [class_Complete__Lattice_Ocomplete__lattice(_1644598), -(c_Complete__Lattice_OInf__class_OInf(_1644598, hAPP(hAPP(c_Set_Oinsert(_1644598), _1644600), _1644602)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1644598), _1644600), c_Complete__Lattice_OInf__class_OInf(_1644598, _1644602)))], (16040 ^ _774244) ^ [_1046781, _1046783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1046783)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1046783), _1046781)), _1046783) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1046783), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046781), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (44795 ^ _774244) ^ [_1650786, _1650788] : [class_Complete__Lattice_Ocomplete__lattice(_1650786), hBOOL(hAPP(c_Finite__Set_Ofinite(_1650786), _1650788)), -(_1650788 = c_Orderings_Obot__class_Obot(tc_fun(_1650786, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1650786, _1650788) = c_Complete__Lattice_OSup__class_OSup(_1650786, _1650788))], (11457 ^ _774244) ^ [_962957, _962959, _962961] : [class_Groups_Oordered__comm__monoid__add(_962957), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962957), c_Groups_Ozero__class_Ozero(_962957)), _962959)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962957), c_Groups_Ozero__class_Ozero(_962957)), _962961)), 11468 ^ _774244 : [(11477 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962957), _962959), _962961) = c_Groups_Ozero__class_Ozero(_962957)), _962959 = c_Groups_Ozero__class_Ozero(_962957), _962961 = c_Groups_Ozero__class_Ozero(_962957)], (11469 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962957), _962959), _962961) = c_Groups_Ozero__class_Ozero(_962957), 11472 ^ _774244 : [(11475 ^ _774244) ^ [] : [-(_962961 = c_Groups_Ozero__class_Ozero(_962957))], (11473 ^ _774244) ^ [] : [-(_962959 = c_Groups_Ozero__class_Ozero(_962957))]]]]], (45353 ^ _774244) ^ [_1663866, _1663868, _1663870, _1663872] : [c_Fun_Oinj__on(_1663866, tc_Option_Ooption(_1663868), _1663872, c_Map_Odom(_1663866, _1663868, _1663872)), -(c_Fun_Oinj__on(_1663866, tc_Option_Ooption(_1663868), c_Map_Omap__add(_1663866, _1663868, _1663870, _1663872), c_Map_Odom(_1663866, _1663868, _1663872)))], (39352 ^ _774244) ^ [_1512316, _1512318, _1512320, _1512322, _1512324, _1512326, _1512328] : [-(hBOOL(hAPP(hAPP(c_member(_1512316), _1512318), _1512320))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1512316, _1512322, _1512324, _1512326, _1512320), _1512328)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1512316, _1512322, _1512324, _1512326, hAPP(hAPP(c_Set_Oinsert(_1512316), _1512318), _1512320)), hAPP(hAPP(_1512324, _1512318), _1512328))))], (24287 ^ _774244) ^ [_1196082, _1196084] : [class_Orderings_Olinorder(_1196082), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196082), _1196084), _1196084) = _1196084)], (42343 ^ _774244) ^ [_1591755, _1591757, _1591759] : [class_Orderings_Olinorder(_1591755), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591755), _1591757)), 42353 ^ _774244 : [(42356 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1591755), 42352 ^ [_1591755, _1591757, _1591759]), _1591759))], (42354 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591755), 42352 ^ [_1591755, _1591757, _1591759]), _1591757)))]], hBOOL(hAPP(hAPP(c_member(_1591755), _1591759), _1591757)), -(c_Big__Operators_Olinorder__class_OMax(_1591755, _1591757) = _1591759)], (26061 ^ _774244) ^ [_1229459, _1229461] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1229459), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229461))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1229459))), _1229461)))], (19603 ^ _774244) ^ [_1108944, _1108946, _1108948] : [class_Int_Onumber__ring(_1108944), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1108944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108944), _1108946), _1108948)), 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(_1108944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108944), hAPP(hAPP(c_Power_Opower__class_Opower(_1108944), _1108946), 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(_1108944), _1108948), 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(_1108944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108944), hAPP(c_Int_Onumber__class_Onumber__of(_1108944), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1108946)), _1108948)))], (5290 ^ _774244) ^ [_856055, _856057] : [_856057 = _856055, -(c_List_Odistinct(_856057) = c_List_Odistinct(_856055))], (26113 ^ _774244) ^ [_1230438, _1230440] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230438), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230440))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230438), _1230440)))], (50326 ^ _774244) ^ [_1782237, _1782239, _1782241] : [hAPP(c_List_Orev(_1782237), _1782239) = _1782241, -(_1782239 = hAPP(c_List_Orev(_1782237), _1782241))], (15152 ^ _774244) ^ [_1029059, _1029061, _1029063, _1029065] : [class_Divides_Oring__div(_1029059), -(c_Divides_Odiv__class_Omod(_1029059, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029059), _1029061), _1029063), _1029065) = c_Divides_Odiv__class_Omod(_1029059, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029059), _1029061), c_Divides_Odiv__class_Omod(_1029059, _1029063, _1029065)), _1029065))], (6688 ^ _774244) ^ [_881914, _881916, _881918] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_881914, _881916, _881918)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_881918)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24395 ^ _774244) ^ [_1198480] : [class_Orderings_Olinorder(_1198480), -(c_Orderings_Oord_Omin(_1198480, hAPP(c_COMBC(_1198480, _1198480, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1198480))) = c_Orderings_Oord__class_Omax(_1198480))], (34097 ^ _774244) ^ [_1394240, _1394242, _1394244, _1394246] : [class_Groups_Ocomm__monoid__mult(_1394240), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1394242), _1394244))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1394242, _1394240), _1394246), _1394244) = c_Groups_Oone__class_Oone(_1394240))], (41348 ^ _774244) ^ [_1567974, _1567976] : [hAPP(hAPP(c_Relation_Orel__comp(_1567974, _1567974, _1567974), _1567976), _1567976) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1567974, _1567974), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1567974, _1567976))], (8039 ^ _774244) ^ [_905828, _905830, _905832, _905834] : [class_Orderings_Oorder(_905828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905828), hAPP(_905830, 8044 ^ [_905828, _905830, _905832, _905834])), hAPP(_905830, hAPP(c_Nat_OSuc, 8044 ^ [_905828, _905830, _905832, _905834])))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905832), _905834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905828), hAPP(_905830, _905832)), hAPP(_905830, _905834))))], (36435 ^ _774244) ^ [_1447091, _1447093, _1447095, _1447097, _1447099] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447091, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447093, tc_fun(_1447091, tc_HOL_Obool)), _1447095), _1447097)), _1447099) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447093, tc_fun(_1447091, tc_HOL_Obool)), _1447095), hAPP(hAPP(c_COMBC(_1447093, tc_fun(_1447091, tc_HOL_Obool), tc_fun(_1447091, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447091, tc_HOL_Obool), tc_fun(tc_fun(_1447091, tc_HOL_Obool), tc_fun(_1447091, tc_HOL_Obool)), _1447093), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447091, tc_HOL_Obool))), _1447097)), _1447099)))], (27759 ^ _774244) ^ [_1263951, _1263953, _1263955, _1263957] : [27773 ^ _774244 : [(27776 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1263957, 27772 ^ [_1263951, _1263953, _1263955, _1263957])))], (27774 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1263951), 27772 ^ [_1263951, _1263953, _1263955, _1263957]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263951, tc_HOL_Obool)), _1263953), _1263955))))]], 27760 ^ _774244 : [(27767 ^ _774244) ^ [_1264160] : [hBOOL(hAPP(hAPP(c_member(_1263951), _1264160), _1263955)), hBOOL(hAPP(_1263957, _1264160))], (27761 ^ _774244) ^ [_1264064] : [hBOOL(hAPP(hAPP(c_member(_1263951), _1264064), _1263953)), hBOOL(hAPP(_1263957, _1264064))]]], (33912 ^ _774244) ^ [_1390300, _1390302, _1390304, _1390306, _1390308, _1390310, _1390312] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1390300, tc_Option_Ooption(_1390302)), _1390304), _1390306), hAPP(c_Option_Ooption_OSome(_1390302), _1390308)), _1390310) = hAPP(c_Option_Ooption_OSome(_1390302), _1390312)), 33913 ^ _774244 : [(33920 ^ _774244) ^ [] : [-(_1390310 = _1390306), hAPP(_1390304, _1390310) = hAPP(c_Option_Ooption_OSome(_1390302), _1390312)], (33914 ^ _774244) ^ [] : [_1390310 = _1390306, _1390308 = _1390312]]], (41158 ^ _774244) ^ [_1561596, _1561598, _1561600, _1561602] : [c_Finite__Set_Ofolding(_1561596, _1561598, _1561600, _1561602), -(hAPP(_1561602, c_Orderings_Obot__class_Obot(tc_fun(_1561596, tc_HOL_Obool))) = c_Fun_Oid(_1561598))], (13740 ^ _774244) ^ [_1003403, _1003405, _1003407, _1003409] : [class_Groups_Ouminus(_1003403), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1003405, _1003403)), _1003407), _1003409) = hAPP(c_Groups_Ouminus__class_Ouminus(_1003403), hAPP(_1003407, _1003409)))], (7249 ^ _774244) ^ [_891807, _891809, _891811, _891813] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_891807), 7252 ^ _774244 : [(7259 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891807), _891809), _891813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_891807), _891809), _891811)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_891807), _891813), _891811))))], (7253 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_891807), _891809), _891811)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_891807), _891813), _891811))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891807), _891809), _891813)))]]], (32860 ^ _774244) ^ [_1369612, _1369614, _1369616] : [class_Orderings_Olinorder(_1369612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1369612, tc_HOL_Obool)), _1369614), _1369616)), -(_1369614 = c_Orderings_Obot__class_Obot(tc_fun(_1369612, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369612), _1369616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369612), c_Big__Operators_Olinorder__class_OMax(_1369612, _1369614)), c_Big__Operators_Olinorder__class_OMax(_1369612, _1369616))))], (29582 ^ _774244) ^ [_1301151, _1301153] : [-(c_Set_Othe__elem(_1301151, hAPP(hAPP(c_Set_Oinsert(_1301151), _1301153), c_Orderings_Obot__class_Obot(tc_fun(_1301151, tc_HOL_Obool)))) = _1301153)], (39964 ^ _774244) ^ [_1529277, _1529279, _1529281] : [c_Relation_Orefl__on(_1529277, _1529279, _1529281), 39967 ^ _774244 : [(39970 ^ _774244) ^ [_1529459] : [hBOOL(hAPP(hAPP(c_member(_1529277), _1529459), _1529279)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1529277, _1529277)), hAPP(hAPP(c_Product__Type_OPair(_1529277, _1529277), _1529459), _1529459)), _1529281)))], (39968 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529277, _1529277), tc_HOL_Obool)), _1529281), hAPP(hAPP(c_Product__Type_OSigma(_1529277, _1529277), _1529279), hAPP(c_COMBK(tc_fun(_1529277, tc_HOL_Obool), _1529277), _1529279)))))]]], (45978 ^ _774244) ^ [_1678523, _1678525, _1678527] : [-(hAPP(hAPP(c_List_Ozip(_1678523, _1678525), hAPP(hAPP(c_List_Omap(tc_prod(_1678523, _1678525), _1678523), c_Product__Type_Ofst(_1678523, _1678525)), _1678527)), hAPP(hAPP(c_List_Omap(tc_prod(_1678523, _1678525), _1678525), c_Product__Type_Osnd(_1678523, _1678525)), _1678527)) = _1678527)], (51385 ^ _774244) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (6325 ^ _774244) ^ [_875869, _875871, _875873, _875875, _875877, _875879] : [c_Com_Ocom_OCall(_875869, _875871, _875873) = c_Com_Ocom_OCond(_875875, _875877, _875879)], (628 ^ _774244) ^ [_783990, _783992, _783994, _783996, _783998, _784000, _784002, _784004] : [-(c_Finite__Set_Ofolding(_784002, _783998, _783994, _783990)), c_Finite__Set_Ofolding(_784004, _784000, _783996, _783992), _784004 = _784002, _784000 = _783998, _783996 = _783994, _783992 = _783990], (41033 ^ _774244) ^ [_1555688, _1555690, _1555692] : [class_Lattices_Odistrib__lattice(_1555688), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555688), _1555690)), -(_1555690 = c_Orderings_Obot__class_Obot(tc_fun(_1555688, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555688), _1555692)), -(_1555692 = c_Orderings_Obot__class_Obot(tc_fun(_1555688, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1555688), c_Big__Operators_Olattice__class_OSup__fin(_1555688, _1555690)), c_Big__Operators_Olattice__class_OSup__fin(_1555688, _1555692)) = c_Big__Operators_Olattice__class_OSup__fin(_1555688, hAPP(c_Set_OCollect(_1555688), hAPP(hAPP(c_COMBB(tc_fun(_1555688, tc_HOL_Obool), tc_HOL_Obool, _1555688), c_HOL_OEx(_1555688)), hAPP(hAPP(c_COMBB(tc_fun(_1555688, tc_fun(_1555688, tc_HOL_Obool)), tc_fun(_1555688, tc_HOL_Obool), _1555688), hAPP(c_COMBB(tc_fun(_1555688, tc_HOL_Obool), tc_HOL_Obool, _1555688), c_HOL_OEx(_1555688))), hAPP(hAPP(c_COMBC(_1555688, tc_fun(_1555688, tc_fun(_1555688, tc_HOL_Obool)), tc_fun(_1555688, tc_fun(_1555688, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1555688, tc_fun(tc_fun(_1555688, tc_HOL_Obool), tc_fun(_1555688, tc_HOL_Obool))), tc_fun(tc_fun(_1555688, tc_fun(_1555688, tc_HOL_Obool)), tc_fun(_1555688, tc_fun(_1555688, tc_HOL_Obool))), _1555688), c_COMBS(_1555688, tc_fun(_1555688, tc_HOL_Obool), tc_fun(_1555688, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1555688, tc_fun(_1555688, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1555688, tc_fun(tc_fun(_1555688, tc_HOL_Obool), tc_fun(_1555688, tc_HOL_Obool))), _1555688), hAPP(c_COMBB(tc_fun(_1555688, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1555688, tc_HOL_Obool), tc_fun(_1555688, tc_HOL_Obool)), _1555688), c_COMBS(_1555688, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1555688, tc_fun(_1555688, tc_HOL_Obool)), tc_fun(_1555688, tc_fun(_1555688, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1555688), hAPP(c_COMBB(tc_fun(_1555688, tc_HOL_Obool), tc_fun(_1555688, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1555688), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1555688), c_fconj))), hAPP(hAPP(c_COMBC(_1555688, tc_fun(_1555688, tc_fun(_1555688, _1555688)), tc_fun(_1555688, tc_fun(_1555688, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1555688, _1555688), tc_fun(_1555688, tc_HOL_Obool)), tc_fun(tc_fun(_1555688, tc_fun(_1555688, _1555688)), tc_fun(_1555688, tc_fun(_1555688, tc_HOL_Obool))), _1555688), c_COMBB(tc_fun(_1555688, _1555688), tc_fun(_1555688, tc_HOL_Obool), _1555688)), hAPP(hAPP(c_COMBB(tc_fun(_1555688, tc_HOL_Obool), tc_fun(tc_fun(_1555688, _1555688), tc_fun(_1555688, tc_HOL_Obool)), _1555688), c_COMBB(_1555688, tc_HOL_Obool, _1555688)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1555688)))))), hAPP(hAPP(c_COMBC(_1555688, tc_fun(_1555688, tc_HOL_Obool), tc_fun(_1555688, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1555688, tc_HOL_Obool), tc_fun(_1555688, tc_HOL_Obool)), _1555688), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1555688)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1555688), c_fconj), hAPP(hAPP(c_COMBC(_1555688, tc_fun(_1555688, tc_HOL_Obool), tc_HOL_Obool), c_member(_1555688)), _1555690)))), hAPP(hAPP(c_COMBC(_1555688, tc_fun(_1555688, tc_HOL_Obool), tc_HOL_Obool), c_member(_1555688)), _1555692))))))))], (49489 ^ _774244) ^ [_1765422, _1765424, _1765426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1765422), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1765424))), c_List_Otranspose(_1765424, _1765426)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1765424)), c_List_Otranspose(_1765424, _1765426)), _1765422) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1765424), _1765424), hAPP(hAPP(c_COMBC(tc_List_Olist(_1765424), tc_Nat_Onat, _1765424), c_List_Onth(_1765424)), _1765422)), hAPP(c_List_Ofilter(tc_List_Olist(_1765424), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1765424)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1765422)), c_Nat_Osize__class_Osize(tc_List_Olist(_1765424)))), _1765426)))], (28489 ^ _774244) ^ [_1278269, _1278271] : [class_Orderings_Olinorder(_1278269), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1278269, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1278269), _1278271)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1278269), _1278271))], (17627 ^ _774244) ^ [_1075983, _1075985, _1075987, _1075989, _1075991] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1075983, _1075985, _1075987), _1075989), hAPP(c_Nat_OSuc, _1075991)) = hAPP(hAPP(_1075987, _1075989), hAPP(hAPP(c_Power_Opower_Opower(_1075983, _1075985, _1075987), _1075989), _1075991)))], (38846 ^ _774244) ^ [_1500582, _1500584, _1500586, _1500588, _1500590] : [hBOOL(hAPP(hAPP(c_member(_1500582), _1500584), hAPP(c_Set_Ovimage(_1500582, _1500586, _1500588), _1500590))), -(hBOOL(hAPP(hAPP(c_member(_1500586), hAPP(_1500588, _1500584)), _1500590)))], (11705 ^ _774244) ^ [_967351, _967353, _967355, _967357] : [class_Rings_Oordered__comm__semiring(_967351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967351), _967353), _967355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967351), c_Groups_Ozero__class_Ozero(_967351)), _967357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967351), _967357), _967353)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967351), _967357), _967355))))], (39748 ^ _774244) ^ [_1522697, _1522699, _1522701, _1522703] : [_1522697 = c_Orderings_Obot__class_Obot(tc_fun(_1522699, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1522701, _1522699), _1522701, c_Product__Type_Ofst(_1522701, _1522699)), hAPP(hAPP(c_Product__Type_OSigma(_1522701, _1522699), _1522703), hAPP(c_COMBK(tc_fun(_1522699, tc_HOL_Obool), _1522701), _1522697))) = c_Orderings_Obot__class_Obot(tc_fun(_1522701, tc_HOL_Obool)))], (25625 ^ _774244) ^ [_1221284, _1221286, _1221288, _1221290] : [class_Divides_Osemiring__div(_1221284), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221284), _1221286), _1221288)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221284), _1221290), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1221284), _1221288), _1221286)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1221284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221284), _1221290), _1221288)), _1221286))], (27426 ^ _774244) ^ [_1257850, _1257852, _1257854, _1257856] : [class_Rings_Osemiring__1(_1257850), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1257852, _1257850), hAPP(c_COMBK(_1257850, _1257852), _1257854)), _1257856) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257850), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1257850), hAPP(c_Finite__Set_Ocard(_1257852), _1257856))), _1257854))], (17017 ^ _774244) ^ [_1065291] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1065291) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15732 ^ _774244) ^ [_1040697, _1040699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040697), hAPP(c_Nat_OSuc, _1040699))), _1040697)))], (49531 ^ _774244) ^ [_1766506, _1766508, _1766510] : [class_Orderings_Olinorder(_1766506), -(c_List_Olinorder__class_Osorted(_1766506, hAPP(c_List_Ofilter(_1766506, hAPP(hAPP(c_COMBC(_1766506, _1766506, tc_HOL_Obool), c_fequal), hAPP(_1766508, _1766510))), _1766510)))], (4088 ^ _774244) ^ [_837388, _837390, _837392, _837394, _837396, _837398] : [-(c_Map_Oran(_837398, _837394, _837390) = c_Map_Oran(_837396, _837392, _837388)), _837398 = _837396, _837394 = _837392, _837390 = _837388], (16283 ^ _774244) ^ [_1051210, _1051212] : [class_Rings_Ocomm__semiring__1(_1051210), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1051210), _1051212), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1051212)], (11381 ^ _774244) ^ [_961615, _961617] : [class_Rings_Olinordered__idom(_961615), 11384 ^ _774244 : [(11391 ^ _774244) ^ [] : [_961617 = c_Groups_Ozero__class_Ozero(_961615), -(c_Groups_Osgn__class_Osgn(_961615, _961617) = c_Groups_Ozero__class_Ozero(_961615))], (11385 ^ _774244) ^ [] : [c_Groups_Osgn__class_Osgn(_961615, _961617) = c_Groups_Ozero__class_Ozero(_961615), -(_961617 = c_Groups_Ozero__class_Ozero(_961615))]]], (32602 ^ _774244) ^ [_1365159] : [class_Rings_Osemiring__1(_1365159), -(hBOOL(hAPP(hAPP(c_member(_1365159), c_Groups_Oone__class_Oone(_1365159)), c_Nat_Osemiring__1__class_ONats(_1365159))))], (23105 ^ _774244) ^ [_1173558, _1173560] : [-(_1173558 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1173560, _1173558), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1173560), _1173558)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1173560, _1173558)))))], (43939 ^ _774244) ^ [_1629703, _1629705, _1629707] : [-(hAPP(c_Relation_Oconverse(_1629703, _1629705), _1629707) = hAPP(c_Set_OCollect(tc_prod(_1629705, _1629703)), hAPP(c_Product__Type_Oprod_Oprod__case(_1629705, _1629703, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1629705, tc_fun(tc_prod(_1629703, _1629705), tc_HOL_Obool), tc_fun(_1629703, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1629703, tc_fun(tc_fun(tc_prod(_1629703, _1629705), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1629703, _1629705), tc_HOL_Obool), tc_fun(_1629703, tc_HOL_Obool)), _1629705), c_COMBC(_1629703, tc_fun(tc_prod(_1629703, _1629705), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1629703, tc_prod(_1629703, _1629705)), tc_fun(_1629703, tc_fun(tc_fun(tc_prod(_1629703, _1629705), tc_HOL_Obool), tc_HOL_Obool)), _1629705), hAPP(c_COMBB(tc_prod(_1629703, _1629705), tc_fun(tc_fun(tc_prod(_1629703, _1629705), tc_HOL_Obool), tc_HOL_Obool), _1629703), c_member(tc_prod(_1629703, _1629705)))), hAPP(c_COMBC(_1629703, _1629705, tc_prod(_1629703, _1629705)), c_Product__Type_OPair(_1629703, _1629705))))), _1629707))))], (17753 ^ _774244) ^ [_1078135, _1078137] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078135)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078135)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078137)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078135)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078137))))], (38043 ^ _774244) ^ [_1483575, _1483577, _1483579, _1483581, _1483583, _1483585] : [c_Fun_Oinj__on(_1483575, _1483577, hAPP(c_Fun_Ocomp(_1483579, _1483577, _1483575, _1483581), _1483583), _1483585), -(c_Fun_Oinj__on(_1483575, _1483579, _1483583, _1483585))], (39940 ^ _774244) ^ [_1528431, _1528433, _1528435, _1528437, _1528439, _1528441] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1528431, _1528433), _1528431, tc_prod(_1528435, _1528437), c_Product__Type_Ofst(_1528431, _1528433)), c_Product__Type_Omap__pair(_1528435, _1528431, _1528437, _1528433, _1528439, _1528441)) = hAPP(c_Fun_Ocomp(_1528435, _1528431, tc_prod(_1528435, _1528437), _1528439), c_Product__Type_Ofst(_1528435, _1528437)))], (7431 ^ _774244) ^ [_894827, _894829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894827), _894829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894827), hAPP(c_Nat_OSuc, _894829))))], (49230 ^ _774244) ^ [_1758986, _1758988, _1758990] : [-(c_List_Obutlast(_1758986, hAPP(hAPP(c_List_Odrop(_1758986), _1758988), _1758990)) = hAPP(hAPP(c_List_Odrop(_1758986), _1758988), c_List_Obutlast(_1758986, _1758990)))], (1734 ^ _774244) ^ [_798643, _798645] : [-(class_Int_Onumber(_798643)), _798645 = _798643, class_Int_Onumber(_798645)], (29866 ^ _774244) ^ [_1306340] : [29868 ^ _774244 : [(29871 ^ _774244) ^ [_1306450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29867 ^ [_1306340, _1306450]), _1306450))], (29869 ^ _774244) ^ [_1306416] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29867 ^ [_1306340, _1306416]), _1306340)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1306340)))], (1424 ^ _774244) ^ [_794768, _794770] : [-(class_Groups_Ocancel__ab__semigroup__add(_794768)), _794770 = _794768, class_Groups_Ocancel__ab__semigroup__add(_794770)], (51267 ^ _774244) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (20287 ^ _774244) ^ [_1121436, _1121438, _1121440, _1121442] : [class_Rings_Odivision__ring(_1121436), -(_1121438 = c_Groups_Ozero__class_Ozero(_1121436)), 20294 ^ _774244 : [(20301 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121436), _1121440), _1121438) = _1121442, -(_1121440 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121436), _1121442), _1121438))], (20295 ^ _774244) ^ [] : [_1121440 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121436), _1121442), _1121438), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121436), _1121440), _1121438) = _1121442)]]], (17333 ^ _774244) ^ [_1070871, _1070873, _1070875, _1070877] : [class_Rings_Olinordered__semidom(_1070871), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070871), hAPP(hAPP(c_Power_Opower__class_Opower(_1070871), _1070873), hAPP(c_Nat_OSuc, _1070875))), hAPP(hAPP(c_Power_Opower__class_Opower(_1070871), _1070877), hAPP(c_Nat_OSuc, _1070875)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070871), c_Groups_Ozero__class_Ozero(_1070871)), _1070877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070871), _1070873), _1070877)))], (14205 ^ _774244) ^ [_1012324, _1012326, _1012328] : [-(_1012324 = 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), _1012324), _1012326)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012324), _1012328)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1012326), _1012328))], (18709 ^ _774244) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (25949 ^ _774244) ^ [_1227577, _1227579, _1227581, _1227583] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1227577, _1227579, _1227581), c_Product__Type_Ocurry(_1227577, _1227579, _1227581, _1227583)) = _1227583)], (44036 ^ _774244) ^ [_1632831, _1632833] : [-(c_Transitive__Closure_Ortrancl(_1632831, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1632831, _1632831), tc_HOL_Obool)), _1632833), c_Relation_OId(_1632831))) = c_Transitive__Closure_Ortrancl(_1632831, _1632833))], (18579 ^ _774244) ^ [_1091312] : [-(c_Int_OBit1(_1091312) = 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)), _1091312)), _1091312))], (19291 ^ _774244) ^ [_1103582, _1103584] : [class_Int_Onumber__ring(_1103582), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103582), hAPP(c_Int_Onumber__class_Onumber__of(_1103582), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1103584) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103582), _1103584), _1103584))], (34293 ^ _774244) ^ [_1398242, _1398244, _1398246, _1398248, _1398250] : [class_Groups_Ocomm__monoid__mult(_1398242), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398244), _1398246)), -(hBOOL(hAPP(hAPP(c_member(_1398244), _1398248), _1398246))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398244, _1398242), _1398250), hAPP(hAPP(c_Set_Oinsert(_1398244), _1398248), _1398246)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398242), hAPP(_1398250, _1398248)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398244, _1398242), _1398250), _1398246)))], (47500 ^ _774244) ^ [_1718076, _1718078, _1718080, _1718082, _1718084] : [-(hAPP(hAPP(c_List_Olist_OCons(_1718076), _1718078), _1718080) = hAPP(hAPP(c_List_Oappend(_1718076), _1718082), _1718084)), 47501 ^ _774244 : [(47508 ^ _774244) ^ [_1718259] : [hAPP(hAPP(c_List_Olist_OCons(_1718076), _1718078), _1718259) = _1718082, _1718080 = hAPP(hAPP(c_List_Oappend(_1718076), _1718259), _1718084)], (47502 ^ _774244) ^ [] : [_1718082 = c_List_Olist_ONil(_1718076), hAPP(hAPP(c_List_Olist_OCons(_1718076), _1718078), _1718080) = _1718084]]], (28596 ^ _774244) ^ [_1280864, _1280866, _1280868, _1280870, _1280872, _1280874] : [class_Complete__Lattice_Ocomplete__lattice(_1280864), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280866, _1280864), _1280868), hAPP(hAPP(c_COMBB(tc_fun(_1280870, _1280864), _1280864, _1280866), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280870, _1280864), _1280872)), _1280874)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280870, _1280864), _1280872), hAPP(hAPP(c_COMBB(tc_fun(_1280866, _1280864), _1280864, _1280870), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280866, _1280864), _1280868)), hAPP(c_COMBC(_1280866, _1280870, _1280864), _1280874))))], (8508 ^ _774244) ^ [_912948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _912948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _912948))))], (34014 ^ _774244) ^ [_1392685, _1392687, _1392689, _1392691, _1392693] : [class_Groups_Ocomm__monoid__mult(_1392685), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392687, _1392685), hAPP(hAPP(c_COMBS(_1392687, _1392685, _1392685), hAPP(hAPP(c_COMBB(_1392685, tc_fun(_1392685, _1392685), _1392687), c_Groups_Otimes__class_Otimes(_1392685)), _1392689)), _1392691)), _1392693) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392685), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392687, _1392685), _1392689), _1392693)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392687, _1392685), _1392691), _1392693)))], (39315 ^ _774244) ^ [_1511107, _1511109, _1511111, _1511113, _1511115] : [hBOOL(hAPP(hAPP(c_member(_1511107), _1511109), c_Map_Oran(_1511111, _1511107, c_Map_Orestrict__map(_1511111, _1511107, _1511113, _1511115)))), 39319 ^ _774244 : [(39322 ^ _774244) ^ [] : [-(hAPP(_1511113, 39318 ^ [_1511107, _1511109, _1511111, _1511113, _1511115]) = hAPP(c_Option_Ooption_OSome(_1511107), _1511109))], (39320 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1511111), 39318 ^ [_1511107, _1511109, _1511111, _1511113, _1511115]), _1511115)))]]], (19155 ^ _774244) ^ [_1101155] : [-(c_Int_Opred(c_Int_OBit1(_1101155)) = c_Int_OBit0(_1101155))], (8724 ^ _774244) ^ [_916585, _916587, _916589, _916591] : [class_Groups_Oab__semigroup__mult(_916585), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916585), _916587), _916589)), _916591) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916585), _916587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916585), _916589), _916591)))], (23525 ^ _774244) ^ [_1181859] : [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), _1181859))), -(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), _1181859)) = 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), _1181859))))], (46818 ^ _774244) ^ [_1702038, _1702040, _1702042] : [-(hAPP(hAPP(c_List_Omap(_1702038, _1702040), _1702042), c_List_Olist_ONil(_1702038)) = c_List_Olist_ONil(_1702040))], (22050 ^ _774244) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (6584 ^ _774244) ^ [_880332, _880334] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _880332), _880334)), 6585 ^ _774244 : [(6592 ^ _774244) ^ [] : [_880332 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _880334 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6586 ^ _774244) ^ [] : [_880332 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _880334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (31146 ^ _774244) ^ [_1333171, _1333173, _1333175, _1333177] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333171, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1333171, tc_fun(_1333171, tc_HOL_Obool), tc_HOL_Obool), c_member(_1333171)), _1333173)), hAPP(hAPP(c_COMBC(_1333171, tc_fun(_1333171, tc_HOL_Obool), tc_HOL_Obool), c_member(_1333171)), _1333175)), _1333177)), -(hBOOL(hAPP(hAPP(c_member(_1333171), _1333177), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333171, tc_HOL_Obool)), _1333173), _1333175))))], (13198 ^ _774244) ^ [_993662, _993664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993662), _993664)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993664), _993662)), -(_993662 = _993664)], (35237 ^ _774244) ^ [_1420109, _1420111, _1420113, _1420115, _1420117] : [hAPP(c_Set_Oimage(_1420109, _1420111, _1420113), c_Orderings_Otop__class_Otop(tc_fun(_1420109, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1420111, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1420111, _1420115, _1420117), c_Orderings_Otop__class_Otop(tc_fun(_1420111, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1420115, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1420109, _1420115, hAPP(c_Fun_Ocomp(_1420111, _1420115, _1420109, _1420117), _1420113)), c_Orderings_Otop__class_Otop(tc_fun(_1420109, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1420115, tc_HOL_Obool)))], (12267 ^ _774244) ^ [_977252, _977254, _977256, _977258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _977252), _977254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _977256), _977258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _977252), _977256)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _977254), _977258))))], (34166 ^ _774244) ^ [_1395608, _1395610, _1395612, _1395614, _1395616] : [-(hBOOL(hAPP(hAPP(c_member(_1395608), _1395610), _1395612))), -(hAPP(c_Map_Orestrict__map(_1395608, _1395614, _1395616, _1395612), _1395610) = c_Option_Ooption_ONone(_1395614))], (3836 ^ _774244) ^ [_833374, _833376] : [_833376 = _833374, -(c_Set_OBall(_833376) = c_Set_OBall(_833374))], (7126 ^ _774244) ^ [_890042, _890044] : [-(_890042 = c_Option_Ooption_ONone(_890044)), -(_890042 = hAPP(c_Option_Ooption_OSome(_890044), 7129 ^ [_890042, _890044]))], (37524 ^ _774244) ^ [_1472947] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1472947)), c_Int_OInteg)))], (30043 ^ _774244) ^ [_1309360] : [class_Orderings_Olinorder(_1309360), -(c_Finite__Set_Ofun__left__comm__idem(_1309360, _1309360, c_Orderings_Oord__class_Omax(_1309360)))], (24625 ^ _774244) ^ [_1203117, _1203119, _1203121, _1203123, _1203125, _1203127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203117, tc_fun(_1203119, tc_HOL_Obool))), _1203121), _1203123)), hBOOL(hAPP(hAPP(_1203121, _1203125), _1203127)), -(hBOOL(hAPP(hAPP(_1203123, _1203125), _1203127)))], (47153 ^ _774244) ^ [_1709667, _1709669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709667), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1709669))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1709669), _1709667)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1709669))))], (46844 ^ _774244) ^ [_1702508, _1702510] : [-(c_List_Oremove1(_1702508, _1702510, c_List_Olist_ONil(_1702508)) = c_List_Olist_ONil(_1702508))], (12021 ^ _774244) ^ [_973125, _973127] : [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), _973125), _973127))), 12024 ^ _774244 : [(12027 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _973127)))], (12025 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _973125)))]]], (31100 ^ _774244) ^ [_1332161, _1332163, _1332165, _1332167, _1332169] : [hBOOL(hAPP(hAPP(c_member(_1332161), _1332163), _1332165)), -(hBOOL(hAPP(hAPP(c_member(_1332167), hAPP(_1332169, _1332163)), hAPP(c_Set_Oimage(_1332161, _1332167, _1332169), _1332165))))], (50298 ^ _774244) ^ [_1781663, _1781665] : [hBOOL(hAPP(c_List_Odistinct(_1781663), hAPP(c_List_Orev(_1781663), _1781665))), -(hBOOL(hAPP(c_List_Odistinct(_1781663), _1781665)))], (25745 ^ _774244) ^ [_1223506, _1223508, _1223510] : [25746 ^ _774244 : [(25749 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223508), _1223510))], (25747 ^ _774244) ^ [] : [_1223506 = 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), _1223506), _1223508)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223506), _1223510))))], (28809 ^ _774244) ^ [_1285999] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1285999)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1285999)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1285999)))], (16637 ^ _774244) ^ [_1057821, _1057823, _1057825] : [class_Int_Onumber__ring(_1057821), class_Rings_Olinordered__idom(_1057821), 16644 ^ _774244 : [(16651 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1057823), _1057825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057821), hAPP(c_Int_Onumber__class_Onumber__of(_1057821), _1057823)), hAPP(c_Int_Onumber__class_Onumber__of(_1057821), _1057825))))], (16645 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057821), hAPP(c_Int_Onumber__class_Onumber__of(_1057821), _1057823)), hAPP(c_Int_Onumber__class_Onumber__of(_1057821), _1057825))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1057823), _1057825)))]]], (21399 ^ _774244) ^ [_1141164, _1141166, _1141168, _1141170] : [class_Fields_Olinordered__field__inverse__zero(_1141164), class_Int_Onumber(_1141164), 21406 ^ _774244 : [(21407 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141164), _1141166), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168))), _1141170)), 21410 ^ _774244 : [(21417 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), c_Groups_Ozero__class_Ozero(_1141164)), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168)))), 21420 ^ _774244 : [(21427 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168)), c_Groups_Ozero__class_Ozero(_1141164)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), c_Groups_Ozero__class_Ozero(_1141164)), _1141170)))], (21421 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168)), c_Groups_Ozero__class_Ozero(_1141164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141164), _1141170), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168))), _1141166)))]]], (21411 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), c_Groups_Ozero__class_Ozero(_1141164)), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), _1141166), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141164), _1141170), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168)))))]]], (21433 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141164), _1141166), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168))), _1141170))), 21436 ^ _774244 : [(21439 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), _1141166), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141164), _1141170), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168))))], (21437 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), c_Groups_Ozero__class_Ozero(_1141164)), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168))))]], 21440 ^ _774244 : [(21443 ^ _774244) ^ [] : [21444 ^ _774244 : [(21447 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141164), _1141170), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168))), _1141166))], (21445 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168)), c_Groups_Ozero__class_Ozero(_1141164))))]], 21448 ^ _774244 : [(21451 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), c_Groups_Ozero__class_Ozero(_1141164)), _1141170))], (21449 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168)), c_Groups_Ozero__class_Ozero(_1141164)))]]], (21441 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141164), c_Groups_Ozero__class_Ozero(_1141164)), hAPP(c_Int_Onumber__class_Onumber__of(_1141164), _1141168)))]]]]], (22328 ^ _774244) ^ [_1159071, _1159073, _1159075] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1159071, _1159073, _1159075, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1159073)], (24679 ^ _774244) ^ [_1204238, _1204240, _1204242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1204238), c_Nitpick_Oplus__frac(_1204238, _1204240, c_Nitpick_Ouminus__frac(_1204238, _1204242)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1204238, _1204240, _1204242))], (49242 ^ _774244) ^ [_1759308, _1759310, _1759312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1759308), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759310)), _1759312))), -(hAPP(hAPP(c_List_Otake(_1759310), _1759308), c_List_Obutlast(_1759310, _1759312)) = hAPP(hAPP(c_List_Otake(_1759310), _1759308), _1759312))], (7917 ^ _774244) ^ [_903589] : [_903589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _903589) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9618 ^ _774244) ^ [_932667] : [class_Rings_Olinordered__semidom(_932667), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932667), c_Groups_Ozero__class_Ozero(_932667)), c_Groups_Oone__class_Oone(_932667))))], (40414 ^ _774244) ^ [_1537562, _1537564, _1537566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537562, _1537562), tc_HOL_Obool)), _1537564), hAPP(hAPP(c_Product__Type_OSigma(_1537562, _1537562), _1537566), hAPP(c_COMBK(tc_fun(_1537562, tc_HOL_Obool), _1537562), _1537566)))), 40420 ^ _774244 : [(40423 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537562, _1537562)), hAPP(hAPP(c_Product__Type_OPair(_1537562, _1537562), 40419 ^ [_1537562, _1537564, _1537566]), 40419 ^ [_1537562, _1537564, _1537566])), _1537564))], (40421 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537562), 40419 ^ [_1537562, _1537564, _1537566]), _1537566)))]], -(c_Relation_Orefl__on(_1537562, _1537566, _1537564))], (35643 ^ _774244) ^ [] : [-(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))], (40675 ^ _774244) ^ [_1543388, _1543390, _1543392, _1543394] : [-(hBOOL(hAPP(hAPP(c_member(_1543388), _1543390), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1543388, tc_HOL_Obool)), _1543392), hAPP(c_Set_OCollect(_1543388), _1543394))))), hBOOL(hAPP(hAPP(c_member(_1543388), _1543390), _1543392)), hBOOL(hAPP(_1543394, _1543390))], (45488 ^ _774244) ^ [_1667314, _1667316, _1667318, _1667320, _1667322, _1667324, _1667326] : [c_Map_Omap__comp(_1667314, _1667316, _1667318, _1667320, _1667322, _1667324) = hAPP(c_Option_Ooption_OSome(_1667316), _1667326), 45492 ^ _774244 : [(45495 ^ _774244) ^ [] : [-(hAPP(_1667320, 45491 ^ [_1667314, _1667316, _1667318, _1667320, _1667322, _1667324, _1667326]) = hAPP(c_Option_Ooption_OSome(_1667316), _1667326))], (45493 ^ _774244) ^ [] : [-(hAPP(_1667322, _1667324) = hAPP(c_Option_Ooption_OSome(_1667314), 45491 ^ [_1667314, _1667316, _1667318, _1667320, _1667322, _1667324, _1667326]))]]], (16373 ^ _774244) ^ [_1052695, _1052697] : [class_Groups_Oordered__ab__group__add__abs(_1052695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052695), c_Groups_Ozero__class_Ozero(_1052695)), _1052697)), -(hAPP(c_Groups_Oabs__class_Oabs(_1052695), _1052697) = _1052697)], (27922 ^ _774244) ^ [_1267326, _1267328, _1267330, _1267332] : [class_Lattices_Osemilattice__sup(_1267326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267326), _1267328), _1267330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267326), _1267328), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267326), _1267330), _1267332))))], (26462 ^ _774244) ^ [_1236920, _1236922, _1236924, _1236926] : [class_Rings_Oring__1(_1236920), -(hAPP(c_Int_Oring__1__class_Oof__int(_1236920), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236922, tc_Int_Oint), _1236924), _1236926)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236922, _1236920), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1236920, _1236922), c_Int_Oring__1__class_Oof__int(_1236920)), _1236924)), _1236926))], (13487 ^ _774244) ^ [_998729, _998731, _998733, _998735] : [class_Divides_Osemiring__div(_998729), -(c_Divides_Odiv__class_Omod(_998729, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998729), _998731), _998733), _998735) = c_Divides_Odiv__class_Omod(_998729, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998729), _998731), c_Divides_Odiv__class_Omod(_998729, _998733, _998735)), _998735))], (49228 ^ _774244) ^ [_1758937, _1758939, _1758941] : [-(hAPP(hAPP(c_List_Odrop(_1758937), _1758939), c_List_Obutlast(_1758937, _1758941)) = c_List_Obutlast(_1758937, hAPP(hAPP(c_List_Odrop(_1758937), _1758939), _1758941)))], (47415 ^ _774244) ^ [_1715876, _1715878, _1715880] : [class_Orderings_Olinorder(_1715876), -(hBOOL(hAPP(hAPP(c_member(_1715876), _1715878), hAPP(c_List_Oset(_1715876), _1715880)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1715876, _1715876, c_COMBI(_1715876), _1715878, _1715880) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1715876, _1715876, c_COMBI(_1715876)), _1715878), _1715880))], (49204 ^ _774244) ^ [_1758589, _1758591, _1758593] : [_1758589 = c_List_Olist_ONil(_1758591), -(c_List_Obutlast(_1758591, hAPP(hAPP(c_List_Olist_OCons(_1758591), _1758593), _1758589)) = c_List_Olist_ONil(_1758591))], (36315 ^ _774244) ^ [_1444557, _1444559, _1444561, _1444563] : [class_Lattices_Olattice(_1444557), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444557), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444557), _1444559), _1444561)), _1444563) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444557), _1444559), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444557), _1444561), _1444563)))], (45692 ^ _774244) ^ [_1672309, _1672311, _1672313, _1672315, _1672317] : [c_Fun_Oinj__on(_1672309, _1672311, _1672313, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1672309, tc_HOL_Obool)), hAPP(c_List_Oset(_1672309), _1672315)), hAPP(c_List_Oset(_1672309), _1672317))), 45695 ^ _774244 : [(45702 ^ _774244) ^ [] : [_1672315 = _1672317, -(hAPP(hAPP(c_List_Omap(_1672309, _1672311), _1672313), _1672315) = hAPP(hAPP(c_List_Omap(_1672309, _1672311), _1672313), _1672317))], (45696 ^ _774244) ^ [] : [hAPP(hAPP(c_List_Omap(_1672309, _1672311), _1672313), _1672315) = hAPP(hAPP(c_List_Omap(_1672309, _1672311), _1672313), _1672317), -(_1672315 = _1672317)]]], (12183 ^ _774244) ^ [_975939] : [-(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), _975939))))], (41324 ^ _774244) ^ [_1567584, _1567586, _1567588, _1567590] : [c_Wellfounded_Owf(_1567584, _1567586), c_Wellfounded_Owf(_1567588, _1567590), -(c_Wellfounded_Owf(tc_prod(_1567584, _1567588), c_Wellfounded_Olex__prod(_1567584, _1567588, _1567586, _1567590)))], (45635 ^ _774244) ^ [_1670979, _1670981, _1670983, _1670985, _1670987] : [-(c_Map_Odom(_1670979, _1670981, hAPP(hAPP(c_COMBS(_1670979, tc_Option_Ooption(_1670983), tc_Option_Ooption(_1670981)), hAPP(hAPP(c_COMBB(tc_fun(_1670983, _1670981), tc_fun(tc_Option_Ooption(_1670983), tc_Option_Ooption(_1670981)), _1670979), c_Option_Omap(_1670983, _1670981)), _1670985)), _1670987)) = c_Map_Odom(_1670979, _1670983, _1670987))], (1724 ^ _774244) ^ [_798518, _798520] : [-(class_Groups_Ozero(_798518)), _798520 = _798518, class_Groups_Ozero(_798520)], (47036 ^ _774244) ^ [_1706796, _1706798, _1706800] : [47038 ^ _774244 : [(47041 ^ _774244) ^ [] : [hBOOL(hAPP(_1706800, 47037 ^ [_1706796, _1706798, _1706800]))], (47039 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1706796), 47037 ^ [_1706796, _1706798, _1706800]), hAPP(c_List_Oset(_1706796), _1706798))))]], 47042 ^ _774244 : [(47043 ^ _774244) ^ [_1706980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706980), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706796)), _1706798))), -(hBOOL(hAPP(_1706800, hAPP(hAPP(c_List_Onth(_1706796), _1706798), _1706980))))]]], (18397 ^ _774244) ^ [_1088161, _1088163] : [class_Int_Onumber__ring(_1088161), -(hAPP(c_Int_Onumber__class_Onumber__of(_1088161), c_Int_Opred(_1088163)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088161), hAPP(c_Groups_Ouminus__class_Ouminus(_1088161), c_Groups_Oone__class_Oone(_1088161))), hAPP(c_Int_Onumber__class_Onumber__of(_1088161), _1088163)))], (6386 ^ _774244) ^ [_876941, _876943] : [hAPP(c_Option_Ooption_OSome(_876941), _876943) = c_Option_Ooption_ONone(_876941)], (35082 ^ _774244) ^ [_1416609, _1416611, _1416613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1416609, tc_HOL_Obool)), _1416611), _1416613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1416609, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1416609, _1416611)), c_Predicate_OPowp(_1416609, _1416613))))], (29444 ^ _774244) ^ [_1298444, _1298446, _1298448, _1298450, _1298452] : [-(_1298444 = c_Orderings_Obot__class_Obot(tc_fun(_1298446, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298446, tc_fun(_1298448, tc_HOL_Obool)), _1298444), hAPP(hAPP(c_COMBB(tc_fun(_1298448, tc_HOL_Obool), tc_fun(_1298448, tc_HOL_Obool), _1298446), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298448, tc_HOL_Obool)), _1298450)), _1298452)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298448, tc_HOL_Obool)), _1298450), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298446, tc_fun(_1298448, tc_HOL_Obool)), _1298444), _1298452)))], (51107 ^ _774244) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (14127 ^ _774244) ^ [_1010880, _1010882] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1010880), _1010882)), _1010880)))], (27135 ^ _774244) ^ [_1251609, _1251611, _1251613, _1251615] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251609), _1251611)), 27138 ^ _774244 : [(27139 ^ _774244) ^ [_1251763] : [27141 ^ _774244 : [(27147 ^ _774244) ^ [] : [-(_1251763 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27143 ^ [_1251609, _1251611, _1251613, _1251615, _1251763]), 27140 ^ [_1251609, _1251611, _1251613, _1251615, _1251763]))], (27145 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27143 ^ [_1251609, _1251611, _1251613, _1251615, _1251763]), _1251613)))], (27142 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27140 ^ [_1251609, _1251611, _1251613, _1251615, _1251763]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1251611))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251609), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1251763), _1251615))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251609), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1251763), _1251611)), _1251615))))]]], (7549 ^ _774244) ^ [_896964, _896966, _896968, _896970] : [c_Com_Ocom_OWhile(_896964, _896966) = c_Com_Ocom_OAss(_896968, _896970)], (40983 ^ _774244) ^ [_1553617, _1553619, _1553621] : [class_Lattices_Odistrib__lattice(_1553617), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553617), _1553619)), -(_1553619 = c_Orderings_Obot__class_Obot(tc_fun(_1553617, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553617), _1553621)), -(_1553621 = c_Orderings_Obot__class_Obot(tc_fun(_1553617, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1553617), c_Big__Operators_Olattice__class_OInf__fin(_1553617, _1553619)), c_Big__Operators_Olattice__class_OInf__fin(_1553617, _1553621)) = c_Big__Operators_Olattice__class_OInf__fin(_1553617, hAPP(c_Set_OCollect(_1553617), hAPP(hAPP(c_COMBB(tc_fun(_1553617, tc_HOL_Obool), tc_HOL_Obool, _1553617), c_HOL_OEx(_1553617)), hAPP(hAPP(c_COMBB(tc_fun(_1553617, tc_fun(_1553617, tc_HOL_Obool)), tc_fun(_1553617, tc_HOL_Obool), _1553617), hAPP(c_COMBB(tc_fun(_1553617, tc_HOL_Obool), tc_HOL_Obool, _1553617), c_HOL_OEx(_1553617))), hAPP(hAPP(c_COMBC(_1553617, tc_fun(_1553617, tc_fun(_1553617, tc_HOL_Obool)), tc_fun(_1553617, tc_fun(_1553617, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1553617, tc_fun(tc_fun(_1553617, tc_HOL_Obool), tc_fun(_1553617, tc_HOL_Obool))), tc_fun(tc_fun(_1553617, tc_fun(_1553617, tc_HOL_Obool)), tc_fun(_1553617, tc_fun(_1553617, tc_HOL_Obool))), _1553617), c_COMBS(_1553617, tc_fun(_1553617, tc_HOL_Obool), tc_fun(_1553617, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1553617, tc_fun(_1553617, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1553617, tc_fun(tc_fun(_1553617, tc_HOL_Obool), tc_fun(_1553617, tc_HOL_Obool))), _1553617), hAPP(c_COMBB(tc_fun(_1553617, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1553617, tc_HOL_Obool), tc_fun(_1553617, tc_HOL_Obool)), _1553617), c_COMBS(_1553617, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1553617, tc_fun(_1553617, tc_HOL_Obool)), tc_fun(_1553617, tc_fun(_1553617, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1553617), hAPP(c_COMBB(tc_fun(_1553617, tc_HOL_Obool), tc_fun(_1553617, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1553617), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1553617), c_fconj))), hAPP(hAPP(c_COMBC(_1553617, tc_fun(_1553617, tc_fun(_1553617, _1553617)), tc_fun(_1553617, tc_fun(_1553617, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1553617, _1553617), tc_fun(_1553617, tc_HOL_Obool)), tc_fun(tc_fun(_1553617, tc_fun(_1553617, _1553617)), tc_fun(_1553617, tc_fun(_1553617, tc_HOL_Obool))), _1553617), c_COMBB(tc_fun(_1553617, _1553617), tc_fun(_1553617, tc_HOL_Obool), _1553617)), hAPP(hAPP(c_COMBB(tc_fun(_1553617, tc_HOL_Obool), tc_fun(tc_fun(_1553617, _1553617), tc_fun(_1553617, tc_HOL_Obool)), _1553617), c_COMBB(_1553617, tc_HOL_Obool, _1553617)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1553617)))))), hAPP(hAPP(c_COMBC(_1553617, tc_fun(_1553617, tc_HOL_Obool), tc_fun(_1553617, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1553617, tc_HOL_Obool), tc_fun(_1553617, tc_HOL_Obool)), _1553617), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1553617)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1553617), c_fconj), hAPP(hAPP(c_COMBC(_1553617, tc_fun(_1553617, tc_HOL_Obool), tc_HOL_Obool), c_member(_1553617)), _1553619)))), hAPP(hAPP(c_COMBC(_1553617, tc_fun(_1553617, tc_HOL_Obool), tc_HOL_Obool), c_member(_1553617)), _1553621))))))))], (12003 ^ _774244) ^ [_972778, _972780, _972782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972778), _972780)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972778), _972782))), 12006 ^ _774244 : [(12009 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972780), _972782)))], (12007 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _972778)))]]], (36581 ^ _774244) ^ [_1450943, _1450945, _1450947] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1450943, tc_HOL_Obool)), _1450945), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1450943, tc_HOL_Obool)), _1450947)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450943, tc_HOL_Obool)), _1450945), _1450947))], (39656 ^ _774244) ^ [_1520268, _1520270, _1520272, _1520274, _1520276] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1520268, _1520270), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520268, tc_HOL_Obool)), _1520272), _1520274)), _1520276) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1520268, _1520270), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1520268, _1520270), _1520272), _1520276)), hAPP(hAPP(c_Product__Type_OSigma(_1520268, _1520270), _1520274), _1520276)))], (11182 ^ _774244) ^ [_958064, _958066] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958064), _958066))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _958064), _958066)), -(_958064 = _958066)], (48889 ^ _774244) ^ [_1751904, _1751906, _1751908, _1751910] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1751904)), hAPP(hAPP(c_List_Oappend(_1751904), _1751906), _1751908)), c_List_Olists(_1751904, _1751910))), 48892 ^ _774244 : [(48895 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1751904)), _1751908), c_List_Olists(_1751904, _1751910))))], (48893 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1751904)), _1751906), c_List_Olists(_1751904, _1751910))))]]], (38049 ^ _774244) ^ [_1483684, _1483686, _1483688, _1483690] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1483684), hAPP(c_Set_Oimage(_1483686, _1483684, _1483688), _1483690))), c_Fun_Oinj__on(_1483686, _1483684, _1483688, _1483690), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1483686), _1483690)))], (36381 ^ _774244) ^ [_1445974, _1445976] : [class_Lattices_Osemilattice__inf(_1445974), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445974), _1445976), _1445976) = _1445976)], (33324 ^ _774244) ^ [_1378691, _1378693, _1378695] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1378691, tc_HOL_Obool), tc_fun(_1378691, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1378691, tc_HOL_Obool), tc_fun(_1378691, tc_HOL_Obool)), _1378693), _1378695)), c_Wellfounded_Ofinite__psubset(_1378691))), 33327 ^ _774244 : [(33330 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1378691), _1378695)))], (33328 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1378691, tc_HOL_Obool)), _1378693), _1378695)))]]], (40487 ^ _774244) ^ [_1539221, _1539223, _1539225] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539221), _1539223)), 40493 ^ _774244 : [(40496 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1539225, 40492 ^ [_1539221, _1539223, _1539225])))], (40494 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539221), 40492 ^ [_1539221, _1539223, _1539225]), _1539223)))]], -(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(_1539221, tc_Nat_Onat), _1539225), _1539223))))], (51247 ^ _774244) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (22758 ^ _774244) ^ [_1167192, _1167194, _1167196, _1167198, _1167200] : [hBOOL(hAPP(hAPP(_1167192, _1167194), _1167196)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1167198, _1167200, tc_HOL_Obool), _1167192), hAPP(hAPP(c_Product__Type_OPair(_1167198, _1167200), _1167194), _1167196))))], (37612 ^ _774244) ^ [_1474976, _1474978, _1474980] : [class_Lattices_Olattice(_1474976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474976), _1474978)), hBOOL(hAPP(hAPP(c_member(_1474976), _1474980), _1474978)), 37623 ^ _774244 : [(37630 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474976, tc_HOL_Obool)), _1474978), hAPP(hAPP(c_Set_Oinsert(_1474976), _1474980), c_Orderings_Obot__class_Obot(tc_fun(_1474976, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1474976, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1474976, _1474978) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1474976), _1474980), c_Big__Operators_Olattice__class_OInf__fin(_1474976, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474976, tc_HOL_Obool)), _1474978), hAPP(hAPP(c_Set_Oinsert(_1474976), _1474980), c_Orderings_Obot__class_Obot(tc_fun(_1474976, tc_HOL_Obool)))))))], (37624 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474976, tc_HOL_Obool)), _1474978), hAPP(hAPP(c_Set_Oinsert(_1474976), _1474980), c_Orderings_Obot__class_Obot(tc_fun(_1474976, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1474976, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1474976, _1474978) = _1474980)]]], (18561 ^ _774244) ^ [_1091015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1091015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1091015))))], (18725 ^ _774244) ^ [] : [-(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)))], (39805 ^ _774244) ^ [_1524541, _1524543, _1524545, _1524547] : [-(c_Fun_Oinj__on(_1524541, tc_prod(_1524543, _1524541), 39803 ^ [_1524541, _1524543, _1524545, _1524547], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524543, tc_fun(_1524541, tc_HOL_Obool)), _1524545), _1524547)))], (10155 ^ _774244) ^ [_941607, _941609] : [class_Rings_Olinordered__idom(_941607), -(c_Groups_Osgn__class_Osgn(_941607, c_Groups_Osgn__class_Osgn(_941607, _941609)) = c_Groups_Osgn__class_Osgn(_941607, _941609))], (51281 ^ _774244) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (43791 ^ _774244) ^ [_1625833, _1625835, _1625837, _1625839] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625833, tc_fun(_1625835, tc_HOL_Obool)), _1625837), _1625839) = hAPP(c_Set_OCollect(_1625835), hAPP(hAPP(c_COMBB(tc_fun(_1625833, tc_HOL_Obool), tc_HOL_Obool, _1625835), c_HOL_OAll(_1625833)), hAPP(hAPP(c_COMBB(tc_fun(_1625833, tc_HOL_Obool), tc_fun(_1625833, tc_HOL_Obool), _1625835), hAPP(c_COMBS(_1625833, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1625833), c_fimplies), hAPP(hAPP(c_COMBC(_1625833, tc_fun(_1625833, tc_HOL_Obool), tc_HOL_Obool), c_member(_1625833)), _1625837)))), hAPP(hAPP(c_COMBC(_1625835, tc_fun(_1625833, tc_fun(_1625835, tc_HOL_Obool)), tc_fun(_1625833, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1625835, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1625833, tc_fun(_1625835, tc_HOL_Obool)), tc_fun(_1625833, tc_HOL_Obool)), _1625835), c_COMBB(tc_fun(_1625835, tc_HOL_Obool), tc_HOL_Obool, _1625833)), c_member(_1625835))), _1625839)))))], (28108 ^ _774244) ^ [_1270651, _1270653, _1270655] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270651, tc_HOL_Obool)), _1270653), _1270655) = _1270655, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270651, tc_HOL_Obool)), _1270653), _1270655)))], (25215 ^ _774244) ^ [_1214112, _1214114] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214112), _1214114))), 25216 ^ _774244 : [(25217 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214112), _1214114)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214114), _1214112)))], (25223 ^ _774244) ^ [] : [_1214112 = _1214114]]], (16237 ^ _774244) ^ [_1050272, _1050274] : [class_Rings_Olinordered__idom(_1050272), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050272), hAPP(c_Groups_Oabs__class_Oabs(_1050272), _1050274)), hAPP(c_Groups_Oabs__class_Oabs(_1050272), _1050274)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050272), _1050274), _1050274))], (34980 ^ _774244) ^ [_1414293, _1414295, _1414297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1414293, tc_HOL_Obool)), _1414295), _1414297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1414293, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1414293), _1414295)), hAPP(c_Set_OPow(_1414293), _1414297))))], (49322 ^ _774244) ^ [_1761103, _1761105, _1761107] : [hAPP(c_List_Ofilter(_1761103, _1761105), _1761107) = _1761107, 49325 ^ _774244 : [(49326 ^ _774244) ^ [_1761194] : [hBOOL(hAPP(hAPP(c_member(_1761103), _1761194), hAPP(c_List_Oset(_1761103), _1761107))), -(hBOOL(hAPP(_1761105, _1761194)))]]], (15934 ^ _774244) ^ [_1044953, _1044955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1044953), _1044955)), -(c_Nat__Transfer_Otsub(_1044955, _1044953) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044955), _1044953))], (22583 ^ _774244) ^ [_1164005, _1164007, _1164009] : [22585 ^ _774244 : [(22588 ^ _774244) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1164005, _1164007), 22584 ^ [_1164005, _1164007, _1164009]))], (22586 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1164007, 22584 ^ [_1164005, _1164007, _1164009]), _1164009)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1164005, _1164007), _1164009)))], (5498 ^ _774244) ^ [_859129, _859131, _859133, _859135] : [-(tc_sum(_859135, _859131) = tc_sum(_859133, _859129)), _859135 = _859133, _859131 = _859129], (5660 ^ _774244) ^ [_864464, _864466] : [hAPP(c_Nat_OSuc, _864464) = hAPP(c_Nat_OSuc, _864466), -(_864464 = _864466)], (18151 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (32878 ^ _774244) ^ [_1369918, _1369920, _1369922] : [class_Orderings_Olinorder(_1369918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1369918, tc_HOL_Obool)), _1369920), _1369922)), -(_1369920 = c_Orderings_Obot__class_Obot(tc_fun(_1369918, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369918), _1369922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369918), c_Big__Operators_Olinorder__class_OMin(_1369918, _1369922)), c_Big__Operators_Olinorder__class_OMin(_1369918, _1369920))))], (20839 ^ _774244) ^ [_1131239, _1131241, _1131243, _1131245] : [class_Fields_Ofield__inverse__zero(_1131239), -(_1131241 = c_Groups_Ozero__class_Ozero(_1131239)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131239), _1131243), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131239), _1131245), _1131241)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131239), _1131245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131239), _1131243), _1131241))), _1131241))], (45825 ^ _774244) ^ [_1675316, _1675318, _1675320, _1675322, _1675324] : [hBOOL(hAPP(c_List_Odistinct(_1675316), hAPP(hAPP(c_List_Omap(tc_prod(_1675316, _1675318), _1675316), c_Product__Type_Ofst(_1675316, _1675318)), _1675320))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1675316, _1675318)), hAPP(hAPP(c_Product__Type_OPair(_1675316, _1675318), _1675322), _1675324)), hAPP(c_List_Oset(tc_prod(_1675316, _1675318)), _1675320))), -(hAPP(c_Map_Omap__of(_1675316, _1675318, _1675320), _1675322) = hAPP(c_Option_Ooption_OSome(_1675318), _1675324))], (5308 ^ _774244) ^ [_856310, _856312] : [_856312 = _856310, -(c_List_Oappend(_856312) = c_List_Oappend(_856310))], (40567 ^ _774244) ^ [_1540828] : [-(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)), _1540828)))))], (18073 ^ _774244) ^ [_1083163] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083163) = 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(_1083163)))))], (47008 ^ _774244) ^ [_1705678, _1705680, _1705682, _1705684, _1705686] : [-(hAPP(hAPP(c_List_Ozip(_1705678, _1705680), _1705682), hAPP(hAPP(c_List_Olist_OCons(_1705680), _1705684), _1705686)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1705678, _1705680)), _1705678, c_List_Olist_ONil(tc_prod(_1705678, _1705680)), hAPP(hAPP(c_COMBC(_1705678, tc_fun(tc_List_Olist(_1705678), tc_List_Olist(tc_prod(_1705678, _1705680))), tc_fun(tc_List_Olist(_1705678), tc_List_Olist(tc_prod(_1705678, _1705680)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1705678, _1705680)), tc_List_Olist(tc_prod(_1705678, _1705680))), tc_fun(tc_fun(tc_List_Olist(_1705678), tc_List_Olist(tc_prod(_1705678, _1705680))), tc_fun(tc_List_Olist(_1705678), tc_List_Olist(tc_prod(_1705678, _1705680)))), _1705678), c_COMBB(tc_List_Olist(tc_prod(_1705678, _1705680)), tc_List_Olist(tc_prod(_1705678, _1705680)), tc_List_Olist(_1705678))), hAPP(hAPP(c_COMBB(tc_prod(_1705678, _1705680), tc_fun(tc_List_Olist(tc_prod(_1705678, _1705680)), tc_List_Olist(tc_prod(_1705678, _1705680))), _1705678), c_List_Olist_OCons(tc_prod(_1705678, _1705680))), hAPP(hAPP(c_COMBC(_1705678, _1705680, tc_prod(_1705678, _1705680)), c_Product__Type_OPair(_1705678, _1705680)), _1705684)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1705678), tc_List_Olist(_1705680), tc_List_Olist(tc_prod(_1705678, _1705680))), c_List_Ozip(_1705678, _1705680)), _1705686))), _1705682))], (39042 ^ _774244) ^ [_1505187, _1505189, _1505191, _1505193] : [class_Groups_Ocomm__monoid__mult(_1505187), 39045 ^ _774244 : [(39052 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505189), _1505191))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1505189, _1505187), _1505193), _1505191) = c_Groups_Oone__class_Oone(_1505187))], (39046 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1505189), _1505191)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1505189, _1505187), _1505193), _1505191) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1505187, _1505189, c_Groups_Otimes__class_Otimes(_1505187)), _1505193), c_Groups_Oone__class_Oone(_1505187)), _1505191))]]], (45403 ^ _774244) ^ [_1665185, _1665187, _1665189] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1665185), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1665187), _1665189)))), 45406 ^ _774244 : [(45413 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1665187), _1665189))), -(c_Smallcheck_Osmall_H(_1665185, _1665187, _1665189) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1665185, _1665187, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1665189), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1665185, _1665189)))], (45407 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1665187), _1665189)), -(c_Smallcheck_Osmall_H(_1665185, _1665187, _1665189) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))]]], (36143 ^ _774244) ^ [_1440561, _1440563, _1440565, _1440567] : [hBOOL(hAPP(hAPP(c_member(_1440561), _1440563), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440561, tc_HOL_Obool)), _1440565), _1440567))), 36146 ^ _774244 : [(36149 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1440561), _1440563), _1440567)))], (36147 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1440561), _1440563), _1440565)))]]], (39279 ^ _774244) ^ [_1510327, _1510329, _1510331, _1510333, _1510335] : [hAPP(_1510327, _1510329) = c_Option_Ooption_ONone(_1510331), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1510333, tc_HOL_Obool)), c_Map_Odom(_1510333, _1510331, _1510327)), hAPP(hAPP(c_Set_Oinsert(_1510333), _1510329), _1510335)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1510333, tc_HOL_Obool)), c_Map_Odom(_1510333, _1510331, _1510327)), _1510335))], (28282 ^ _774244) ^ [_1274276, _1274278, _1274280, _1274282] : [class_Orderings_Olinorder(_1274276), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274276), _1274278), _1274280)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274276), _1274280), _1274282)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274276, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1274276, _1274278, _1274280)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1274276, _1274280, _1274282)) = c_SetInterval_Oord__class_OatLeastAtMost(_1274276, _1274278, _1274282))], (26031 ^ _774244) ^ [_1228988, _1228990] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1228988)), _1228990)), 26034 ^ _774244 : [(26041 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228988))), -(_1228990 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26035 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228988)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1228988), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228990))))]]], (37687 ^ _774244) ^ [_1476418, _1476420, _1476422] : [class_Lattices_Olattice(_1476418), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476418), _1476420)), -(_1476420 = c_Orderings_Obot__class_Obot(tc_fun(_1476418, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1476418, hAPP(hAPP(c_Set_Oinsert(_1476418), _1476422), _1476420)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1476418), _1476422), c_Big__Operators_Olattice__class_OInf__fin(_1476418, _1476420)))], (20119 ^ _774244) ^ [_1118627, _1118629, _1118631] : [class_Fields_Olinordered__field(_1118627), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118627), _1118629), c_Groups_Ozero__class_Ozero(_1118627))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118627), c_Groups_Ozero__class_Ozero(_1118627)), _1118631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118627), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118627), _1118629), _1118631)), c_Groups_Ozero__class_Ozero(_1118627))))], (45021 ^ _774244) ^ [_1656589, _1656591, _1656593, _1656595] : [class_Orderings_Olinorder(_1656589), hBOOL(hAPP(c_Finite__Set_Ofinite(_1656589), _1656591)), 45031 ^ _774244 : [(45034 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656589), 45030 ^ [_1656589, _1656591, _1656593, _1656595]), _1656593))], (45032 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1656589), 45030 ^ [_1656589, _1656591, _1656593, _1656595]), _1656591)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656589), hAPP(hAPP(c_Finite__Set_Ofold(_1656589, _1656589, c_Orderings_Oord__class_Omax(_1656589)), _1656595), _1656591)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1656589), _1656593), _1656595))))], (14650 ^ _774244) ^ [_1019607, _1019609, _1019611] : [-(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), _1019607), _1019609)), _1019609)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019607, _1019609))), _1019611) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019607), _1019611))], (44202 ^ _774244) ^ [_1636843, _1636845] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1636843, _1636843), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1636845) = c_Relation_OId(_1636843))], (18529 ^ _774244) ^ [_1090538] : [c_Int_OMin = c_Int_OBit1(_1090538), -(c_Int_OMin = _1090538)], (4750 ^ _774244) ^ [_847645, _847647] : [_847647 = _847645, -(c_Option_Ooption_ONone(_847647) = c_Option_Ooption_ONone(_847645))], (49392 ^ _774244) ^ [_1762404, _1762406, _1762408] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1762404), tc_List_Olist(_1762404)), c_List_Opartition(_1762404, _1762406, _1762408)) = hAPP(c_List_Ofilter(_1762404, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1762404, c_fNot), _1762406)), _1762408))], (18167 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (21255 ^ _774244) ^ [_1138496, _1138498, _1138500, _1138502] : [class_Fields_Olinordered__field(_1138496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138496), c_Groups_Ozero__class_Ozero(_1138496)), _1138498)), 21262 ^ _774244 : [(21269 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138496), _1138500), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138496), _1138502), _1138498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138496), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138496), _1138500), _1138498)), _1138502)))], (21263 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138496), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138496), _1138500), _1138498)), _1138502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138496), _1138500), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138496), _1138502), _1138498))))]]], (14314 ^ _774244) ^ [_1014042, _1014044] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1014042), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1014044)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1014042, _1014044)))], (26644 ^ _774244) ^ [_1241653, _1241655, _1241657, _1241659, _1241661] : [class_Orderings_Olinorder(_1241653), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241653), _1241655), _1241657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241653), _1241659), _1241661)), 26655 ^ _774244 : [(26664 ^ _774244) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241653, _1241655), _1241657) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241653, _1241659), _1241661)), _1241655 = _1241659, _1241657 = _1241661], (26656 ^ _774244) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241653, _1241655), _1241657) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241653, _1241659), _1241661), 26659 ^ _774244 : [(26662 ^ _774244) ^ [] : [-(_1241657 = _1241661)], (26660 ^ _774244) ^ [] : [-(_1241655 = _1241659)]]]]], (14137 ^ _774244) ^ [_1011065, _1011067] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1011065), _1011067) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1011065, _1011067)), _1011067))], (34694 ^ _774244) ^ [_1407979, _1407981, _1407983] : [class_Orderings_Olinorder(_1407979), hAPP(_1407981, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1407979), 34699 ^ [_1407979, _1407981, _1407983]), 34700 ^ [_1407979, _1407981, _1407983])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1407979), hAPP(_1407981, 34699 ^ [_1407979, _1407981, _1407983])), hAPP(_1407981, 34700 ^ [_1407979, _1407981, _1407983])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407979), _1407983)), -(_1407983 = c_Orderings_Obot__class_Obot(tc_fun(_1407979, tc_HOL_Obool))), -(hAPP(_1407981, c_Big__Operators_Olinorder__class_OMax(_1407979, _1407983)) = c_Big__Operators_Olinorder__class_OMax(_1407979, hAPP(c_Set_Oimage(_1407979, _1407979, _1407981), _1407983)))], (13022 ^ _774244) ^ [_990494, _990496] : [class_Rings_Olinordered__idom(_990494), 13025 ^ _774244 : [(13032 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990494), c_Groups_Ozero__class_Ozero(_990494)), _990496)), -(c_Groups_Osgn__class_Osgn(_990494, _990496) = c_Groups_Oone__class_Oone(_990494))], (13026 ^ _774244) ^ [] : [c_Groups_Osgn__class_Osgn(_990494, _990496) = c_Groups_Oone__class_Oone(_990494), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990494), c_Groups_Ozero__class_Ozero(_990494)), _990496)))]]], (16441 ^ _774244) ^ [_1053951, _1053953, _1053955] : [class_Groups_Oordered__ab__group__add__abs(_1053951), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053951), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1053951), hAPP(c_Groups_Oabs__class_Oabs(_1053951), _1053953)), hAPP(c_Groups_Oabs__class_Oabs(_1053951), _1053955))), hAPP(c_Groups_Oabs__class_Oabs(_1053951), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1053951), _1053953), _1053955)))))], (11281 ^ _774244) ^ [_959934, _959936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _959934), _959936)), 11284 ^ _774244 : [(11287 ^ _774244) ^ [] : [_959934 = _959936], (11285 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _959934), _959936)))]]], (43075 ^ _774244) ^ [_1607033, _1607035, _1607037, _1607039, _1607041] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607033, _1607033)), hAPP(hAPP(c_Product__Type_OPair(_1607033, _1607033), _1607035), _1607037)), c_Transitive__Closure_Ortrancl(_1607033, _1607039))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1607033, _1607033)), hAPP(hAPP(c_Product__Type_OPair(_1607033, _1607033), _1607037), _1607041)), c_Transitive__Closure_Ortrancl(_1607033, _1607039))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607033, _1607033)), hAPP(hAPP(c_Product__Type_OPair(_1607033, _1607033), _1607035), _1607041)), c_Transitive__Closure_Ortrancl(_1607033, _1607039))))], (46455 ^ _774244) ^ [_1692589, _1692591, _1692593] : [hAPP(hAPP(c_List_Olist_OCons(_1692589), _1692591), _1692593) = _1692593], (41198 ^ _774244) ^ [_1562362, _1562364] : [41199 ^ _774244 : [(41200 ^ _774244) ^ [_1562426, _1562428] : [_1562364 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1562362, _1562426), 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)), _1562428)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1562362), _1562364)))], (38209 ^ _774244) ^ [_1486585, _1486587, _1486589, _1486591, _1486593] : [c_Fun_Oinj__on(_1486585, _1486587, _1486589, c_Orderings_Otop__class_Otop(tc_fun(_1486585, tc_HOL_Obool))), 38212 ^ _774244 : [(38219 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1486585), _1486591), _1486593)), -(hBOOL(hAPP(hAPP(c_member(_1486587), hAPP(_1486589, _1486591)), hAPP(c_Set_Oimage(_1486585, _1486587, _1486589), _1486593))))], (38213 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1486587), hAPP(_1486589, _1486591)), hAPP(c_Set_Oimage(_1486585, _1486587, _1486589), _1486593))), -(hBOOL(hAPP(hAPP(c_member(_1486585), _1486591), _1486593)))]]], (17295 ^ _774244) ^ [_1070082, _1070084, _1070086] : [class_Groups_Omonoid__mult(_1070082), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1070082), _1070084), hAPP(c_Nat_OSuc, _1070086)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070082), hAPP(hAPP(c_Power_Opower__class_Opower(_1070082), _1070084), _1070086)), _1070084))], (16255 ^ _774244) ^ [_1050619, _1050621] : [class_Groups_Oordered__ab__group__add__abs(_1050619), -(hAPP(c_Groups_Oabs__class_Oabs(_1050619), hAPP(c_Groups_Ouminus__class_Ouminus(_1050619), _1050621)) = hAPP(c_Groups_Oabs__class_Oabs(_1050619), _1050621))], (43049 ^ _774244) ^ [_1606330, _1606332, _1606334, _1606336] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606330, _1606330)), hAPP(hAPP(c_Product__Type_OPair(_1606330, _1606330), _1606332), _1606334)), c_Transitive__Closure_Otrancl(_1606330, _1606336))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606330, _1606330)), hAPP(hAPP(c_Product__Type_OPair(_1606330, _1606330), _1606332), _1606334)), c_Transitive__Closure_Ortrancl(_1606330, _1606336))))], (43429 ^ _774244) ^ [_1615276, _1615278, _1615280, _1615282, _1615284, _1615286] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615276, tc_fun(_1615278, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615280, tc_fun(_1615276, tc_HOL_Obool)), _1615282), _1615284)), _1615286) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615280, tc_fun(_1615278, tc_HOL_Obool)), _1615282), hAPP(hAPP(c_COMBC(_1615280, tc_fun(_1615276, tc_fun(_1615278, tc_HOL_Obool)), tc_fun(_1615278, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615276, tc_HOL_Obool), tc_fun(tc_fun(_1615276, tc_fun(_1615278, tc_HOL_Obool)), tc_fun(_1615278, tc_HOL_Obool)), _1615280), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615276, tc_fun(_1615278, tc_HOL_Obool))), _1615284)), _1615286)))], (24493 ^ _774244) ^ [_1200399] : [-(hAPP(c_Code__Numeral_Onat__of, _1200399) = c_Code__Numeral_Onat__of__aux(_1200399, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24343 ^ _774244) ^ [_1197259, _1197261, _1197263] : [class_Int_Onumber(_1197259), class_Orderings_Oord(_1197259), 24350 ^ _774244 : [(24357 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197259), hAPP(c_Int_Onumber__class_Onumber__of(_1197259), _1197261)), hAPP(c_Int_Onumber__class_Onumber__of(_1197259), _1197263)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197259), hAPP(c_Int_Onumber__class_Onumber__of(_1197259), _1197261)), hAPP(c_Int_Onumber__class_Onumber__of(_1197259), _1197263)) = hAPP(c_Int_Onumber__class_Onumber__of(_1197259), _1197261))], (24351 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197259), hAPP(c_Int_Onumber__class_Onumber__of(_1197259), _1197261)), hAPP(c_Int_Onumber__class_Onumber__of(_1197259), _1197263))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197259), hAPP(c_Int_Onumber__class_Onumber__of(_1197259), _1197261)), hAPP(c_Int_Onumber__class_Onumber__of(_1197259), _1197263)) = hAPP(c_Int_Onumber__class_Onumber__of(_1197259), _1197263))]]], (34227 ^ _774244) ^ [_1396693, _1396695, _1396697, _1396699, _1396701] : [-(c_Map_Orestrict__map(_1396693, _1396695, _1396697, hAPP(hAPP(c_Set_Oinsert(_1396693), _1396699), _1396701)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1396693, tc_Option_Ooption(_1396695)), c_Map_Orestrict__map(_1396693, _1396695, _1396697, _1396701)), _1396699), hAPP(_1396697, _1396699)))], (45269 ^ _774244) ^ [_1662210, _1662212, _1662214, _1662216, _1662218, _1662220] : [-(hAPP(c_Map_Omap__add(_1662210, _1662212, _1662214, _1662216), _1662218) = hAPP(c_Option_Ooption_OSome(_1662212), _1662220)), 45270 ^ _774244 : [(45273 ^ _774244) ^ [] : [hAPP(_1662216, _1662218) = c_Option_Ooption_ONone(_1662212), hAPP(_1662214, _1662218) = hAPP(c_Option_Ooption_OSome(_1662212), _1662220)], (45271 ^ _774244) ^ [] : [hAPP(_1662216, _1662218) = hAPP(c_Option_Ooption_OSome(_1662212), _1662220)]]], (46294 ^ _774244) ^ [_1687024, _1687026, _1687028, _1687030] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687024)), _1687026) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687028)), _1687030), hBOOL(hAPP(c_List_Odistinct(_1687024), _1687026)), -(c_Map_Odom(_1687024, _1687028, c_Map_Omap__of(_1687024, _1687028, hAPP(hAPP(c_List_Ozip(_1687024, _1687028), _1687026), _1687030))) = hAPP(c_List_Oset(_1687024), _1687026))], (7565 ^ _774244) ^ [_897424, _897426, _897428, _897430] : [c_Com_Ocom_OSemi(_897424, _897426) = c_Com_Ocom_OAss(_897428, _897430)], (1514 ^ _774244) ^ [_795893, _795895] : [-(class_Rings_Oordered__semiring(_795893)), _795895 = _795893, class_Rings_Oordered__semiring(_795895)], (50432 ^ _774244) ^ [_1785147, _1785149, _1785151, _1785153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1785147), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1785149)), _1785151))), -(hAPP(c_List_Orev(_1785149), hAPP(hAPP(c_List_Olist__update(_1785149, _1785151), _1785147), _1785153)) = hAPP(hAPP(c_List_Olist__update(_1785149, hAPP(c_List_Orev(_1785149), _1785151)), 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(_1785149)), _1785151)), _1785147)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1785153))], (17707 ^ _774244) ^ [_1077450] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077450))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077450)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7637 ^ _774244) ^ [_898769, _898771, _898773] : [class_Groups_Oordered__comm__monoid__add(_898769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_898769), _898771), c_Groups_Ozero__class_Ozero(_898769))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_898769), _898773), c_Groups_Ozero__class_Ozero(_898769))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_898769), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898769), _898771), _898773)), c_Groups_Ozero__class_Ozero(_898769))))], (21946 ^ _774244) ^ [_1151393] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1151393)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1151393)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (13668 ^ _774244) ^ [_1002209, _1002211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002209)), -(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, _1002211, _1002209))))], (46282 ^ _774244) ^ [_1686809, _1686811, _1686813] : [hBOOL(hAPP(hAPP(c_member(_1686809), _1686811), hAPP(c_List_Oset(_1686809), _1686813))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686809)), c_List_Oremove1(_1686809, _1686811, _1686813)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686809)), _1686813)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (13469 ^ _774244) ^ [_998316, _998318, _998320, _998322] : [class_Divides_Osemiring__div(_998316), -(c_Divides_Odiv__class_Omod(_998316, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998316), _998318), c_Divides_Odiv__class_Omod(_998316, _998320, _998322)), _998322) = c_Divides_Odiv__class_Omod(_998316, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998316), _998318), _998320), _998322))], (45781 ^ _774244) ^ [_1674225, _1674227, _1674229] : [hBOOL(hAPP(c_List_Odistinct(_1674225), hAPP(hAPP(c_List_Omap(tc_prod(_1674225, _1674227), _1674225), c_Product__Type_Ofst(_1674225, _1674227)), _1674229))), -(hAPP(c_List_Oset(tc_prod(_1674225, _1674227)), _1674229) = hAPP(c_Set_OCollect(tc_prod(_1674225, _1674227)), hAPP(c_Product__Type_Oprod_Oprod__case(_1674225, _1674227, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1674225, tc_fun(_1674227, tc_Option_Ooption(_1674227)), tc_fun(_1674227, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1674227), tc_HOL_Obool), tc_fun(tc_fun(_1674227, tc_Option_Ooption(_1674227)), tc_fun(_1674227, tc_HOL_Obool)), _1674225), c_COMBB(tc_Option_Ooption(_1674227), tc_HOL_Obool, _1674227)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1674227), tc_fun(tc_Option_Ooption(_1674227), tc_HOL_Obool), _1674225), c_fequal), c_Map_Omap__of(_1674225, _1674227, _1674229)))), c_Option_Ooption_OSome(_1674227)))))], (38385 ^ _774244) ^ [_1490126, _1490128, _1490130, _1490132, _1490134, _1490136] : [c_Fun_Oinj__on(_1490126, _1490128, _1490130, _1490132), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1490126, tc_HOL_Obool)), _1490134), _1490132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1490126, tc_HOL_Obool)), _1490136), _1490132)), -(hAPP(c_Set_Oimage(_1490126, _1490128, _1490130), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1490126, tc_HOL_Obool)), _1490134), _1490136)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1490128, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1490126, _1490128, _1490130), _1490134)), hAPP(c_Set_Oimage(_1490126, _1490128, _1490130), _1490136)))], (22032 ^ _774244) ^ [_1152798, _1152800] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1152798), _1152800))), -(c_Quickcheck_Obeyond(_1152798, _1152800) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (3858 ^ _774244) ^ [_833693, _833695] : [_833695 = _833693, -(c_Nat_Ofunpow(_833695) = c_Nat_Ofunpow(_833693))], (15018 ^ _774244) ^ [_1026650, _1026652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026650), _1026652)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1026652)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1026650)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026652), _1026650)))], (47943 ^ _774244) ^ [_1728538, _1728540, _1728542, _1728544] : [hBOOL(hAPP(hAPP(c_member(_1728538), _1728540), hAPP(c_List_Oset(_1728538), hAPP(hAPP(c_List_Otake(_1728538), _1728542), _1728544)))), -(hBOOL(hAPP(hAPP(c_member(_1728538), _1728540), hAPP(c_List_Oset(_1728538), _1728544))))], (45105 ^ _774244) ^ [_1658418, _1658420] : [c_Wellfounded_Owf(_1658418, _1658420), 45108 ^ _774244 : [(45109 ^ _774244) ^ [_1658550] : [45110 ^ _774244 : [(45111 ^ _774244) ^ [_1658655] : [hBOOL(hAPP(hAPP(c_member(_1658418), _1658655), _1658550))]], 45113 ^ _774244 : [(45116 ^ _774244) ^ [_1658777] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1658418, _1658418)), hAPP(hAPP(c_Product__Type_OPair(_1658418, _1658418), _1658777), 45112 ^ [_1658418, _1658420, _1658550])), _1658420)), hBOOL(hAPP(hAPP(c_member(_1658418), _1658777), _1658550))], (45114 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1658418), 45112 ^ [_1658418, _1658420, _1658550]), _1658550)))]]]]], (18115 ^ _774244) ^ [_1083780] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1083780) = c_Int_OPls)], (6217 ^ _774244) ^ [_874038, _874040, _874042, _874044, _874046, _874048, _874050, _874052, _874054, _874056, _874058, _874060] : [-(c_Com_Ocom_Ocom__rec(_874038, _874040, _874042, _874044, _874046, _874048, _874050, _874052, _874054, c_Com_Ocom_OCond(_874056, _874058, _874060)) = hAPP(hAPP(hAPP(hAPP(hAPP(_874048, _874056), _874058), _874060), c_Com_Ocom_Ocom__rec(_874038, _874040, _874042, _874044, _874046, _874048, _874050, _874052, _874054, _874058)), c_Com_Ocom_Ocom__rec(_874038, _874040, _874042, _874044, _874046, _874048, _874050, _874052, _874054, _874060)))], (8830 ^ _774244) ^ [_918680, _918682, _918684, _918686, _918688] : [class_Rings_Ocomm__semiring__1(_918680), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918680), _918682), _918684)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918680), _918686), _918688)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918680), _918686), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918680), _918682), _918684)), _918688)))], (44184 ^ _774244) ^ [_1636404, _1636406, _1636408] : [c_Relation_Ototal__on(_1636404, _1636406, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1636404, _1636404), tc_HOL_Obool)), _1636408), c_Relation_OId(_1636404))), -(c_Relation_Ototal__on(_1636404, _1636406, _1636408))], (33450 ^ _774244) ^ [_1381351, _1381353, _1381355] : [class_Orderings_Olinorder(_1381351), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381351), _1381353)), hBOOL(hAPP(hAPP(c_member(_1381351), _1381355), _1381353)), 33461 ^ _774244 : [(33468 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1381351, tc_HOL_Obool)), _1381353), hAPP(hAPP(c_Set_Oinsert(_1381351), _1381355), c_Orderings_Obot__class_Obot(tc_fun(_1381351, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1381351, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1381351, c_Orderings_Oord__class_Omin(_1381351), _1381353) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1381351), _1381355), c_Big__Operators_Olattice_OInf__fin(_1381351, c_Orderings_Oord__class_Omin(_1381351), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1381351, tc_HOL_Obool)), _1381353), hAPP(hAPP(c_Set_Oinsert(_1381351), _1381355), c_Orderings_Obot__class_Obot(tc_fun(_1381351, tc_HOL_Obool)))))))], (33462 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1381351, tc_HOL_Obool)), _1381353), hAPP(hAPP(c_Set_Oinsert(_1381351), _1381355), c_Orderings_Obot__class_Obot(tc_fun(_1381351, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1381351, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1381351, c_Orderings_Oord__class_Omin(_1381351), _1381353) = _1381355)]]], (21761 ^ _774244) ^ [_1148196, _1148198, _1148200, _1148202] : [class_Fields_Olinordered__field__inverse__zero(_1148196), class_Int_Onumber(_1148196), 21768 ^ _774244 : [(21769 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148196), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148196), _1148198), _1148200)), hAPP(c_Int_Onumber__class_Onumber__of(_1148196), _1148202))), 21772 ^ _774244 : [(21779 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148196), c_Groups_Ozero__class_Ozero(_1148196)), _1148200))), 21782 ^ _774244 : [(21789 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148196), _1148200), c_Groups_Ozero__class_Ozero(_1148196)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148196), c_Groups_Ozero__class_Ozero(_1148196)), hAPP(c_Int_Onumber__class_Onumber__of(_1148196), _1148202))))], (21783 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148196), _1148200), c_Groups_Ozero__class_Ozero(_1148196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148196), hAPP(c_Int_Onumber__class_Onumber__of(_1148196), _1148202)), _1148200)), _1148198)))]]], (21773 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148196), c_Groups_Ozero__class_Ozero(_1148196)), _1148200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148196), _1148198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148196), hAPP(c_Int_Onumber__class_Onumber__of(_1148196), _1148202)), _1148200))))]]], (21795 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148196), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148196), _1148198), _1148200)), hAPP(c_Int_Onumber__class_Onumber__of(_1148196), _1148202)))), 21798 ^ _774244 : [(21801 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148196), _1148198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148196), hAPP(c_Int_Onumber__class_Onumber__of(_1148196), _1148202)), _1148200)))], (21799 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148196), c_Groups_Ozero__class_Ozero(_1148196)), _1148200)))]], 21802 ^ _774244 : [(21805 ^ _774244) ^ [] : [21806 ^ _774244 : [(21809 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148196), hAPP(c_Int_Onumber__class_Onumber__of(_1148196), _1148202)), _1148200)), _1148198))], (21807 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148196), _1148200), c_Groups_Ozero__class_Ozero(_1148196))))]], 21810 ^ _774244 : [(21813 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148196), c_Groups_Ozero__class_Ozero(_1148196)), hAPP(c_Int_Onumber__class_Onumber__of(_1148196), _1148202)))], (21811 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148196), _1148200), c_Groups_Ozero__class_Ozero(_1148196)))]]], (21803 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148196), c_Groups_Ozero__class_Ozero(_1148196)), _1148200))]]]]], (7923 ^ _774244) ^ [_903687, _903689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _903687), _903689)), -(_903689 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _903687), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 7926 ^ [_903687, _903689]))))], (27314 ^ _774244) ^ [_1255629, _1255631] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1255629), _1255631) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1255629, _1255631))], (40603 ^ _774244) ^ [_1541690, _1541692] : [-(hBOOL(hAPP(_1541692, 40604 ^ [_1541690, _1541692]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1541690, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1541690), _1541692))], (22072 ^ _774244) ^ [_1153426, _1153428, _1153430, _1153432, _1153434] : [class_Groups_Ominus(_1153426), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1153428, _1153426)), _1153430), _1153432), _1153434) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1153426), hAPP(_1153430, _1153434)), hAPP(_1153432, _1153434)))], (49579 ^ _774244) ^ [_1767443, _1767445] : [class_Orderings_Olinorder(_1767443), -(_1767445 = c_List_Olist_ONil(_1767443)), c_List_Olinorder__class_Osorted(_1767443, _1767445), -(c_List_Olinorder__class_Osorted(_1767443, c_List_Obutlast(_1767443, _1767445)))], (8086 ^ _774244) ^ [_906730, _906732, _906734] : [class_Orderings_Olinorder(_906730), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906730), _906732), _906734))), -(_906732 = _906734), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906730), _906734), _906732)))], (48919 ^ _774244) ^ [_1752577, _1752579, _1752581, _1752583] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1752577)), hAPP(hAPP(c_List_Olist_OCons(_1752577), _1752579), _1752581)), c_List_Olists(_1752577, _1752583))), 48922 ^ _774244 : [(48925 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1752577)), _1752581), c_List_Olists(_1752577, _1752583))))], (48923 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752577), _1752579), _1752583)))]]], (272 ^ _774244) ^ [_778244, _778246] : [-(c_Nat__Transfer_Ois__nat(_778244)), _778246 = _778244, c_Nat__Transfer_Ois__nat(_778246)], (33508 ^ _774244) ^ [_1382559, _1382561, _1382563] : [class_Orderings_Olinorder(_1382559), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382559), _1382561)), hBOOL(hAPP(hAPP(c_member(_1382559), _1382563), _1382561)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1382559), _1382563), c_Big__Operators_Olattice_OInf__fin(_1382559, c_Orderings_Oord__class_Omin(_1382559), _1382561)) = c_Big__Operators_Olattice_OInf__fin(_1382559, c_Orderings_Oord__class_Omin(_1382559), _1382561))], (6373 ^ _774244) ^ [_876777, _876779] : [-(_876777 = hAPP(c_Option_Ooption_OSome(_876779), 6374 ^ [_876777, _876779])), -(_876777 = c_Option_Ooption_ONone(_876779))], (20431 ^ _774244) ^ [_1123664, _1123666, _1123668] : [class_Fields_Olinordered__field(_1123664), -(_1123666 = c_Groups_Ozero__class_Ozero(_1123664)), -(hAPP(c_Groups_Oabs__class_Oabs(_1123664), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123664), _1123668), _1123666)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123664), hAPP(c_Groups_Oabs__class_Oabs(_1123664), _1123668)), hAPP(c_Groups_Oabs__class_Oabs(_1123664), _1123666)))], (8012 ^ _774244) ^ [_905275, _905277, _905279] : [class_Rings_Osemiring__1(_905275), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_905275), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _905277), _905279)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_905275), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_905275), _905277)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_905275), _905279)))], (21899 ^ _774244) ^ [_1150730, _1150732] : [-(c_Random_Olog(_1150730, _1150732) = 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(_1150730, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1150732), _1150730)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1150730), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1150732), _1150730)))], (44606 ^ _774244) ^ [_1646330, _1646332, _1646334] : [-(hAPP(c_Relation_ODomain(_1646330, _1646332), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1646330, _1646332), tc_HOL_Obool), _1646334)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1646330, _1646332), tc_HOL_Obool), tc_fun(_1646330, tc_HOL_Obool)), _1646334), c_Relation_ODomain(_1646330, _1646332)))], (11887 ^ _774244) ^ [_970757, _970759] : [class_Groups_Oordered__ab__group__add(_970757), 11890 ^ _774244 : [(11897 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970757), c_Groups_Ozero__class_Ozero(_970757)), _970759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970757), hAPP(c_Groups_Ouminus__class_Ouminus(_970757), _970759)), c_Groups_Ozero__class_Ozero(_970757))))], (11891 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970757), hAPP(c_Groups_Ouminus__class_Ouminus(_970757), _970759)), c_Groups_Ozero__class_Ozero(_970757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970757), c_Groups_Ozero__class_Ozero(_970757)), _970759)))]]], (35799 ^ _774244) ^ [_1433676, _1433678, _1433680, _1433682, _1433684, _1433686] : [c_Equiv__Relations_Oequiv(_1433676, _1433678, _1433680), c_Equiv__Relations_Ocongruent(_1433676, tc_fun(_1433682, tc_HOL_Obool), _1433680, _1433684), hBOOL(hAPP(hAPP(c_member(_1433676), _1433686), _1433678)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433676, tc_fun(_1433682, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1433676, _1433676, _1433680), hAPP(hAPP(c_Set_Oinsert(_1433676), _1433686), c_Orderings_Obot__class_Obot(tc_fun(_1433676, tc_HOL_Obool))))), _1433684) = hAPP(_1433684, _1433686))], (47913 ^ _774244) ^ [_1727834, _1727836, _1727838] : [47914 ^ _774244 : [(47917 ^ _774244) ^ [] : [_1727838 = c_List_Olist_ONil(_1727834)], (47915 ^ _774244) ^ [] : [_1727836 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1727834), _1727836), _1727838) = c_List_Olist_ONil(_1727834))], (29426 ^ _774244) ^ [_1297923, _1297925, _1297927, _1297929, _1297931] : [_1297923 = c_Orderings_Obot__class_Obot(tc_fun(_1297925, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297925, tc_fun(_1297927, tc_HOL_Obool)), _1297923), hAPP(hAPP(c_COMBC(_1297925, tc_fun(_1297927, tc_HOL_Obool), tc_fun(_1297927, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297927, tc_HOL_Obool), tc_fun(tc_fun(_1297927, tc_HOL_Obool), tc_fun(_1297927, tc_HOL_Obool)), _1297925), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297927, tc_HOL_Obool))), _1297929)), _1297931)) = c_Orderings_Obot__class_Obot(tc_fun(_1297927, tc_HOL_Obool)))], (6317 ^ _774244) ^ [_875672, _875674, _875676] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCall(_875672, _875674, _875676)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14710 ^ _774244) ^ [_1020751, _1020753, _1020755, _1020757] : [class_Divides_Osemiring__div(_1020751), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020751), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020751), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020751), _1020753), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020751), _1020755), _1020753))), c_Divides_Odiv__class_Omod(_1020751, _1020755, _1020753))), _1020757) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020751), _1020755), _1020757))], (36655 ^ _774244) ^ [_1452479, _1452481, _1452483, _1452485, _1452487] : [class_Orderings_Olinorder(_1452479), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452479, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1452479, _1452481), _1452483)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1452479, _1452485), _1452487)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1452479, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1452479), _1452481), _1452485)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1452479), _1452483), _1452487)))], (48502 ^ _774244) ^ [_1743565, _1743567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743565)), _1743567)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1743565), _1743567) = _1743567)], (50603 ^ _774244) ^ [_1789403, _1789405, _1789407, _1789409, _1789411] : [-(hBOOL(hAPP(_1789403, _1789405))), -(c_List_OtakeWhile(_1789407, _1789403, hAPP(hAPP(c_List_Oappend(_1789407), _1789409), hAPP(hAPP(c_List_Olist_OCons(_1789407), _1789405), _1789411))) = c_List_OtakeWhile(_1789407, _1789403, _1789409))], (5748 ^ _774244) ^ [_865889] : [-(c_Natural_Oevalc(c_Com_Ocom_OSKIP, _865889, _865889))], (34771 ^ _774244) ^ [_1409708, _1409710, _1409712, _1409714] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1409708, _1409708)), hAPP(hAPP(c_Product__Type_OPair(_1409708, _1409708), _1409710), _1409712)), c_Relation_OId__on(_1409708, _1409714)))), _1409710 = _1409712, hBOOL(hAPP(hAPP(c_member(_1409708), _1409710), _1409714))], (36443 ^ _774244) ^ [_1447489, _1447491, _1447493, _1447495, _1447497] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447489, tc_fun(_1447491, tc_HOL_Obool)), _1447493), hAPP(hAPP(c_COMBB(tc_fun(_1447491, tc_HOL_Obool), tc_fun(_1447491, tc_HOL_Obool), _1447489), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447491, tc_HOL_Obool)), _1447495)), _1447497)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447491, tc_HOL_Obool)), _1447495), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1447489, tc_fun(_1447491, tc_HOL_Obool)), _1447493), _1447497)))], (37063 ^ _774244) ^ [_1461761, _1461763, _1461765] : [class_Lattices_Olattice(_1461761), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461761), _1461763)), -(_1461763 = c_Orderings_Obot__class_Obot(tc_fun(_1461761, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461761), _1461765)), -(_1461765 = c_Orderings_Obot__class_Obot(tc_fun(_1461761, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461761, tc_HOL_Obool)), _1461763), _1461765) = c_Orderings_Obot__class_Obot(tc_fun(_1461761, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1461761, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461761, tc_HOL_Obool)), _1461763), _1461765)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1461761), c_Big__Operators_Olattice__class_OSup__fin(_1461761, _1461763)), c_Big__Operators_Olattice__class_OSup__fin(_1461761, _1461765)))], (31899 ^ _774244) ^ [_1350933, _1350935, _1350937] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1350933), _1350935)), hBOOL(hAPP(hAPP(c_member(_1350933), _1350937), _1350935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1350933), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350933, tc_HOL_Obool)), _1350935), hAPP(hAPP(c_Set_Oinsert(_1350933), _1350937), c_Orderings_Obot__class_Obot(tc_fun(_1350933, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1350933), _1350935))))], (18201 ^ _774244) ^ [_1085016] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085016), c_Int_OMin) = c_Int_Opred(_1085016))], (27057 ^ _774244) ^ [_1250099, _1250101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250099)), 27066 ^ _774244 : [(27069 ^ _774244) ^ [] : [hBOOL(hAPP(_1250101, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27062 ^ [_1250099, _1250101]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 27063 ^ [_1250099, _1250101]), _1250099))))], (27067 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1250101, 27062 ^ [_1250099, _1250101])))]], 27070 ^ _774244 : [(27073 ^ _774244) ^ [] : [hBOOL(hAPP(_1250101, 27062 ^ [_1250099, _1250101]))], (27071 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1250101, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27062 ^ [_1250099, _1250101]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 27063 ^ [_1250099, _1250101]), _1250099)))))]], 27074 ^ _774244 : [(27084 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1250101, 27091 ^ [_1250099, _1250101]))), 27085 ^ _774244 : [(27086 ^ _774244) ^ [_1250646] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1250646), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1250099))), hBOOL(hAPP(_1250101, _1250646))]]], (27075 ^ _774244) ^ [] : [27076 ^ _774244 : [(27077 ^ _774244) ^ [_1250531] : [hBOOL(hAPP(_1250101, _1250531))]], 27079 ^ _774244 : [(27082 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1250101, 27078 ^ [_1250099, _1250101])))], (27080 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27078 ^ [_1250099, _1250101]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1250099))))]]]]], (8530 ^ _774244) ^ [_913352, _913354] : [class_Rings_Ocomm__semiring__1(_913352), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913352), _913354), _913354) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913352), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913352), c_Groups_Oone__class_Oone(_913352)), c_Groups_Oone__class_Oone(_913352))), _913354))], (16985 ^ _774244) ^ [_1064676] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1064676) = _1064676)], (50484 ^ _774244) ^ [_1786617, _1786619] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1786617), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1786617))), _1786619))), 50487 ^ _774244 : [(50494 ^ _774244) ^ [] : [-(_1786619 = c_List_Olist_ONil(tc_List_Olist(_1786617))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1786617))), c_List_Otranspose(_1786617, _1786619)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786617)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1786617)), _1786619), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50488 ^ _774244) ^ [] : [_1786619 = c_List_Olist_ONil(tc_List_Olist(_1786617)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1786617))), c_List_Otranspose(_1786617, _1786619)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (51105 ^ _774244) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (14648 ^ _774244) ^ [_1019546, _1019548, _1019550] : [-(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), _1019546), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019548), _1019546))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019548, _1019546))), _1019550) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019548), _1019550))], (24519 ^ _774244) ^ [_1200828, _1200830] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1200828), _1200830) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1200828)), hAPP(c_Code__Numeral_Onat__of, _1200830))))], (48226 ^ _774244) ^ [_1736433, _1736435, _1736437, _1736439, _1736441, _1736443, _1736445, _1736447] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1736433, _1736433)), hAPP(hAPP(c_Product__Type_OPair(_1736433, _1736433), _1736435), _1736437)), _1736439)), _1736441 = hAPP(hAPP(c_List_Oappend(_1736433), _1736443), hAPP(hAPP(c_List_Olist_OCons(_1736433), _1736435), _1736445)), _1736447 = hAPP(hAPP(c_List_Oappend(_1736433), _1736443), hAPP(hAPP(c_List_Olist_OCons(_1736433), _1736437), _1736445)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1736433), tc_List_Olist(_1736433))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1736433), tc_List_Olist(_1736433)), _1736441), _1736447)), c_List_Olistrel1(_1736433, _1736439))))], (28803 ^ _774244) ^ [_1285863, _1285865] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285863, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1285863, tc_HOL_Obool)), _1285865)), _1285865) = c_Orderings_Otop__class_Otop(tc_fun(_1285863, tc_HOL_Obool)))], (31375 ^ _774244) ^ [_1337901, _1337903, _1337905] : [class_Orderings_Oord(_1337901), 31378 ^ _774244 : [(31385 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337901), _1337903), _1337905)), -(hBOOL(hAPP(hAPP(c_member(_1337901), _1337903), hAPP(c_SetInterval_Oord__class_OatMost(_1337901), _1337905))))], (31379 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1337901), _1337903), hAPP(c_SetInterval_Oord__class_OatMost(_1337901), _1337905))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337901), _1337903), _1337905)))]]], (43817 ^ _774244) ^ [_1626663, _1626665, _1626667, _1626669, _1626671] : [_1626663 = c_Orderings_Obot__class_Obot(tc_fun(_1626665, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1626667, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626665, tc_fun(_1626667, tc_HOL_Obool)), _1626663), _1626669)), _1626671) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1626667, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1626667, tc_HOL_Obool))), _1626671))], (39402 ^ _774244) ^ [_1513393, _1513395, _1513397] : [39404 ^ _774244 : [(39407 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1513393), 39403 ^ [_1513393, _1513395, _1513397]), c_Wellfounded_Oacc(_1513393, _1513397)))], (39405 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1513393, _1513393)), hAPP(hAPP(c_Product__Type_OPair(_1513393, _1513393), 39403 ^ [_1513393, _1513395, _1513397]), _1513395)), _1513397)))]], -(hBOOL(hAPP(hAPP(c_member(_1513393), _1513395), c_Wellfounded_Oacc(_1513393, _1513397))))], (39942 ^ _774244) ^ [_1528502, _1528504, _1528506, _1528508, _1528510, _1528512] : [-(c_Product__Type_Omap__pair(_1528502, _1528504, _1528506, _1528508, _1528510, _1528512) = hAPP(c_Product__Type_Oprod_Oprod__case(_1528502, _1528506, tc_prod(_1528504, _1528508)), hAPP(hAPP(c_COMBC(_1528502, tc_fun(_1528506, _1528508), tc_fun(_1528506, tc_prod(_1528504, _1528508))), hAPP(hAPP(c_COMBB(tc_fun(_1528508, tc_prod(_1528504, _1528508)), tc_fun(tc_fun(_1528506, _1528508), tc_fun(_1528506, tc_prod(_1528504, _1528508))), _1528502), c_COMBB(_1528508, tc_prod(_1528504, _1528508), _1528506)), hAPP(hAPP(c_COMBB(_1528504, tc_fun(_1528508, tc_prod(_1528504, _1528508)), _1528502), c_Product__Type_OPair(_1528504, _1528508)), _1528510))), _1528512)))], (10770 ^ _774244) ^ [_951129, _951131, _951133, _951135] : [class_Orderings_Opreorder(_951129), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951129), _951131), _951133)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951129), _951133), _951135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951129), _951131), _951135)))], (18655 ^ _774244) ^ [_1092531, _1092533] : [class_Int_Onumber__ring(_1092531), -(hAPP(c_Int_Onumber__class_Onumber__of(_1092531), c_Int_OBit1(_1092533)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092531), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092531), c_Groups_Oone__class_Oone(_1092531)), hAPP(c_Int_Onumber__class_Onumber__of(_1092531), _1092533))), hAPP(c_Int_Onumber__class_Onumber__of(_1092531), _1092533)))], (24191 ^ _774244) ^ [_1194393, _1194395, _1194397] : [class_Orderings_Olinorder(_1194393), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194393), _1194395), _1194397)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194393), _1194397), _1194395) = _1194397)], (43544 ^ _774244) ^ [_1619423, _1619425, _1619427, _1619429, _1619431] : [class_Complete__Lattice_Ocomplete__lattice(_1619423), class_Orderings_Olinorder(_1619423), 43551 ^ _774244 : [(43561 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1619423), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1619425, _1619423), _1619427), _1619429)), _1619431))), 43562 ^ _774244 : [(43563 ^ _774244) ^ [_1619771] : [hBOOL(hAPP(hAPP(c_member(_1619425), _1619771), _1619427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1619423), hAPP(_1619429, _1619771)), _1619431))]]], (43552 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1619423), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1619425, _1619423), _1619427), _1619429)), _1619431)), 43556 ^ _774244 : [(43559 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1619423), hAPP(_1619429, 43555 ^ [_1619423, _1619425, _1619427, _1619429, _1619431])), _1619431)))], (43557 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1619425), 43555 ^ [_1619423, _1619425, _1619427, _1619429, _1619431]), _1619427)))]]]]], (25665 ^ _774244) ^ [_1222068, _1222070, _1222072, _1222074] : [class_Rings_Ocomm__semiring__1(_1222068), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1222070), _1222072)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222068), hAPP(hAPP(c_Power_Opower__class_Opower(_1222068), _1222074), _1222070)), hAPP(hAPP(c_Power_Opower__class_Opower(_1222068), _1222074), _1222072))))], (11719 ^ _774244) ^ [_967620, _967622, _967624, _967626] : [class_Rings_Oordered__ring(_967620), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967620), _967622), _967624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967620), _967626), c_Groups_Ozero__class_Ozero(_967620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967620), _967624), _967626)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967620), _967622), _967626))))], (14185 ^ _774244) ^ [_1011952, _1011954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011952)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1011952), _1011954)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1011952)), hAPP(c_Int_Onat, _1011954)))], (48578 ^ _774244) ^ [_1744980, _1744982, _1744984] : [-(_1744980 = c_List_Olist_ONil(_1744982)), -(hAPP(c_List_Ohd(_1744982), hAPP(c_List_Orotate(_1744982, _1744984), _1744980)) = hAPP(hAPP(c_List_Onth(_1744982), _1744980), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1744984, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744982)), _1744980))))], (24095 ^ _774244) ^ [_1192659, _1192661, _1192663, _1192665] : [class_Orderings_Olinorder(_1192659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192659), _1192661), _1192663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192659), _1192661), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1192659), _1192665), _1192663))))], (7794 ^ _774244) ^ [_901497, _901499, _901501, _901503] : [_901501 = _901503, -(hAPP(c_Sum__Type_OInr(_901497, _901499), _901501) = hAPP(c_Sum__Type_OInr(_901497, _901499), _901503))], (18955 ^ _774244) ^ [_1097717] : [c_Int_OPls = c_Int_OBit0(_1097717), -(c_Int_OPls = _1097717)], (17581 ^ _774244) ^ [_1075376, _1075378] : [-(c_Nitpick_Oint__lcm(_1075376, _1075378) = 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), _1075376)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1075378)))))], (35076 ^ _774244) ^ [_1416514, _1416516, _1416518, _1416520] : [c_Finite__Set_Ofolding__one__idem(_1416514, _1416516, _1416518), -(hAPP(hAPP(_1416516, _1416520), _1416520) = _1416520)], (47575 ^ _774244) ^ [_1719880, _1719882, _1719884, _1719886] : [-(hAPP(hAPP(c_List_Oappend(_1719880), hAPP(hAPP(c_List_Oappend(_1719880), _1719882), _1719884)), _1719886) = hAPP(hAPP(c_List_Oappend(_1719880), _1719882), hAPP(hAPP(c_List_Oappend(_1719880), _1719884), _1719886)))], (5016 ^ _774244) ^ [_851778, _851780, _851782, _851784] : [-(c_Wellfounded_Oaccp(_851784, _851780) = c_Wellfounded_Oaccp(_851782, _851778)), _851784 = _851782, _851780 = _851778], (45343 ^ _774244) ^ [_1663588, _1663590, _1663592, _1663594, _1663596, _1663598] : [-(c_Map_Omap__add(_1663588, _1663590, _1663592, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1663588, tc_Option_Ooption(_1663590)), _1663594), _1663596), hAPP(c_Option_Ooption_OSome(_1663590), _1663598))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1663588, tc_Option_Ooption(_1663590)), c_Map_Omap__add(_1663588, _1663590, _1663592, _1663594)), _1663596), hAPP(c_Option_Ooption_OSome(_1663590), _1663598)))], (35269 ^ _774244) ^ [_1420933, _1420935, _1420937, _1420939, _1420941] : [hBOOL(hAPP(hAPP(c_member(_1420933), _1420935), hAPP(c_Relation_OImage(_1420937, _1420933, _1420939), _1420941))), 35273 ^ _774244 : [(35276 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1420937, _1420933)), hAPP(hAPP(c_Product__Type_OPair(_1420937, _1420933), 35272 ^ [_1420933, _1420935, _1420937, _1420939, _1420941]), _1420935)), _1420939)))], (35274 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1420937), 35272 ^ [_1420933, _1420935, _1420937, _1420939, _1420941]), _1420941)))]]], (50929 ^ _774244) ^ [_1796132, _1796134] : [class_Complete__Lattice_Ocomplete__lattice(_1796132), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1796134, _1796132)))], (36257 ^ _774244) ^ [_1443332, _1443334, _1443336, _1443338] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443332, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443332, tc_HOL_Obool)), _1443334), _1443336)), _1443338) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443332, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443332, tc_HOL_Obool)), _1443334), _1443338)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443332, tc_HOL_Obool)), _1443336), _1443338)))], (11649 ^ _774244) ^ [_966303, _966305, _966307] : [class_Rings_Oordered__cancel__semiring(_966303), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966303), _966305), c_Groups_Ozero__class_Ozero(_966303))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966303), c_Groups_Ozero__class_Ozero(_966303)), _966307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966303), _966305), _966307)), c_Groups_Ozero__class_Ozero(_966303))))], (12436 ^ _774244) ^ [_980324, _980326, _980328, _980330, _980332] : [class_Rings_Olinordered__semiring__strict(_980324), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980324), _980326), _980328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980324), _980330), _980332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980324), c_Groups_Ozero__class_Ozero(_980324)), _980328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980324), c_Groups_Ozero__class_Ozero(_980324)), _980330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980324), _980326), _980330)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980324), _980328), _980332))))], (22194 ^ _774244) ^ [_1156106, _1156108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1156106), _1156108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1156106)), hAPP(c_Code__Numeral_Oof__nat, _1156108))))], (49930 ^ _774244) ^ [_1773380, _1773382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1773380)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1773382))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1773380), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1773382)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1773380)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1773380)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1773382))))], (27434 ^ _774244) ^ [_1258027, _1258029] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1258027), _1258029)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1258029), _1258027)))], (48986 ^ _774244) ^ [_1754291, _1754293, _1754295, _1754297] : [-(_1754291 = c_List_Olist_ONil(_1754293)), 48989 ^ _774244 : [(48996 ^ _774244) ^ [] : [-(_1754295 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754293)), _1754291)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1754293, hAPP(hAPP(c_List_Olist__update(_1754293, _1754291), _1754295), _1754297)) = c_List_Olast(_1754293, _1754291))], (48990 ^ _774244) ^ [] : [_1754295 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754293)), _1754291)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1754293, hAPP(hAPP(c_List_Olist__update(_1754293, _1754291), _1754295), _1754297)) = _1754297)]]], (19093 ^ _774244) ^ [_1100058, _1100060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1100058)), c_Int_OBit0(_1100060))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100058), _1100060)))], (37013 ^ _774244) ^ [_1460672, _1460674, _1460676, _1460678, _1460680] : [class_Groups_Ocomm__monoid__mult(_1460672), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460674), _1460676)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460674), _1460678)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460674, tc_HOL_Obool)), _1460676), _1460678) = c_Orderings_Obot__class_Obot(tc_fun(_1460674, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1460674, _1460672), _1460680), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460674, tc_HOL_Obool)), _1460676), _1460678)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1460672), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1460674, _1460672), _1460680), _1460676)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1460674, _1460672), _1460680), _1460678)))], (43625 ^ _774244) ^ [_1621475, _1621477, _1621479] : [c_Relation_Orefl__on(_1621475, _1621477, _1621479), -(c_Relation_Orefl__on(_1621475, _1621477, hAPP(c_Relation_Oconverse(_1621475, _1621475), _1621479)))], (47776 ^ _774244) ^ [_1724108, _1724110, _1724112] : [-(hBOOL(hAPP(c_List_Odistinct(_1724108), hAPP(hAPP(c_List_Oappend(_1724108), _1724110), _1724112)))), hBOOL(hAPP(c_List_Odistinct(_1724108), _1724110)), hBOOL(hAPP(c_List_Odistinct(_1724108), _1724112)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1724108, tc_HOL_Obool)), hAPP(c_List_Oset(_1724108), _1724110)), hAPP(c_List_Oset(_1724108), _1724112)) = c_Orderings_Obot__class_Obot(tc_fun(_1724108, tc_HOL_Obool))], (8848 ^ _774244) ^ [_919169] : [class_Rings_Osemiring__1(_919169), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919169), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_919169))], (42033 ^ _774244) ^ [_1584329, _1584331, _1584333] : [hBOOL(hAPP(hAPP(c_member(_1584331), _1584329), c_Orderings_Obot__class_Obot(tc_fun(_1584331, tc_HOL_Obool)))), -(hBOOL(hAPP(_1584333, _1584329)))], (14620 ^ _774244) ^ [_1018984, _1018986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1018984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1018986, _1018984)), _1018984)))], (51095 ^ _774244) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (50526 ^ _774244) ^ [_1787811, _1787813] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1787811), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1787811))), _1787813))), -(c_List_Otranspose(_1787811, c_List_Otranspose(_1787811, _1787813)) = c_List_OtakeWhile(tc_List_Olist(_1787811), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1787811)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1787811), tc_List_Olist(_1787811), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1787811))), _1787813))], (7836 ^ _774244) ^ [_902277, _902279, _902281, _902283, _902285, _902287] : [-(c_Sum__Type_Osum_Osum__rec(_902277, _902279, _902281, _902283, _902285, hAPP(c_Sum__Type_OInr(_902281, _902277), _902287)) = hAPP(_902285, _902287))], (47959 ^ _774244) ^ [_1728900, _1728902, _1728904, _1728906, _1728908, _1728910, _1728912] : [hBOOL(hAPP(hAPP(c_member(_1728900), _1728902), hAPP(c_List_Oset(_1728900), hAPP(hAPP(c_List_Otake(_1728900), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728904)), _1728906)), _1728908)))), -(c_Map_Omap__upds(_1728900, _1728904, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1728900, tc_Option_Ooption(_1728904)), _1728910), _1728902), hAPP(c_Option_Ooption_OSome(_1728904), _1728912)), _1728908, _1728906) = c_Map_Omap__upds(_1728900, _1728904, _1728910, _1728908, _1728906))], (42425 ^ _774244) ^ [_1593423, _1593425, _1593427] : [class_Orderings_Olinorder(_1593423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593423), _1593425)), -(hBOOL(hAPP(hAPP(c_member(_1593423), _1593427), _1593425))), -(c_Big__Operators_Olattice_OSup__fin(_1593423, c_Orderings_Oord__class_Omax(_1593423), hAPP(hAPP(c_Set_Oinsert(_1593423), _1593427), _1593425)) = hAPP(hAPP(c_Finite__Set_Ofold(_1593423, _1593423, c_Orderings_Oord__class_Omax(_1593423)), _1593427), _1593425))], (40882 ^ _774244) ^ [_1550056, _1550058] : [c_Relation_Orefl__on(_1550056, c_Orderings_Otop__class_Otop(tc_fun(_1550056, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1550056, _1550056)), hAPP(c_Product__Type_Oprod_Oprod__case(_1550056, _1550056, tc_HOL_Obool), _1550058))), -(c_Predicate_Oreflp(_1550056, _1550058))], (39058 ^ _774244) ^ [_1505459, _1505461, _1505463, _1505465] : [class_Groups_Ocomm__monoid__mult(_1505459), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505461), _1505463)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1505461, _1505459), _1505465), _1505463) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1505459, _1505461, c_Groups_Otimes__class_Otimes(_1505459)), _1505465), c_Groups_Oone__class_Oone(_1505459)), _1505463))], (44414 ^ _774244) ^ [_1642162, _1642164, _1642166, _1642168] : [hBOOL(hAPP(hAPP(c_member(_1642162), _1642164), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1642162, tc_HOL_Obool), _1642166))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1642162, tc_HOL_Obool)), _1642168), _1642166)), -(hBOOL(hAPP(hAPP(c_member(_1642162), _1642164), _1642168)))], (26237 ^ _774244) ^ [_1232594, _1232596] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232594)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232596))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232594), _1232596)))], (14552 ^ _774244) ^ [_1017952, _1017954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017952)), 14555 ^ _774244 : [(14562 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1017952), _1017954)), -(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), _1017954), _1017952))))], (14556 ^ _774244) ^ [] : [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), _1017954), _1017952))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1017952), _1017954)))]]], (8154 ^ _774244) ^ [_907694, _907696, _907698] : [-(c_Natural_Oevalc(c_Com_Ocom_OAss(_907694, _907696), _907698, c_Natural_Oupdate(_907698, _907694, hAPP(_907696, _907698))))], (39640 ^ _774244) ^ [_1519922, _1519924, _1519926, _1519928] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1519922), _1519924)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519926), _1519928)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1519922, _1519926)), hAPP(hAPP(c_Product__Type_OSigma(_1519922, _1519926), _1519924), hAPP(c_COMBK(tc_fun(_1519926, tc_HOL_Obool), _1519922), _1519928)))))], (4560 ^ _774244) ^ [_844750, _844752, _844754, _844756] : [-(c_Product__Type_OSigma(_844756, _844752) = c_Product__Type_OSigma(_844754, _844750)), _844756 = _844754, _844752 = _844750], (35187 ^ _774244) ^ [_1418758, _1418760, _1418762, _1418764, _1418766] : [-(hAPP(c_Relation_OImage(_1418758, _1418760, _1418762), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1418758, tc_HOL_Obool)), _1418764), _1418766)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1418760, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1418758, _1418760, _1418762), _1418764)), hAPP(c_Relation_OImage(_1418758, _1418760, _1418762), _1418766)))], (2684 ^ _774244) ^ [_814912, _814914, _814916, _814918] : [-(c_Nitpick_Onorm__frac(_814918, _814914) = c_Nitpick_Onorm__frac(_814916, _814912)), _814918 = _814916, _814914 = _814912], (16113 ^ _774244) ^ [_1048231] : [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), _1048231))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1048231) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1048231)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (42808 ^ _774244) ^ [_1600750, _1600752] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1600750, _1600750), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1600750, _1600752)), hAPP(hAPP(c_Product__Type_OSigma(_1600750, _1600750), hAPP(c_Relation_OField(_1600750), _1600752)), hAPP(c_COMBK(tc_fun(_1600750, tc_HOL_Obool), _1600750), hAPP(c_Relation_OField(_1600750), _1600752))))))], (25961 ^ _774244) ^ [_1227771, _1227773, _1227775] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227771), _1227773)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227771), _1227775))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227771)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227773), _1227775)))], (21241 ^ _774244) ^ [_1138227, _1138229, _1138231, _1138233] : [class_Fields_Olinordered__field(_1138227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138227), c_Groups_Ozero__class_Ozero(_1138227)), _1138229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138227), _1138231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138227), _1138233), _1138229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138227), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138227), _1138231), _1138229)), _1138233)))], (34467 ^ _774244) ^ [_1402206, _1402208, _1402210, _1402212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1402206), _1402208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1402210), _1402212)), -(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), _1402206), _1402210)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1402208), _1402212))), c_FunDef_Opair__leq)))], (4240 ^ _774244) ^ [_839832, _839834, _839836, _839838, _839840, _839842, _839844, _839846] : [-(c_Lazy__Sequence_Oanamorph(_839846, _839842, _839838, _839834) = c_Lazy__Sequence_Oanamorph(_839844, _839840, _839836, _839832)), _839846 = _839844, _839842 = _839840, _839838 = _839836, _839834 = _839832], (19063 ^ _774244) ^ [_1099523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1099523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1099523))))], (7523 ^ _774244) ^ [_896447, _896449, _896451, _896453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _896447), _896449)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _896451), _896449) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _896447), _896453), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _896451), _896453)))], (51037 ^ _774244) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (40743 ^ _774244) ^ [_1545011, _1545013, _1545015, _1545017, _1545019, _1545021, _1545023] : [class_Groups_Ocomm__monoid__add(_1545011), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545013), _1545015)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545017), _1545019)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545013, _1545011), hAPP(hAPP(c_COMBS(_1545013, tc_fun(_1545017, tc_HOL_Obool), _1545011), hAPP(hAPP(c_COMBB(tc_fun(_1545017, _1545011), tc_fun(tc_fun(_1545017, tc_HOL_Obool), _1545011), _1545013), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545017, _1545011)), _1545021)), hAPP(hAPP(c_COMBB(tc_fun(_1545017, tc_HOL_Obool), tc_fun(_1545017, tc_HOL_Obool), _1545013), c_Set_OCollect(_1545017)), hAPP(hAPP(c_COMBB(tc_fun(_1545017, tc_HOL_Obool), tc_fun(_1545017, tc_HOL_Obool), _1545013), hAPP(c_COMBS(_1545017, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545017), c_fconj), hAPP(hAPP(c_COMBC(_1545017, tc_fun(_1545017, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545017)), _1545019)))), _1545023)))), _1545015) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545017, _1545011), hAPP(hAPP(c_COMBS(_1545017, tc_fun(_1545013, tc_HOL_Obool), _1545011), hAPP(hAPP(c_COMBB(tc_fun(_1545013, _1545011), tc_fun(tc_fun(_1545013, tc_HOL_Obool), _1545011), _1545017), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545013, _1545011)), hAPP(c_COMBC(_1545013, _1545017, _1545011), _1545021))), hAPP(hAPP(c_COMBB(tc_fun(_1545013, tc_HOL_Obool), tc_fun(_1545013, tc_HOL_Obool), _1545017), c_Set_OCollect(_1545013)), hAPP(hAPP(c_COMBB(tc_fun(_1545013, tc_HOL_Obool), tc_fun(_1545013, tc_HOL_Obool), _1545017), hAPP(c_COMBS(_1545013, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545013), c_fconj), hAPP(hAPP(c_COMBC(_1545013, tc_fun(_1545013, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545013)), _1545015)))), hAPP(c_COMBC(_1545013, _1545017, tc_HOL_Obool), _1545023))))), _1545019))], (118 ^ _774244) ^ [_775887, _775889] : [-(class_Rings_Oinverse(_775887)), _775889 = _775887, class_Rings_Oinverse(_775889)], (22146 ^ _774244) ^ [_1154957, _1154959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1154957)), hAPP(c_Code__Numeral_Oof__nat, _1154959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1154957), _1154959)))], (18113 ^ _774244) ^ [_1083754] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1083754) = _1083754)], (42964 ^ _774244) ^ [_1604432, _1604434, _1604436, _1604438, _1604440, _1604442] : [c_Finite__Set_Ofun__left__comm(_1604432, _1604434, _1604436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1604432), _1604438)), -(hAPP(hAPP(_1604436, _1604440), hAPP(hAPP(c_Finite__Set_Ofold(_1604432, _1604434, _1604436), _1604442), _1604438)) = hAPP(hAPP(c_Finite__Set_Ofold(_1604432, _1604434, _1604436), hAPP(hAPP(_1604436, _1604440), _1604442)), _1604438))], (36399 ^ _774244) ^ [_1446293, _1446295] : [class_Lattices_Olattice(_1446293), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1446293), _1446295), _1446295) = _1446295)], (17771 ^ _774244) ^ [_1078397] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078397))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078397)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31195 ^ _774244) ^ [_1334456, _1334458, _1334460, _1334462, _1334464, _1334466] : [hBOOL(hAPP(hAPP(c_member(_1334456), _1334458), c_SetInterval_Oord_OgreaterThanAtMost(_1334456, _1334460, _1334462, _1334464, _1334466))), 31198 ^ _774244 : [(31201 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1334460, _1334458), _1334466)))], (31199 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1334462, _1334464), _1334458)))]]], (42892 ^ _774244) ^ [_1602848, _1602850, _1602852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602848, _1602848), tc_HOL_Obool)), _1602850), _1602852)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602848, _1602848), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1602848, _1602848, _1602848), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1602848, _1602848), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1602848, _1602850)), _1602852)), _1602850)), _1602852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602848, _1602848), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1602848, _1602850)), _1602852)))], (30613 ^ _774244) ^ [_1320781, _1320783, _1320785, _1320787] : [hBOOL(hAPP(hAPP(c_member(_1320781), _1320783), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320781, tc_HOL_Obool)), _1320785), _1320787))), -(hBOOL(hAPP(hAPP(c_member(_1320781), _1320783), _1320785))), -(hBOOL(hAPP(hAPP(c_member(_1320781), _1320783), _1320787)))], (27573 ^ _774244) ^ [_1260320, _1260322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1260320), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1260322), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1260322), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1260320))))), -(_1260320 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1260322), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1260322), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1260320))))], (43157 ^ _774244) ^ [_1608973, _1608975, _1608977, _1608979] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608973, _1608973)), hAPP(hAPP(c_Product__Type_OPair(_1608973, _1608973), _1608975), _1608977)), c_Transitive__Closure_Ortrancl(_1608973, _1608979)))), 43158 ^ _774244 : [(43161 ^ _774244) ^ [] : [-(_1608975 = _1608977), hBOOL(hAPP(hAPP(c_member(tc_prod(_1608973, _1608973)), hAPP(hAPP(c_Product__Type_OPair(_1608973, _1608973), _1608975), _1608977)), c_Transitive__Closure_Otrancl(_1608973, _1608979)))], (43159 ^ _774244) ^ [] : [_1608975 = _1608977]]], (47897 ^ _774244) ^ [_1727595, _1727597, _1727599, _1727601] : [-(c_Map_Omap__upds(_1727595, _1727597, _1727599, _1727601, c_List_Olist_ONil(_1727597)) = _1727599)], (3062 ^ _774244) ^ [_821089, _821091, _821093, _821095, _821097, _821099, _821101, _821103] : [-(c_New__DSequence_Opos__bind(_821103, _821099, _821095, _821091) = c_New__DSequence_Opos__bind(_821101, _821097, _821093, _821089)), _821103 = _821101, _821099 = _821097, _821095 = _821093, _821091 = _821089], (49025 ^ _774244) ^ [_1755112, _1755114, _1755116] : [-(_1755112 = c_List_Olist_ONil(_1755114)), -(c_List_Olast(_1755114, hAPP(hAPP(c_List_Oappend(_1755114), _1755116), _1755112)) = c_List_Olast(_1755114, _1755112))], (45869 ^ _774244) ^ [_1676380, _1676382, _1676384, _1676386, _1676388] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1676380, _1676382)), hAPP(hAPP(c_Product__Type_OPair(_1676380, _1676382), _1676384), _1676386)), hAPP(c_List_Oset(tc_prod(_1676380, _1676382)), _1676388))), -(hAPP(c_Map_Omap__of(_1676380, _1676382, _1676388), _1676384) = hAPP(c_Option_Ooption_OSome(_1676382), 45872 ^ [_1676380, _1676382, _1676384, _1676386, _1676388]))], (29574 ^ _774244) ^ [_1301021] : [-(hAPP(c_Finite__Set_Ocard(_1301021), c_Orderings_Obot__class_Obot(tc_fun(_1301021, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50663 ^ _774244) ^ [_1790635, _1790637] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790635)), c_List_Oremdups(_1790635, _1790637))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790635)), _1790637))))], (45335 ^ _774244) ^ [_1663410, _1663412, _1663414, _1663416, _1663418, _1663420] : [hAPP(_1663410, _1663412) = hAPP(c_Option_Ooption_OSome(_1663414), _1663416), -(hAPP(c_Map_Omap__add(_1663418, _1663414, _1663420, _1663410), _1663412) = hAPP(c_Option_Ooption_OSome(_1663414), _1663416))], (42818 ^ _774244) ^ [_1600986, _1600988] : [-(hAPP(c_Relation_ODomain(_1600986, _1600986), c_Transitive__Closure_Otrancl(_1600986, _1600988)) = hAPP(c_Relation_ODomain(_1600986, _1600986), _1600988))], (32059 ^ _774244) ^ [_1354477, _1354479] : [c_Nitpick_Orefl_H(_1354477, _1354479), 32062 ^ _774244 : [(32063 ^ _774244) ^ [_1354555] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1354477, _1354477)), hAPP(hAPP(c_Product__Type_OPair(_1354477, _1354477), _1354555), _1354555)), _1354479)))]]], (24877 ^ _774244) ^ [_1208623, _1208625, _1208627, _1208629] : [class_Rings_Ocomm__semiring__1(_1208623), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208623), _1208625), _1208627)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208623), _1208625), _1208629)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208623), _1208625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208623), _1208627), _1208629))))], (11953 ^ _774244) ^ [_971842, _971844] : [class_Rings_Olinordered__semidom(_971842), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971842), c_Groups_Ozero__class_Ozero(_971842)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_971842), _971844))))], (29977 ^ _774244) ^ [_1308298, _1308300, _1308302] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1308298), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308298, tc_HOL_Obool)), _1308300), _1308302))), 29980 ^ _774244 : [(29983 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308298), _1308302)))], (29981 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308298), _1308300)))]]], (25689 ^ _774244) ^ [_1222526, _1222528, _1222530, _1222532, _1222534] : [class_Rings_Ocomm__semiring__1(_1222526), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222526), hAPP(hAPP(c_Power_Opower__class_Opower(_1222526), _1222528), _1222530)), _1222532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1222534), _1222530)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222526), hAPP(hAPP(c_Power_Opower__class_Opower(_1222526), _1222528), _1222534)), _1222532)))], (19105 ^ _774244) ^ [_1100266, _1100268] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1100266)), c_Int_OBit1(_1100268)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1100266), _1100268)))], (44404 ^ _774244) ^ [_1641954, _1641956] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1641954), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1641954, tc_HOL_Obool), _1641956)))), 44405 ^ _774244 : [(44406 ^ _774244) ^ [_1642018] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1641954, tc_HOL_Obool)), _1642018), _1641956)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641954), _1642018))]]], (7076 ^ _774244) ^ [_889177, _889179, _889181, _889183, _889185, _889187, _889189, _889191, _889193, _889195, _889197] : [-(c_Com_Ocom_Ocom__case(_889177, _889179, _889181, _889183, _889185, _889187, _889189, _889191, _889193, c_Com_Ocom_OWhile(_889195, _889197)) = hAPP(hAPP(_889189, _889195), _889197))], (23807 ^ _774244) ^ [_1187298, _1187300, _1187302] : [class_Orderings_Olinorder(_1187298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187298), _1187300), _1187302)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187298), _1187302), _1187300) = _1187300)], (19609 ^ _774244) ^ [_1109159, _1109161, _1109163] : [class_Rings_Olinordered__idom(_1109159), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109159), c_Groups_Ozero__class_Ozero(_1109159)), hAPP(hAPP(c_Power_Opower__class_Opower(_1109159), _1109161), 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)))), _1109163)))))], (18929 ^ _774244) ^ [_1097256, _1097258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1097256)), c_Int_OBit0(_1097258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097256), _1097258)))], (42932 ^ _774244) ^ [_1603832, _1603834, _1603836, _1603838, _1603840, _1603842] : [c_Finite__Set_Ofun__left__comm(_1603832, _1603834, _1603836), -(hAPP(hAPP(_1603836, _1603838), hAPP(hAPP(_1603836, _1603840), _1603842)) = hAPP(hAPP(_1603836, _1603840), hAPP(hAPP(_1603836, _1603838), _1603842)))], (41935 ^ _774244) ^ [_1581661, _1581663, _1581665, _1581667, _1581669] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1581661), _1581663), _1581665), _1581667), _1581669) = c_New__DSequence_Opos__single(_1581661, _1581663))], (48262 ^ _774244) ^ [_1737542, _1737544, _1737546, _1737548] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1737542), tc_List_Olist(_1737542))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1737542), tc_List_Olist(_1737542)), _1737544), _1737546)), c_List_Olistrel1(_1737542, _1737548)))), 48263 ^ _774244 : [(48264 ^ _774244) ^ [_1737675, _1737677] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1737542, _1737542)), hAPP(hAPP(c_Product__Type_OPair(_1737542, _1737542), hAPP(hAPP(c_List_Onth(_1737542), _1737544), _1737675)), _1737677)), _1737548)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737675), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737542)), _1737544))), _1737546 = hAPP(hAPP(c_List_Olist__update(_1737542, _1737544), _1737675), _1737677)]]], (43927 ^ _774244) ^ [_1629426, _1629428, _1629430, _1629432, _1629434] : [_1629426 = c_Orderings_Obot__class_Obot(tc_fun(_1629428, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629428, tc_fun(_1629430, tc_HOL_Obool)), _1629426), hAPP(hAPP(c_COMBB(tc_fun(_1629430, tc_HOL_Obool), tc_fun(_1629430, tc_HOL_Obool), _1629428), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1629430, tc_HOL_Obool)), _1629432)), _1629434)) = c_Orderings_Otop__class_Otop(tc_fun(_1629430, tc_HOL_Obool)))], (26149 ^ _774244) ^ [_1231046, _1231048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231048)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231046), _1231048)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231048), _1231046)), -(_1231046 = _1231048)], (45754 ^ _774244) ^ [] : [c_Com_OWT__bodies, 45757 ^ _774244 : [(45758 ^ _774244) ^ [_1673776] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1673776), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), _1673776)))]]], (16291 ^ _774244) ^ [_1051352, _1051354] : [class_Int_Onumber__ring(_1051352), 16294 ^ _774244 : [(16301 ^ _774244) ^ [] : [-(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), _1051354)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1051352), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1051354)) = c_Groups_Ozero__class_Ozero(_1051352))], (16295 ^ _774244) ^ [] : [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), _1051354))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1051352), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1051354)) = hAPP(c_Int_Onumber__class_Onumber__of(_1051352), _1051354))]]], (49294 ^ _774244) ^ [_1760289, _1760291, _1760293, _1760295] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760289)), _1760291))), c_List_Ofoldr(tc_List_Olist(_1760293), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1760293)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1760293))), _1760295, 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(_1760289)), _1760291)), c_List_Ofoldr(tc_List_Olist(_1760293), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1760293)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1760293), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1760293)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1760293)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1760293), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1760293)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1760293), tc_List_Olist(_1760293), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1760293)))), _1760295), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (7337 ^ _774244) ^ [_893515] : [-(_893515 = 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)), _893515)))], (11985 ^ _774244) ^ [_972428, _972430, _972432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972428), _972430)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972432), _972430))), 11988 ^ _774244 : [(11991 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972428), _972432)))], (11989 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _972430)))]]], (568 ^ _774244) ^ [_783126, _783128, _783130, _783132] : [-(c_Nitpick_Owf_H(_783130, _783126)), c_Nitpick_Owf_H(_783132, _783128), _783132 = _783130, _783128 = _783126], (51109 ^ _774244) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (17175 ^ _774244) ^ [_1068056, _1068058] : [class_Groups_Omonoid__mult(_1068056), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1068056), _1068058), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1068058)], (17075 ^ _774244) ^ [_1066156] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1066156)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066156))], (6896 ^ _774244) ^ [_885839, _885841, _885843, _885845] : [-(c_Com_Ocom_OWhile(_885839, _885841) = c_Com_Ocom_OWhile(_885843, _885845)), _885839 = _885843, _885841 = _885845], (24579 ^ _774244) ^ [_1202218, _1202220] : [-(c_Nitpick_Onumber__of__frac(_1202218, _1202220) = c_Nitpick_OAbs__Frac(_1202218, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1202220), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (48590 ^ _774244) ^ [_1745203, _1745205, _1745207] : [-(_1745203 = c_List_Olist_ONil(_1745205)), -(hAPP(c_List_Otl(_1745205), hAPP(hAPP(c_List_Oappend(_1745205), _1745203), _1745207)) = hAPP(hAPP(c_List_Oappend(_1745205), hAPP(c_List_Otl(_1745205), _1745203)), _1745207))], (36649 ^ _774244) ^ [_1452320, _1452322, _1452324, _1452326, _1452328] : [class_Orderings_Olinorder(_1452320), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452320, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1452320, _1452322, _1452324)), c_SetInterval_Oord__class_OatLeastAtMost(_1452320, _1452326, _1452328)) = c_SetInterval_Oord__class_OatLeastAtMost(_1452320, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1452320), _1452322), _1452326), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1452320), _1452324), _1452328)))], (27400 ^ _774244) ^ [_1257324, _1257326] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1257324, _1257326)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1257324), hAPP(c_Nat_OSuc, _1257326)))], (6762 ^ _774244) ^ [_883405, _883407, _883409, _883411, _883413] : [c_Com_Ocom_OLocal(_883405, _883407, _883409) = c_Com_Ocom_OSemi(_883411, _883413)], (43299 ^ _774244) ^ [_1612322, _1612324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1612322), _1612324)), -(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), _1612322), _1612324)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (41146 ^ _774244) ^ [_1561342, _1561344, _1561346] : [-(hAPP(c_Fun_Ocomp(_1561342, _1561342, _1561344, c_Fun_Oid(_1561342)), _1561346) = _1561346)], (42392 ^ _774244) ^ [_1592700, _1592702, _1592704, _1592706, _1592708, _1592710, _1592712, _1592714] : [class_Groups_Ocomm__monoid__add(_1592700), c_Fun_Oinj__on(_1592702, _1592704, _1592706, _1592708), _1592710 = hAPP(c_Set_Oimage(_1592702, _1592704, _1592706), _1592708), 42406 ^ _774244 : [(42409 ^ _774244) ^ [] : [hAPP(_1592712, 42405 ^ [_1592700, _1592702, _1592704, _1592706, _1592708, _1592710, _1592712, _1592714]) = hAPP(_1592714, hAPP(_1592706, 42405 ^ [_1592700, _1592702, _1592704, _1592706, _1592708, _1592710, _1592712, _1592714]))], (42407 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1592702), 42405 ^ [_1592700, _1592702, _1592704, _1592706, _1592708, _1592710, _1592712, _1592714]), _1592708)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1592704, _1592700), _1592714), _1592710) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1592702, _1592700), _1592712), _1592708))], (30727 ^ _774244) ^ [_1322940, _1322942, _1322944, _1322946, _1322948, _1322950] : [c_Typedef_Otype__definition(_1322940, _1322942, _1322944, _1322946, _1322948), -(hBOOL(hAPP(hAPP(c_member(_1322942), hAPP(_1322944, _1322950)), _1322948)))], (39704 ^ _774244) ^ [_1521678, _1521680, _1521682, _1521684] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1521678, _1521680)), hAPP(hAPP(c_Product__Type_OSigma(_1521678, _1521680), hAPP(hAPP(c_Set_Oinsert(_1521678), _1521682), c_Orderings_Obot__class_Obot(tc_fun(_1521678, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1521680, tc_HOL_Obool), _1521678), _1521684))) = hAPP(c_Finite__Set_Ocard(_1521680), _1521684))], (25005 ^ _774244) ^ [_1210753, _1210755] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210753), _1210755))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210753), _1210755)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210755), _1210753)))], (50868 ^ _774244) ^ [_1794639, _1794641, _1794643, _1794645, _1794647] : [-(c_List_OdropWhile(_1794639, _1794641, _1794643) = hAPP(hAPP(c_List_Olist_OCons(_1794639), _1794645), _1794647)), _1794643 = hAPP(hAPP(c_List_Oappend(_1794639), c_List_OtakeWhile(_1794639, _1794641, _1794643)), hAPP(hAPP(c_List_Olist_OCons(_1794639), _1794645), _1794647)), -(hBOOL(hAPP(_1794641, _1794645)))], (11919 ^ _774244) ^ [_971299, _971301] : [class_Groups_Oordered__ab__group__add(_971299), 11922 ^ _774244 : [(11929 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971299), _971301), c_Groups_Ozero__class_Ozero(_971299))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971299), c_Groups_Ozero__class_Ozero(_971299)), hAPP(c_Groups_Ouminus__class_Ouminus(_971299), _971301))))], (11923 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971299), c_Groups_Ozero__class_Ozero(_971299)), hAPP(c_Groups_Ouminus__class_Ouminus(_971299), _971301))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971299), _971301), c_Groups_Ozero__class_Ozero(_971299))))]]], (36243 ^ _774244) ^ [_1442944, _1442946] : [class_Lattices_Obounded__lattice__bot(_1442944), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1442944), c_Orderings_Obot__class_Obot(_1442944)), _1442946) = c_Orderings_Obot__class_Obot(_1442944))], (35835 ^ _774244) ^ [_1434560, _1434562, _1434564, _1434566, _1434568, _1434570] : [c_Equiv__Relations_Oequiv(_1434560, _1434562, _1434564), hBOOL(hAPP(hAPP(c_member(_1434560), _1434566), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434560, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1434560, _1434560, _1434564), hAPP(hAPP(c_Set_Oinsert(_1434560), _1434568), c_Orderings_Obot__class_Obot(tc_fun(_1434560, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1434560, _1434560, _1434564), hAPP(hAPP(c_Set_Oinsert(_1434560), _1434570), c_Orderings_Obot__class_Obot(tc_fun(_1434560, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1434560, _1434560)), hAPP(hAPP(c_Product__Type_OPair(_1434560, _1434560), _1434568), _1434570)), _1434564)))], (36369 ^ _774244) ^ [_1445756, _1445758, _1445760] : [class_Lattices_Olattice(_1445756), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445756), _1445758), _1445760) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1445756), _1445760), _1445758))], (13674 ^ _774244) ^ [_1002302, _1002304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002302)), 13677 ^ _774244 : [(13680 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1002304, _1002302)), _1002302)))], (13678 ^ _774244) ^ [] : [-(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, _1002304, _1002302))))]]], (36603 ^ _774244) ^ [_1451399, _1451401, _1451403, _1451405, _1451407, _1451409, _1451411, _1451413] : [c_Equiv__Relations_Oequiv(_1451399, _1451401, _1451403), c_Equiv__Relations_Ocongruent2(_1451399, _1451405, _1451407, _1451403, _1451409, _1451411), hBOOL(hAPP(hAPP(c_member(_1451399), _1451413), _1451401)), -(c_Equiv__Relations_Ocongruent(_1451405, _1451407, _1451409, hAPP(_1451411, _1451413)))], (252 ^ _774244) ^ [_777994, _777996] : [-(class_Fields_Olinordered__field(_777994)), _777996 = _777994, class_Fields_Olinordered__field(_777996)], (8076 ^ _774244) ^ [_906544, _906546, _906548] : [-(c_Natural_Oevalc(c_Com_Ocom_OAss(_906544, _906546), _906548, c_Natural_Oupdate(_906548, _906544, hAPP(_906546, _906548))))], (18997 ^ _774244) ^ [_1098394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1098394)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098394), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35020 ^ _774244) ^ [_1415333, _1415335, _1415337] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1415333, tc_HOL_Obool)), _1415337), hAPP(c_Set_OPow(_1415333), _1415335))), -(hBOOL(hAPP(c_Predicate_OPowp(_1415333, hAPP(hAPP(c_COMBC(_1415333, tc_fun(_1415333, tc_HOL_Obool), tc_HOL_Obool), c_member(_1415333)), _1415335)), _1415337)))], (7838 ^ _774244) ^ [_902326, _902328, _902330, _902332, _902334] : [-(hAPP(c_Sum__Type_OSuml(_902326, _902328, _902330, _902332), hAPP(c_Sum__Type_OInl(_902326, _902330), _902334)) = hAPP(_902332, _902334))], (38676 ^ _774244) ^ [_1496633, _1496635, _1496637, _1496639, _1496641, _1496643, _1496645, _1496647] : [c_Finite__Set_Ofolding__image(_1496633, _1496635, _1496637, _1496639, _1496641), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496635), _1496643)), -(hAPP(hAPP(_1496641, hAPP(hAPP(c_COMBS(_1496635, _1496633, _1496633), hAPP(hAPP(c_COMBB(_1496633, tc_fun(_1496633, _1496633), _1496635), _1496637), _1496645)), _1496647)), _1496643) = hAPP(hAPP(_1496637, hAPP(hAPP(_1496641, _1496645), _1496643)), hAPP(hAPP(_1496641, _1496647), _1496643)))], (18845 ^ _774244) ^ [_1095580, _1095582] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1095580))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1095582)) = 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)))), _1095580), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1095582)))], (43335 ^ _774244) ^ [_1613108, _1613110, _1613112, _1613114, _1613116, _1613118] : [hBOOL(hAPP(hAPP(c_member(_1613108), _1613110), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613112, tc_fun(_1613108, tc_HOL_Obool)), _1613114), _1613116))), hBOOL(hAPP(hAPP(c_member(_1613112), _1613118), _1613114)), -(hBOOL(hAPP(hAPP(c_member(_1613108), _1613110), hAPP(_1613116, _1613118))))], (9032 ^ _774244) ^ [_922122, _922124, _922126] : [class_Groups_Ogroup__add(_922122), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922122), hAPP(c_Groups_Ouminus__class_Ouminus(_922122), _922124)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922122), _922124), _922126)) = _922126)], (3544 ^ _774244) ^ [_828828, _828830] : [_828830 = _828828, -(c_Int_Oint__ge__less__than(_828830) = c_Int_Oint__ge__less__than(_828828))], (3188 ^ _774244) ^ [_823174, _823176, _823178, _823180, _823182, _823184, _823186, _823188] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_823188, _823184, _823180, _823176) = c_SetInterval_Oord_OgreaterThanLessThan(_823186, _823182, _823178, _823174)), _823188 = _823186, _823184 = _823182, _823180 = _823178, _823176 = _823174], (36299 ^ _774244) ^ [_1444192, _1444194, _1444196] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444192, tc_HOL_Obool)), _1444194), _1444196) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444192, tc_HOL_Obool)), _1444196), _1444194))], (8824 ^ _774244) ^ [_918503, _918505, _918507, _918509, _918511] : [class_Rings_Ocomm__semiring__1(_918503), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918503), _918505), _918507)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918503), _918509), _918511)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918503), _918505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918503), _918507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918503), _918509), _918511))))], (28835 ^ _774244) ^ [_1286574, _1286576, _1286578, _1286580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286574, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1286574, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28836 ^ [_1286574, _1286576, _1286578, _1286580])), _1286576)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1286574, 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), 28836 ^ [_1286574, _1286576, _1286578, _1286580]), _1286578))), _1286580))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286574, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1286574, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1286576)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1286574, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1286580))))], (47563 ^ _774244) ^ [_1719545, _1719547, _1719549, _1719551] : [-(hAPP(hAPP(c_List_Oappend(_1719545), hAPP(hAPP(c_List_Olist_OCons(_1719545), _1719547), _1719549)), _1719551) = hAPP(hAPP(c_List_Olist_OCons(_1719545), _1719547), hAPP(hAPP(c_List_Oappend(_1719545), _1719549), _1719551)))], (44012 ^ _774244) ^ [_1632353, _1632355, _1632357] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1632353, _1632353, _1632355), c_Relation_OId(_1632353)), _1632357) = _1632357)], (32120 ^ _774244) ^ [_1355694, _1355696, _1355698, _1355700] : [hBOOL(hAPP(hAPP(c_member(_1355694), _1355696), c_SetInterval_Oord_OgreaterThan(_1355694, _1355698, _1355700))), -(hBOOL(hAPP(hAPP(_1355698, _1355700), _1355696)))], (16143 ^ _774244) ^ [_1048706, _1048708] : [class_Groups_Oordered__ab__group__add__abs(_1048706), -(hAPP(c_Groups_Oabs__class_Oabs(_1048706), hAPP(c_Groups_Oabs__class_Oabs(_1048706), _1048708)) = hAPP(c_Groups_Oabs__class_Oabs(_1048706), _1048708))], (49308 ^ _774244) ^ [_1760795, _1760797, _1760799] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760795)), hAPP(c_List_Ofilter(_1760795, _1760797), _1760799))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760795)), hAPP(c_List_Ofilter(_1760795, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1760795), c_fNot), _1760797)), _1760799))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760795)), _1760799))], (24549 ^ _774244) ^ [_1201476, _1201478, _1201480, _1201482, _1201484, _1201486, _1201488, _1201490, _1201492] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1201476, _1201478, _1201480, _1201482), hAPP(hAPP(c_Product__Type_Oscomp(_1201476, _1201484, _1201486, tc_prod(_1201478, _1201480)), _1201488), _1201490)), _1201492) = hAPP(hAPP(c_Product__Type_Oscomp(_1201476, _1201484, _1201486, _1201482), _1201488), hAPP(hAPP(c_COMBC(_1201484, tc_fun(_1201478, tc_fun(_1201480, _1201482)), tc_fun(_1201486, _1201482)), hAPP(hAPP(c_COMBB(tc_fun(_1201486, tc_prod(_1201478, _1201480)), tc_fun(tc_fun(_1201478, tc_fun(_1201480, _1201482)), tc_fun(_1201486, _1201482)), _1201484), c_Product__Type_Oscomp(_1201486, _1201478, _1201480, _1201482)), _1201490)), _1201492)))], (33494 ^ _774244) ^ [_1382361, _1382363] : [class_Orderings_Olinorder(_1382361), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382361), _1382363)), -(_1382363 = c_Orderings_Obot__class_Obot(tc_fun(_1382361, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382361), c_Big__Operators_Olattice_OInf__fin(_1382361, c_Orderings_Oord__class_Omin(_1382361), _1382363)), c_Big__Operators_Olattice_OSup__fin(_1382361, c_Orderings_Oord__class_Omax(_1382361), _1382363))))], (27968 ^ _774244) ^ [_1268178, _1268180, _1268182, _1268184] : [class_Lattices_Osemilattice__sup(_1268178), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268178), _1268180), _1268182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268178), _1268184), _1268182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268178), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268178), _1268180), _1268184)), _1268182)))], (51073 ^ _774244) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (45604 ^ _774244) ^ [_1670050, _1670052] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1670050), hAPP(c_List_Oset(_1670050), _1670052))))], (46098 ^ _774244) ^ [_1682052, _1682054, _1682056, _1682058, _1682060] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682052), tc_List_Olist(_1682052))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682052), tc_List_Olist(_1682052)), _1682054), _1682056)), hAPP(c_List_Olexn(_1682052, _1682058), _1682060))), 46101 ^ _774244 : [(46104 ^ _774244) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682052)), _1682056) = _1682060)], (46102 ^ _774244) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682052)), _1682054) = _1682060)]]], (48662 ^ _774244) ^ [_1746679, _1746681, _1746683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746679)), _1746681)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1746679, _1746683), _1746681) = _1746681)], (13334 ^ _774244) ^ [_995882, _995884] : [-(hBOOL(hAPP(_995882, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_995882, _995884)), 13342 ^ _774244 : [(13345 ^ _774244) ^ [_996120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996120), 13341 ^ [_995882, _995884])), hBOOL(hAPP(_995882, _996120))], (13351 ^ _774244) ^ [] : [-(hBOOL(hAPP(_995882, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 13341 ^ [_995882, _995884]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (13343 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13341 ^ [_995882, _995884]), _995884)))]]], (10223 ^ _774244) ^ [_942684, _942686, _942688] : [class_Orderings_Oorder(_942684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942684), _942686), _942688)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942684), _942688), _942686)), -(_942686 = _942688)], (6772 ^ _774244) ^ [_883687, _883689, _883691, _883693, _883695] : [class_Rings_Ocomm__semiring__1(_883687), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883687), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883687), _883689), _883691)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883687), _883693), _883695)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883687), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883687), _883689), _883693)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883687), _883691), _883695)))], (16137 ^ _774244) ^ [_1048605, _1048607] : [class_Int_Onumber__ring(_1048605), -(hAPP(c_Int_Oring__1__class_Oof__int(_1048605), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1048607)) = hAPP(c_Int_Onumber__class_Onumber__of(_1048605), _1048607))], (38199 ^ _774244) ^ [_1486372, _1486374, _1486376, _1486378, _1486380] : [c_Fun_Oinj__on(_1486372, _1486374, _1486376, _1486378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1486372, tc_HOL_Obool)), _1486380), _1486378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1486374, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1486372, _1486374, _1486376), _1486380)), hAPP(c_Set_Oimage(_1486372, _1486374, _1486376), _1486378))))], (18741 ^ _774244) ^ [] : [-(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)))))], (9240 ^ _774244) ^ [_925875, _925877] : [class_Groups_Oordered__ab__group__add(_925875), 9243 ^ _774244 : [(9250 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925875), c_Groups_Ozero__class_Ozero(_925875)), _925877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925875), hAPP(c_Groups_Ouminus__class_Ouminus(_925875), _925877)), c_Groups_Ozero__class_Ozero(_925875))))], (9244 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925875), hAPP(c_Groups_Ouminus__class_Ouminus(_925875), _925877)), c_Groups_Ozero__class_Ozero(_925875))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925875), c_Groups_Ozero__class_Ozero(_925875)), _925877)))]]], (5923 ^ _774244) ^ [_869033, _869035, _869037, _869039, _869041] : [-(hBOOL(hAPP(_869033, _869035))), c_Natural_Oevalc(_869037, _869035, _869039), -(c_Natural_Oevalc(c_Com_Ocom_OCond(_869033, _869041, _869037), _869035, _869039))], (42718 ^ _774244) ^ [_1599287, _1599289, _1599291] : [class_Groups_Oab__semigroup__mult(_1599287), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599287), _1599289)), -(hBOOL(hAPP(hAPP(c_member(_1599287), _1599291), _1599289))), -(hAPP(c_Finite__Set_Ofold1(_1599287, c_Groups_Otimes__class_Otimes(_1599287)), hAPP(hAPP(c_Set_Oinsert(_1599287), _1599291), _1599289)) = hAPP(hAPP(c_Finite__Set_Ofold(_1599287, _1599287, c_Groups_Otimes__class_Otimes(_1599287)), _1599291), _1599289))], (47143 ^ _774244) ^ [_1709388, _1709390, _1709392, _1709394, _1709396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709388), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709390)), _1709392))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709388), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709394)), _1709396))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1709390, _1709394)), hAPP(hAPP(c_List_Ozip(_1709390, _1709394), _1709392), _1709396)), _1709388) = hAPP(hAPP(c_Product__Type_OPair(_1709390, _1709394), hAPP(hAPP(c_List_Onth(_1709390), _1709392), _1709388)), hAPP(hAPP(c_List_Onth(_1709394), _1709396), _1709388)))], (31611 ^ _774244) ^ [_1344567, _1344569, _1344571, _1344573, _1344575] : [class_Groups_Ocomm__monoid__add(_1344567), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344569), _1344571)), 31618 ^ _774244 : [(31625 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344569), _1344573), _1344571))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344569, _1344567), hAPP(hAPP(c_COMBC(_1344569, _1344567, _1344567), hAPP(hAPP(c_COMBS(_1344569, _1344567, tc_fun(_1344567, _1344567)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1344567, tc_fun(_1344567, _1344567)), _1344569), c_If(_1344567)), hAPP(c_fequal, _1344573))), _1344575)), c_Groups_Ozero__class_Ozero(_1344567))), _1344571) = c_Groups_Ozero__class_Ozero(_1344567))], (31619 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1344569), _1344573), _1344571)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344569, _1344567), hAPP(hAPP(c_COMBC(_1344569, _1344567, _1344567), hAPP(hAPP(c_COMBS(_1344569, _1344567, tc_fun(_1344567, _1344567)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1344567, tc_fun(_1344567, _1344567)), _1344569), c_If(_1344567)), hAPP(c_fequal, _1344573))), _1344575)), c_Groups_Ozero__class_Ozero(_1344567))), _1344571) = hAPP(_1344575, _1344573))]]], (28767 ^ _774244) ^ [_1285138, _1285140, _1285142, _1285144, _1285146] : [-(hAPP(c_Set_Oimage(_1285138, _1285140, _1285142), hAPP(hAPP(c_Set_Oinsert(_1285138), _1285144), _1285146)) = hAPP(hAPP(c_Set_Oinsert(_1285140), hAPP(_1285142, _1285144)), hAPP(c_Set_Oimage(_1285138, _1285140, _1285142), _1285146)))], (17503 ^ _774244) ^ [_1074091, _1074093, _1074095, _1074097] : [class_Rings_Olinordered__semidom(_1074091), hAPP(hAPP(c_Power_Opower__class_Opower(_1074091), _1074093), _1074095) = hAPP(hAPP(c_Power_Opower__class_Opower(_1074091), _1074097), _1074095), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074091), c_Groups_Ozero__class_Ozero(_1074091)), _1074093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074091), c_Groups_Ozero__class_Ozero(_1074091)), _1074097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1074095)), -(_1074093 = _1074097)], (45584 ^ _774244) ^ [_1669455, _1669457, _1669459, _1669461, _1669463, _1669465] : [-(c_Map_Omap__comp(_1669455, _1669457, _1669459, _1669461, _1669463, _1669465) = c_Option_Ooption_ONone(_1669457)), 45585 ^ _774244 : [(45588 ^ _774244) ^ [_1669567] : [hAPP(_1669463, _1669465) = hAPP(c_Option_Ooption_OSome(_1669455), _1669567), hAPP(_1669461, _1669567) = c_Option_Ooption_ONone(_1669457)], (45586 ^ _774244) ^ [] : [hAPP(_1669463, _1669465) = c_Option_Ooption_ONone(_1669455)]]], (18381 ^ _774244) ^ [_1087888, _1087890] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087888), c_Int_OPls))), 18384 ^ _774244 : [(18391 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087890), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087888)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087890)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1087888), _1087890)))], (18385 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087890), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087888)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087890)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087888))]]], (30871 ^ _774244) ^ [_1327949, _1327951] : [30872 ^ _774244 : [(30873 ^ _774244) ^ [_1328002] : [hBOOL(hAPP(hAPP(c_member(_1327949), _1328002), _1327951))]], _1327951 = c_Orderings_Obot__class_Obot(tc_fun(_1327949, tc_HOL_Obool))], (4112 ^ _774244) ^ [_837758, _837760, _837762, _837764] : [-(c_Relation_Oinv__image(_837764, _837760) = c_Relation_Oinv__image(_837762, _837758)), _837764 = _837762, _837760 = _837758], (42509 ^ _774244) ^ [_1595126, _1595128] : [c_Wellfounded_Oacyclic(_1595126, _1595128), 42512 ^ _774244 : [(42513 ^ _774244) ^ [_1595211] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595126, _1595126)), hAPP(hAPP(c_Product__Type_OPair(_1595126, _1595126), _1595211), _1595211)), c_Transitive__Closure_Otrancl(_1595126, _1595128)))]]], (27866 ^ _774244) ^ [_1266342, _1266344] : [class_Lattices_Osemilattice__sup(_1266342), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266342), _1266344), _1266344) = _1266344)], (18935 ^ _774244) ^ [_1097357, _1097359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097357), _1097359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1097357)), c_Int_OBit0(_1097359))))], (11110 ^ _774244) ^ [_957014, _957016] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957014), _957016))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _957016)), _957014)))], (7124 ^ _774244) ^ [_889994, _889996, _889998, _890000, _890002] : [-(c_Sum__Type_Osum_Osum__size(_889994, _889996, _889998, _890000, hAPP(c_Sum__Type_OInr(_889996, _889994), _890002)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_890000, _890002)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48250 ^ _774244) ^ [_1737194, _1737196, _1737198, _1737200] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1737194), tc_List_Olist(_1737194))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1737194), tc_List_Olist(_1737194)), _1737196), _1737198)), c_List_Olistrel1(_1737194, _1737200))), 48255 ^ _774244 : [(48260 ^ _774244) ^ [] : [-(_1737198 = hAPP(hAPP(c_List_Olist__update(_1737194, _1737196), 48254 ^ [_1737194, _1737196, _1737198, _1737200]), 48253 ^ [_1737194, _1737196, _1737198, _1737200]))], (48258 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48254 ^ [_1737194, _1737196, _1737198, _1737200]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737194)), _1737196))))], (48256 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1737194, _1737194)), hAPP(hAPP(c_Product__Type_OPair(_1737194, _1737194), hAPP(hAPP(c_List_Onth(_1737194), _1737196), 48254 ^ [_1737194, _1737196, _1737198, _1737200])), 48253 ^ [_1737194, _1737196, _1737198, _1737200])), _1737200)))]]], (15660 ^ _774244) ^ [_1038793, _1038795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038793), _1038795)), -(c_Nat__Transfer_Otsub(_1038795, _1038793) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1038795), _1038793))], (24523 ^ _774244) ^ [_1200920, _1200922] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1200920), _1200922) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1200920)), hAPP(c_Code__Numeral_Onat__of, _1200922))))], (50693 ^ _774244) ^ [_1791147, _1791149] : [c_List_Olist_ONil(_1791147) = c_List_Oremdups(_1791147, _1791149), -(_1791149 = c_List_Olist_ONil(_1791147))], (30218 ^ _774244) ^ [_1312581, _1312583, _1312585, _1312587] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312581), _1312583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1312585), hAPP(c_Set_Oimage(_1312581, _1312585, _1312587), _1312583))), hAPP(c_Finite__Set_Ocard(_1312581), _1312583))))], (872 ^ _774244) ^ [_787684, _787686, _787688, _787690, _787692, _787694] : [-(c_Equiv__Relations_Oequiv(_787692, _787688, _787684)), c_Equiv__Relations_Oequiv(_787694, _787690, _787686), _787694 = _787692, _787690 = _787688, _787686 = _787684], (32426 ^ _774244) ^ [_1361970, _1361972, _1361974] : [-(hAPP(c_Finite__Set_Ocard(_1361970), _1361972) = hAPP(c_Nat_OSuc, _1361974)), 32427 ^ _774244 : [(32428 ^ _774244) ^ [_1362070, _1362072] : [_1361972 = hAPP(hAPP(c_Set_Oinsert(_1361970), _1362072), _1362070), -(hBOOL(hAPP(hAPP(c_member(_1361970), _1362072), _1362070))), hAPP(c_Finite__Set_Ocard(_1361970), _1362070) = _1361974, 32439 ^ _774244 : [(32442 ^ _774244) ^ [] : [_1362070 = c_Orderings_Obot__class_Obot(tc_fun(_1361970, tc_HOL_Obool))], (32440 ^ _774244) ^ [] : [-(_1361974 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (8792 ^ _774244) ^ [_917882, _917884] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _917882)), _917884) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _917882), _917884)))], (46611 ^ _774244) ^ [_1697128, _1697130, _1697132, _1697134] : [hBOOL(hAPP(hAPP(c_member(_1697128), _1697130), hAPP(c_List_Oset(_1697128), c_List_Osublist(_1697128, _1697132, _1697134)))), -(hBOOL(hAPP(hAPP(c_member(_1697128), _1697130), hAPP(c_List_Oset(_1697128), _1697132))))], (7573 ^ _774244) ^ [_897602, _897604, _897606, _897608, _897610, _897612, _897614, _897616, _897618, _897620, _897622] : [-(c_Com_Ocom_Ocom__case(_897602, _897604, _897606, _897608, _897610, _897612, _897614, _897616, _897618, c_Com_Ocom_OAss(_897620, _897622)) = hAPP(hAPP(_897606, _897620), _897622))], (24603 ^ _774244) ^ [_1202749, _1202751, _1202753, _1202755, _1202757] : [_1202749 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1202751, _1202753, _1202755, _1202757), _1202749) = c_Lazy__Sequence_Ohit__bound(_1202753))], (6758 ^ _774244) ^ [_883284, _883286, _883288, _883290, _883292, _883294] : [c_Com_Ocom_OLocal(_883284, _883286, _883288) = c_Com_Ocom_OCall(_883290, _883292, _883294)], (49499 ^ _774244) ^ [_1765852, _1765854, _1765856, _1765858, _1765860] : [class_Orderings_Olinorder(_1765852), hBOOL(hAPP(hAPP(c_member(_1765854), _1765856), hAPP(c_List_Oset(_1765854), _1765858))), c_List_Olinorder__class_Osorted(_1765852, hAPP(hAPP(c_List_Omap(_1765854, _1765852), _1765860), _1765858)), hAPP(c_List_Ohd(_1765854), hAPP(c_List_Ofilter(_1765854, hAPP(hAPP(c_COMBB(_1765852, tc_HOL_Obool, _1765854), hAPP(c_fequal, hAPP(_1765860, _1765856))), _1765860)), _1765858)) = _1765856, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1765854, _1765852, _1765860), _1765856), c_List_Oremove1(_1765854, _1765856, _1765858)) = _1765858)], (48362 ^ _774244) ^ [_1740084, _1740086] : [-(hAPP(hAPP(c_List_Odrop(_1740084), _1740086), c_List_Olist_ONil(_1740084)) = c_List_Olist_ONil(_1740084))], (9206 ^ _774244) ^ [_925300, _925302, _925304] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _925300), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _925302), _925304)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _925300), _925302)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _925300), _925304)))], (20057 ^ _774244) ^ [_1117527, _1117529, _1117531] : [class_Fields_Olinordered__field__inverse__zero(_1117527), 20060 ^ _774244 : [(20075 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117527), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117527), _1117529), _1117531)), c_Groups_Ozero__class_Ozero(_1117527)))), 20076 ^ _774244 : [(20083 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117527), _1117529), c_Groups_Ozero__class_Ozero(_1117527))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117527), c_Groups_Ozero__class_Ozero(_1117527)), _1117531))], (20077 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117527), c_Groups_Ozero__class_Ozero(_1117527)), _1117529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117527), _1117531), c_Groups_Ozero__class_Ozero(_1117527)))]]], (20061 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117527), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117527), _1117529), _1117531)), c_Groups_Ozero__class_Ozero(_1117527))), 20066 ^ _774244 : [(20069 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117527), _1117531), c_Groups_Ozero__class_Ozero(_1117527))))], (20067 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117527), c_Groups_Ozero__class_Ozero(_1117527)), _1117529)))]], 20070 ^ _774244 : [(20073 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117527), c_Groups_Ozero__class_Ozero(_1117527)), _1117531)))], (20071 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117527), _1117529), c_Groups_Ozero__class_Ozero(_1117527))))]]]]], (26904 ^ _774244) ^ [_1247014, _1247016] : [26912 ^ _774244 : [(26915 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1247016, 26911 ^ [_1247014, _1247016])))], (26913 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26911 ^ [_1247014, _1247016]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1247014))))]], 26905 ^ _774244 : [(26906 ^ _774244) ^ [_1247083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1247083), _1247014)), hBOOL(hAPP(_1247016, _1247083))]]], (42874 ^ _774244) ^ [_1602369, _1602371, _1602373, _1602375] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602369, _1602369)), _1602371), c_Transitive__Closure_Otrancl(_1602369, _1602373))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602369, _1602369), tc_HOL_Obool)), _1602373), _1602375)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602369, _1602369)), _1602371), c_Transitive__Closure_Otrancl(_1602369, _1602375))))], (31309 ^ _774244) ^ [_1336728, _1336730, _1336732, _1336734] : [-(hBOOL(hAPP(hAPP(c_member(_1336728), _1336730), _1336732))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336728, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1336728), _1336730), _1336734)), _1336732) = hAPP(hAPP(c_Set_Oinsert(_1336728), _1336730), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336728, tc_HOL_Obool)), _1336734), _1336732)))], (18923 ^ _774244) ^ [_1097134, _1097136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097134), _1097136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1097134)), c_Int_OBit0(_1097136))))], (36999 ^ _774244) ^ [_1460311, _1460313, _1460315, _1460317, _1460319] : [class_Groups_Oab__group__add(_1460311), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460313), _1460315)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460313), _1460317)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460313, _1460311), _1460319), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460313, tc_HOL_Obool)), _1460315), _1460317)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1460311), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1460311), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460313, _1460311), _1460319), _1460315)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460313, _1460311), _1460319), _1460317))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460313, _1460311), _1460319), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460313, tc_HOL_Obool)), _1460315), _1460317))))], (42322 ^ _774244) ^ [_1591259, _1591261, _1591263, _1591265, _1591267, _1591269] : [class_Rings_Ocomm__semiring__1(_1591259), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591261), _1591263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1591261, tc_HOL_Obool)), _1591265), _1591263)), 42336 ^ _774244 : [(42339 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1591259), hAPP(_1591267, 42335 ^ [_1591259, _1591261, _1591263, _1591265, _1591267, _1591269])), hAPP(_1591269, 42335 ^ [_1591259, _1591261, _1591263, _1591265, _1591267, _1591269])))], (42337 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591261), 42335 ^ [_1591259, _1591261, _1591263, _1591265, _1591267, _1591269]), _1591265)))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1591259), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1591261, _1591259), _1591267), _1591265)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1591261, _1591259), _1591269), _1591263))))], (1744 ^ _774244) ^ [_798768, _798770] : [-(class_Groups_Oone(_798768)), _798770 = _798768, class_Groups_Oone(_798770)], (38656 ^ _774244) ^ [_1496320, _1496322] : [-(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)), _1496320), _1496322))], (51017 ^ _774244) ^ [_1797288, _1797290] : [class_Groups_Ouminus(_1797288), -(class_Groups_Ouminus(tc_fun(_1797290, _1797288)))], (2308 ^ _774244) ^ [_809038, _809040] : [_809040 = _809038, -(c_Int_Osucc(_809040) = c_Int_Osucc(_809038))], (3368 ^ _774244) ^ [_825990, _825992, _825994, _825996, _825998, _826000, _826002, _826004] : [-(c_Random__Sequence_Obind(_826004, _826000, _825996, _825992) = c_Random__Sequence_Obind(_826002, _825998, _825994, _825990)), _826004 = _826002, _826000 = _825998, _825996 = _825994, _825992 = _825990], (36425 ^ _774244) ^ [_1446742] : [class_Lattices_Osemilattice__inf(_1446742), -(c_Finite__Set_Ofun__left__comm__idem(_1446742, _1446742, c_Lattices_Osemilattice__inf__class_Oinf(_1446742)))], (48831 ^ _774244) ^ [_1750278, _1750280, _1750282, _1750284] : [class_Complete__Lattice_Ocomplete__lattice(_1750278), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1750280, _1750278), hAPP(c_List_Oset(_1750280), _1750282)), _1750284) = hAPP(c_List_Ofoldl(_1750278, _1750280, hAPP(c_COMBC(_1750280, _1750278, _1750278), hAPP(hAPP(c_COMBB(_1750278, tc_fun(_1750278, _1750278), _1750280), c_Lattices_Osemilattice__inf__class_Oinf(_1750278)), _1750284)), c_Orderings_Otop__class_Otop(_1750278)), _1750282))], (44358 ^ _774244) ^ [_1640901, _1640903, _1640905, _1640907, _1640909] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1640901, _1640901)), hAPP(hAPP(c_Product__Type_OPair(_1640901, _1640901), _1640903), _1640905)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1640901, _1640901), tc_HOL_Obool), _1640907), _1640909))), 44363 ^ _774244 : [(44366 ^ _774244) ^ [] : [-(_1640903 = _1640905)], (44364 ^ _774244) ^ [] : [-(_1640907 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 44369 ^ _774244 : [(44374 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1640901, _1640901)), hAPP(hAPP(c_Product__Type_OPair(_1640901, _1640901), 44367 ^ [_1640901, _1640903, _1640905, _1640907, _1640909]), _1640905)), _1640909)))], (44372 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1640901, _1640901)), hAPP(hAPP(c_Product__Type_OPair(_1640901, _1640901), _1640903), 44367 ^ [_1640901, _1640903, _1640905, _1640907, _1640909])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1640901, _1640901), tc_HOL_Obool), 44368 ^ [_1640901, _1640903, _1640905, _1640907, _1640909]), _1640909))))], (44370 ^ _774244) ^ [] : [-(_1640907 = hAPP(c_Nat_OSuc, 44368 ^ [_1640901, _1640903, _1640905, _1640907, _1640909]))]]], (17195 ^ _774244) ^ [_1068416, _1068418, _1068420] : [class_Rings_Olinordered__semidom(_1068416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068416), c_Groups_Ozero__class_Ozero(_1068416)), _1068418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068416), c_Groups_Ozero__class_Ozero(_1068416)), hAPP(hAPP(c_Power_Opower__class_Opower(_1068416), _1068418), _1068420))))], (39508 ^ _774244) ^ [_1515787, _1515789, _1515791, _1515793] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1515787, _1515789, hAPP(hAPP(c_Set_Oinsert(_1515787), _1515791), c_Orderings_Obot__class_Obot(tc_fun(_1515787, tc_HOL_Obool)))), _1515793)), -(_1515791 = _1515793)], (46070 ^ _774244) ^ [_1681545, _1681547, _1681549, _1681551, _1681553, _1681555] : [class_Orderings_Olinorder(_1681545), -(hAPP(_1681547, _1681549) = hAPP(_1681547, _1681551)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681553, _1681545, _1681547), _1681551), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681553, _1681545, _1681547), _1681549), _1681555)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681553, _1681545, _1681547), _1681549), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681553, _1681545, _1681547), _1681551), _1681555)))], (47455 ^ _774244) ^ [_1716972, _1716974, _1716976, _1716978, _1716980, _1716982] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716972)), _1716974) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716976)), _1716978), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716972)), _1716980) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716976)), _1716982), -(hAPP(hAPP(c_List_Ozip(_1716972, _1716976), hAPP(hAPP(c_List_Oappend(_1716972), _1716974), _1716980)), hAPP(hAPP(c_List_Oappend(_1716976), _1716978), _1716982)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1716972, _1716976)), hAPP(hAPP(c_List_Ozip(_1716972, _1716976), _1716974), _1716978)), hAPP(hAPP(c_List_Ozip(_1716972, _1716976), _1716980), _1716982)))], (35195 ^ _774244) ^ [_1419028, _1419030, _1419032, _1419034, _1419036, _1419038, _1419040, _1419042] : [hAPP(c_Fun_Ocomp(_1419028, _1419030, _1419032, _1419034), _1419036) = hAPP(c_Fun_Ocomp(_1419038, _1419030, _1419032, _1419040), _1419042), 35198 ^ _774244 : [(35199 ^ _774244) ^ [_1419143] : [-(hAPP(_1419034, hAPP(_1419036, _1419143)) = hAPP(_1419040, hAPP(_1419042, _1419143)))]]], (50188 ^ _774244) ^ [_1779232, _1779234, _1779236] : [_1779236 = hAPP(hAPP(c_List_Olist_OCons(_1779232), _1779234), c_List_Olist_ONil(_1779232)), -(hAPP(hAPP(c_List_Olist_OCons(_1779232), _1779234), c_List_Olist_ONil(_1779232)) = hAPP(c_List_Orev(_1779232), _1779236))], (9256 ^ _774244) ^ [_926149, _926151] : [class_Groups_Olinordered__ab__group__add(_926149), 9259 ^ _774244 : [(9266 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926149), c_Groups_Ozero__class_Ozero(_926149)), _926151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926149), hAPP(c_Groups_Ouminus__class_Ouminus(_926149), _926151)), _926151)))], (9260 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926149), hAPP(c_Groups_Ouminus__class_Ouminus(_926149), _926151)), _926151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926149), c_Groups_Ozero__class_Ozero(_926149)), _926151)))]]], (6059 ^ _774244) ^ [_871292, _871294] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_871292, _871294))), 6062 ^ _774244 : [(6065 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _871294)))], (6063 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _871292)))]]], (37526 ^ _774244) ^ [] : [-(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))], (50977 ^ _774244) ^ [_1796764, _1796766] : [-(class_Finite__Set_Ofinite(tc_fun(_1796764, _1796766))), class_Finite__Set_Ofinite(_1796764), class_Finite__Set_Ofinite(_1796766)], (34321 ^ _774244) ^ [_1398742, _1398744, _1398746, _1398748, _1398750] : [hAPP(_1398742, _1398744) = hAPP(c_Option_Ooption_OSome(_1398746), _1398748), -(hBOOL(hAPP(hAPP(c_member(_1398746), _1398748), c_Map_Oran(_1398750, _1398746, _1398742))))], (22520 ^ _774244) ^ [_1162916, _1162918] : [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), _1162916), _1162918))), 22523 ^ _774244 : [(22532 ^ _774244) ^ [] : [-(c_Divides_OnegDivAlg(_1162916, _1162918) = hAPP(c_Divides_Oadjust(_1162918), c_Divides_OnegDivAlg(_1162916, 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)))), _1162918)))), -(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), _1162916), _1162918)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1162918), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22524 ^ _774244) ^ [] : [22525 ^ _774244 : [(22528 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1162918), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22526 ^ _774244) ^ [] : [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), _1162916), _1162918)))]], -(c_Divides_OnegDivAlg(_1162916, _1162918) = 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), _1162916), _1162918)))]]], (17985 ^ _774244) ^ [_1081803] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1081803), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1081803))], (24581 ^ _774244) ^ [_1202255, _1202257, _1202259] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1202255), _1202257), _1202259) = c_Nitpick_OAbs__Frac(_1202255, c_Nitpick_Onorm__frac(_1202257, _1202259)))], (42085 ^ _774244) ^ [_1585725, _1585727] : [42087 ^ _774244 : [(42090 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1585727), 42086 ^ [_1585725, _1585727]))], (42088 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42086 ^ [_1585725, _1585727]), _1585725)))]], -(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)), _1585727), _1585725))], (28723 ^ _774244) ^ [_1284274, _1284276, _1284278, _1284280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284274, tc_HOL_Obool)), _1284276), _1284278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284274, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1284274), _1284280), _1284276)), hAPP(hAPP(c_Set_Oinsert(_1284274), _1284280), _1284278))))], (23627 ^ _774244) ^ [_1184124, _1184126, _1184128] : [class_Orderings_Olinorder(_1184124), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184124), _1184126), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184124), _1184126), _1184128)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184124), _1184126), _1184128))], (48518 ^ _774244) ^ [_1744079, _1744081, _1744083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744079), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744081)), _1744083))), -(hAPP(hAPP(c_List_Oappend(_1744081), hAPP(hAPP(c_List_Otake(_1744081), _1744079), _1744083)), hAPP(hAPP(c_List_Olist_OCons(_1744081), hAPP(c_List_Ohd(_1744081), hAPP(hAPP(c_List_Odrop(_1744081), _1744079), _1744083))), c_List_Olist_ONil(_1744081))) = hAPP(hAPP(c_List_Otake(_1744081), hAPP(c_Nat_OSuc, _1744079)), _1744083))], (43496 ^ _774244) ^ [_1618054, _1618056, _1618058, _1618060, _1618062] : [-(hAPP(c_Relation_Oconverse(_1618054, _1618056), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618058, tc_fun(tc_prod(_1618054, _1618056), tc_HOL_Obool)), _1618060), _1618062)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618058, tc_fun(tc_prod(_1618056, _1618054), tc_HOL_Obool)), _1618060), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1618054, _1618056), tc_HOL_Obool), tc_fun(tc_prod(_1618056, _1618054), tc_HOL_Obool), _1618058), c_Relation_Oconverse(_1618054, _1618056)), _1618062)))], (48813 ^ _774244) ^ [_1749837, _1749839, _1749841] : [class_Orderings_Olinorder(_1749837), -(c_Big__Operators_Olattice_OInf__fin(_1749837, c_Orderings_Oord__class_Omin(_1749837), hAPP(c_List_Oset(_1749837), hAPP(hAPP(c_List_Olist_OCons(_1749837), _1749839), _1749841))) = hAPP(c_List_Ofoldl(_1749837, _1749837, c_Orderings_Oord__class_Omin(_1749837), _1749839), _1749841))], (18451 ^ _774244) ^ [_1089166, _1089168] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1089166), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1089168)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1089166), 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)))), _1089168)))], (15650 ^ _774244) ^ [_1038574, _1038576] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1038574), hAPP(c_Nat_OSuc, _1038576)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1038574), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1038576))], (45509 ^ _774244) ^ [_1667793] : [-(hAPP(c_List_Omap(_1667793, _1667793), c_Fun_Oid(_1667793)) = c_Fun_Oid(tc_List_Olist(_1667793)))], (8928 ^ _774244) ^ [_920327, _920329] : [class_Groups_Olinordered__ab__group__add(_920327), 8931 ^ _774244 : [(8938 ^ _774244) ^ [] : [_920329 = c_Groups_Ozero__class_Ozero(_920327), -(_920329 = hAPP(c_Groups_Ouminus__class_Ouminus(_920327), _920329))], (8932 ^ _774244) ^ [] : [_920329 = hAPP(c_Groups_Ouminus__class_Ouminus(_920327), _920329), -(_920329 = c_Groups_Ozero__class_Ozero(_920327))]]], (44095 ^ _774244) ^ [_1634379] : [-(c_Relation_Osingle__valued(_1634379, _1634379, c_Relation_OId(_1634379)))], (922 ^ _774244) ^ [_788431, _788433, _788435, _788437, _788439, _788441] : [-(c_Finite__Set_Ofun__left__comm(_788439, _788435, _788431)), c_Finite__Set_Ofun__left__comm(_788441, _788437, _788433), _788441 = _788439, _788437 = _788435, _788433 = _788431], (6766 ^ _774244) ^ [_883504, _883506, _883508] : [c_Com_Ocom_OLocal(_883504, _883506, _883508) = c_Com_Ocom_OSKIP], (48857 ^ _774244) ^ [_1750847, _1750849, _1750851, _1750853, _1750855] : [-(c_Map_Omap__upds(_1750847, _1750849, _1750851, _1750853, _1750855) = hAPP(c_List_Ofoldl(tc_fun(_1750847, tc_Option_Ooption(_1750849)), tc_prod(_1750847, _1750849), hAPP(hAPP(c_COMBB(tc_fun(_1750847, tc_fun(_1750849, tc_fun(_1750847, tc_Option_Ooption(_1750849)))), tc_fun(tc_prod(_1750847, _1750849), tc_fun(_1750847, tc_Option_Ooption(_1750849))), tc_fun(_1750847, tc_Option_Ooption(_1750849))), c_Product__Type_Oprod_Oprod__case(_1750847, _1750849, tc_fun(_1750847, tc_Option_Ooption(_1750849)))), hAPP(hAPP(c_COMBC(tc_fun(_1750847, tc_Option_Ooption(_1750849)), tc_fun(_1750849, tc_Option_Ooption(_1750849)), tc_fun(_1750847, tc_fun(_1750849, tc_fun(_1750847, tc_Option_Ooption(_1750849))))), hAPP(hAPP(c_COMBB(tc_fun(_1750847, tc_fun(tc_fun(_1750849, tc_Option_Ooption(_1750849)), tc_fun(_1750849, tc_fun(_1750847, tc_Option_Ooption(_1750849))))), tc_fun(tc_fun(_1750849, tc_Option_Ooption(_1750849)), tc_fun(_1750847, tc_fun(_1750849, tc_fun(_1750847, tc_Option_Ooption(_1750849))))), tc_fun(_1750847, tc_Option_Ooption(_1750849))), c_COMBC(_1750847, tc_fun(_1750849, tc_Option_Ooption(_1750849)), tc_fun(_1750849, tc_fun(_1750847, tc_Option_Ooption(_1750849))))), hAPP(hAPP(c_COMBB(tc_fun(_1750847, tc_fun(tc_Option_Ooption(_1750849), tc_fun(_1750847, tc_Option_Ooption(_1750849)))), tc_fun(_1750847, tc_fun(tc_fun(_1750849, tc_Option_Ooption(_1750849)), tc_fun(_1750849, tc_fun(_1750847, tc_Option_Ooption(_1750849))))), tc_fun(_1750847, tc_Option_Ooption(_1750849))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1750849), tc_fun(_1750847, tc_Option_Ooption(_1750849))), tc_fun(tc_fun(_1750849, tc_Option_Ooption(_1750849)), tc_fun(_1750849, tc_fun(_1750847, tc_Option_Ooption(_1750849)))), _1750847), c_COMBB(tc_Option_Ooption(_1750849), tc_fun(_1750847, tc_Option_Ooption(_1750849)), _1750849))), c_Fun_Ofun__upd(_1750847, tc_Option_Ooption(_1750849))))), c_Option_Ooption_OSome(_1750849))), _1750851), hAPP(hAPP(c_List_Ozip(_1750847, _1750849), _1750853), _1750855)))], (40733 ^ _774244) ^ [_1544676, _1544678] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1544676, tc_HOL_Obool)), _1544678) = hAPP(c_Set_OCollect(_1544676), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1544676), c_fNot), hAPP(hAPP(c_COMBC(_1544676, tc_fun(_1544676, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544676)), _1544678))))], (10528 ^ _774244) ^ [_947741, _947743, _947745] : [class_Orderings_Olinorder(_947741), 10531 ^ _774244 : [(10538 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947741), _947745), _947743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947741), _947743), _947745))], (10532 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947741), _947743), _947745))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947741), _947745), _947743)))]]], (42816 ^ _774244) ^ [_1600944] : [-(c_Transitive__Closure_Otrancl(_1600944, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1600944, _1600944), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1600944, _1600944), tc_HOL_Obool)))], (46826 ^ _774244) ^ [_1702202, _1702204, _1702206, _1702208] : [_1702208 = c_List_Olist_ONil(_1702202), -(hAPP(hAPP(c_List_Omap(_1702202, _1702204), _1702206), _1702208) = c_List_Olist_ONil(_1702204))], (23347 ^ _774244) ^ [_1178253, _1178255, _1178257, _1178259, _1178261, _1178263] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1178253, _1178255), _1178255, _1178257), hAPP(hAPP(c_COMBB(_1178259, tc_fun(_1178255, _1178257), tc_prod(_1178253, _1178255)), _1178261), hAPP(hAPP(c_COMBB(_1178253, _1178259, tc_prod(_1178253, _1178255)), _1178263), c_Product__Type_Ofst(_1178253, _1178255)))), c_Product__Type_Osnd(_1178253, _1178255)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1178253, _1178255, _1178257), hAPP(hAPP(c_COMBB(_1178259, tc_fun(_1178255, _1178257), _1178253), _1178261), _1178263)))], (42487 ^ _774244) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (13274 ^ _774244) ^ [_994867, _994869, _994871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _994867)), 13277 ^ _774244 : [(13284 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994869), _994871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994867), _994869)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994867), _994871))))], (13278 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994867), _994869)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994867), _994871))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994869), _994871)))]]], (51413 ^ _774244) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (33854 ^ _774244) ^ [_1389019, _1389021, _1389023, _1389025, _1389027] : [hAPP(_1389019, _1389021) = _1389023, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1389025, _1389027), _1389019), _1389021), _1389023) = _1389019)], (17127 ^ _774244) ^ [_1067067, _1067069, _1067071] : [class_Rings_Oring__1__no__zero__divisors(_1067067), -(_1067069 = c_Groups_Ozero__class_Ozero(_1067067)), hAPP(hAPP(c_Power_Opower__class_Opower(_1067067), _1067069), _1067071) = c_Groups_Ozero__class_Ozero(_1067067)], (10293 ^ _774244) ^ [_943773, _943775, _943777] : [class_Orderings_Oorder(_943773), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943773), _943775), _943777)), 10300 ^ _774244 : [(10307 ^ _774244) ^ [] : [_943777 = _943775, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943773), _943777), _943775)))], (10301 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943773), _943777), _943775)), -(_943777 = _943775)]]], (47118 ^ _774244) ^ [_1708786, _1708788, _1708790] : [_1708786 = _1708788, 47121 ^ _774244 : [(47124 ^ _774244) ^ [_1708934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708934), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708790)), _1708786))), -(hAPP(hAPP(c_List_Onth(_1708790), _1708786), _1708934) = hAPP(hAPP(c_List_Onth(_1708790), _1708788), _1708934))], (47122 ^ _774244) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708790)), _1708786) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708790)), _1708788))]]], (43169 ^ _774244) ^ [_1609239, _1609241, _1609243, _1609245, _1609247] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609239, _1609239)), hAPP(hAPP(c_Product__Type_OPair(_1609239, _1609239), _1609241), _1609243)), _1609245)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1609239, _1609239)), hAPP(hAPP(c_Product__Type_OPair(_1609239, _1609239), _1609243), _1609247)), c_Transitive__Closure_Ortrancl(_1609239, _1609245))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609239, _1609239)), hAPP(hAPP(c_Product__Type_OPair(_1609239, _1609239), _1609241), _1609247)), c_Transitive__Closure_Otrancl(_1609239, _1609245))))], (35558 ^ _774244) ^ [_1428261, _1428263, _1428265, _1428267, _1428269] : [c_Finite__Set_Ofolding__idem(_1428261, _1428263, _1428265, _1428267), -(hAPP(c_Fun_Ocomp(_1428263, _1428263, _1428263, hAPP(_1428265, _1428269)), hAPP(_1428265, _1428269)) = hAPP(_1428265, _1428269))], (34391 ^ _774244) ^ [_1400598, _1400600, _1400602, _1400604, _1400606, _1400608] : [-(hBOOL(hAPP(hAPP(c_member(_1400598), _1400600), _1400602))), -(c_Map_Orestrict__map(_1400598, _1400604, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1400598, tc_Option_Ooption(_1400604)), _1400606), _1400600), _1400608), _1400602) = c_Map_Orestrict__map(_1400598, _1400604, _1400606, _1400602))], (41304 ^ _774244) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (3722 ^ _774244) ^ [_831647, _831649] : [_831649 = _831647, -(c_New__Random__Sequence_Oneg__single(_831649) = c_New__Random__Sequence_Oneg__single(_831647))], (4030 ^ _774244) ^ [_836365, _836367, _836369, _836371, _836373, _836375, _836377, _836379, _836381, _836383, _836385, _836387] : [-(c_Map_Omap__comp(_836387, _836383, _836379, _836375, _836371, _836367) = c_Map_Omap__comp(_836385, _836381, _836377, _836373, _836369, _836365)), _836387 = _836385, _836383 = _836381, _836379 = _836377, _836375 = _836373, _836371 = _836369, _836367 = _836365], (23541 ^ _774244) ^ [_1182159, _1182161, _1182163, _1182165, _1182167] : [-(c_Product__Type_Oprod_Oprod__size(_1182159, _1182161, _1182163, _1182165, _1182167) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1182163, hAPP(c_Product__Type_Ofst(_1182159, _1182161), _1182167))), hAPP(_1182165, hAPP(c_Product__Type_Osnd(_1182159, _1182161), _1182167)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49061 ^ _774244) ^ [_1755605, _1755607, _1755609] : [-(_1755605 = c_List_Olist_ONil(_1755607)), -(c_List_Olast(_1755607, hAPP(hAPP(c_List_Olist_OCons(_1755607), _1755609), _1755605)) = c_List_Olast(_1755607, _1755605))], (27115 ^ _774244) ^ [_1251201, _1251203, _1251205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251201)), 27118 ^ _774244 : [(27119 ^ _774244) ^ [_1251335] : [27121 ^ _774244 : [(27127 ^ _774244) ^ [] : [-(_1251335 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27123 ^ [_1251201, _1251203, _1251205, _1251335]), 27120 ^ [_1251201, _1251203, _1251205, _1251335]))], (27125 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27123 ^ [_1251201, _1251203, _1251205, _1251335]), _1251203)))], (27122 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27120 ^ [_1251201, _1251203, _1251205, _1251335]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1251201))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251205), _1251335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251205), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1251335), _1251201))))]]], (11845 ^ _774244) ^ [_970027, _970029, _970031, _970033, _970035] : [class_Groups_Oordered__cancel__ab__semigroup__add(_970027), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970027), _970029), _970031)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970027), _970033), _970035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970027), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970027), _970029), _970033)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970027), _970031), _970035))))], (40306 ^ _774244) ^ [_1535644, _1535646, _1535648] : [class_Orderings_Olinorder(_1535644), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535644), _1535646)), -(_1535646 = c_Orderings_Obot__class_Obot(tc_fun(_1535644, tc_HOL_Obool))), 40317 ^ _774244 : [(40327 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1535644), hAPP(c_Finite__Set_Ofold1(_1535644, c_Orderings_Oord__class_Omin(_1535644)), _1535646)), _1535648))), 40328 ^ _774244 : [(40329 ^ _774244) ^ [_1536033] : [hBOOL(hAPP(hAPP(c_member(_1535644), _1536033), _1535646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1535644), _1536033), _1535648))]]], (40318 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1535644), hAPP(c_Finite__Set_Ofold1(_1535644, c_Orderings_Oord__class_Omin(_1535644)), _1535646)), _1535648)), 40322 ^ _774244 : [(40325 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1535644), 40321 ^ [_1535644, _1535646, _1535648]), _1535648)))], (40323 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1535644), 40321 ^ [_1535644, _1535646, _1535648]), _1535646)))]]]]], (15890 ^ _774244) ^ [_1044137, _1044139, _1044141, _1044143, _1044145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044137), _1044139)), 15893 ^ _774244 : [(15900 ^ _774244) ^ [] : [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), _1044139), _1044137)), _1044141)), _1044143)), _1044145)), -(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), _1044139), _1044141)), _1044143)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1044137), _1044141)), _1044145))))], (15894 ^ _774244) ^ [] : [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), _1044139), _1044141)), _1044143)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1044137), _1044141)), _1044145))), -(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), _1044139), _1044137)), _1044141)), _1044143)), _1044145)))]]], (35322 ^ _774244) ^ [_1422397, _1422399] : [-(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), _1422397), _1422399)), 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), _1422399), _1422397)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (50133 ^ _774244) ^ [_1777426, _1777428, _1777430, _1777432] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1777426, tc_Nat_Onat), _1777426), c_Product__Type_Ofst(_1777426, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1777426, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1777426, 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(_1777426, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1777426, tc_Nat_Onat))), _1777428)), hAPP(hAPP(c_List_Ozip(_1777426, tc_Nat_Onat), _1777430), c_List_Oupt(_1777432, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1777432), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777426)), _1777430)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1777426, tc_Nat_Onat), _1777426), c_Product__Type_Ofst(_1777426, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1777426, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1777426, 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(_1777426, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1777426, 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(_1777426, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1777426, tc_Nat_Onat))), _1777432))), _1777428)), hAPP(hAPP(c_List_Ozip(_1777426, tc_Nat_Onat), _1777430), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777426)), _1777430))))))], (39520 ^ _774244) ^ [_1516047, _1516049, _1516051, _1516053, _1516055] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1516047, _1516049, hAPP(hAPP(c_Set_Oinsert(_1516047), _1516051), _1516053)), _1516055)), 39525 ^ _774244 : [(39530 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1516047), 39523 ^ [_1516047, _1516049, _1516051, _1516053, _1516055]), 39524 ^ [_1516047, _1516049, _1516051, _1516053, _1516055]))], (39528 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1516047, _1516047, _1516049, 39523 ^ [_1516047, _1516049, _1516051, _1516053, _1516055], 39524 ^ [_1516047, _1516049, _1516051, _1516053, _1516055]), _1516055)))], (39526 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1516047), _1516051), _1516053) = hAPP(hAPP(c_Set_Oinsert(_1516047), 39523 ^ [_1516047, _1516049, _1516051, _1516053, _1516055]), 39524 ^ [_1516047, _1516049, _1516051, _1516053, _1516055]))]]], (11102 ^ _774244) ^ [_956856, _956858] : [11103 ^ _774244 : [(11106 ^ _774244) ^ [] : [_956856 = hAPP(c_Nat_OSuc, _956858)], (11104 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956856), _956858))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956856), hAPP(c_Nat_OSuc, _956858))))], (43065 ^ _774244) ^ [_1606766, _1606768, _1606770, _1606772, _1606774] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606766, _1606766)), hAPP(hAPP(c_Product__Type_OPair(_1606766, _1606766), _1606768), _1606770)), c_Transitive__Closure_Ortrancl(_1606766, _1606772))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1606766, _1606766)), hAPP(hAPP(c_Product__Type_OPair(_1606766, _1606766), _1606770), _1606774)), _1606772)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606766, _1606766)), hAPP(hAPP(c_Product__Type_OPair(_1606766, _1606766), _1606768), _1606774)), c_Transitive__Closure_Ortrancl(_1606766, _1606772))))], (49055 ^ _774244) ^ [_1755506, _1755508, _1755510] : [_1755506 = c_List_Olist_ONil(_1755508), -(c_List_Olast(_1755508, hAPP(hAPP(c_List_Olist_OCons(_1755508), _1755510), _1755506)) = _1755510)], (47049 ^ _774244) ^ [_1707107, _1707109, _1707111] : [47051 ^ _774244 : [(47054 ^ _774244) ^ [] : [hBOOL(hAPP(_1707111, hAPP(hAPP(c_List_Onth(_1707107), _1707109), 47050 ^ [_1707107, _1707109, _1707111])))], (47052 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47050 ^ [_1707107, _1707109, _1707111]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707107)), _1707109))))]], 47055 ^ _774244 : [(47056 ^ _774244) ^ [_1707309] : [hBOOL(hAPP(hAPP(c_member(_1707107), _1707309), hAPP(c_List_Oset(_1707107), _1707109))), -(hBOOL(hAPP(_1707111, _1707309)))]]], (34576 ^ _774244) ^ [] : [-(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)))], (9272 ^ _774244) ^ [_926417, _926419] : [class_Rings_Olinordered__idom(_926417), 9275 ^ _774244 : [(9282 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926417), _926419), c_Groups_Ozero__class_Ozero(_926417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926417), _926419), hAPP(c_Groups_Ouminus__class_Ouminus(_926417), _926419))))], (9276 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926417), _926419), hAPP(c_Groups_Ouminus__class_Ouminus(_926417), _926419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926417), _926419), c_Groups_Ozero__class_Ozero(_926417))))]]], (43727 ^ _774244) ^ [_1624600, _1624602, _1624604] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1624600, tc_fun(_1624602, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1624600, tc_HOL_Obool))), _1624604) = c_Orderings_Otop__class_Otop(tc_fun(_1624602, tc_HOL_Obool)))], (31875 ^ _774244) ^ [_1350349, _1350351, _1350353] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1350349), _1350351)), hBOOL(hAPP(hAPP(c_member(_1350349), _1350353), _1350351)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1350349), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350349, tc_HOL_Obool)), _1350351), hAPP(hAPP(c_Set_Oinsert(_1350349), _1350353), c_Orderings_Obot__class_Obot(tc_fun(_1350349, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1350349), _1350351))], (22642 ^ _774244) ^ [_1165096, _1165098, _1165100, _1165102, _1165104, _1165106, _1165108] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1165096, _1165098), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1165100), _1165102))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1165104, _1165098), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1165106), _1165108))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1165098)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1165096), _1165104), _1165098), 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), _1165100), _1165106)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1165102), _1165108)), _1165098))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1165102), _1165108), _1165098)))))], (28886 ^ _774244) ^ [_1288059, _1288061, _1288063, _1288065, _1288067] : [hAPP(hAPP(c_Set_Oinsert(_1288059), _1288061), hAPP(hAPP(c_Set_Oinsert(_1288059), _1288063), c_Orderings_Obot__class_Obot(tc_fun(_1288059, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1288059), _1288065), hAPP(hAPP(c_Set_Oinsert(_1288059), _1288067), c_Orderings_Obot__class_Obot(tc_fun(_1288059, tc_HOL_Obool)))), 28891 ^ _774244 : [(28894 ^ _774244) ^ [] : [-(_1288063 = _1288067)], (28892 ^ _774244) ^ [] : [-(_1288061 = _1288065)]], 28895 ^ _774244 : [(28898 ^ _774244) ^ [] : [-(_1288063 = _1288065)], (28896 ^ _774244) ^ [] : [-(_1288061 = _1288067)]]], (6494 ^ _774244) ^ [_878933, _878935] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878933), _878935) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878935), _878933))], (22860 ^ _774244) ^ [_1169038, _1169040, _1169042, _1169044, _1169046, _1169048] : [hAPP(hAPP(c_Product__Type_OPair(_1169038, _1169040), _1169042), _1169044) = hAPP(hAPP(c_Product__Type_OPair(_1169038, _1169040), _1169046), _1169048), 22863 ^ _774244 : [(22866 ^ _774244) ^ [] : [-(_1169044 = _1169048)], (22864 ^ _774244) ^ [] : [-(_1169042 = _1169046)]]], (50643 ^ _774244) ^ [_1790209, _1790211, _1790213, _1790215, _1790217] : [class_Orderings_Olinorder(_1790209), c_List_Olinorder__class_Osorted(_1790209, hAPP(c_List_Orev(_1790209), hAPP(hAPP(c_List_Omap(_1790211, _1790209), _1790213), _1790215))), -(hAPP(c_List_Ofilter(_1790211, hAPP(hAPP(c_COMBB(_1790209, tc_HOL_Obool, _1790211), hAPP(c_Orderings_Oord__class_Oless(_1790209), _1790217)), _1790213)), _1790215) = c_List_OtakeWhile(_1790211, hAPP(hAPP(c_COMBB(_1790209, tc_HOL_Obool, _1790211), hAPP(c_Orderings_Oord__class_Oless(_1790209), _1790217)), _1790213), _1790215))], (17319 ^ _774244) ^ [_1070602, _1070604, _1070606, _1070608] : [class_Rings_Olinordered__semidom(_1070602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070602), hAPP(hAPP(c_Power_Opower__class_Opower(_1070602), _1070604), _1070606)), hAPP(hAPP(c_Power_Opower__class_Opower(_1070602), _1070608), _1070606))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070602), c_Groups_Ozero__class_Ozero(_1070602)), _1070608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070602), _1070604), _1070608)))], (20371 ^ _774244) ^ [_1122774, _1122776] : [class_Rings_Odivision__ring(_1122774), -(_1122776 = c_Groups_Ozero__class_Ozero(_1122774)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122774), _1122776), _1122776) = c_Groups_Oone__class_Oone(_1122774))], (9648 ^ _774244) ^ [_933196, _933198, _933200] : [class_Rings_Olinordered__ring__strict(_933196), 9651 ^ _774244 : [(9660 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933196), _933198), _933198)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933196), _933200), _933200)) = c_Groups_Ozero__class_Ozero(_933196)), _933198 = c_Groups_Ozero__class_Ozero(_933196), _933200 = c_Groups_Ozero__class_Ozero(_933196)], (9652 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933196), _933198), _933198)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933196), _933200), _933200)) = c_Groups_Ozero__class_Ozero(_933196), 9655 ^ _774244 : [(9658 ^ _774244) ^ [] : [-(_933200 = c_Groups_Ozero__class_Ozero(_933196))], (9656 ^ _774244) ^ [] : [-(_933198 = c_Groups_Ozero__class_Ozero(_933196))]]]]], (13854 ^ _774244) ^ [_1005543, _1005545, _1005547, _1005549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005543)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1005545), _1005547)), -(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), _1005547), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005549, _1005543))), _1005545))))], (3050 ^ _774244) ^ [_820919, _820921] : [_820921 = _820919, -(c_DSequence_Oempty(_820921) = c_DSequence_Oempty(_820919))], (5812 ^ _774244) ^ [_866944, _866946, _866948, _866950, _866952, _866954, _866956, _866958, _866960] : [-(c_Com_Ocom_Ocom__case(_866944, _866946, _866948, _866950, _866952, _866954, _866956, _866958, _866960, c_Com_Ocom_OSKIP) = _866946)], (41099 ^ _774244) ^ [_1559021, _1559023, _1559025, _1559027, _1559029, _1559031, _1559033] : [class_Rings_Osemiring__0(_1559021), c_Fun_Oinj__on(tc_prod(_1559023, _1559025), _1559021, hAPP(c_Product__Type_Oprod_Oprod__case(_1559023, _1559025, _1559021), hAPP(hAPP(c_COMBC(_1559023, tc_fun(_1559025, _1559021), tc_fun(_1559025, _1559021)), hAPP(hAPP(c_COMBB(tc_fun(_1559021, _1559021), tc_fun(tc_fun(_1559025, _1559021), tc_fun(_1559025, _1559021)), _1559023), c_COMBB(_1559021, _1559021, _1559025)), hAPP(hAPP(c_COMBB(_1559021, tc_fun(_1559021, _1559021), _1559023), c_Groups_Otimes__class_Otimes(_1559021)), _1559027))), _1559029)), hAPP(hAPP(c_Product__Type_OSigma(_1559023, _1559025), _1559031), hAPP(c_COMBK(tc_fun(_1559025, tc_HOL_Obool), _1559023), _1559033))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1559021), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1559023, _1559021), _1559027), _1559031)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1559025, _1559021), _1559029), _1559033)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1559021, _1559021), c_Fun_Oid(_1559021)), hAPP(c_Set_OCollect(_1559021), hAPP(hAPP(c_COMBB(tc_fun(_1559023, tc_HOL_Obool), tc_HOL_Obool, _1559021), c_HOL_OEx(_1559023)), hAPP(hAPP(c_COMBB(tc_fun(_1559023, tc_fun(_1559025, tc_HOL_Obool)), tc_fun(_1559023, tc_HOL_Obool), _1559021), hAPP(c_COMBB(tc_fun(_1559025, tc_HOL_Obool), tc_HOL_Obool, _1559023), c_HOL_OEx(_1559025))), hAPP(hAPP(c_COMBC(_1559021, tc_fun(_1559023, tc_fun(_1559025, tc_HOL_Obool)), tc_fun(_1559023, tc_fun(_1559025, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1559023, tc_fun(tc_fun(_1559025, tc_HOL_Obool), tc_fun(_1559025, tc_HOL_Obool))), tc_fun(tc_fun(_1559023, tc_fun(_1559025, tc_HOL_Obool)), tc_fun(_1559023, tc_fun(_1559025, tc_HOL_Obool))), _1559021), c_COMBS(_1559023, tc_fun(_1559025, tc_HOL_Obool), tc_fun(_1559025, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1559023, tc_fun(_1559025, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1559023, tc_fun(tc_fun(_1559025, tc_HOL_Obool), tc_fun(_1559025, tc_HOL_Obool))), _1559021), hAPP(c_COMBB(tc_fun(_1559025, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1559025, tc_HOL_Obool), tc_fun(_1559025, tc_HOL_Obool)), _1559023), c_COMBS(_1559025, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1559023, tc_fun(_1559025, tc_HOL_Obool)), tc_fun(_1559023, tc_fun(_1559025, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1559021), hAPP(c_COMBB(tc_fun(_1559025, tc_HOL_Obool), tc_fun(_1559025, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1559023), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1559025), c_fconj))), hAPP(hAPP(c_COMBC(_1559021, tc_fun(_1559023, tc_fun(_1559025, _1559021)), tc_fun(_1559023, tc_fun(_1559025, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1559025, _1559021), tc_fun(_1559025, tc_HOL_Obool)), tc_fun(tc_fun(_1559023, tc_fun(_1559025, _1559021)), tc_fun(_1559023, tc_fun(_1559025, tc_HOL_Obool))), _1559021), c_COMBB(tc_fun(_1559025, _1559021), tc_fun(_1559025, tc_HOL_Obool), _1559023)), hAPP(hAPP(c_COMBB(tc_fun(_1559021, tc_HOL_Obool), tc_fun(tc_fun(_1559025, _1559021), tc_fun(_1559025, tc_HOL_Obool)), _1559021), c_COMBB(_1559021, tc_HOL_Obool, _1559025)), c_fequal))), hAPP(hAPP(c_COMBC(_1559023, tc_fun(_1559025, _1559021), tc_fun(_1559025, _1559021)), hAPP(hAPP(c_COMBB(tc_fun(_1559021, _1559021), tc_fun(tc_fun(_1559025, _1559021), tc_fun(_1559025, _1559021)), _1559023), c_COMBB(_1559021, _1559021, _1559025)), hAPP(hAPP(c_COMBB(_1559021, tc_fun(_1559021, _1559021), _1559023), c_Groups_Otimes__class_Otimes(_1559021)), _1559027))), _1559029)))))), hAPP(hAPP(c_COMBC(_1559023, tc_fun(_1559025, tc_HOL_Obool), tc_fun(_1559025, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1559025, tc_HOL_Obool), tc_fun(_1559025, tc_HOL_Obool)), _1559023), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1559025)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1559023), c_fconj), hAPP(hAPP(c_COMBC(_1559023, tc_fun(_1559023, tc_HOL_Obool), tc_HOL_Obool), c_member(_1559023)), _1559031)))), hAPP(hAPP(c_COMBC(_1559025, tc_fun(_1559025, tc_HOL_Obool), tc_HOL_Obool), c_member(_1559025)), _1559033))))))))], (41839 ^ _774244) ^ [_1579255, _1579257] : [c_Wellfounded_Owf(_1579255, _1579257), -(c_Wellfounded_OwfP(_1579255, hAPP(hAPP(c_COMBC(_1579255, tc_fun(tc_prod(_1579255, _1579255), tc_HOL_Obool), tc_fun(_1579255, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1579255, tc_fun(tc_fun(tc_prod(_1579255, _1579255), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1579255, _1579255), tc_HOL_Obool), tc_fun(_1579255, tc_HOL_Obool)), _1579255), c_COMBC(_1579255, tc_fun(tc_prod(_1579255, _1579255), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1579255, tc_prod(_1579255, _1579255)), tc_fun(_1579255, tc_fun(tc_fun(tc_prod(_1579255, _1579255), tc_HOL_Obool), tc_HOL_Obool)), _1579255), hAPP(c_COMBB(tc_prod(_1579255, _1579255), tc_fun(tc_fun(tc_prod(_1579255, _1579255), tc_HOL_Obool), tc_HOL_Obool), _1579255), c_member(tc_prod(_1579255, _1579255)))), c_Product__Type_OPair(_1579255, _1579255)))), _1579257)))], (46731 ^ _774244) ^ [_1700245, _1700247, _1700249] : [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, _1700245), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1700245)), _1700247)))), -(hBOOL(hAPP(hAPP(c_member(_1700245), hAPP(c_Product__Type_Ofst(_1700245, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1700245, _1700247), _1700249))), hAPP(c_List_Oset(_1700245), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1700245), _1700245), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1700245)), _1700247)))))], (6816 ^ _774244) ^ [_884687] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_884687)), c_Option_Ooption_ONone(_884687)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40862 ^ _774244) ^ [_1549223] : [-(c_Wellfounded_Ofinite__psubset(_1549223) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1549223, tc_HOL_Obool), tc_fun(_1549223, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1549223, tc_HOL_Obool), tc_fun(_1549223, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1549223, tc_HOL_Obool), tc_fun(tc_fun(_1549223, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1549223, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1549223, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1549223, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1549223, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1549223, tc_HOL_Obool)), c_COMBS(tc_fun(_1549223, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1549223, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1549223, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1549223, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1549223, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1549223, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1549223)))))], (47393 ^ _774244) ^ [_1715391, _1715393, _1715395] : [class_Orderings_Olinorder(_1715391), -(hAPP(c_List_Oset(_1715391), c_List_Olinorder__class_Oinsort__insert__key(_1715391, _1715391, c_COMBI(_1715391), _1715393, _1715395)) = hAPP(hAPP(c_Set_Oinsert(_1715391), _1715393), hAPP(c_List_Oset(_1715391), _1715395)))], (33342 ^ _774244) ^ [_1379115, _1379117, _1379119, _1379121, _1379123] : [hBOOL(hAPP(hAPP(c_member(_1379115), _1379117), _1379119)), -(hBOOL(hAPP(hAPP(c_member(tc_sum(_1379121, _1379115)), hAPP(c_Sum__Type_OInr(_1379115, _1379121), _1379117)), c_Sum__Type_OPlus(_1379121, _1379115, _1379123, _1379119))))], (24381 ^ _774244) ^ [_1198136, _1198138, _1198140] : [class_Groups_Olinordered__ab__group__add(_1198136), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1198136), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198136), _1198138), _1198140)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198136), hAPP(c_Groups_Ouminus__class_Ouminus(_1198136), _1198138)), hAPP(c_Groups_Ouminus__class_Ouminus(_1198136), _1198140)))], (19713 ^ _774244) ^ [_1111314] : [_1111314 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1111314) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (42231 ^ _774244) ^ [_1589153, _1589155, _1589157, _1589159] : [class_Groups_Ocomm__monoid__mult(_1589153), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589155), _1589157)), 42241 ^ _774244 : [(42244 ^ _774244) ^ [] : [hAPP(_1589159, 42240 ^ [_1589153, _1589155, _1589157, _1589159]) = c_Groups_Oone__class_Oone(_1589153)], (42242 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589155), 42240 ^ [_1589153, _1589155, _1589157, _1589159]), _1589157)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1589153, _1589155, c_Groups_Otimes__class_Otimes(_1589153)), _1589159), c_Groups_Oone__class_Oone(_1589153)), _1589157) = c_Groups_Oone__class_Oone(_1589153))], (40832 ^ _774244) ^ [_1548650, _1548652, _1548654, _1548656, _1548658, _1548660] : [hBOOL(hAPP(hAPP(c_member(_1548650), _1548652), _1548654)), -(hAPP(c_Fun_Ooverride__on(_1548650, _1548656, _1548658, _1548660, _1548654), _1548652) = hAPP(_1548660, _1548652))], (44809 ^ _774244) ^ [_1650958, _1650960] : [class_Complete__Lattice_Ocomplete__lattice(_1650958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1650958), _1650960)), -(c_Complete__Lattice_OSup__class_OSup(_1650958, _1650960) = hAPP(hAPP(c_Finite__Set_Ofold(_1650958, _1650958, c_Lattices_Osemilattice__sup__class_Osup(_1650958)), c_Orderings_Obot__class_Obot(_1650958)), _1650960))], (18035 ^ _774244) ^ [_1082542, _1082544] : [class_Int_Onumber__ring(_1082542), 18038 ^ _774244 : [(18045 ^ _774244) ^ [] : [c_Int_Oiszero(_1082542, hAPP(c_Int_Onumber__class_Onumber__of(_1082542), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1082544), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1082542), _1082544) = c_Groups_Ozero__class_Ozero(_1082542))], (18039 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1082542), _1082544) = c_Groups_Ozero__class_Ozero(_1082542), -(c_Int_Oiszero(_1082542, hAPP(c_Int_Onumber__class_Onumber__of(_1082542), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1082544), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (43933 ^ _774244) ^ [_1629595, _1629597, _1629599, _1629601, _1629603] : [-(_1629595 = c_Orderings_Obot__class_Obot(tc_fun(_1629597, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629597, tc_fun(_1629599, tc_HOL_Obool)), _1629595), hAPP(hAPP(c_COMBB(tc_fun(_1629599, tc_HOL_Obool), tc_fun(_1629599, tc_HOL_Obool), _1629597), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1629599, tc_HOL_Obool)), _1629601)), _1629603)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1629599, tc_HOL_Obool)), _1629601), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1629597, tc_fun(_1629599, tc_HOL_Obool)), _1629595), _1629603)))], (8502 ^ _774244) ^ [_912863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _912863))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _912863)))], (12185 ^ _774244) ^ [] : [-(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))))], (38628 ^ _774244) ^ [_1495670, _1495672, _1495674, _1495676, _1495678, _1495680, _1495682] : [c_Fun_Oinj__on(_1495670, _1495672, _1495674, hAPP(c_Set_Oimage(_1495676, _1495670, _1495678), _1495680)), c_Fun_Oinj__on(_1495676, _1495670, _1495678, _1495680), hBOOL(hAPP(hAPP(c_member(_1495672), _1495682), hAPP(c_Set_Oimage(_1495670, _1495672, _1495674), hAPP(c_Set_Oimage(_1495676, _1495670, _1495678), _1495680)))), -(hAPP(c_Fun_Othe__inv__into(_1495676, _1495672, _1495680, hAPP(c_Fun_Ocomp(_1495670, _1495672, _1495676, _1495674), _1495678)), _1495682) = hAPP(hAPP(c_Fun_Ocomp(_1495670, _1495676, _1495672, c_Fun_Othe__inv__into(_1495676, _1495670, _1495680, _1495678)), c_Fun_Othe__inv__into(_1495670, _1495672, hAPP(c_Set_Oimage(_1495676, _1495670, _1495678), _1495680), _1495674)), _1495682))], (48927 ^ _774244) ^ [_1752758, _1752760, _1752762, _1752764] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1752758)), hAPP(hAPP(c_List_Olist_OCons(_1752758), _1752760), _1752762)), c_List_Olists(_1752758, _1752764)))), hBOOL(hAPP(hAPP(c_member(_1752758), _1752760), _1752764)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1752758)), _1752762), c_List_Olists(_1752758, _1752764)))], (34810 ^ _774244) ^ [_1410507, _1410509, _1410511] : [class_Lattices_Olattice(_1410507), hAPP(_1410509, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1410507), 34815 ^ [_1410507, _1410509, _1410511]), 34816 ^ [_1410507, _1410509, _1410511])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1410507), hAPP(_1410509, 34815 ^ [_1410507, _1410509, _1410511])), hAPP(_1410509, 34816 ^ [_1410507, _1410509, _1410511])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410507), _1410511)), -(_1410511 = c_Orderings_Obot__class_Obot(tc_fun(_1410507, tc_HOL_Obool))), -(hAPP(_1410509, c_Big__Operators_Olattice__class_OSup__fin(_1410507, _1410511)) = c_Big__Operators_Olattice__class_OSup__fin(_1410507, hAPP(c_Set_Oimage(_1410507, _1410507, _1410509), _1410511)))], (36283 ^ _774244) ^ [_1443857] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1443857) = c_Orderings_Oord__class_Omin(_1443857)), class_Lattices_Osemilattice__inf(_1443857), class_Orderings_Olinorder(_1443857)], (34401 ^ _774244) ^ [_1400848, _1400850, _1400852, _1400854, _1400856, _1400858] : [class_Groups_Oordered__ab__group__add(_1400848), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400850), _1400852)), 34411 ^ _774244 : [(34414 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400848), c_Groups_Ozero__class_Ozero(_1400848)), hAPP(_1400854, 34410 ^ [_1400848, _1400850, _1400852, _1400854, _1400856, _1400858])))], (34412 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1400850), 34410 ^ [_1400848, _1400850, _1400852, _1400854, _1400856, _1400858]), _1400852)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400850, _1400848), _1400854), _1400852) = _1400856, hBOOL(hAPP(hAPP(c_member(_1400850), _1400858), _1400852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400848), hAPP(_1400854, _1400858)), _1400856)))], (43039 ^ _774244) ^ [_1605909, _1605911, _1605913, _1605915] : [-(c_Transitive__Closure_Otrancl(_1605909, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1605909, _1605909)), hAPP(hAPP(c_Product__Type_OPair(_1605909, _1605909), _1605911), _1605913)), _1605915)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1605909, _1605909), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1605909, _1605915)), hAPP(c_Set_OCollect(tc_prod(_1605909, _1605909)), hAPP(c_Product__Type_Oprod_Oprod__case(_1605909, _1605909, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1605909, tc_fun(_1605909, tc_HOL_Obool), tc_fun(_1605909, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1605909, tc_HOL_Obool), tc_fun(_1605909, tc_HOL_Obool)), _1605909), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1605909)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1605909), c_fconj), hAPP(hAPP(c_COMBC(_1605909, tc_fun(tc_prod(_1605909, _1605909), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1605909, _1605909), tc_fun(tc_fun(tc_prod(_1605909, _1605909), tc_HOL_Obool), tc_HOL_Obool), _1605909), c_member(tc_prod(_1605909, _1605909))), hAPP(hAPP(c_COMBC(_1605909, _1605909, tc_prod(_1605909, _1605909)), c_Product__Type_OPair(_1605909, _1605909)), _1605911))), c_Transitive__Closure_Ortrancl(_1605909, _1605915))))), hAPP(hAPP(c_COMBC(_1605909, tc_fun(tc_prod(_1605909, _1605909), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1605909, _1605909), tc_fun(tc_fun(tc_prod(_1605909, _1605909), tc_HOL_Obool), tc_HOL_Obool), _1605909), c_member(tc_prod(_1605909, _1605909))), hAPP(c_Product__Type_OPair(_1605909, _1605909), _1605913))), c_Transitive__Closure_Ortrancl(_1605909, _1605915)))))))], (25605 ^ _774244) ^ [_1220894, _1220896, _1220898, _1220900] : [class_Divides_Osemiring__div(_1220894), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220894), _1220896), _1220898)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220894), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1220894), _1220898), _1220896)), _1220900) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1220894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220894), _1220898), _1220900)), _1220896))], (16605 ^ _774244) ^ [_1057240, _1057242, _1057244] : [class_Int_Onumber__ring(_1057240), class_Rings_Olinordered__idom(_1057240), 16612 ^ _774244 : [(16619 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1057242), _1057244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057240), hAPP(c_Int_Onumber__class_Onumber__of(_1057240), _1057242)), hAPP(c_Int_Onumber__class_Onumber__of(_1057240), _1057244))))], (16613 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057240), hAPP(c_Int_Onumber__class_Onumber__of(_1057240), _1057242)), hAPP(c_Int_Onumber__class_Onumber__of(_1057240), _1057244))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1057242), _1057244)))]]], (25309 ^ _774244) ^ [_1215669, _1215671, _1215673, _1215675] : [class_Divides_Osemiring__div(_1215669), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215669), _1215671), c_Divides_Odiv__class_Omod(_1215669, _1215673, _1215675))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215669), _1215671), _1215675)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215669), _1215671), _1215673)))], (24375 ^ _774244) ^ [_1197997, _1197999, _1198001] : [class_Groups_Olinordered__ab__group__add(_1197997), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1197997), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197997), _1197999), _1198001)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197997), hAPP(c_Groups_Ouminus__class_Ouminus(_1197997), _1197999)), hAPP(c_Groups_Ouminus__class_Ouminus(_1197997), _1198001)))], (18215 ^ _774244) ^ [_1085217] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085217) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085217), c_Int_OPls)))], (15996 ^ _774244) ^ [_1046166, _1046168] : [-(_1046166 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046166), _1046168) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046166), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1046168)))], (18727 ^ _774244) ^ [] : [-(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)))))], (11258 ^ _774244) ^ [_959486, _959488, _959490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959488), _959490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959486), _959488)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959486), _959490))))], (28745 ^ _774244) ^ [_1284746, _1284748, _1284750] : [-(hAPP(hAPP(c_Set_Oinsert(_1284746), _1284748), hAPP(hAPP(c_Set_Oinsert(_1284746), _1284748), _1284750)) = hAPP(hAPP(c_Set_Oinsert(_1284746), _1284748), _1284750))], (44196 ^ _774244) ^ [_1636632, _1636634, _1636636] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636632, _1636632)), _1636634), c_Transitive__Closure_Ortrancl(_1636632, _1636636))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636632, _1636632)), _1636634), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1636632, _1636632), 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(_1636632, _1636632), tc_HOL_Obool), tc_fun(tc_prod(_1636632, _1636632), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1636632, _1636632), tc_HOL_Obool)), _1636636)))))], (30957 ^ _774244) ^ [_1329486, _1329488, _1329490] : [hBOOL(hAPP(hAPP(c_member(_1329486), _1329488), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1329486, tc_HOL_Obool)), _1329490))), hBOOL(hAPP(hAPP(c_member(_1329486), _1329488), _1329490))], (51101 ^ _774244) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (4460 ^ _774244) ^ [_843244, _843246, _843248, _843250] : [-(c_Big__Operators_Olattice__class_OSup__fin(_843250, _843246) = c_Big__Operators_Olattice__class_OSup__fin(_843248, _843244)), _843250 = _843248, _843246 = _843244], (23157 ^ _774244) ^ [_1174579, _1174581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1174581), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1174579, _1174581) = 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), _1174579), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1174581)))))], (27438 ^ _774244) ^ [_1258112, _1258114] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1258112), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1258114) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1258112, _1258114))], (47405 ^ _774244) ^ [_1715681, _1715683, _1715685, _1715687, _1715689] : [class_Orderings_Olinorder(_1715681), hBOOL(hAPP(hAPP(c_member(_1715681), hAPP(_1715683, _1715685)), hAPP(c_Set_Oimage(_1715687, _1715681, _1715683), hAPP(c_List_Oset(_1715687), _1715689)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1715687, _1715681, _1715683, _1715685, _1715689) = _1715689)], (26317 ^ _774244) ^ [_1234036, _1234038] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1234038), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1234036)) = 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), _1234036)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1234038))))], (49543 ^ _774244) ^ [_1766784, _1766786, _1766788, _1766790, _1766792] : [class_Orderings_Olinorder(_1766784), c_List_Olinorder__class_Osorted(_1766784, hAPP(hAPP(c_List_Omap(_1766786, _1766784), _1766788), _1766790)), -(c_List_Olinorder__class_Osorted(_1766784, hAPP(hAPP(c_List_Omap(_1766786, _1766784), _1766788), hAPP(c_List_Ofilter(_1766786, _1766792), _1766790))))], (29855 ^ _774244) ^ [_1306153] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1306153)), 29859 ^ _774244 : [(29860 ^ _774244) ^ [_1306233] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1306233), _1306153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1306233), 29858 ^ [_1306153])))]]], (46563 ^ _774244) ^ [_1695277, _1695279, _1695281, _1695283] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1695277), tc_List_Olist(_1695277), c_List_Olistrel(_1695277, _1695279)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1695277)), hAPP(hAPP(c_List_Olist_OCons(_1695277), _1695281), _1695283)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1695277), tc_HOL_Obool)))) = c_List_Oset__Cons(_1695277, hAPP(c_Relation_OImage(_1695277, _1695277, _1695279), hAPP(hAPP(c_Set_Oinsert(_1695277), _1695281), c_Orderings_Obot__class_Obot(tc_fun(_1695277, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1695277), tc_List_Olist(_1695277), c_List_Olistrel(_1695277, _1695279)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1695277)), _1695283), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1695277), tc_HOL_Obool))))))], (47571 ^ _774244) ^ [_1719745, _1719747, _1719749, _1719751, _1719753] : [-(hAPP(hAPP(c_List_Omap(_1719745, _1719747), _1719749), hAPP(hAPP(c_List_Oappend(_1719745), _1719751), _1719753)) = hAPP(hAPP(c_List_Oappend(_1719747), hAPP(hAPP(c_List_Omap(_1719745, _1719747), _1719749), _1719751)), hAPP(hAPP(c_List_Omap(_1719745, _1719747), _1719749), _1719753)))], (36433 ^ _774244) ^ [_1446888, _1446890, _1446892, _1446894, _1446896, _1446898, _1446900] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446888, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1446890, tc_fun(_1446888, tc_HOL_Obool)), _1446892), _1446894)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1446896, tc_fun(_1446888, tc_HOL_Obool)), _1446898), _1446900)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1446890, tc_fun(_1446888, tc_HOL_Obool)), _1446892), hAPP(hAPP(c_COMBB(tc_fun(_1446896, tc_fun(_1446888, tc_HOL_Obool)), tc_fun(_1446888, tc_HOL_Obool), _1446890), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1446896, tc_fun(_1446888, tc_HOL_Obool)), _1446898)), hAPP(hAPP(c_COMBC(_1446890, tc_fun(_1446896, tc_fun(_1446888, tc_HOL_Obool)), tc_fun(_1446896, tc_fun(_1446888, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1446888, tc_HOL_Obool), tc_fun(_1446888, tc_HOL_Obool)), tc_fun(tc_fun(_1446896, tc_fun(_1446888, tc_HOL_Obool)), tc_fun(_1446896, tc_fun(_1446888, tc_HOL_Obool))), _1446890), c_COMBB(tc_fun(_1446888, tc_HOL_Obool), tc_fun(_1446888, tc_HOL_Obool), _1446896)), hAPP(hAPP(c_COMBB(tc_fun(_1446888, tc_HOL_Obool), tc_fun(tc_fun(_1446888, tc_HOL_Obool), tc_fun(_1446888, tc_HOL_Obool)), _1446890), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446888, tc_HOL_Obool))), _1446894))), _1446900))))], (47218 ^ _774244) ^ [_1711206, _1711208, _1711210, _1711212] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711206), tc_List_Olist(_1711206))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711206), tc_List_Olist(_1711206)), _1711208), _1711210)), c_List_Olistrel(_1711206, _1711212))), 47221 ^ _774244 : [(47224 ^ _774244) ^ [_1711435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711435), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711206)), _1711208))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1711206, _1711206)), hAPP(hAPP(c_Product__Type_OPair(_1711206, _1711206), hAPP(hAPP(c_List_Onth(_1711206), _1711208), _1711435)), hAPP(hAPP(c_List_Onth(_1711206), _1711210), _1711435))), _1711212)))], (47222 ^ _774244) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711206)), _1711208) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711206)), _1711210))]]], (1224 ^ _774244) ^ [_792268, _792270] : [-(class_Complete__Lattice_Ocomplete__lattice(_792268)), _792270 = _792268, class_Complete__Lattice_Ocomplete__lattice(_792270)], (1164 ^ _774244) ^ [_791518, _791520] : [-(class_Groups_Oabs__if(_791518)), _791520 = _791518, class_Groups_Oabs__if(_791520)], (3670 ^ _774244) ^ [_830811, _830813, _830815, _830817] : [-(c_Lazy__Sequence_Osingle(_830817, _830813) = c_Lazy__Sequence_Osingle(_830815, _830811)), _830817 = _830815, _830813 = _830811], (39674 ^ _774244) ^ [_1520920, _1520922, _1520924, _1520926, _1520928, _1520930] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1520920, _1520922)), hAPP(hAPP(c_Product__Type_OPair(_1520920, _1520922), _1520924), _1520926)), hAPP(hAPP(c_Product__Type_OSigma(_1520920, _1520922), _1520928), _1520930)))), hBOOL(hAPP(hAPP(c_member(_1520920), _1520924), _1520928)), hBOOL(hAPP(hAPP(c_member(_1520922), _1520926), hAPP(_1520930, _1520924)))], (8128 ^ _774244) ^ [_907313] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907313), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _907313)], (6696 ^ _774244) ^ [_882090, _882092, _882094, _882096] : [-(c_Option_Ooption_Ooption__rec(_882090, _882092, _882094, _882096, c_Option_Ooption_ONone(_882092)) = _882094)], (46675 ^ _774244) ^ [_1698926, _1698928, _1698930, _1698932] : [class_Groups_Oab__group__add(_1698926), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1698926), hAPP(c_List_Omonoid__add__class_Olistsum(_1698926), hAPP(hAPP(c_List_Omap(_1698928, _1698926), _1698930), _1698932))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1698926), hAPP(hAPP(c_List_Omap(_1698928, _1698926), hAPP(c_Fun_Ocomp(_1698926, _1698926, _1698928, c_Groups_Ouminus__class_Ouminus(_1698926)), _1698930)), _1698932)))], (10095 ^ _774244) ^ [_940646, _940648, _940650, _940652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940646), _940648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940650), _940652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940646), _940650)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940648), _940652))))], (47746 ^ _774244) ^ [_1723379, _1723381, _1723383, _1723385, _1723387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723379), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723381)), _1723383))), -(hAPP(hAPP(c_List_Olist__update(_1723381, hAPP(hAPP(c_List_Oappend(_1723381), _1723383), _1723385)), _1723379), _1723387) = hAPP(hAPP(c_List_Oappend(_1723381), hAPP(hAPP(c_List_Olist__update(_1723381, _1723383), _1723379), _1723387)), _1723385))], (46461 ^ _774244) ^ [_1692757, _1692759, _1692761, _1692763] : [_1692757 = _1692759, -(c_List_Oremove1(_1692761, _1692757, hAPP(hAPP(c_List_Olist_OCons(_1692761), _1692759), _1692763)) = _1692763)], (30927 ^ _774244) ^ [_1328913, _1328915, _1328917, _1328919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328913, tc_HOL_Obool)), _1328915), _1328917)), hBOOL(hAPP(hAPP(c_member(_1328913), _1328919), _1328915)), -(hBOOL(hAPP(hAPP(c_member(_1328913), _1328919), _1328917)))], (50274 ^ _774244) ^ [_1781015, _1781017, _1781019, _1781021] : [hAPP(c_List_Orev(_1781015), _1781017) = hAPP(hAPP(c_List_Olist_OCons(_1781015), _1781019), _1781021), -(_1781017 = hAPP(hAPP(c_List_Oappend(_1781015), hAPP(c_List_Orev(_1781015), _1781021)), hAPP(hAPP(c_List_Olist_OCons(_1781015), _1781019), c_List_Olist_ONil(_1781015))))], (686 ^ _774244) ^ [_784881, _784883, _784885, _784887] : [-(c_Relation_Oirrefl(_784885, _784881)), c_Relation_Oirrefl(_784887, _784883), _784887 = _784885, _784883 = _784881], (35257 ^ _774244) ^ [_1420607, _1420609, _1420611, _1420613, _1420615] : [-(hAPP(c_Relation_OImage(_1420607, _1420609, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1420607, _1420609), tc_HOL_Obool)), _1420611), _1420613)), _1420615) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420609, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1420607, _1420609, _1420611), _1420615)), hAPP(c_Relation_OImage(_1420607, _1420609, _1420613), _1420615)))], (33740 ^ _774244) ^ [_1386573, _1386575, _1386577] : [class_Orderings_Olinorder(_1386573), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386573), _1386575)), 33747 ^ _774244 : [(33754 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386573, tc_HOL_Obool)), _1386575), hAPP(hAPP(c_Set_Oinsert(_1386573), _1386577), c_Orderings_Obot__class_Obot(tc_fun(_1386573, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1386573, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1386573, c_Orderings_Oord__class_Omax(_1386573), hAPP(hAPP(c_Set_Oinsert(_1386573), _1386577), _1386575)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1386573), _1386577), c_Big__Operators_Olattice_OSup__fin(_1386573, c_Orderings_Oord__class_Omax(_1386573), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386573, tc_HOL_Obool)), _1386575), hAPP(hAPP(c_Set_Oinsert(_1386573), _1386577), c_Orderings_Obot__class_Obot(tc_fun(_1386573, tc_HOL_Obool)))))))], (33748 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386573, tc_HOL_Obool)), _1386575), hAPP(hAPP(c_Set_Oinsert(_1386573), _1386577), c_Orderings_Obot__class_Obot(tc_fun(_1386573, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1386573, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1386573, c_Orderings_Oord__class_Omax(_1386573), hAPP(hAPP(c_Set_Oinsert(_1386573), _1386577), _1386575)) = _1386577)]]], (3848 ^ _774244) ^ [_833544, _833546, _833548, _833550] : [-(c_Relation_OId__on(_833550, _833546) = c_Relation_OId__on(_833548, _833544)), _833550 = _833548, _833546 = _833544], (36697 ^ _774244) ^ [_1453448, _1453450, _1453452, _1453454] : [class_Orderings_Oorder(_1453448), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453448, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1453448, _1453450, _1453452)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1453448, _1453452), _1453454)) = c_Orderings_Obot__class_Obot(tc_fun(_1453448, tc_HOL_Obool)))], (29995 ^ _774244) ^ [_1308638] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1308638)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1308638), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308638), c_Orderings_Otop__class_Otop(tc_fun(_1308638, tc_HOL_Obool)))))], (14506 ^ _774244) ^ [_1017220, _1017222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017222), 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), _1017220), _1017222)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (49593 ^ _774244) ^ [_1767635, _1767637, _1767639] : [class_Orderings_Olinorder(_1767635), 49596 ^ _774244 : [(49615 ^ _774244) ^ [] : [-(c_List_Olinorder__class_Osorted(_1767635, hAPP(hAPP(c_List_Oappend(_1767635), _1767637), _1767639))), c_List_Olinorder__class_Osorted(_1767635, _1767637), c_List_Olinorder__class_Osorted(_1767635, _1767639), 49625 ^ _774244 : [(49631 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1767635), 49624 ^ [_1767635, _1767637, _1767639]), 49627 ^ [_1767635, _1767637, _1767639]))], (49629 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767635), 49627 ^ [_1767635, _1767637, _1767639]), hAPP(c_List_Oset(_1767635), _1767639))))], (49626 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767635), 49624 ^ [_1767635, _1767637, _1767639]), hAPP(c_List_Oset(_1767635), _1767637))))]]], (49597 ^ _774244) ^ [] : [c_List_Olinorder__class_Osorted(_1767635, hAPP(hAPP(c_List_Oappend(_1767635), _1767637), _1767639)), 49600 ^ _774244 : [(49605 ^ _774244) ^ [_1767871] : [hBOOL(hAPP(hAPP(c_member(_1767635), _1767871), hAPP(c_List_Oset(_1767635), _1767637))), 49608 ^ _774244 : [(49609 ^ _774244) ^ [_1767981] : [hBOOL(hAPP(hAPP(c_member(_1767635), _1767981), hAPP(c_List_Oset(_1767635), _1767639))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1767635), _1767871), _1767981)))]]], (49603 ^ _774244) ^ [] : [-(c_List_Olinorder__class_Osorted(_1767635, _1767639))], (49601 ^ _774244) ^ [] : [-(c_List_Olinorder__class_Osorted(_1767635, _1767637))]]]]], (33392 ^ _774244) ^ [_1380165, _1380167, _1380169, _1380171] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1380165), _1380167)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380169), _1380171)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1380165, _1380169)), c_Sum__Type_OPlus(_1380165, _1380169, _1380167, _1380171))))], (34994 ^ _774244) ^ [_1414662, _1414664] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1414662, tc_HOL_Obool)), hAPP(c_Set_OPow(_1414662), _1414664))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1414662), _1414664)))], (26047 ^ _774244) ^ [_1229200, _1229202] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1229200)), _1229202))), 26050 ^ _774244 : [(26053 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1229200), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229202)))], (26051 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229200)))]], 26054 ^ _774244 : [(26057 ^ _774244) ^ [] : [_1229202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26055 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229200))]]], (51253 ^ _774244) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (36249 ^ _774244) ^ [_1443043, _1443045, _1443047, _1443049] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443043, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1443043), _1443045), _1443047)), hAPP(hAPP(c_Set_Oinsert(_1443043), _1443045), _1443049)) = hAPP(hAPP(c_Set_Oinsert(_1443043), _1443045), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443043, tc_HOL_Obool)), _1443047), _1443049)))], (43639 ^ _774244) ^ [_1621909, _1621911, _1621913, _1621915, _1621917] : [hBOOL(hAPP(hAPP(c_member(_1621909), _1621911), _1621913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621915, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1621909, tc_fun(_1621915, tc_HOL_Obool)), _1621913), _1621917)), hAPP(_1621917, _1621911))))], (11124 ^ _774244) ^ [] : [-(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))))], (9350 ^ _774244) ^ [_927722, _927724, _927726, _927728] : [class_Rings_Olinordered__ring__strict(_927722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927722), _927724), _927726)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927722), _927728), c_Groups_Ozero__class_Ozero(_927722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927722), _927726), _927728)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927722), _927724), _927728))))], (22092 ^ _774244) ^ [_1153822, _1153824] : [-(c_Divides_Odivmod__nat(_1153822, _1153824) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1153822), _1153824)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1153822, _1153824)))], (8156 ^ _774244) ^ [_907732, _907734] : [class_Orderings_Opreorder(_907732), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907732), _907734), _907734))], (36033 ^ _774244) ^ [_1438238, _1438240, _1438242] : [class_Lattices_Osemilattice__inf(_1438238), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438238), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1438238), _1438240), _1438242)), _1438240)))], (40870 ^ _774244) ^ [_1549706, _1549708, _1549710, _1549712] : [-(c_Nitpick_Oprod(_1549706, _1549708, _1549710, _1549712) = hAPP(c_Set_OCollect(tc_prod(_1549706, _1549708)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549706, _1549708, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1549706, tc_fun(_1549708, tc_HOL_Obool), tc_fun(_1549708, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1549708, tc_HOL_Obool), tc_fun(_1549708, tc_HOL_Obool)), _1549706), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1549708)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549706), c_fconj), hAPP(hAPP(c_COMBC(_1549706, tc_fun(_1549706, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549706)), _1549710)))), hAPP(hAPP(c_COMBC(_1549708, tc_fun(_1549708, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549708)), _1549712)))))], (1664 ^ _774244) ^ [_797768, _797770] : [-(class_Rings_Omult__zero(_797768)), _797770 = _797768, class_Rings_Omult__zero(_797770)], (37979 ^ _774244) ^ [_1482237, _1482239, _1482241, _1482243, _1482245] : [c_Equiv__Relations_Oequivp(_1482237, _1482239), hBOOL(hAPP(hAPP(_1482239, _1482241), _1482243)), hBOOL(hAPP(hAPP(_1482239, _1482243), _1482245)), -(hBOOL(hAPP(hAPP(_1482239, _1482241), _1482245)))], (24971 ^ _774244) ^ [_1210217, _1210219] : [_1210219 = _1210217, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210217), _1210219)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210219), _1210217)))], (24479 ^ _774244) ^ [_1200136] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1200136)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1200136))], (11277 ^ _774244) ^ [_959847, _959849] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959847), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959847), _959849))))], (30107 ^ _774244) ^ [_1310439, _1310441] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310439), _1310441)), 30110 ^ _774244 : [(30117 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310439), c_Orderings_Otop__class_Otop(tc_fun(_1310439, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1310439), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1310439, tc_HOL_Obool)), _1310441))))], (30111 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310439), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1310439, tc_HOL_Obool)), _1310441))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1310439), c_Orderings_Otop__class_Otop(tc_fun(_1310439, tc_HOL_Obool)))))]]], (12552 ^ _774244) ^ [_982554, _982556, _982558, _982560] : [class_Rings_Olinordered__semiring(_982554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982554), _982556), _982558)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982554), _982556), _982560))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982554), c_Groups_Ozero__class_Ozero(_982554)), _982556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982554), _982558), _982560)))], (47531 ^ _774244) ^ [_1718740, _1718742, _1718744, _1718746, _1718748] : [-(hAPP(hAPP(c_List_Oappend(_1718740), _1718742), _1718744) = hAPP(hAPP(c_List_Olist_OCons(_1718740), _1718746), _1718748)), 47532 ^ _774244 : [(47539 ^ _774244) ^ [_1718923] : [_1718742 = hAPP(hAPP(c_List_Olist_OCons(_1718740), _1718746), _1718923), hAPP(hAPP(c_List_Oappend(_1718740), _1718923), _1718744) = _1718748], (47533 ^ _774244) ^ [] : [_1718742 = c_List_Olist_ONil(_1718740), _1718744 = hAPP(hAPP(c_List_Olist_OCons(_1718740), _1718746), _1718748)]]], (41132 ^ _774244) ^ [_1561119, _1561121] : [-(hAPP(c_Set_Ovimage(_1561119, _1561119, c_Fun_Oid(_1561119)), _1561121) = _1561121)], (9378 ^ _774244) ^ [_928260, _928262, _928264, _928266] : [class_Rings_Olinordered__semiring__strict(_928260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928260), _928262), _928264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928260), c_Groups_Ozero__class_Ozero(_928260)), _928266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928260), _928266), _928262)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928260), _928266), _928264))))], (15438 ^ _774244) ^ [_1034566, _1034568, _1034570] : [class_Rings_Ocomm__ring__1(_1034566), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034566), _1034568), _1034570) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034566), _1034568), hAPP(c_Groups_Ouminus__class_Ouminus(_1034566), _1034570)))], (50789 ^ _774244) ^ [_1793122, _1793124, _1793126, _1793128, _1793130] : [-(c_List_OdropWhile(_1793122, _1793124, hAPP(hAPP(c_List_Omap(_1793126, _1793122), _1793128), _1793130)) = hAPP(hAPP(c_List_Omap(_1793126, _1793122), _1793128), c_List_OdropWhile(_1793126, hAPP(c_Fun_Ocomp(_1793122, tc_HOL_Obool, _1793126, _1793124), _1793128), _1793130)))], (43619 ^ _774244) ^ [_1621384, _1621386, _1621388] : [c_Relation_Orefl__on(_1621384, _1621386, hAPP(c_Relation_Oconverse(_1621384, _1621384), _1621388)), -(c_Relation_Orefl__on(_1621384, _1621386, _1621388))], (24533 ^ _774244) ^ [_1201166, _1201168, _1201170, _1201172, _1201174] : [_1201166 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1201168, _1201170, _1201166, _1201172), _1201174) = hAPP(c_Product__Type_OPair(_1201168, _1201170), _1201174))], (16351 ^ _774244) ^ [_1052339, _1052341] : [class_Groups_Oordered__ab__group__add__abs(_1052339), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052339), c_Groups_Ozero__class_Ozero(_1052339)), hAPP(c_Groups_Oabs__class_Oabs(_1052339), _1052341))))], (32322 ^ _774244) ^ [_1359582, _1359584, _1359586, _1359588] : [hBOOL(hAPP(hAPP(_1359586, _1359584), _1359588)), -(hBOOL(hAPP(hAPP(c_member(_1359582), _1359584), c_SetInterval_Oord_OatMost(_1359582, _1359586, _1359588))))], (43385 ^ _774244) ^ [_1614167, _1614169, _1614171, _1614173, _1614175, _1614177, _1614179, _1614181] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614167, tc_fun(_1614169, tc_fun(_1614171, tc_HOL_Obool))), _1614173), _1614175), _1614177), _1614179)), -(hBOOL(hAPP(hAPP(hAPP(_1614175, _1614181), _1614177), _1614179))), hBOOL(hAPP(hAPP(c_member(_1614167), _1614181), _1614173))], (31909 ^ _774244) ^ [_1351166, _1351168, _1351170, _1351172] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1351166), _1351168)), hBOOL(hAPP(hAPP(c_member(_1351166), _1351170), _1351168)), -(hBOOL(hAPP(hAPP(c_member(_1351166), _1351170), _1351172))), -(hAPP(c_Finite__Set_Ocard(_1351166), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351166, tc_HOL_Obool)), _1351168), hAPP(hAPP(c_Set_Oinsert(_1351166), _1351170), _1351172))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1351166), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351166, tc_HOL_Obool)), _1351168), _1351172))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (48718 ^ _774244) ^ [_1747830, _1747832, _1747834, _1747836, _1747838, _1747840, _1747842] : [-(hAPP(c_List_Ofoldl(_1747830, _1747832, _1747834, _1747836), hAPP(hAPP(c_List_Omap(_1747838, _1747832), _1747840), _1747842)) = hAPP(c_List_Ofoldl(_1747830, _1747838, hAPP(hAPP(c_COMBC(_1747830, tc_fun(_1747838, _1747832), tc_fun(_1747838, _1747830)), hAPP(hAPP(c_COMBB(tc_fun(_1747832, _1747830), tc_fun(tc_fun(_1747838, _1747832), tc_fun(_1747838, _1747830)), _1747830), c_COMBB(_1747832, _1747830, _1747838)), _1747834)), _1747840), _1747836), _1747842))], (28878 ^ _774244) ^ [_1287843, _1287845] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287843, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1287843, tc_HOL_Obool))), _1287845)))], (24701 ^ _774244) ^ [_1204779, _1204781] : [-(hAPP(c_New__DSequence_Opos__empty(_1204779), _1204781) = c_Lazy__Sequence_Oempty(_1204779))], (23297 ^ _774244) ^ [_1177228, _1177230, _1177232, _1177234] : [-(hAPP(c_Product__Type_Ofst(_1177228, _1177230), hAPP(hAPP(c_Product__Type_OPair(_1177228, _1177230), _1177232), _1177234)) = _1177232)], (19297 ^ _774244) ^ [_1103699] : [class_Int_Onumber__ring(_1103699), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103699), c_Groups_Oone__class_Oone(_1103699)), c_Groups_Oone__class_Oone(_1103699)) = hAPP(c_Int_Onumber__class_Onumber__of(_1103699), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (34745 ^ _774244) ^ [_1409155, _1409157, _1409159] : [-(hAPP(c_Relation_OField(_1409155), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1409155, _1409155), tc_HOL_Obool)), _1409157), _1409159)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409155, tc_HOL_Obool)), hAPP(c_Relation_OField(_1409155), _1409157)), hAPP(c_Relation_OField(_1409155), _1409159)))], (28158 ^ _774244) ^ [_1271707, _1271709, _1271711] : [class_Orderings_Olinorder(_1271707), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271707), _1271709), _1271711)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271707, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1271707), _1271709)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1271707, _1271709, _1271711)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1271707), _1271711))], (43022 ^ _774244) ^ [_1605525, _1605527, _1605529, _1605531, _1605533, _1605535, _1605537] : [c_Finite__Set_Ofun__left__comm(_1605525, _1605527, _1605529), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1605525, _1605527, _1605529, _1605531, _1605533), _1605535)), hBOOL(hAPP(hAPP(c_member(_1605525), _1605537), _1605533)), 43034 ^ _774244 : [(43037 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1605525, _1605527, _1605529, _1605531, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1605525, tc_HOL_Obool)), _1605533), hAPP(hAPP(c_Set_Oinsert(_1605525), _1605537), c_Orderings_Obot__class_Obot(tc_fun(_1605525, tc_HOL_Obool))))), 43033 ^ [_1605525, _1605527, _1605529, _1605531, _1605533, _1605535, _1605537])))], (43035 ^ _774244) ^ [] : [-(_1605535 = hAPP(hAPP(_1605529, _1605537), 43033 ^ [_1605525, _1605527, _1605529, _1605531, _1605533, _1605535, _1605537]))]]], (21649 ^ _774244) ^ [_1146013, _1146015, _1146017, _1146019] : [class_Fields_Olinordered__field__inverse__zero(_1146013), class_Int_Onumber(_1146013), 21656 ^ _774244 : [(21657 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146013), _1146015), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146013), _1146017), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019)))), 21660 ^ _774244 : [(21667 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146013), c_Groups_Ozero__class_Ozero(_1146013)), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019)))), 21670 ^ _774244 : [(21677 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146013), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019)), c_Groups_Ozero__class_Ozero(_1146013)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146013), _1146015), c_Groups_Ozero__class_Ozero(_1146013))))], (21671 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146013), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019)), c_Groups_Ozero__class_Ozero(_1146013))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146013), _1146017), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146013), _1146015), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019)))))]]], (21661 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146013), c_Groups_Ozero__class_Ozero(_1146013)), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146013), _1146015), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019))), _1146017)))]]], (21683 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146013), _1146015), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146013), _1146017), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019))))), 21686 ^ _774244 : [(21689 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146013), _1146015), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019))), _1146017))], (21687 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146013), c_Groups_Ozero__class_Ozero(_1146013)), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019))))]], 21690 ^ _774244 : [(21693 ^ _774244) ^ [] : [21694 ^ _774244 : [(21697 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146013), _1146017), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146013), _1146015), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019))))], (21695 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146013), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019)), c_Groups_Ozero__class_Ozero(_1146013))))]], 21698 ^ _774244 : [(21701 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146013), _1146015), c_Groups_Ozero__class_Ozero(_1146013)))], (21699 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146013), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019)), c_Groups_Ozero__class_Ozero(_1146013)))]]], (21691 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146013), c_Groups_Ozero__class_Ozero(_1146013)), hAPP(c_Int_Onumber__class_Onumber__of(_1146013), _1146019)))]]]]], (24811 ^ _774244) ^ [_1207517] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1207517)))], (22262 ^ _774244) ^ [_1157585, _1157587, _1157589, _1157591, _1157593] : [-(c_Nat_Onat_Onat__case(_1157585, _1157587, _1157589, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157591)), _1157593)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1157585), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1157591))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1157585, _1157585), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1157585, tc_fun(_1157585, _1157585)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1157585, tc_fun(_1157585, _1157585)), tc_Int_Oint), c_If(_1157585)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1157585, _1157587, _1157589, _1157593))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1157585, tc_Int_Oint), _1157589), 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)), _1157593)))))], (33536 ^ _774244) ^ [_1383053, _1383055] : [class_Orderings_Olinorder(_1383053), -(c_Big__Operators_Olattice_OInf__fin(_1383053, c_Orderings_Oord__class_Omin(_1383053), hAPP(hAPP(c_Set_Oinsert(_1383053), _1383055), c_Orderings_Obot__class_Obot(tc_fun(_1383053, tc_HOL_Obool)))) = _1383055)], (30745 ^ _774244) ^ [_1323318, _1323320, _1323322, _1323324, _1323326] : [hBOOL(hAPP(hAPP(c_member(_1323318), _1323320), c_SetInterval_Oord_OatLeastAtMost(_1323318, _1323322, _1323324, _1323326))), 30748 ^ _774244 : [(30751 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1323322, _1323320), _1323326)))], (30749 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1323322, _1323324), _1323320)))]]], (18175 ^ _774244) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (28602 ^ _774244) ^ [_1281073, _1281075, _1281077, _1281079, _1281081, _1281083] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281073, tc_fun(_1281075, tc_HOL_Obool)), _1281077), hAPP(hAPP(c_COMBC(_1281073, tc_fun(_1281079, tc_fun(_1281075, tc_HOL_Obool)), tc_fun(_1281075, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1281079, tc_HOL_Obool), tc_fun(tc_fun(_1281079, tc_fun(_1281075, tc_HOL_Obool)), tc_fun(_1281075, tc_HOL_Obool)), _1281073), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281079, tc_fun(_1281075, tc_HOL_Obool))), _1281081)), _1281083)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281079, tc_fun(_1281075, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281073, tc_fun(_1281079, tc_HOL_Obool)), _1281077), _1281081)), _1281083))], (45740 ^ _774244) ^ [_1673445, _1673447, _1673449, _1673451] : [hAPP(c_Map_Omap__of(_1673445, _1673447, _1673449), _1673451) = c_Option_Ooption_ONone(_1673447), hBOOL(hAPP(hAPP(c_member(_1673445), _1673451), hAPP(c_Set_Oimage(tc_prod(_1673445, _1673447), _1673445, c_Product__Type_Ofst(_1673445, _1673447)), hAPP(c_List_Oset(tc_prod(_1673445, _1673447)), _1673449))))], (19891 ^ _774244) ^ [_1114733, _1114735] : [c_Nat__Transfer_Ois__nat(_1114733), c_Nat__Transfer_Ois__nat(_1114735), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1114733), _1114735)))], (40969 ^ _774244) ^ [_1553131, _1553133, _1553135] : [class_Groups_Olinordered__ab__semigroup__add(_1553131), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553131), _1553133)), -(_1553133 = c_Orderings_Obot__class_Obot(tc_fun(_1553131, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1553131), _1553135), c_Big__Operators_Olinorder__class_OMax(_1553131, _1553133)) = c_Big__Operators_Olinorder__class_OMax(_1553131, hAPP(c_Set_OCollect(_1553131), hAPP(hAPP(c_COMBB(tc_fun(_1553131, tc_HOL_Obool), tc_HOL_Obool, _1553131), c_HOL_OEx(_1553131)), hAPP(hAPP(c_COMBC(_1553131, tc_fun(_1553131, tc_HOL_Obool), tc_fun(_1553131, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553131, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1553131, tc_HOL_Obool), tc_fun(_1553131, tc_HOL_Obool)), _1553131), c_COMBS(_1553131, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553131, tc_HOL_Obool), tc_fun(_1553131, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1553131), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1553131), c_fconj)), hAPP(hAPP(c_COMBC(_1553131, tc_fun(_1553131, _1553131), tc_fun(_1553131, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553131, tc_HOL_Obool), tc_fun(tc_fun(_1553131, _1553131), tc_fun(_1553131, tc_HOL_Obool)), _1553131), c_COMBB(_1553131, tc_HOL_Obool, _1553131)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1553131), _1553135))))), hAPP(hAPP(c_COMBC(_1553131, tc_fun(_1553131, tc_HOL_Obool), tc_HOL_Obool), c_member(_1553131)), _1553133))))))], (46721 ^ _774244) ^ [_1699996, _1699998, _1700000, _1700002, _1700004] : [class_Groups_Ocomm__monoid__add(_1699996), hBOOL(hAPP(hAPP(c_member(_1699998), _1700000), hAPP(c_List_Oset(_1699998), _1700002))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1699996), hAPP(hAPP(c_List_Omap(_1699998, _1699996), _1700004), _1700002)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1699996), hAPP(_1700004, _1700000)), hAPP(c_List_Omonoid__add__class_Olistsum(_1699996), hAPP(hAPP(c_List_Omap(_1699998, _1699996), _1700004), c_List_Oremove1(_1699998, _1700000, _1700002)))))], (34399 ^ _774244) ^ [_1400746, _1400748, _1400750, _1400752, _1400754] : [-(c_Map_Orestrict__map(_1400746, _1400748, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1400746, tc_Option_Ooption(_1400748)), _1400750), _1400752), hAPP(c_Option_Ooption_OSome(_1400748), _1400754)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1400746, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1400746), _1400752), c_Orderings_Obot__class_Obot(tc_fun(_1400746, tc_HOL_Obool))))) = c_Map_Orestrict__map(_1400746, _1400748, _1400750, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1400746, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1400746), _1400752), c_Orderings_Obot__class_Obot(tc_fun(_1400746, tc_HOL_Obool))))))], (9196 ^ _774244) ^ [_925038, _925040, _925042, _925044] : [class_Rings_Ocomm__semiring(_925038), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925038), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925038), _925040), _925042)), _925044) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925038), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925038), _925040), _925044)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925038), _925042), _925044)))], (45958 ^ _774244) ^ [_1678134, _1678136, _1678138, _1678140, _1678142] : [-(hBOOL(hAPP(hAPP(c_member(_1678134), _1678136), hAPP(c_List_Oset(_1678134), _1678138)))), -(hAPP(c_Map_Omap__of(_1678134, _1678140, hAPP(hAPP(c_List_Ozip(_1678134, _1678140), _1678138), hAPP(hAPP(c_List_Omap(_1678134, _1678140), _1678142), _1678138))), _1678136) = c_Option_Ooption_ONone(_1678140))], (7050 ^ _774244) ^ [_888481, _888483, _888485] : [c_Com_Ocom_OWhile(_888481, _888483) = c_Com_Ocom_OBODY(_888485)], (21817 ^ _774244) ^ [_1149265, _1149267, _1149269, _1149271] : [class_Fields_Olinordered__field__inverse__zero(_1149265), class_Int_Onumber(_1149265), 21824 ^ _774244 : [(21825 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149265), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149265), _1149267), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269))), _1149271)), 21828 ^ _774244 : [(21835 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149265), c_Groups_Ozero__class_Ozero(_1149265)), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269)))), 21838 ^ _774244 : [(21845 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149265), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269)), c_Groups_Ozero__class_Ozero(_1149265)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149265), c_Groups_Ozero__class_Ozero(_1149265)), _1149271)))], (21839 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149265), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269)), c_Groups_Ozero__class_Ozero(_1149265))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149265), _1149271), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269))), _1149267)))]]], (21829 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149265), c_Groups_Ozero__class_Ozero(_1149265)), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149265), _1149267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149265), _1149271), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269)))))]]], (21851 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149265), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149265), _1149267), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269))), _1149271))), 21854 ^ _774244 : [(21857 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149265), _1149267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149265), _1149271), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269))))], (21855 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149265), c_Groups_Ozero__class_Ozero(_1149265)), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269))))]], 21858 ^ _774244 : [(21861 ^ _774244) ^ [] : [21862 ^ _774244 : [(21865 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149265), _1149271), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269))), _1149267))], (21863 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149265), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269)), c_Groups_Ozero__class_Ozero(_1149265))))]], 21866 ^ _774244 : [(21869 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149265), c_Groups_Ozero__class_Ozero(_1149265)), _1149271))], (21867 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149265), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269)), c_Groups_Ozero__class_Ozero(_1149265)))]]], (21859 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149265), c_Groups_Ozero__class_Ozero(_1149265)), hAPP(c_Int_Onumber__class_Onumber__of(_1149265), _1149269)))]]]]], (17735 ^ _774244) ^ [_1077840, _1077842] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077840))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077840)), _1077842) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1077842))], (1194 ^ _774244) ^ [_791893, _791895] : [-(class_Rings_Oidom(_791893)), _791895 = _791893, class_Rings_Oidom(_791895)], (33252 ^ _774244) ^ [_1376794, _1376796, _1376798, _1376800, _1376802, _1376804, _1376806] : [-(c_Nitpick_Ofold__graph_H(_1376794, _1376796, _1376798, _1376800, _1376802, hAPP(hAPP(_1376798, _1376804), _1376806))), 33253 ^ _774244 : [(33260 ^ _774244) ^ [_1377023, _1377025] : [hAPP(hAPP(_1376798, _1376804), _1376806) = hAPP(hAPP(_1376798, _1377025), _1377023), hBOOL(hAPP(hAPP(c_member(_1376794), _1377025), _1376802)), c_Nitpick_Ofold__graph_H(_1376794, _1376796, _1376798, _1376800, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1376794, tc_HOL_Obool)), _1376802), hAPP(hAPP(c_Set_Oinsert(_1376794), _1377025), c_Orderings_Obot__class_Obot(tc_fun(_1376794, tc_HOL_Obool)))), _1377023)], (33254 ^ _774244) ^ [] : [_1376802 = c_Orderings_Obot__class_Obot(tc_fun(_1376794, tc_HOL_Obool)), hAPP(hAPP(_1376798, _1376804), _1376806) = _1376800]]], (39243 ^ _774244) ^ [_1509620, _1509622, _1509624, _1509626] : [-(hAPP(_1509626, _1509622) = c_Option_Ooption_ONone(_1509624)), -(hBOOL(hAPP(hAPP(c_member(_1509620), _1509622), c_Map_Odom(_1509620, _1509624, _1509626))))], (6820 ^ _774244) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37283 ^ _774244) ^ [_1465970, _1465972, _1465974, _1465976, _1465978, _1465980, _1465982, _1465984, _1465986, _1465988] : [c_Equiv__Relations_Ocongruent2(_1465970, _1465972, _1465974, _1465976, _1465978, _1465980), hBOOL(hAPP(hAPP(c_member(tc_prod(_1465970, _1465970)), hAPP(hAPP(c_Product__Type_OPair(_1465970, _1465970), _1465982), _1465984)), _1465976)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1465972, _1465972)), hAPP(hAPP(c_Product__Type_OPair(_1465972, _1465972), _1465986), _1465988)), _1465978)), -(hAPP(hAPP(_1465980, _1465982), _1465986) = hAPP(hAPP(_1465980, _1465984), _1465988))], (40866 ^ _774244) ^ [_1549624] : [-(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)))), _1549624)) = 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), _1549624), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (22959 ^ _774244) ^ [_1171120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1171120)), 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), _1171120)) = 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), _1171120))))))], (41005 ^ _774244) ^ [_1554716, _1554718, _1554720] : [class_Lattices_Odistrib__lattice(_1554716), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554716), _1554718)), -(_1554718 = c_Orderings_Obot__class_Obot(tc_fun(_1554716, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1554716), _1554720), c_Big__Operators_Olattice__class_OInf__fin(_1554716, _1554718)) = c_Big__Operators_Olattice__class_OInf__fin(_1554716, hAPP(c_Set_OCollect(_1554716), hAPP(hAPP(c_COMBB(tc_fun(_1554716, tc_HOL_Obool), tc_HOL_Obool, _1554716), c_HOL_OEx(_1554716)), hAPP(hAPP(c_COMBC(_1554716, tc_fun(_1554716, tc_HOL_Obool), tc_fun(_1554716, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554716, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1554716, tc_HOL_Obool), tc_fun(_1554716, tc_HOL_Obool)), _1554716), c_COMBS(_1554716, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554716, tc_HOL_Obool), tc_fun(_1554716, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1554716), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1554716), c_fconj)), hAPP(hAPP(c_COMBC(_1554716, tc_fun(_1554716, _1554716), tc_fun(_1554716, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554716, tc_HOL_Obool), tc_fun(tc_fun(_1554716, _1554716), tc_fun(_1554716, tc_HOL_Obool)), _1554716), c_COMBB(_1554716, tc_HOL_Obool, _1554716)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1554716), _1554720))))), hAPP(hAPP(c_COMBC(_1554716, tc_fun(_1554716, tc_HOL_Obool), tc_HOL_Obool), c_member(_1554716)), _1554718))))))], (32530 ^ _774244) ^ [_1363897] : [class_Rings_Oring__1(_1363897), -(hBOOL(hAPP(hAPP(c_member(_1363897), c_Groups_Oone__class_Oone(_1363897)), c_Int_Oring__1__class_OInts(_1363897))))], (27504 ^ _774244) ^ [_1259222] : [c_Nat__Transfer_Onat__set(_1259222), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1259222) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259222)))], (28136 ^ _774244) ^ [_1271235, _1271237, _1271239, _1271241, _1271243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271235, tc_HOL_Obool)), _1271237), _1271239)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271235, tc_HOL_Obool)), _1271241), _1271243)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271235, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271235, tc_HOL_Obool)), _1271237), _1271241)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271235, tc_HOL_Obool)), _1271239), _1271243))))], (23111 ^ _774244) ^ [_1173615, _1173617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173617)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1173615, _1173617), c_Divides_OposDivAlg(_1173615, _1173617))))], (44727 ^ _774244) ^ [_1649262, _1649264] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1649262, tc_HOL_Obool), tc_HOL_Obool)), _1649264), hAPP(c_Set_OPow(_1649262), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649262, tc_HOL_Obool), _1649264)))))], (19773 ^ _774244) ^ [_1112277, _1112279, _1112281, _1112283] : [19775 ^ _774244 : [(19780 ^ _774244) ^ [] : [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(_1112281, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 19774 ^ [_1112277, _1112279, _1112281, _1112283]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1112281, 19774 ^ [_1112277, _1112279, _1112281, _1112283])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19778 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19774 ^ [_1112277, _1112279, _1112281, _1112283]), _1112279)))], (19776 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112277), 19774 ^ [_1112277, _1112279, _1112281, _1112283])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112277), _1112279)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1112281, _1112277)), _1112283)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1112283), hAPP(_1112281, _1112279))), 19794 ^ _774244 : [(19799 ^ _774244) ^ [] : [-(hAPP(_1112281, 19793 ^ [_1112277, _1112279, _1112281, _1112283]) = _1112283)], (19797 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 19793 ^ [_1112277, _1112279, _1112281, _1112283]), _1112279)))], (19795 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112277), 19793 ^ [_1112277, _1112279, _1112281, _1112283])))]]], (49942 ^ _774244) ^ [_1773591, _1773593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1773591), _1773593)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1773591, _1773593)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1773593), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (24813 ^ _774244) ^ [_1207557, _1207559] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1207557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1207559), _1207557))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1207557), _1207559)))], (19027 ^ _774244) ^ [_1098881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098881), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1098881)), c_Int_OPls)))], (23987 ^ _774244) ^ [_1190539, _1190541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1190539)), -(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(_1190539), _1190541))), _1190539)))], (19181 ^ _774244) ^ [_1101526] : [-(c_Int_Osucc(c_Int_OBit0(_1101526)) = c_Int_OBit1(_1101526))], (32536 ^ _774244) ^ [_1363992, _1363994] : [class_Rings_Oring__1(_1363992), hBOOL(hAPP(hAPP(c_member(_1363992), _1363994), c_Int_Oring__1__class_OInts(_1363992))), -(hBOOL(hAPP(hAPP(c_member(_1363992), hAPP(c_Groups_Ouminus__class_Ouminus(_1363992), _1363994)), c_Int_Oring__1__class_OInts(_1363992))))], (26209 ^ _774244) ^ [_1232012, _1232014, _1232016] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1232012), _1232014)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1232012), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1232014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232012), _1232016)))))], (43143 ^ _774244) ^ [_1608660, _1608662] : [-(c_Transitive__Closure_Otrancl(_1608660, c_Transitive__Closure_Ortrancl(_1608660, _1608662)) = c_Transitive__Closure_Ortrancl(_1608660, _1608662))], (45980 ^ _774244) ^ [_1678589, _1678591, _1678593, _1678595, _1678597, _1678599, _1678601, _1678603] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1678589, _1678591), _1678593), _1678595), hAPP(hAPP(c_List_Ozip(_1678589, _1678591), hAPP(hAPP(c_List_Omap(_1678597, _1678589), _1678599), _1678601)), _1678603)) = hAPP(hAPP(c_List_Omap(tc_prod(_1678597, _1678591), _1678593), hAPP(c_Product__Type_Oprod_Oprod__case(_1678597, _1678591, _1678593), hAPP(hAPP(c_COMBB(tc_fun(_1678591, tc_prod(_1678589, _1678591)), tc_fun(_1678591, _1678593), _1678597), hAPP(c_COMBB(tc_prod(_1678589, _1678591), _1678593, _1678591), _1678595)), hAPP(hAPP(c_COMBB(_1678589, tc_fun(_1678591, tc_prod(_1678589, _1678591)), _1678597), c_Product__Type_OPair(_1678589, _1678591)), _1678599)))), hAPP(hAPP(c_List_Ozip(_1678597, _1678591), _1678601), _1678603)))], (9026 ^ _774244) ^ [_922003, _922005, _922007] : [class_Groups_Ogroup__add(_922003), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922003), _922005), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922003), hAPP(c_Groups_Ouminus__class_Ouminus(_922003), _922005)), _922007)) = _922007)], (43407 ^ _774244) ^ [_1614665, _1614667] : [c_Wellfounded_Owf(_1614665, hAPP(c_Relation_Oconverse(_1614665, _1614665), _1614667)), -(c_Wellfounded_Owf(_1614665, hAPP(c_Relation_Oconverse(_1614665, _1614665), c_Transitive__Closure_Otrancl(_1614665, _1614667))))], (27656 ^ _774244) ^ [_1261868, _1261870, _1261872, _1261874] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261868, tc_HOL_Obool)), _1261870), _1261872), _1261874)), -(hBOOL(hAPP(_1261870, _1261874))), -(hBOOL(hAPP(_1261872, _1261874)))], (51289 ^ _774244) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (44223 ^ _774244) ^ [_1637317, _1637319, _1637321] : [44224 ^ _774244 : [(44225 ^ _774244) ^ [_1637393] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637317, _1637317)), _1637319), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1637317, _1637317), tc_HOL_Obool), _1637393), _1637321)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637317, _1637317)), _1637319), c_Transitive__Closure_Ortrancl(_1637317, _1637321))))], (16631 ^ _774244) ^ [_1057666, _1057668, _1057670, _1057672] : [class_Rings_Ocomm__semiring__1(_1057666), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057666), hAPP(hAPP(c_Power_Opower__class_Opower(_1057666), _1057668), _1057670)), hAPP(hAPP(c_Power_Opower__class_Opower(_1057666), _1057668), _1057672)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1057666), _1057668), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1057670), _1057672)))], (8536 ^ _774244) ^ [_913483, _913485, _913487] : [class_Rings_Ocomm__semiring__1(_913483), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913483), _913485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913483), _913487), _913485)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913483), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913483), _913487), c_Groups_Oone__class_Oone(_913483))), _913485))], (41288 ^ _774244) ^ [_1566403, _1566405, _1566407, _1566409, _1566411, _1566413, _1566415] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566403, _1566407)), hAPP(hAPP(c_Product__Type_OPair(_1566403, _1566407), _1566413), _1566415)), hAPP(hAPP(c_Relation_Orel__comp(_1566403, _1566405, _1566407), _1566409), _1566411))), -(c_Predicate_Opred__comp(_1566403, _1566405, _1566407, hAPP(hAPP(c_COMBC(_1566403, tc_fun(tc_prod(_1566403, _1566405), tc_HOL_Obool), tc_fun(_1566405, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566405, tc_fun(tc_fun(tc_prod(_1566403, _1566405), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1566403, _1566405), tc_HOL_Obool), tc_fun(_1566405, tc_HOL_Obool)), _1566403), c_COMBC(_1566405, tc_fun(tc_prod(_1566403, _1566405), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566405, tc_prod(_1566403, _1566405)), tc_fun(_1566405, tc_fun(tc_fun(tc_prod(_1566403, _1566405), tc_HOL_Obool), tc_HOL_Obool)), _1566403), hAPP(c_COMBB(tc_prod(_1566403, _1566405), tc_fun(tc_fun(tc_prod(_1566403, _1566405), tc_HOL_Obool), tc_HOL_Obool), _1566405), c_member(tc_prod(_1566403, _1566405)))), c_Product__Type_OPair(_1566403, _1566405)))), _1566409), hAPP(hAPP(c_COMBC(_1566405, tc_fun(tc_prod(_1566405, _1566407), tc_HOL_Obool), tc_fun(_1566407, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566407, tc_fun(tc_fun(tc_prod(_1566405, _1566407), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1566405, _1566407), tc_HOL_Obool), tc_fun(_1566407, tc_HOL_Obool)), _1566405), c_COMBC(_1566407, tc_fun(tc_prod(_1566405, _1566407), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566407, tc_prod(_1566405, _1566407)), tc_fun(_1566407, tc_fun(tc_fun(tc_prod(_1566405, _1566407), tc_HOL_Obool), tc_HOL_Obool)), _1566405), hAPP(c_COMBB(tc_prod(_1566405, _1566407), tc_fun(tc_fun(tc_prod(_1566405, _1566407), tc_HOL_Obool), tc_HOL_Obool), _1566407), c_member(tc_prod(_1566405, _1566407)))), c_Product__Type_OPair(_1566405, _1566407)))), _1566411), _1566413, _1566415))], (36523 ^ _774244) ^ [_1449294, _1449296, _1449298, _1449300] : [hBOOL(hAPP(hAPP(c_member(_1449294), _1449296), _1449298)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449294, tc_HOL_Obool)), _1449298), hAPP(hAPP(c_Set_Oinsert(_1449294), _1449296), _1449300)) = hAPP(hAPP(c_Set_Oinsert(_1449294), _1449296), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449294, tc_HOL_Obool)), _1449298), _1449300)))], (36789 ^ _774244) ^ [_1455536, _1455538, _1455540] : [class_Lattices_Oboolean__algebra(_1455536), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455536), _1455538), _1455540) = c_Orderings_Obot__class_Obot(_1455536), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1455536), _1455538), _1455540) = c_Orderings_Otop__class_Otop(_1455536), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1455536), _1455538) = _1455540)], (20579 ^ _774244) ^ [_1126389, _1126391, _1126393, _1126395] : [class_Fields_Olinordered__field__inverse__zero(_1126389), 20582 ^ _774244 : [(20583 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), _1126391), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126389), _1126393), _1126395))), 20586 ^ _774244 : [(20593 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), c_Groups_Ozero__class_Ozero(_1126389)), _1126395))), 20596 ^ _774244 : [(20603 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), _1126395), c_Groups_Ozero__class_Ozero(_1126389)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), _1126391), c_Groups_Ozero__class_Ozero(_1126389))))], (20597 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), _1126395), c_Groups_Ozero__class_Ozero(_1126389))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), _1126393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126389), _1126391), _1126395))))]]], (20587 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), c_Groups_Ozero__class_Ozero(_1126389)), _1126395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126389), _1126391), _1126395)), _1126393)))]]], (20609 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), _1126391), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126389), _1126393), _1126395)))), 20612 ^ _774244 : [(20615 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126389), _1126391), _1126395)), _1126393))], (20613 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), c_Groups_Ozero__class_Ozero(_1126389)), _1126395)))]], 20616 ^ _774244 : [(20619 ^ _774244) ^ [] : [20620 ^ _774244 : [(20623 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), _1126393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126389), _1126391), _1126395)))], (20621 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), _1126395), c_Groups_Ozero__class_Ozero(_1126389))))]], 20624 ^ _774244 : [(20627 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), _1126391), c_Groups_Ozero__class_Ozero(_1126389)))], (20625 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), _1126395), c_Groups_Ozero__class_Ozero(_1126389)))]]], (20617 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126389), c_Groups_Ozero__class_Ozero(_1126389)), _1126395))]]]]], (45898 ^ _774244) ^ [_1676907, _1676909, _1676911] : [hBOOL(hAPP(c_List_Odistinct(_1676907), _1676909)), -(hAPP(c_List_Oset(_1676907), c_List_Oremove1(_1676907, _1676911, _1676909)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1676907, tc_HOL_Obool)), hAPP(c_List_Oset(_1676907), _1676909)), hAPP(hAPP(c_Set_Oinsert(_1676907), _1676911), c_Orderings_Obot__class_Obot(tc_fun(_1676907, tc_HOL_Obool)))))], (36115 ^ _774244) ^ [_1439771, _1439773] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439771, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1439771, tc_HOL_Obool))), _1439773) = _1439773)], (43613 ^ _774244) ^ [_1621245, _1621247, _1621249] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1621247, _1621245)), _1621249)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1621245, _1621247)), hAPP(c_Relation_Oconverse(_1621247, _1621245), _1621249))))], (14416 ^ _774244) ^ [_1015711, _1015713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1015711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1015713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1015713), _1015711)), _1015713)))], (50290 ^ _774244) ^ [_1781439, _1781441] : [-(hAPP(c_List_Orev(_1781439), c_List_Oconcat(_1781439, _1781441)) = c_List_Oconcat(_1781439, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1781439), tc_List_Olist(_1781439)), c_List_Orev(_1781439)), hAPP(c_List_Orev(tc_List_Olist(_1781439)), _1781441))))], (48356 ^ _774244) ^ [_1739987, _1739989] : [_1739989 = c_List_Olist_ONil(_1739987), -(hAPP(c_List_Orotate1(_1739987), _1739989) = c_List_Olist_ONil(_1739987))], (43747 ^ _774244) ^ [_1625059, _1625061, _1625063, _1625065, _1625067] : [-(_1625059 = c_Orderings_Obot__class_Obot(tc_fun(_1625061, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1625063, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625061, tc_fun(_1625063, tc_HOL_Obool)), _1625059), _1625065)), _1625067) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625061, tc_fun(_1625063, tc_HOL_Obool)), _1625059), hAPP(hAPP(c_COMBC(_1625061, tc_fun(_1625063, tc_HOL_Obool), tc_fun(_1625063, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1625063, tc_HOL_Obool), tc_fun(tc_fun(_1625063, tc_HOL_Obool), tc_fun(_1625063, tc_HOL_Obool)), _1625061), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1625063, tc_HOL_Obool))), _1625065)), _1625067)))], (44295 ^ _774244) ^ [_1639211, _1639213] : [-(hAPP(hAPP(c_Nat_Ocompow(_1639211, _1639211), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1639213) = c_Fun_Oid(_1639211))], (24709 ^ _774244) ^ [_1205029, _1205031, _1205033] : [-(c_HOL_OThe(tc_prod(_1205029, _1205031), hAPP(c_Product__Type_Oprod_Oprod__case(_1205029, _1205031, tc_HOL_Obool), _1205033)) = c_HOL_OThe(tc_prod(_1205029, _1205031), hAPP(hAPP(c_COMBS(tc_prod(_1205029, _1205031), _1205031, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1205029, tc_fun(_1205031, tc_HOL_Obool), tc_prod(_1205029, _1205031)), _1205033), c_Product__Type_Ofst(_1205029, _1205031))), c_Product__Type_Osnd(_1205029, _1205031))))], (1034 ^ _774244) ^ [_789893, _789895] : [-(class_Groups_Oordered__ab__group__add(_789893)), _789895 = _789893, class_Groups_Oordered__ab__group__add(_789895)], (19737 ^ _774244) ^ [_1111668, _1111670] : [class_Fields_Olinordered__field__inverse__zero(_1111668), class_Int_Onumber__ring(_1111668), 19744 ^ _774244 : [(19751 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111668), c_Groups_Ozero__class_Ozero(_1111668)), _1111670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111668), c_Groups_Ozero__class_Ozero(_1111668)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111668), _1111670), hAPP(c_Int_Onumber__class_Onumber__of(_1111668), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (19745 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111668), c_Groups_Ozero__class_Ozero(_1111668)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111668), _1111670), hAPP(c_Int_Onumber__class_Onumber__of(_1111668), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111668), c_Groups_Ozero__class_Ozero(_1111668)), _1111670)))]]], (29330 ^ _774244) ^ [_1296086, _1296088, _1296090, _1296092] : [_1296086 = c_Orderings_Obot__class_Obot(tc_fun(_1296088, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1296088, _1296090, hAPP(c_COMBK(_1296090, _1296088), _1296092)), _1296086) = c_Orderings_Obot__class_Obot(tc_fun(_1296090, tc_HOL_Obool)))], (29730 ^ _774244) ^ [_1303740, _1303742, _1303744] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1303740), _1303742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1303740), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1303740, tc_HOL_Obool)), _1303742), hAPP(hAPP(c_Set_Oinsert(_1303740), _1303744), c_Orderings_Obot__class_Obot(tc_fun(_1303740, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1303740), _1303742))))], (39082 ^ _774244) ^ [_1506079, _1506081, _1506083, _1506085, _1506087, _1506089, _1506091] : [class_Groups_Oab__semigroup__mult(_1506079), hBOOL(hAPP(c_Finite__Set_Ofinite(_1506081), _1506083)), c_Fun_Oinj__on(_1506081, _1506085, _1506087, _1506083), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1506079, _1506085, c_Groups_Otimes__class_Otimes(_1506079)), _1506089), _1506091), hAPP(c_Set_Oimage(_1506081, _1506085, _1506087), _1506083)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1506079, _1506081, c_Groups_Otimes__class_Otimes(_1506079)), hAPP(c_Fun_Ocomp(_1506085, _1506079, _1506081, _1506089), _1506087)), _1506091), _1506083))], (44001 ^ _774244) ^ [_1632097, _1632099, _1632101, _1632103, _1632105] : [44003 ^ _774244 : [(44006 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1632103, 44002 ^ [_1632097, _1632099, _1632101, _1632103, _1632105]), _1632105))], (44004 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1632097), 44002 ^ [_1632097, _1632099, _1632101, _1632103, _1632105]), _1632101)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632097, tc_fun(_1632099, tc_HOL_Obool)), _1632101), _1632103), _1632105)))], (35221 ^ _774244) ^ [_1419743, _1419745, _1419747, _1419749] : [c_Finite__Set_Ofun__left__comm__idem(_1419743, _1419745, _1419747), -(hAPP(c_Fun_Ocomp(_1419745, _1419745, _1419745, hAPP(_1419747, _1419749)), hAPP(_1419747, _1419749)) = hAPP(_1419747, _1419749))], (10698 ^ _774244) ^ [_950194, _950196, _950198] : [class_Orderings_Opreorder(_950194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950194), _950196), _950198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950194), _950196), _950198)))], (29116 ^ _774244) ^ [_1292571, _1292573, _1292575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1292571, tc_HOL_Obool)), _1292573), hAPP(hAPP(c_Set_Oinsert(_1292571), _1292575), c_Orderings_Obot__class_Obot(tc_fun(_1292571, tc_HOL_Obool))))), -(_1292573 = c_Orderings_Obot__class_Obot(tc_fun(_1292571, tc_HOL_Obool))), -(_1292573 = hAPP(hAPP(c_Set_Oinsert(_1292571), _1292575), c_Orderings_Obot__class_Obot(tc_fun(_1292571, tc_HOL_Obool))))], (5254 ^ _774244) ^ [_855499, _855501] : [_855501 = _855499, -(c_List_Oembed__list(_855501) = c_List_Oembed__list(_855499))], (48138 ^ _774244) ^ [_1733768, _1733770, _1733772] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733768), tc_List_Olist(_1733768))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733768), tc_List_Olist(_1733768)), _1733770), c_List_Olist_ONil(_1733768))), c_List_Olistrel1(_1733768, _1733772)))], (24955 ^ _774244) ^ [_1209951, _1209953, _1209955] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209951), _1209953)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209953), _1209951))), _1209953 = _1209955, 24966 ^ _774244 : [(24969 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209955), _1209951))], (24967 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209951), _1209955)))]]], (43635 ^ _774244) ^ [_1621726, _1621728, _1621730, _1621732, _1621734, _1621736] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621726, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1621728, _1621726, _1621730), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1621732, tc_fun(_1621728, tc_HOL_Obool)), _1621734), _1621736))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1621732, tc_fun(_1621726, tc_HOL_Obool)), _1621734), hAPP(hAPP(c_COMBB(tc_fun(_1621728, tc_HOL_Obool), tc_fun(_1621726, tc_HOL_Obool), _1621732), c_Relation_OImage(_1621728, _1621726, _1621730)), _1621736)))))], (24729 ^ _774244) ^ [_1205853, _1205855, _1205857] : [-(c_Random__Sequence_Oempty(_1205853, _1205855, _1205857) = 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(_1205853)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1205853)))], (43668 ^ _774244) ^ [_1622550, _1622552, _1622554, _1622556, _1622558, _1622560] : [hBOOL(hAPP(hAPP(c_member(_1622550), _1622552), _1622554)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622550, tc_fun(_1622556, tc_HOL_Obool)), _1622554), hAPP(hAPP(c_COMBB(tc_fun(_1622556, tc_HOL_Obool), tc_fun(_1622556, tc_HOL_Obool), _1622550), hAPP(c_Set_Oinsert(_1622556), _1622558)), _1622560)) = hAPP(hAPP(c_Set_Oinsert(_1622556), _1622558), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622550, tc_fun(_1622556, tc_HOL_Obool)), _1622554), _1622560)))], (20341 ^ _774244) ^ [_1122322, _1122324, _1122326, _1122328] : [class_Rings_Odivision__ring(_1122322), -(_1122324 = c_Groups_Ozero__class_Ozero(_1122322)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122322), _1122326), _1122324) = _1122328, -(_1122326 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122322), _1122328), _1122324))], (8636 ^ _774244) ^ [_915265, _915267] : [class_Groups_Omonoid__mult(_915265), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915265), c_Groups_Oone__class_Oone(_915265)), _915267) = _915267)], (48088 ^ _774244) ^ [_1732254, _1732256, _1732258, _1732260] : [hBOOL(hAPP(hAPP(c_member(_1732254), _1732256), c_Wellfounded_Oacc(_1732254, _1732258))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1732254)), _1732260), c_Wellfounded_Oacc(tc_List_Olist(_1732254), c_List_Olistrel1(_1732254, _1732258)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1732254)), hAPP(hAPP(c_List_Olist_OCons(_1732254), _1732256), _1732260)), c_Wellfounded_Oacc(tc_List_Olist(_1732254), c_List_Olistrel1(_1732254, _1732258)))))], (30025 ^ _774244) ^ [_1309123] : [class_Lattices_Oab__semigroup__idem__mult(_1309123), -(c_Finite__Set_Ofun__left__comm__idem(_1309123, _1309123, c_Groups_Otimes__class_Otimes(_1309123)))], (31203 ^ _774244) ^ [_1334609, _1334611, _1334613, _1334615, _1334617, _1334619] : [-(hBOOL(hAPP(hAPP(c_member(_1334609), _1334611), c_SetInterval_Oord_OgreaterThanAtMost(_1334609, _1334613, _1334615, _1334617, _1334619)))), hBOOL(hAPP(hAPP(_1334615, _1334617), _1334611)), hBOOL(hAPP(hAPP(_1334613, _1334611), _1334619))], (50542 ^ _774244) ^ [_1788263, _1788265, _1788267, _1788269] : [hBOOL(hAPP(hAPP(c_member(_1788263), _1788265), hAPP(c_List_Oset(_1788263), c_List_OtakeWhile(_1788263, _1788267, _1788269)))), 50545 ^ _774244 : [(50548 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1788267, _1788265)))], (50546 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1788263), _1788265), hAPP(c_List_Oset(_1788263), _1788269))))]]], (14312 ^ _774244) ^ [_1014000, _1014002] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1014000, _1014002)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1014000), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1014002)))], (40610 ^ _774244) ^ [_1541762, _1541764] : [hAPP(c_Set_OCollect(_1541762), _1541764) = c_Orderings_Obot__class_Obot(tc_fun(_1541762, tc_HOL_Obool)), 40613 ^ _774244 : [(40614 ^ _774244) ^ [_1541847] : [hBOOL(hAPP(_1541764, _1541847))]]], (5588 ^ _774244) ^ [_860494, _860496] : [_860496 = _860494, -(c_Com_Ocom_OBODY(_860496) = c_Com_Ocom_OBODY(_860494))], (36087 ^ _774244) ^ [_1439349, _1439351] : [class_Lattices_Obounded__lattice__top(_1439349), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1439349), _1439351), c_Orderings_Otop__class_Otop(_1439349)) = _1439351)], (32456 ^ _774244) ^ [_1362551, _1362553] : [class_Rings_Olinordered__idom(_1362551), hBOOL(hAPP(hAPP(c_member(_1362551), _1362553), c_Int_Oring__1__class_OInts(_1362551))), 32463 ^ _774244 : [(32470 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362551), _1362553), c_Groups_Ozero__class_Ozero(_1362551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362551), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362551), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362551), c_Groups_Oone__class_Oone(_1362551)), _1362553)), _1362553)), c_Groups_Ozero__class_Ozero(_1362551))))], (32464 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362551), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362551), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362551), c_Groups_Oone__class_Oone(_1362551)), _1362553)), _1362553)), c_Groups_Ozero__class_Ozero(_1362551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362551), _1362553), c_Groups_Ozero__class_Ozero(_1362551))))]]], (50745 ^ _774244) ^ [_1792039, _1792041, _1792043] : [-(c_List_Oremdups(_1792039, hAPP(c_List_Ofilter(_1792039, _1792041), _1792043)) = hAPP(c_List_Ofilter(_1792039, _1792041), c_List_Oremdups(_1792039, _1792043)))], (13762 ^ _774244) ^ [_1003761, _1003763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003761)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1003761), _1003763)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1003761, _1003763) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1003761), _1003763))], (49210 ^ _774244) ^ [_1758692, _1758694, _1758696] : [-(_1758692 = c_List_Olist_ONil(_1758694)), -(c_List_Obutlast(_1758694, hAPP(hAPP(c_List_Olist_OCons(_1758694), _1758696), _1758692)) = hAPP(hAPP(c_List_Olist_OCons(_1758694), _1758696), c_List_Obutlast(_1758694, _1758692)))], (36511 ^ _774244) ^ [_1449035, _1449037, _1449039, _1449041] : [hBOOL(hAPP(hAPP(c_member(_1449035), _1449037), _1449039)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449035, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1449035), _1449037), _1449041)), _1449039) = hAPP(hAPP(c_Set_Oinsert(_1449035), _1449037), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449035, tc_HOL_Obool)), _1449041), _1449039)))], (9842 ^ _774244) ^ [_936425, _936427, _936429] : [class_Rings_Olinordered__ring(_936425), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936425), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936425), _936427), _936427)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936425), _936429), _936429))), c_Groups_Ozero__class_Ozero(_936425)))], (43179 ^ _774244) ^ [_1609506, _1609508, _1609510, _1609512] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609506, _1609506)), hAPP(hAPP(c_Product__Type_OPair(_1609506, _1609506), _1609508), _1609510)), c_Transitive__Closure_Ortrancl(_1609506, _1609512))), -(_1609508 = _1609510), 43186 ^ _774244 : [(43189 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609506, _1609506)), hAPP(hAPP(c_Product__Type_OPair(_1609506, _1609506), _1609508), _1609510)), c_Transitive__Closure_Otrancl(_1609506, _1609512))))], (43187 ^ _774244) ^ [] : [_1609508 = _1609510]]], (39936 ^ _774244) ^ [_1528265, _1528267, _1528269, _1528271, _1528273, _1528275, _1528277, _1528279, _1528281, _1528283] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1528265, _1528267), tc_prod(_1528269, _1528271), tc_prod(_1528273, _1528275), c_Product__Type_Omap__pair(_1528265, _1528269, _1528267, _1528271, _1528277, _1528279)), c_Product__Type_Omap__pair(_1528273, _1528265, _1528275, _1528267, _1528281, _1528283)) = c_Product__Type_Omap__pair(_1528273, _1528269, _1528275, _1528271, hAPP(c_Fun_Ocomp(_1528265, _1528269, _1528273, _1528277), _1528281), hAPP(c_Fun_Ocomp(_1528267, _1528271, _1528275, _1528279), _1528283)))], (21149 ^ _774244) ^ [] : [-(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))], (3286 ^ _774244) ^ [_824729, _824731] : [_824731 = _824729, -(c_Nat_Osemiring__1__class_ONats(_824731) = c_Nat_Osemiring__1__class_ONats(_824729))], (44078 ^ _774244) ^ [_1633890, _1633892, _1633894, _1633896, _1633898, _1633900, _1633902, _1633904] : [c_Fun_Oinj__on(_1633890, _1633892, _1633894, _1633896), 44084 ^ _774244 : [(44087 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1633890, tc_HOL_Obool)), hAPP(_1633902, 44083 ^ [_1633890, _1633892, _1633894, _1633896, _1633898, _1633900, _1633902, _1633904])), _1633896))], (44085 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633898), 44083 ^ [_1633890, _1633892, _1633894, _1633896, _1633898, _1633900, _1633902, _1633904]), _1633900)))]], hBOOL(hAPP(hAPP(c_member(_1633898), _1633904), _1633900)), -(hAPP(c_Set_Oimage(_1633890, _1633892, _1633894), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633898, tc_fun(_1633890, tc_HOL_Obool)), _1633900), _1633902)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633898, tc_fun(_1633892, tc_HOL_Obool)), _1633900), hAPP(hAPP(c_COMBB(tc_fun(_1633890, tc_HOL_Obool), tc_fun(_1633892, tc_HOL_Obool), _1633898), c_Set_Oimage(_1633890, _1633892, _1633894)), _1633902)))], (27888 ^ _774244) ^ [_1266805, _1266807, _1266809] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266805, tc_HOL_Obool)), _1266807), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266805, tc_HOL_Obool)), _1266809), _1266807)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266805, tc_HOL_Obool)), _1266807), _1266809))], (29384 ^ _774244) ^ [_1297165, _1297167] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297165), _1297167))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297165, _1297167) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (50591 ^ _774244) ^ [_1789222, _1789224, _1789226, _1789228] : [hBOOL(hAPP(_1789222, _1789224)), -(c_List_OtakeWhile(_1789226, _1789222, hAPP(hAPP(c_List_Olist_OCons(_1789226), _1789224), _1789228)) = hAPP(hAPP(c_List_Olist_OCons(_1789226), _1789224), c_List_OtakeWhile(_1789226, _1789222, _1789228)))], (47971 ^ _774244) ^ [_1729222, _1729224, _1729226, _1729228, _1729230] : [-(c_Map_Odom(_1729222, _1729224, c_Map_Omap__upds(_1729222, _1729224, _1729226, _1729228, _1729230)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1729222, tc_HOL_Obool)), hAPP(c_List_Oset(_1729222), hAPP(hAPP(c_List_Otake(_1729222), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729224)), _1729230)), _1729228))), c_Map_Odom(_1729222, _1729224, _1729226)))], (44832 ^ _774244) ^ [_1651387, _1651389, _1651391] : [44834 ^ _774244 : [(44837 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1651387, tc_HOL_Obool)), 44833 ^ [_1651387, _1651389, _1651391]), _1651391))], (44835 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1651387, tc_HOL_Obool)), 44833 ^ [_1651387, _1651389, _1651391]), _1651389)))]], -(_1651389 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1651387, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1651387, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1651387, tc_HOL_Obool), _1651389)), _1651391)))], (16803 ^ _774244) ^ [_1061269, _1061271] : [class_Groups_Oabs__if(_1061269), 16806 ^ _774244 : [(16813 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061269), _1061271), c_Groups_Ozero__class_Ozero(_1061269)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1061269), _1061271) = _1061271)], (16807 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061269), _1061271), c_Groups_Ozero__class_Ozero(_1061269))), -(hAPP(c_Groups_Oabs__class_Oabs(_1061269), _1061271) = hAPP(c_Groups_Ouminus__class_Ouminus(_1061269), _1061271))]]], (33800 ^ _774244) ^ [_1387982, _1387984, _1387986, _1387988, _1387990, _1387992] : [hBOOL(hAPP(hAPP(c_member(_1387982), _1387984), _1387986)), -(hAPP(c_Set_Oimage(_1387982, _1387988, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1387982, _1387988), _1387990), _1387984), _1387992)), _1387986) = hAPP(hAPP(c_Set_Oinsert(_1387988), _1387992), hAPP(c_Set_Oimage(_1387982, _1387988, _1387990), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1387982, tc_HOL_Obool)), _1387986), hAPP(hAPP(c_Set_Oinsert(_1387982), _1387984), c_Orderings_Obot__class_Obot(tc_fun(_1387982, tc_HOL_Obool)))))))], (22122 ^ _774244) ^ [_1154483, _1154485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154483), 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)), _1154485)), -(c_Divides_OnegDivAlg(_1154483, _1154485) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1154483), _1154485)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1154483, _1154485)))], (47620 ^ _774244) ^ [_1720950, _1720952, _1720954, _1720956] : [hAPP(hAPP(c_List_Oappend(_1720950), _1720952), _1720954) = hAPP(hAPP(c_List_Oappend(_1720950), _1720956), _1720954), -(_1720952 = _1720956)], (6466 ^ _774244) ^ [_878405, _878407, _878409] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878405), _878407) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878409), _878407), -(_878405 = _878409)], (4818 ^ _774244) ^ [_848723, _848725, _848727, _848729, _848731, _848733] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_848733, _848729, _848725) = c_SetInterval_Oord__class_OatLeastAtMost(_848731, _848727, _848723)), _848733 = _848731, _848729 = _848727, _848725 = _848723], (44058 ^ _774244) ^ [_1633389, _1633391, _1633393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1633389, _1633389), tc_HOL_Obool)), c_Relation_OId(_1633389)), _1633391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1633389, _1633389), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1633389, _1633389, _1633389), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1633389, _1633389), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1633389, _1633393)), _1633391)), _1633393)), _1633391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1633389, _1633389), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1633389, _1633393)), _1633391)))], (49357 ^ _774244) ^ [_1761744, _1761746, _1761748, _1761750] : [-(hBOOL(hAPP(_1761744, _1761746))), -(c_List_Oremove1(_1761748, _1761746, hAPP(c_List_Ofilter(_1761748, _1761744), _1761750)) = hAPP(c_List_Ofilter(_1761748, _1761744), _1761750))], (28715 ^ _774244) ^ [_1284048, _1284050, _1284052, _1284054] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284048, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1284048), _1284050), _1284052)), _1284054) = hAPP(hAPP(c_Set_Oinsert(_1284048), _1284050), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284048, tc_HOL_Obool)), _1284052), _1284054)))], (14296 ^ _774244) ^ [_1013670, _1013672] : [14297 ^ _774244 : [(14298 ^ _774244) ^ [_1013719] : [_1013670 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013672), _1013719)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1013670, _1013672) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11234 ^ _774244) ^ [_959004, _959006, _959008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959004), _959006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959004), _959008)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959006), _959008))))], (45627 ^ _774244) ^ [_1670664, _1670666, _1670668, _1670670, _1670672, _1670674] : [-(hAPP(hAPP(c_Option_Omap(_1670664, _1670666), _1670668), hAPP(hAPP(c_Option_Omap(_1670670, _1670664), _1670672), _1670674)) = hAPP(hAPP(c_Option_Omap(_1670670, _1670666), hAPP(c_Fun_Ocomp(_1670664, _1670666, _1670670, _1670668), _1670672)), _1670674))], (44338 ^ _774244) ^ [_1640220, _1640222, _1640224] : [44340 ^ _774244 : [(44341 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1640220), 44339 ^ [_1640220, _1640222, _1640224]), _1640222)))], (44346 ^ _774244) ^ [] : [44339 ^ [_1640220, _1640222, _1640224] = 44342 ^ [_1640220, _1640222, _1640224]], (44350 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1640220, _1640220)), hAPP(hAPP(c_Product__Type_OPair(_1640220, _1640220), 44342 ^ [_1640220, _1640222, _1640224]), 44339 ^ [_1640220, _1640222, _1640224])), _1640224))], (44348 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1640220, _1640220)), hAPP(hAPP(c_Product__Type_OPair(_1640220, _1640220), 44339 ^ [_1640220, _1640222, _1640224]), 44342 ^ [_1640220, _1640222, _1640224])), _1640224))], (44344 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1640220), 44342 ^ [_1640220, _1640222, _1640224]), _1640222)))]], -(c_Relation_Ototal__on(_1640220, _1640222, _1640224))], (2836 ^ _774244) ^ [_817380, _817382, _817384, _817386, _817388, _817390] : [-(c_Nitpick_Oplus__frac(_817390, _817386, _817382) = c_Nitpick_Oplus__frac(_817388, _817384, _817380)), _817390 = _817388, _817386 = _817384, _817382 = _817380], (34600 ^ _774244) ^ [_1405087, _1405089, _1405091, _1405093] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1405087, tc_HOL_Obool), tc_fun(_1405087, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1405087, tc_HOL_Obool), tc_fun(_1405087, tc_HOL_Obool)), _1405091), _1405093)), c_Wellfounded_Omax__ext(_1405087, _1405089))), -(c_Wellfounded_Omax__extp(_1405087, hAPP(hAPP(c_COMBC(_1405087, tc_fun(tc_prod(_1405087, _1405087), tc_HOL_Obool), tc_fun(_1405087, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405087, tc_fun(tc_fun(tc_prod(_1405087, _1405087), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1405087, _1405087), tc_HOL_Obool), tc_fun(_1405087, tc_HOL_Obool)), _1405087), c_COMBC(_1405087, tc_fun(tc_prod(_1405087, _1405087), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405087, tc_prod(_1405087, _1405087)), tc_fun(_1405087, tc_fun(tc_fun(tc_prod(_1405087, _1405087), tc_HOL_Obool), tc_HOL_Obool)), _1405087), hAPP(c_COMBB(tc_prod(_1405087, _1405087), tc_fun(tc_fun(tc_prod(_1405087, _1405087), tc_HOL_Obool), tc_HOL_Obool), _1405087), c_member(tc_prod(_1405087, _1405087)))), c_Product__Type_OPair(_1405087, _1405087)))), _1405089), _1405091, _1405093))], (25753 ^ _774244) ^ [_1223669, _1223671, _1223673] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223669), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223671), _1223673))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223669), _1223673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223673), _1223671)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223669), _1223671)))], (48292 ^ _774244) ^ [_1738474, _1738476, _1738478, _1738480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738474), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738476)), _1738478))), -(hAPP(hAPP(c_List_Olist__update(_1738476, _1738478), _1738474), _1738480) = hAPP(hAPP(c_List_Oappend(_1738476), hAPP(hAPP(c_List_Otake(_1738476), _1738474), _1738478)), hAPP(hAPP(c_List_Olist_OCons(_1738476), _1738480), hAPP(hAPP(c_List_Odrop(_1738476), hAPP(c_Nat_OSuc, _1738474)), _1738478))))], (13565 ^ _774244) ^ [_1000386, _1000388, _1000390] : [class_Divides_Oring__div(_1000386), -(c_Divides_Odiv__class_Omod(_1000386, hAPP(c_Groups_Ouminus__class_Ouminus(_1000386), _1000388), _1000390) = c_Divides_Odiv__class_Omod(_1000386, hAPP(c_Groups_Ouminus__class_Ouminus(_1000386), c_Divides_Odiv__class_Omod(_1000386, _1000388, _1000390)), _1000390))], (11965 ^ _774244) ^ [_972048, _972050, _972052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972048), _972050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _972052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972052), _972048)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972052), _972050))))], (15002 ^ _774244) ^ [_1026314, _1026316, _1026318, _1026320, _1026322] : [class_Groups_Ominus(_1026314), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026316, _1026314)), _1026318), _1026320), _1026322) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1026314), hAPP(_1026318, _1026322)), hAPP(_1026320, _1026322)))], (4024 ^ _774244) ^ [_836280, _836282] : [_836282 = _836280, -(c_Smallcheck_Osmall__class_Osmall(_836282) = c_Smallcheck_Osmall__class_Osmall(_836280))], (16050 ^ _774244) ^ [_1046966, _1046968, _1046970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1046966)), 16056 ^ _774244 : [(16059 ^ _774244) ^ [] : [hBOOL(hAPP(_1046968, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 16055 ^ [_1046966, _1046968, _1046970]), _1046966)))], (16057 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1046968, 16055 ^ [_1046966, _1046968, _1046970])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1046970)), 16064 ^ _774244 : [(16065 ^ _774244) ^ [_1047255] : [hBOOL(hAPP(_1046968, _1047255)), -(hBOOL(hAPP(_1046968, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1047255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046970), _1046966)))))]]], (48678 ^ _774244) ^ [_1746976, _1746978, _1746980] : [-(hAPP(c_List_Orotate(_1746976, _1746978), _1746980) = hAPP(hAPP(c_List_Oappend(_1746976), hAPP(hAPP(c_List_Odrop(_1746976), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1746978, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746976)), _1746980))), _1746980)), hAPP(hAPP(c_List_Otake(_1746976), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1746978, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746976)), _1746980))), _1746980)))], (1204 ^ _774244) ^ [_792018, _792020] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_792018)), _792020 = _792018, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_792020)], (28372 ^ _774244) ^ [_1276041, _1276043, _1276045] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1276041, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1276043)), _1276045) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276041, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1276041, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1276043)), _1276045)), hAPP(_1276045, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (15214 ^ _774244) ^ [_1030086, _1030088, _1030090] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030086), _1030088)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030086), _1030090)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030088), _1030090))], (18419 ^ _774244) ^ [_1088549, _1088551] : [class_Int_Onumber__ring(_1088549), 18422 ^ _774244 : [(18429 ^ _774244) ^ [] : [c_Int_Oiszero(_1088549, hAPP(c_Int_Onumber__class_Onumber__of(_1088549), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088551), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1088549), _1088551) = c_Groups_Oone__class_Oone(_1088549))], (18423 ^ _774244) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1088549), _1088551) = c_Groups_Oone__class_Oone(_1088549), -(c_Int_Oiszero(_1088549, hAPP(c_Int_Onumber__class_Onumber__of(_1088549), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088551), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (36047 ^ _774244) ^ [_1438500, _1438502, _1438504] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438500, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438500, tc_HOL_Obool)), _1438502), _1438504)), _1438504)))], (49388 ^ _774244) ^ [_1762305, _1762307] : [-(hAPP(c_List_Ofilter(_1762305, _1762307), c_List_Olist_ONil(_1762305)) = c_List_Olist_ONil(_1762305))], (41480 ^ _774244) ^ [_1570485, _1570487, _1570489] : [c_Wellfounded_Owf(_1570485, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570485, _1570485), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570485, _1570485), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1570485, _1570485, _1570485), _1570487), _1570487)), hAPP(hAPP(c_Relation_Orel__comp(_1570485, _1570485, _1570485), _1570489), _1570487))), _1570489)), -(c_Wellfounded_Owf(_1570485, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570485, _1570485), tc_HOL_Obool)), _1570487), _1570489)))], (51445 ^ _774244) ^ [] : [hBOOL(c_fFalse)], (49250 ^ _774244) ^ [_1759497, _1759499] : [-(c_List_Obutlast(_1759497, _1759499) = hAPP(hAPP(c_List_Otake(_1759497), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759497)), _1759499)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1759499))], (19857 ^ _774244) ^ [_1114110, _1114112, _1114114] : [class_Rings_Odivision__ring(_1114110), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1114110), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114110), _1114112), _1114114)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114110), hAPP(c_Groups_Ouminus__class_Ouminus(_1114110), _1114112)), _1114114))], (24587 ^ _774244) ^ [_1202349, _1202351, _1202353, _1202355, _1202357, _1202359] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1202349, _1202351, _1202353), _1202355), hAPP(hAPP(c_Product__Type_OPair(_1202349, _1202351), _1202357), _1202359)) = hAPP(hAPP(_1202355, _1202357), _1202359))], (39594 ^ _774244) ^ [_1518334, _1518336, _1518338, _1518340] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1518334, _1518336)), hAPP(hAPP(c_Product__Type_OSigma(_1518334, _1518336), _1518338), hAPP(c_COMBK(tc_fun(_1518336, tc_HOL_Obool), _1518334), _1518340))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1518334), _1518338)), hAPP(c_Finite__Set_Ocard(_1518336), _1518340)))], (40625 ^ _774244) ^ [_1542000, _1542002, _1542004] : [hBOOL(hAPP(hAPP(c_member(_1542000), _1542002), hAPP(c_Set_OCollect(_1542000), _1542004))), -(hBOOL(hAPP(_1542004, _1542002)))], (29328 ^ _774244) ^ [] : [-(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)))], (32756 ^ _774244) ^ [_1367986, _1367988] : [class_Lattices_Olattice(_1367986), -(c_Big__Operators_Olattice__class_OSup__fin(_1367986, hAPP(hAPP(c_Set_Oinsert(_1367986), _1367988), c_Orderings_Obot__class_Obot(tc_fun(_1367986, tc_HOL_Obool)))) = _1367988)], (34580 ^ _774244) ^ [_1404252, _1404254, _1404256, _1404258, _1404260, _1404262] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1404252, tc_HOL_Obool), tc_fun(_1404252, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1404252, tc_HOL_Obool), tc_fun(_1404252, tc_HOL_Obool)), _1404254), _1404256)), c_Wellfounded_Omax__ext(_1404252, _1404258))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1404252, tc_HOL_Obool), tc_fun(_1404252, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1404252, tc_HOL_Obool), tc_fun(_1404252, tc_HOL_Obool)), _1404260), _1404262)), c_Wellfounded_Omax__ext(_1404252, _1404258))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1404252, tc_HOL_Obool), tc_fun(_1404252, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1404252, tc_HOL_Obool), tc_fun(_1404252, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404252, tc_HOL_Obool)), _1404254), _1404260)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404252, tc_HOL_Obool)), _1404256), _1404262))), c_Wellfounded_Omax__ext(_1404252, _1404258))))], (10161 ^ _774244) ^ [_941700, _941702, _941704] : [class_Orderings_Olinorder(_941700), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941700), _941702), _941704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941700), _941704), _941702)))], (45984 ^ _774244) ^ [_1678913, _1678915, _1678917, _1678919, _1678921, _1678923] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1678913, _1678915)), hAPP(hAPP(c_Product__Type_OPair(_1678913, _1678915), _1678917), _1678919)), hAPP(c_List_Oset(tc_prod(_1678913, _1678915)), hAPP(hAPP(c_List_Ozip(_1678913, _1678915), _1678921), _1678923)))), 45987 ^ _774244 : [(45990 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678915), _1678919), hAPP(c_List_Oset(_1678915), _1678923))))], (45988 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678913), _1678917), hAPP(c_List_Oset(_1678913), _1678921))))]]], (7688 ^ _774244) ^ [_899633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _899633)), -(_899633 = hAPP(c_Nat_OSuc, 7691 ^ [_899633]))], (29378 ^ _774244) ^ [_1297073, _1297075] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297073, _1297075) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297073), _1297075))], (49517 ^ _774244) ^ [_1766231, _1766233, _1766235] : [-(c_List_Osublist(_1766231, _1766233, _1766235) = hAPP(hAPP(c_List_Omap(tc_prod(_1766231, tc_Nat_Onat), _1766231), c_Product__Type_Ofst(_1766231, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1766231, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1766231, 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(_1766231, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1766231, tc_Nat_Onat))), _1766235)), hAPP(hAPP(c_List_Ozip(_1766231, tc_Nat_Onat), _1766233), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766231)), _1766233))))))], (38614 ^ _774244) ^ [_1495381, _1495383, _1495385, _1495387, _1495389, _1495391, _1495393, _1495395] : [c_Finite__Set_Ofolding__image(_1495381, _1495383, _1495385, _1495387, _1495389), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495383), _1495391)), c_Fun_Oinj__on(_1495383, _1495383, _1495393, _1495391), -(hAPP(hAPP(_1495389, _1495395), hAPP(c_Set_Oimage(_1495383, _1495383, _1495393), _1495391)) = hAPP(hAPP(_1495389, hAPP(c_Fun_Ocomp(_1495383, _1495381, _1495383, _1495395), _1495393)), _1495391))], (30633 ^ _774244) ^ [_1321101, _1321103, _1321105, _1321107] : [hBOOL(hAPP(hAPP(c_member(_1321101), _1321103), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321101, tc_HOL_Obool)), _1321105), _1321107))), 30636 ^ _774244 : [(30639 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1321101), _1321103), _1321107))], (30637 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1321101), _1321103), _1321105)))]]], (36197 ^ _774244) ^ [_1441785, _1441787, _1441789, _1441791] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441785, tc_HOL_Obool)), _1441787), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441785, tc_HOL_Obool)), _1441789), _1441791)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441785, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441785, tc_HOL_Obool)), _1441787), _1441789)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441785, tc_HOL_Obool)), _1441787), _1441791)))], (14308 ^ _774244) ^ [_1013870, _1013872, _1013874] : [-(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), _1013870), _1013872)), _1013874), _1013872) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1013874, _1013872))], (2584 ^ _774244) ^ [_813374, _813376, _813378, _813380] : [-(c_Orderings_Oord_Omin(_813380, _813376) = c_Orderings_Oord_Omin(_813378, _813374)), _813380 = _813378, _813376 = _813374], (27464 ^ _774244) ^ [_1258616, _1258618] : [c_Nat__Transfer_Onat__set(_1258616), c_Nat__Transfer_Onat__set(_1258618), 27471 ^ _774244 : [(27478 ^ _774244) ^ [] : [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), _1258616)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258618))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258616), _1258618)))], (27472 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258616), _1258618)), -(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), _1258616)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258618))))]]], (38816 ^ _774244) ^ [_1499823, _1499825, _1499827, _1499829] : [-(hAPP(c_Set_Ovimage(_1499823, _1499825, _1499827), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1499825, tc_HOL_Obool)), _1499829)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1499823, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1499823, _1499825, _1499827), _1499829)))], (26079 ^ _774244) ^ [_1229813, _1229815] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229813), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1229815)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229813)), _1229815)))], (22002 ^ _774244) ^ [_1152324, _1152326, _1152328, _1152330] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1152324, _1152326, _1152328, c_Code__Numeral_OSuc__code__numeral(_1152330)) = hAPP(hAPP(_1152328, _1152330), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1152324, _1152326, _1152328, _1152330)))], (18635 ^ _774244) ^ [_1092237] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092237))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1092237)))))], (12141 ^ _774244) ^ [_975232] : [12143 ^ _774244 : [(12146 ^ _774244) ^ [] : [hBOOL(hAPP(_975232, 12142 ^ [_975232]))], (12144 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12142 ^ [_975232])))]], 12147 ^ _774244 : [(12148 ^ _774244) ^ [_975359] : [-(hBOOL(hAPP(_975232, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _975359))))]]], (43405 ^ _774244) ^ [_1614622, _1614624] : [-(c_Transitive__Closure_Ortrancl(_1614622, hAPP(c_Relation_Oconverse(_1614622, _1614622), _1614624)) = hAPP(c_Relation_Oconverse(_1614622, _1614622), c_Transitive__Closure_Ortrancl(_1614622, _1614624)))], (4882 ^ _774244) ^ [_849705, _849707, _849709, _849711] : [-(c_List_Olinorder__class_Osorted__list__of__set(_849711, _849707) = c_List_Olinorder__class_Osorted__list__of__set(_849709, _849705)), _849711 = _849709, _849707 = _849705], (46878 ^ _774244) ^ [_1703085] : [-(hAPP(c_List_Oset(_1703085), c_List_Olist_ONil(_1703085)) = c_Orderings_Obot__class_Obot(tc_fun(_1703085, tc_HOL_Obool)))], (4010 ^ _774244) ^ [_836059, _836061, _836063, _836065, _836067, _836069] : [-(c_Smallcheck_Osmall_H(_836069, _836065, _836061) = c_Smallcheck_Osmall_H(_836067, _836063, _836059)), _836069 = _836067, _836065 = _836063, _836061 = _836059], (8068 ^ _774244) ^ [] : [-(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)))], (37897 ^ _774244) ^ [_1480755, _1480757, _1480759, _1480761] : [c_Fun_Oinj__on(_1480755, _1480757, _1480759, c_Orderings_Otop__class_Otop(tc_fun(_1480755, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1480755, tc_fun(_1480761, _1480757), hAPP(hAPP(c_COMBB(_1480757, tc_fun(_1480761, _1480757), _1480755), c_COMBK(_1480757, _1480761)), _1480759), c_Orderings_Otop__class_Otop(tc_fun(_1480755, tc_HOL_Obool))))], (16585 ^ _774244) ^ [_1056754, _1056756, _1056758, _1056760] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056754), hAPP(c_Int_Onumber__class_Onumber__of(_1056754), _1056756)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056754), _1056758), _1056760)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056754), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056754), hAPP(c_Int_Onumber__class_Onumber__of(_1056754), _1056756)), _1056758)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056754), hAPP(c_Int_Onumber__class_Onumber__of(_1056754), _1056756)), _1056760))), class_Int_Onumber(_1056754), class_Rings_Oring(_1056754)], (28455 ^ _774244) ^ [_1277610, _1277612, _1277614, _1277616, _1277618] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1277610, tc_fun(_1277612, tc_HOL_Obool)), _1277614), _1277616), _1277618))), 28456 ^ _774244 : [(28457 ^ _774244) ^ [_1277682] : [hBOOL(hAPP(hAPP(c_member(_1277610), _1277682), _1277614)), hBOOL(hAPP(hAPP(_1277616, _1277682), _1277618))]]], (23037 ^ _774244) ^ [_1172672] : [-(_1172672 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1172672), 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)))))], (51225 ^ _774244) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (7950 ^ _774244) ^ [_904209, _904211, _904213] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _904209)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _904211)), _904213)) = 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), _904209), _904211))), _904213))], (28658 ^ _774244) ^ [_1282466, _1282468, _1282470, _1282472, _1282474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282466, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1282468, tc_fun(_1282466, tc_HOL_Obool)), _1282470), _1282472)), _1282474)), 28661 ^ _774244 : [(28662 ^ _774244) ^ [_1282599] : [hBOOL(hAPP(hAPP(c_member(_1282468), _1282599), _1282470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282466, tc_HOL_Obool)), hAPP(_1282472, _1282599)), _1282474)))]]], (29638 ^ _774244) ^ [_1302027, _1302029] : [29639 ^ _774244 : [(29642 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1302029), _1302027))], (29640 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1302027), _1302029)))]], -(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)))), _1302027, _1302029))], (13571 ^ _774244) ^ [_1000507] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1000507, _1000507) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28789 ^ _774244) ^ [] : [-(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)))], (43490 ^ _774244) ^ [_1617845, _1617847, _1617849, _1617851, _1617853, _1617855] : [class_Complete__Lattice_Ocomplete__lattice(_1617845), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1617847, _1617845), _1617849), hAPP(hAPP(c_COMBB(tc_fun(_1617851, _1617845), _1617845, _1617847), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1617851, _1617845), _1617853)), _1617855)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1617851, _1617845), _1617853), hAPP(hAPP(c_COMBB(tc_fun(_1617847, _1617845), _1617845, _1617851), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1617847, _1617845), _1617849)), hAPP(c_COMBC(_1617847, _1617851, _1617845), _1617855))))], (41790 ^ _774244) ^ [_1577838, _1577840, _1577842, _1577844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1577838, _1577840), tc_HOL_Obool)), _1577842), _1577844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1577838, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1577838, _1577840), _1577842)), hAPP(c_Relation_ODomain(_1577838, _1577840), _1577844))))], (44542 ^ _774244) ^ [_1644719, _1644721, _1644723, _1644725] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644719, tc_fun(_1644721, tc_HOL_Obool)), _1644723), _1644725) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1644721, tc_HOL_Obool), hAPP(c_Set_Oimage(_1644719, tc_fun(_1644721, tc_HOL_Obool), _1644725), _1644723)))], (27239 ^ _774244) ^ [_1253987, _1253989] : [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)), _1253987)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1253989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1253987), _1253989)))], (21647 ^ _774244) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (50795 ^ _774244) ^ [_1793280, _1793282, _1793284] : [hBOOL(hAPP(c_List_Odistinct(_1793280), _1793282)), -(hBOOL(hAPP(c_List_Odistinct(_1793280), c_List_OdropWhile(_1793280, _1793284, _1793282))))], (41667 ^ _774244) ^ [_1574866, _1574868, _1574870, _1574872, _1574874] : [-(hAPP(c_Relation_ORange(_1574866, _1574868), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1574866, _1574868)), hAPP(hAPP(c_Product__Type_OPair(_1574866, _1574868), _1574870), _1574872)), _1574874)) = hAPP(hAPP(c_Set_Oinsert(_1574868), _1574872), hAPP(c_Relation_ORange(_1574866, _1574868), _1574874)))], (47981 ^ _774244) ^ [_1729472, _1729474, _1729476, _1729478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729472), _1729474)), -(hAPP(hAPP(c_List_Onth(_1729476), hAPP(hAPP(c_List_Otake(_1729476), _1729474), _1729478)), _1729472) = hAPP(hAPP(c_List_Onth(_1729476), _1729478), _1729472))], (48298 ^ _774244) ^ [_1738667, _1738669, _1738671, _1738673] : [-(hAPP(hAPP(c_List_Odrop(_1738667), _1738669), hAPP(hAPP(c_List_Oappend(_1738667), _1738671), _1738673)) = hAPP(hAPP(c_List_Oappend(_1738667), hAPP(hAPP(c_List_Odrop(_1738667), _1738669), _1738671)), hAPP(hAPP(c_List_Odrop(_1738667), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1738669), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738667)), _1738671))), _1738673)))], (6201 ^ _774244) ^ [_873656, _873658, _873660] : [-(c_Nat_Onat_Onat__case(_873656, _873658, _873660, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _873658)], (40208 ^ _774244) ^ [_1533867, _1533869, _1533871] : [class_Lattices_Oab__semigroup__idem__mult(_1533867), -(_1533869 = c_Orderings_Obot__class_Obot(tc_fun(_1533867, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533867), _1533869)), -(hAPP(c_Finite__Set_Ofold1(_1533867, c_Groups_Otimes__class_Otimes(_1533867)), hAPP(hAPP(c_Set_Oinsert(_1533867), _1533871), _1533869)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1533867), _1533871), hAPP(c_Finite__Set_Ofold1(_1533867, c_Groups_Otimes__class_Otimes(_1533867)), _1533869)))], (17535 ^ _774244) ^ [_1074657] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074657)))), -(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), _1074657)) = 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), _1074657))))], (47425 ^ _774244) ^ [_1716032, _1716034, _1716036, _1716038] : [-(c_List_Osublist(_1716032, hAPP(hAPP(c_List_Olist_OCons(_1716032), _1716034), _1716036), _1716038) = hAPP(hAPP(c_List_Oappend(_1716032), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1716032)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1716038)), hAPP(hAPP(c_List_Olist_OCons(_1716032), _1716034), c_List_Olist_ONil(_1716032))), c_List_Olist_ONil(_1716032))), c_List_Osublist(_1716032, _1716036, 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)), _1716038)))))], (47754 ^ _774244) ^ [_1723648, _1723650, _1723652, _1723654] : [hBOOL(hAPP(hAPP(c_member(_1723648), _1723650), hAPP(c_List_Oset(_1723648), _1723652))), -(c_List_Oremove1(_1723648, _1723650, hAPP(hAPP(c_List_Oappend(_1723648), _1723652), _1723654)) = hAPP(hAPP(c_List_Oappend(_1723648), c_List_Oremove1(_1723648, _1723650, _1723652)), _1723654))], (10544 ^ _774244) ^ [_947950, _947952, _947954] : [class_Orderings_Olinorder(_947950), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947950), _947952), _947954))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947950), _947954), _947952)))], (32790 ^ _774244) ^ [_1368547, _1368549] : [class_Orderings_Olinorder(_1368547), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368547), _1368549)), -(_1368549 = c_Orderings_Obot__class_Obot(tc_fun(_1368547, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1368547), c_Big__Operators_Olinorder__class_OMax(_1368547, _1368549)), _1368549)))], (24063 ^ _774244) ^ [_1192131, _1192133, _1192135, _1192137] : [class_Orderings_Olinorder(_1192131), 24066 ^ _774244 : [(24067 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192131), _1192133), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1192131), _1192135), _1192137))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192131), _1192133), _1192135))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192131), _1192133), _1192137)))], (24077 ^ _774244) ^ [] : [24078 ^ _774244 : [(24081 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192131), _1192133), _1192137))], (24079 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192131), _1192133), _1192135))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192131), _1192133), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1192131), _1192135), _1192137))))]]], (6392 ^ _774244) ^ [_877066, _877068] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_877066, _877068)) = 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(_877066)), c_Com_Ocom_Ocom__size(_877068))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27954 ^ _774244) ^ [_1267907, _1267909, _1267911, _1267913, _1267915] : [class_Lattices_Osemilattice__sup(_1267907), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267907), _1267909), _1267911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267907), _1267913), _1267915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267907), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267907), _1267909), _1267913)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267907), _1267911), _1267915))))], (30775 ^ _774244) ^ [_1324806, _1324808, _1324810, _1324812, _1324814, _1324816] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1324806, tc_fun(_1324808, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1324806, tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_fun(_1324808, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324808, tc_fun(tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_fun(_1324808, tc_HOL_Obool)), _1324806), c_COMBC(_1324808, tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324808, tc_prod(_1324806, _1324808)), tc_fun(_1324808, tc_fun(tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_HOL_Obool)), _1324806), hAPP(c_COMBB(tc_prod(_1324806, _1324808), tc_fun(tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_HOL_Obool), _1324808), c_member(tc_prod(_1324806, _1324808)))), c_Product__Type_OPair(_1324806, _1324808)))), _1324810)), hAPP(hAPP(c_COMBC(_1324806, tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_fun(_1324808, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324808, tc_fun(tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_fun(_1324808, tc_HOL_Obool)), _1324806), c_COMBC(_1324808, tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324808, tc_prod(_1324806, _1324808)), tc_fun(_1324808, tc_fun(tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_HOL_Obool)), _1324806), hAPP(c_COMBB(tc_prod(_1324806, _1324808), tc_fun(tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool), tc_HOL_Obool), _1324808), c_member(tc_prod(_1324806, _1324808)))), c_Product__Type_OPair(_1324806, _1324808)))), _1324812)), _1324814), _1324816)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1324806, _1324808)), hAPP(hAPP(c_Product__Type_OPair(_1324806, _1324808), _1324814), _1324816)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1324806, _1324808), tc_HOL_Obool)), _1324810), _1324812))))], (27569 ^ _774244) ^ [_1260247, _1260249] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1260247, _1260249)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1260249)), _1260247))], (36661 ^ _774244) ^ [_1452650, _1452652, _1452654] : [class_Orderings_Oorder(_1452650), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452650, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1452650), _1452652)), c_SetInterval_Oord__class_OatLeastAtMost(_1452650, _1452652, _1452654)) = c_Orderings_Obot__class_Obot(tc_fun(_1452650, tc_HOL_Obool)))], (44042 ^ _774244) ^ [_1632956, _1632958] : [-(c_Transitive__Closure_Ortrancl(_1632956, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1632956, _1632956), tc_HOL_Obool)), _1632958), c_Relation_OId(_1632956))) = c_Transitive__Closure_Ortrancl(_1632956, _1632958))], (25227 ^ _774244) ^ [_1214322, _1214324] : [_1214322 = _1214324, 25230 ^ _774244 : [(25233 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214324), _1214322)))], (25231 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214322), _1214324)))]]], (48897 ^ _774244) ^ [_1752095, _1752097, _1752099, _1752101] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1752095)), hAPP(hAPP(c_List_Oappend(_1752095), _1752097), _1752099)), c_List_Olists(_1752095, _1752101)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1752095)), _1752097), c_List_Olists(_1752095, _1752101))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1752095)), _1752099), c_List_Olists(_1752095, _1752101)))], (41654 ^ _774244) ^ [_1574549, _1574551, _1574553, _1574555] : [hBOOL(hAPP(hAPP(c_member(_1574549), _1574551), hAPP(c_Relation_ORange(_1574553, _1574549), _1574555))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574553, _1574549)), hAPP(hAPP(c_Product__Type_OPair(_1574553, _1574549), 41657 ^ [_1574549, _1574551, _1574553, _1574555]), _1574551)), _1574555)))], (36715 ^ _774244) ^ [_1453881, _1453883, _1453885, _1453887] : [class_Orderings_Olinorder(_1453881), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453881, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1453881, _1453883, _1453885)), hAPP(c_SetInterval_Oord__class_OatMost(_1453881), _1453887)) = c_SetInterval_Oord__class_OatLeastAtMost(_1453881, _1453883, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1453881), _1453885), _1453887)))], (14241 ^ _774244) ^ [_1012834, _1012836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012834), 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)), _1012836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1012834), _1012836)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24567 ^ _774244) ^ [_1201913, _1201915, _1201917, _1201919, _1201921] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1201913, _1201915, _1201913, _1201917), hAPP(c_Product__Type_OPair(_1201915, _1201913), _1201919)), _1201921) = hAPP(_1201921, _1201919))], (50316 ^ _774244) ^ [_1782035, _1782037] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782035)), hAPP(c_List_Orev(_1782035), _1782037)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782035)), _1782037))], (22632 ^ _774244) ^ [_1164891, _1164893, _1164895, _1164897] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1164891, _1164893), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1164895), _1164897))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1164891), _1164893) = _1164895)], (38059 ^ _774244) ^ [_1483855, _1483857, _1483859, _1483861] : [c_Fun_Oinj__on(_1483855, _1483857, _1483859, _1483861), -(hAPP(c_Finite__Set_Ocard(_1483857), hAPP(c_Set_Oimage(_1483855, _1483857, _1483859), _1483861)) = hAPP(c_Finite__Set_Ocard(_1483855), _1483861))], (12291 ^ _774244) ^ [_977688, _977690] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _977688)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _977690)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977688), _977690)))], (41216 ^ _774244) ^ [_1563233, _1563235, _1563237, _1563239, _1563241, _1563243, _1563245] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1563233, _1563235, _1563237), hAPP(hAPP(c_Relation_Orel__comp(_1563233, _1563239, _1563235), _1563241), _1563243)), _1563245) = hAPP(hAPP(c_Relation_Orel__comp(_1563233, _1563239, _1563237), _1563241), hAPP(hAPP(c_Relation_Orel__comp(_1563239, _1563235, _1563237), _1563243), _1563245)))], (18169 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (18947 ^ _774244) ^ [_1097580, _1097582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097580), _1097582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1097580)), c_Int_OBit0(_1097582))))], (38139 ^ _774244) ^ [_1485349, _1485351, _1485353, _1485355, _1485357, _1485359] : [c_Fun_Oinj__on(_1485349, _1485351, _1485353, _1485355), hAPP(_1485353, _1485357) = hAPP(_1485353, _1485359), hBOOL(hAPP(hAPP(c_member(_1485349), _1485357), _1485355)), hBOOL(hAPP(hAPP(c_member(_1485349), _1485359), _1485355)), -(_1485357 = _1485359)], (33542 ^ _774244) ^ [_1383166, _1383168] : [class_Orderings_Olinorder(_1383166), -(c_Big__Operators_Olattice_OSup__fin(_1383166, c_Orderings_Oord__class_Omax(_1383166), hAPP(hAPP(c_Set_Oinsert(_1383166), _1383168), c_Orderings_Obot__class_Obot(tc_fun(_1383166, tc_HOL_Obool)))) = _1383168)], (14626 ^ _774244) ^ [_1019083, _1019085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019083)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1019085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019083), _1019085)), _1019083)))], (49390 ^ _774244) ^ [_1762340, _1762342, _1762344] : [-(c_List_Opartition(_1762340, _1762342, _1762344) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762340), tc_List_Olist(_1762340)), hAPP(c_List_Ofilter(_1762340, _1762342), _1762344)), hAPP(c_List_Ofilter(_1762340, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1762340, c_fNot), _1762342)), _1762344)))], (21227 ^ _774244) ^ [_1137958, _1137960, _1137962, _1137964] : [class_Fields_Olinordered__field(_1137958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137958), c_Groups_Ozero__class_Ozero(_1137958)), _1137960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137958), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137958), _1137962), _1137960)), _1137964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137958), _1137962), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137958), _1137964), _1137960))))], (14846 ^ _774244) ^ [_1023476, _1023478, _1023480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1023476)), 14849 ^ _774244 : [(14850 ^ _774244) ^ [] : [-(_1023478 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1023480), _1023476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023476), _1023478)), _1023480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1023480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023476), hAPP(c_Nat_OSuc, _1023478))))], (14860 ^ _774244) ^ [] : [_1023478 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1023480), _1023476), 14863 ^ _774244 : [(14866 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1023480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023476), hAPP(c_Nat_OSuc, _1023478)))))], (14864 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023476), _1023478)), _1023480)))]]]]], (45992 ^ _774244) ^ [_1679148, _1679150, _1679152, _1679154, _1679156, _1679158] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1679148, _1679150)), hAPP(hAPP(c_Product__Type_OPair(_1679148, _1679150), _1679152), _1679154)), hAPP(c_List_Oset(tc_prod(_1679148, _1679150)), hAPP(hAPP(c_List_Ozip(_1679148, _1679150), _1679156), _1679158)))), -(hBOOL(hAPP(hAPP(c_member(_1679150), _1679154), hAPP(c_List_Oset(_1679150), _1679158))))], (44677 ^ _774244) ^ [_1648106, _1648108, _1648110] : [class_Complete__Lattice_Ocomplete__lattice(_1648106), 44680 ^ _774244 : [(44681 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1648106), c_Complete__Lattice_OSup__class_OSup(_1648106, _1648108)), _1648110)), 44684 ^ _774244 : [(44685 ^ _774244) ^ [_1648264] : [hBOOL(hAPP(hAPP(c_member(_1648106), _1648264), _1648108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1648106), _1648264), _1648110)))]]], (44691 ^ _774244) ^ [] : [44693 ^ _774244 : [(44696 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1648106), 44692 ^ [_1648106, _1648108, _1648110]), _1648110))], (44694 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1648106), 44692 ^ [_1648106, _1648108, _1648110]), _1648108)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1648106), c_Complete__Lattice_OSup__class_OSup(_1648106, _1648108)), _1648110)))]]], (28604 ^ _774244) ^ [_1281192, _1281194, _1281196, _1281198, _1281200, _1281202] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281192, tc_fun(_1281194, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281196, tc_fun(_1281192, tc_HOL_Obool)), _1281198), _1281200)), _1281202) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281196, tc_fun(_1281194, tc_HOL_Obool)), _1281198), hAPP(hAPP(c_COMBC(_1281196, tc_fun(_1281192, tc_fun(_1281194, tc_HOL_Obool)), tc_fun(_1281194, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1281192, tc_HOL_Obool), tc_fun(tc_fun(_1281192, tc_fun(_1281194, tc_HOL_Obool)), tc_fun(_1281194, tc_HOL_Obool)), _1281196), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281192, tc_fun(_1281194, tc_HOL_Obool))), _1281200)), _1281202)))], (44024 ^ _774244) ^ [_1632600, _1632602, _1632604] : [_1632602 = _1632604, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632600, _1632600)), hAPP(hAPP(c_Product__Type_OPair(_1632600, _1632600), _1632602), _1632604)), c_Relation_OId(_1632600))))], (47377 ^ _774244) ^ [_1715073, _1715075, _1715077, _1715079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715073), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715075)), _1715077))), -(hBOOL(hAPP(hAPP(c_member(_1715075), _1715079), hAPP(c_List_Oset(_1715075), hAPP(hAPP(c_List_Olist__update(_1715075, _1715077), _1715073), _1715079)))))], (15426 ^ _774244) ^ [_1034328, _1034330, _1034332] : [class_Groups_Oab__group__add(_1034328), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034328), _1034330), _1034332) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034328), _1034330), hAPP(c_Groups_Ouminus__class_Ouminus(_1034328), _1034332)))], (15206 ^ _774244) ^ [_1029978, _1029980] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029978), _1029980))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029978, _1029980) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029978), _1029980), _1029980))], (48314 ^ _774244) ^ [_1739078, _1739080, _1739082, _1739084, _1739086] : [-(hAPP(hAPP(c_List_Odrop(_1739078), _1739080), hAPP(hAPP(c_List_Omap(_1739082, _1739078), _1739084), _1739086)) = hAPP(hAPP(c_List_Omap(_1739082, _1739078), _1739084), hAPP(hAPP(c_List_Odrop(_1739082), _1739080), _1739086)))], (51191 ^ _774244) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (4272 ^ _774244) ^ [_840354, _840356, _840358, _840360] : [-(c_List_Olistset(_840360, _840356) = c_List_Olistset(_840358, _840354)), _840360 = _840358, _840356 = _840354], (16737 ^ _774244) ^ [_1059856, _1059858, _1059860] : [class_Rings_Oordered__ring__abs(_1059856), -(hAPP(c_Groups_Oabs__class_Oabs(_1059856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059856), _1059858), _1059860)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059856), hAPP(c_Groups_Oabs__class_Oabs(_1059856), _1059858)), hAPP(c_Groups_Oabs__class_Oabs(_1059856), _1059860))), 16744 ^ _774244 : [(16747 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059856), _1059858), c_Groups_Ozero__class_Ozero(_1059856)))], (16745 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059856), c_Groups_Ozero__class_Ozero(_1059856)), _1059858))]], 16748 ^ _774244 : [(16751 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059856), _1059860), c_Groups_Ozero__class_Ozero(_1059856)))], (16749 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059856), c_Groups_Ozero__class_Ozero(_1059856)), _1059860))]]], (36919 ^ _774244) ^ [_1458670, _1458672, _1458674, _1458676, _1458678, _1458680, _1458682, _1458684] : [c_Finite__Set_Ofolding__image__simple(_1458670, _1458672, _1458674, _1458676, _1458678, _1458680), hBOOL(hAPP(c_Finite__Set_Ofinite(_1458672), _1458682)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1458672), _1458684)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458672, tc_HOL_Obool)), _1458682), _1458684) = c_Orderings_Obot__class_Obot(tc_fun(_1458672, tc_HOL_Obool)), -(hAPP(_1458680, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458672, tc_HOL_Obool)), _1458682), _1458684)) = hAPP(hAPP(_1458674, hAPP(_1458680, _1458682)), hAPP(_1458680, _1458684)))], (14372 ^ _774244) ^ [_1014970, _1014972] : [class_Divides_Osemiring__div(_1014970), -(_1014972 = c_Groups_Ozero__class_Ozero(_1014970)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1014970), _1014972), _1014972) = c_Groups_Oone__class_Oone(_1014970))], (15242 ^ _774244) ^ [_1030655, _1030657, _1030659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030655), _1030657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030655), _1030659)), 15249 ^ _774244 : [(15256 ^ _774244) ^ [] : [_1030657 = _1030659, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030657), _1030655) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030659), _1030655))], (15250 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030657), _1030655) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030659), _1030655), -(_1030657 = _1030659)]]], (31303 ^ _774244) ^ [_1336579, _1336581, _1336583, _1336585] : [hBOOL(hAPP(hAPP(c_member(_1336579), _1336581), _1336583)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336579, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1336579), _1336581), _1336585)), _1336583) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336579, tc_HOL_Obool)), _1336585), _1336583))], (14874 ^ _774244) ^ [_1023962, _1023964] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023962))), -(c_SMT_Oz3div(_1023964, _1023962) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023964), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1023962))))], (8427 ^ _774244) ^ [_911565, _911567] : [class_Rings_Olinordered__idom(_911565), 8430 ^ _774244 : [(8437 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _911567), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911565), hAPP(c_Int_Oring__1__class_Oof__int(_911565), _911567)), c_Groups_Ozero__class_Ozero(_911565))))], (8431 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911565), hAPP(c_Int_Oring__1__class_Oof__int(_911565), _911567)), c_Groups_Ozero__class_Ozero(_911565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _911567), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (30079 ^ _774244) ^ [_1309899, _1309901, _1309903, _1309905] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1309899), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309899, tc_HOL_Obool)), _1309901), hAPP(hAPP(c_Set_Oinsert(_1309899), _1309903), _1309905)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1309899), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309899, tc_HOL_Obool)), _1309901), _1309905))))], (36125 ^ _774244) ^ [_1440073, _1440075, _1440077, _1440079] : [hBOOL(hAPP(hAPP(c_member(_1440073), _1440079), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440073, tc_HOL_Obool)), _1440075), _1440077))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440073, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1440073, tc_fun(_1440073, tc_HOL_Obool), tc_HOL_Obool), c_member(_1440073)), _1440075)), hAPP(hAPP(c_COMBC(_1440073, tc_fun(_1440073, tc_HOL_Obool), tc_HOL_Obool), c_member(_1440073)), _1440077)), _1440079)))], (45371 ^ _774244) ^ [_1664319, _1664321, _1664323, _1664325] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1664319, _1664321)), _1664323), hAPP(c_Relation_Oconverse(_1664321, _1664319), _1664325))), 45376 ^ _774244 : [(45379 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1664321, _1664319)), hAPP(hAPP(c_Product__Type_OPair(_1664321, _1664319), 45374 ^ [_1664319, _1664321, _1664323, _1664325]), 45375 ^ [_1664319, _1664321, _1664323, _1664325])), _1664325)))], (45377 ^ _774244) ^ [] : [-(_1664323 = hAPP(hAPP(c_Product__Type_OPair(_1664319, _1664321), 45375 ^ [_1664319, _1664321, _1664323, _1664325]), 45374 ^ [_1664319, _1664321, _1664323, _1664325]))]]], (34660 ^ _774244) ^ [_1406644, _1406646] : [-(c_FunDef_Orp__inv__image(_1406644, _1406646) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1406644, _1406644), tc_HOL_Obool), tc_fun(tc_prod(_1406644, _1406644), tc_HOL_Obool), tc_fun(tc_fun(_1406646, _1406644), tc_prod(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1406644, _1406644), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1406644, _1406644), tc_HOL_Obool), tc_fun(tc_fun(_1406646, _1406644), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1406644, _1406644), tc_HOL_Obool), tc_fun(tc_fun(_1406646, _1406644), tc_prod(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1406646, _1406644), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool)), tc_fun(tc_fun(_1406646, _1406644), tc_prod(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1406644, _1406644), tc_HOL_Obool), tc_fun(tc_fun(_1406646, _1406644), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1406644, _1406644), tc_HOL_Obool), tc_fun(tc_fun(_1406646, _1406644), tc_prod(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool))))), tc_fun(tc_prod(_1406644, _1406644), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1406646, _1406644), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool)), tc_fun(tc_fun(_1406646, _1406644), tc_prod(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool))), tc_fun(tc_prod(_1406644, _1406644), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1406646, _1406644), tc_fun(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1406646, _1406644), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool)), tc_fun(tc_fun(_1406646, _1406644), tc_prod(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool)))), tc_fun(tc_prod(_1406644, _1406644), tc_HOL_Obool)), c_COMBS(tc_fun(_1406646, _1406644), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1406646, _1406644), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool)), tc_fun(tc_fun(_1406646, _1406644), tc_fun(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool)))), tc_fun(tc_prod(_1406644, _1406644), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool))), tc_fun(_1406646, _1406644)), c_Product__Type_OPair(tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool), tc_fun(tc_prod(_1406646, _1406646), tc_HOL_Obool)))), c_Relation_Oinv__image(_1406644, _1406646))))), c_Relation_Oinv__image(_1406644, _1406646))))], (28783 ^ _774244) ^ [_1285466, _1285468] : [class_Lattices_Obounded__lattice__top(_1285466), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285466), _1285468), c_Orderings_Otop__class_Otop(_1285466)) = c_Orderings_Otop__class_Otop(_1285466))], (50244 ^ _774244) ^ [_1780476, _1780478] : [hAPP(c_List_Orev(_1780476), _1780478) = c_List_Olist_ONil(_1780476), -(_1780478 = c_List_Olist_ONil(_1780476))], (11747 ^ _774244) ^ [_968158, _968160, _968162, _968164, _968166] : [class_Rings_Oordered__semiring(_968158), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968158), _968160), _968162)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968158), _968164), _968166)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968158), c_Groups_Ozero__class_Ozero(_968158)), _968160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968158), c_Groups_Ozero__class_Ozero(_968158)), _968164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968158), _968160), _968164)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968158), _968162), _968166))))], (22102 ^ _774244) ^ [_1154088] : [-(c_Quickcheck_Obeyond(_1154088, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (30595 ^ _774244) ^ [_1320403, _1320405, _1320407, _1320409, _1320411, _1320413] : [_1320403 = hAPP(_1320405, _1320407), hBOOL(hAPP(hAPP(c_member(_1320409), _1320407), _1320411)), -(hBOOL(hAPP(hAPP(c_member(_1320413), _1320403), hAPP(c_Set_Oimage(_1320409, _1320413, _1320405), _1320411))))], (36151 ^ _774244) ^ [_1440728, _1440730, _1440732, _1440734] : [-(hBOOL(hAPP(hAPP(c_member(_1440728), _1440730), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440728, tc_HOL_Obool)), _1440732), _1440734)))), hBOOL(hAPP(hAPP(c_member(_1440728), _1440730), _1440732)), hBOOL(hAPP(hAPP(c_member(_1440728), _1440730), _1440734))], (5617 ^ _774244) ^ [_863713, _863715, _863717, _863719] : [c_Natural_Oevaln(c_Com_Ocom_OBODY(_863713), _863715, hAPP(c_Nat_OSuc, _863717), _863719), -(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _863713)), _863715, _863717, _863719))], (44516 ^ _774244) ^ [_1644235, _1644237, _1644239] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1644235, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1644235, tc_HOL_Obool), tc_HOL_Obool)), _1644237), _1644239)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1644235, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1644235, tc_HOL_Obool), _1644237)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1644235, tc_HOL_Obool), _1644239)))], (33348 ^ _774244) ^ [_1379254, _1379256, _1379258, _1379260, _1379262] : [hBOOL(hAPP(hAPP(c_member(_1379254), _1379256), _1379258)), -(hBOOL(hAPP(hAPP(c_member(tc_sum(_1379254, _1379260)), hAPP(c_Sum__Type_OInl(_1379254, _1379260), _1379256)), c_Sum__Type_OPlus(_1379254, _1379260, _1379258, _1379262))))], (51033 ^ _774244) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (41582 ^ _774244) ^ [_1572858, _1572860, _1572862, _1572864] : [41584 ^ _774244 : [(41587 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1572860, hAPP(_1572862, 41583 ^ [_1572858, _1572860, _1572862, _1572864]))), hAPP(_1572860, 41583 ^ [_1572858, _1572860, _1572862, _1572864])))], (41585 ^ _774244) ^ [] : [-(hBOOL(hAPP(_1572858, 41583 ^ [_1572858, _1572860, _1572862, _1572864])))]], -(c_Wellfounded_Owf(_1572864, hAPP(c_Set_OCollect(tc_prod(_1572864, _1572864)), hAPP(c_Product__Type_Oprod_Oprod__case(_1572864, _1572864, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1572864, tc_HOL_Obool), tc_fun(_1572864, tc_HOL_Obool), _1572864), hAPP(c_COMBS(_1572864, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572864), c_fconj), _1572858))), hAPP(hAPP(c_COMBC(_1572864, tc_fun(_1572864, _1572864), tc_fun(_1572864, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572864, tc_HOL_Obool), tc_fun(tc_fun(_1572864, _1572864), tc_fun(_1572864, tc_HOL_Obool)), _1572864), c_COMBB(_1572864, tc_HOL_Obool, _1572864)), c_fequal)), _1572862))))))], (35915 ^ _774244) ^ [_1436210, _1436212, _1436214, _1436216] : [class_Lattices_Osemilattice__inf(_1436210), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436210), _1436212), _1436214)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436210), _1436212), _1436216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436210), _1436212), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1436210), _1436214), _1436216))))], (42604 ^ _774244) ^ [_1596999, _1597001, _1597003, _1597005] : [class_Orderings_Olinorder(_1596999), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596999), _1597001)), hBOOL(hAPP(hAPP(c_member(_1596999), _1597003), _1597001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1596999), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1596999), _1597003), _1597005)), hAPP(hAPP(c_Finite__Set_Ofold(_1596999, _1596999, c_Orderings_Oord__class_Omax(_1596999)), _1597005), _1597001))))], (3758 ^ _774244) ^ [_832179, _832181, _832183, _832185, _832187, _832189] : [-(c_Predicate_ODomainP(_832189, _832185, _832181) = c_Predicate_ODomainP(_832187, _832183, _832179)), _832189 = _832187, _832185 = _832183, _832181 = _832179], (30799 ^ _774244) ^ [_1326485, _1326487, _1326489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326485, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1326485, tc_fun(_1326485, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326485)), _1326487)), hAPP(hAPP(c_COMBC(_1326485, tc_fun(_1326485, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326485)), _1326489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326485, tc_HOL_Obool)), _1326487), _1326489)))], (36295 ^ _774244) ^ [_1444059, _1444061, _1444063, _1444065] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444059, tc_HOL_Obool)), _1444061), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444059, tc_HOL_Obool)), _1444063), _1444065)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444059, tc_HOL_Obool)), _1444063), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444059, tc_HOL_Obool)), _1444061), _1444065)))], (86 ^ _774244) ^ [_775409, _775411] : [-(class_Fields_Olinordered__field__inverse__zero(_775409)), _775411 = _775409, class_Fields_Olinordered__field__inverse__zero(_775411)], (40659 ^ _774244) ^ [_1542844, _1542846, _1542848] : [-(hAPP(hAPP(c_Set_Oinsert(_1542844), _1542846), _1542848) = hAPP(c_Set_OCollect(_1542844), hAPP(hAPP(c_COMBS(_1542844, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542844), c_fdisj), hAPP(hAPP(c_COMBC(_1542844, _1542844, tc_HOL_Obool), c_fequal), _1542846))), hAPP(hAPP(c_COMBC(_1542844, tc_fun(_1542844, tc_HOL_Obool), tc_HOL_Obool), c_member(_1542844)), _1542848))))], (49713 ^ _774244) ^ [_1769877, _1769879] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1769877), _1769879))), -(c_List_Oupt(_1769877, hAPP(c_Nat_OSuc, _1769879)) = c_List_Olist_ONil(tc_Nat_Onat))], (30739 ^ _774244) ^ [_1323177, _1323179] : [hBOOL(hAPP(hAPP(c_member(_1323177), _1323179), c_Orderings_Obot__class_Obot(tc_fun(_1323177, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1323177, tc_HOL_Obool)), _1323179)))], (30769 ^ _774244) ^ [_1324224, _1324226, _1324228, _1324230] : [_1324228 = _1324230, -(hAPP(hAPP(c_COMBC(_1324224, tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_fun(_1324226, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324226, tc_fun(tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_fun(_1324226, tc_HOL_Obool)), _1324224), c_COMBC(_1324226, tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324226, tc_prod(_1324224, _1324226)), tc_fun(_1324226, tc_fun(tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_HOL_Obool)), _1324224), hAPP(c_COMBB(tc_prod(_1324224, _1324226), tc_fun(tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_HOL_Obool), _1324226), c_member(tc_prod(_1324224, _1324226)))), c_Product__Type_OPair(_1324224, _1324226)))), _1324228) = hAPP(hAPP(c_COMBC(_1324224, tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_fun(_1324226, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324226, tc_fun(tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_fun(_1324226, tc_HOL_Obool)), _1324224), c_COMBC(_1324226, tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324226, tc_prod(_1324224, _1324226)), tc_fun(_1324226, tc_fun(tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_HOL_Obool)), _1324224), hAPP(c_COMBB(tc_prod(_1324224, _1324226), tc_fun(tc_fun(tc_prod(_1324224, _1324226), tc_HOL_Obool), tc_HOL_Obool), _1324226), c_member(tc_prod(_1324224, _1324226)))), c_Product__Type_OPair(_1324224, _1324226)))), _1324230))], (46972 ^ _774244) ^ [_1704799, _1704801] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1704799), tc_List_Olist(_1704799), c_List_Olistrel(_1704799, _1704801)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1704799)), c_List_Olist_ONil(_1704799)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1704799), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1704799)), c_List_Olist_ONil(_1704799)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1704799), tc_HOL_Obool))))], (29746 ^ _774244) ^ [_1304056, _1304058] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1304056), _1304058))))], (1354 ^ _774244) ^ [_793893, _793895] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_793893)), _793895 = _793893, class_Groups_Oordered__cancel__ab__semigroup__add(_793895)], (9496 ^ _774244) ^ [_930454, _930456, _930458] : [class_Rings_Olinordered__semiring__strict(_930454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930454), c_Groups_Ozero__class_Ozero(_930454)), _930456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930454), _930458), c_Groups_Ozero__class_Ozero(_930454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930454), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930454), _930456), _930458)), c_Groups_Ozero__class_Ozero(_930454))))], (22110 ^ _774244) ^ [_1154314, _1154316] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1154314)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1154316)), hAPP(c_Int_Onat, _1154314)) = hAPP(c_Int_Onat, _1154316))], (50540 ^ _774244) ^ [_1788189, _1788191, _1788193, _1788195, _1788197] : [-(hAPP(hAPP(c_List_Ozip(_1788189, _1788191), c_List_OtakeWhile(_1788189, _1788193, _1788195)), _1788197) = c_List_OtakeWhile(tc_prod(_1788189, _1788191), hAPP(c_Fun_Ocomp(_1788189, tc_HOL_Obool, tc_prod(_1788189, _1788191), _1788193), c_Product__Type_Ofst(_1788189, _1788191)), hAPP(hAPP(c_List_Ozip(_1788189, _1788191), _1788195), _1788197)))], (41998 ^ _774244) ^ [_1583307, _1583309, _1583311] : [-(c_Relation_Orefl__on(_1583307, _1583309, _1583311)), 42002 ^ _774244 : [(42005 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1583307, _1583307, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1583307, tc_fun(_1583307, tc_HOL_Obool), tc_fun(_1583307, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1583307, tc_HOL_Obool), tc_fun(_1583307, tc_HOL_Obool)), _1583307), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1583307)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1583307), c_fconj), hAPP(hAPP(c_COMBC(_1583307, tc_fun(_1583307, tc_HOL_Obool), tc_HOL_Obool), c_member(_1583307)), _1583309)))), hAPP(hAPP(c_COMBC(_1583307, tc_fun(_1583307, tc_HOL_Obool), tc_HOL_Obool), c_member(_1583307)), _1583309))), 42001 ^ [_1583307, _1583309, _1583311]))], (42003 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583307, _1583307)), 42001 ^ [_1583307, _1583309, _1583311]), _1583311)))]], 42007 ^ _774244 : [(42010 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583307, _1583307)), hAPP(hAPP(c_Product__Type_OPair(_1583307, _1583307), 42006 ^ [_1583307, _1583309, _1583311]), 42006 ^ [_1583307, _1583309, _1583311])), _1583311))], (42008 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1583307), 42006 ^ [_1583307, _1583309, _1583311]), _1583309)))]]], (41358 ^ _774244) ^ [_1568130, _1568132, _1568134] : [c_Wellfounded_Owf(_1568130, _1568132), -(hBOOL(hAPP(hAPP(c_member(_1568130), _1568134), c_Wellfounded_Oacc(_1568130, _1568132))))], (39324 ^ _774244) ^ [_1511327, _1511329, _1511331] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1511327, hAPP(hAPP(c_COMBC(_1511327, tc_fun(tc_prod(_1511327, _1511327), tc_HOL_Obool), tc_fun(_1511327, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511327, tc_fun(tc_fun(tc_prod(_1511327, _1511327), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511327, _1511327), tc_HOL_Obool), tc_fun(_1511327, tc_HOL_Obool)), _1511327), c_COMBC(_1511327, tc_fun(tc_prod(_1511327, _1511327), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511327, tc_prod(_1511327, _1511327)), tc_fun(_1511327, tc_fun(tc_fun(tc_prod(_1511327, _1511327), tc_HOL_Obool), tc_HOL_Obool)), _1511327), hAPP(c_COMBB(tc_prod(_1511327, _1511327), tc_fun(tc_fun(tc_prod(_1511327, _1511327), tc_HOL_Obool), tc_HOL_Obool), _1511327), c_member(tc_prod(_1511327, _1511327)))), c_Product__Type_OPair(_1511327, _1511327)))), _1511329)), _1511331)), -(hBOOL(hAPP(hAPP(c_member(_1511327), _1511331), c_Wellfounded_Oacc(_1511327, _1511329))))], (23231 ^ _774244) ^ [_1175836, _1175838, _1175840] : [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), _1175836), _1175838))), -(hBOOL(hAPP(hAPP(_1175840, _1175836), _1175838))), 23238 ^ _774244 : [(23241 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23237 ^ [_1175836, _1175838, _1175840]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1175840, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23236 ^ [_1175836, _1175838, _1175840])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23237 ^ [_1175836, _1175838, _1175840]))))], (23247 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1175840, 23236 ^ [_1175836, _1175838, _1175840]), 23237 ^ [_1175836, _1175838, _1175840]))], (23239 ^ _774244) ^ [] : [-(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), 23236 ^ [_1175836, _1175838, _1175840]), 23237 ^ [_1175836, _1175838, _1175840]))))]]], (17899 ^ _774244) ^ [_1080548] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1080548) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1080548))], (30897 ^ _774244) ^ [_1328291, _1328293, _1328295, _1328297] : [hBOOL(hAPP(hAPP(c_member(_1328291), _1328293), _1328295)), -(hBOOL(hAPP(hAPP(c_member(_1328291), _1328293), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328291, tc_HOL_Obool)), _1328297), _1328295))))], (19009 ^ _774244) ^ [_1098602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1098602))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1098602)))], (41891 ^ _774244) ^ [_1580998, _1581000, _1581002, _1581004] : [-(c_New__Random__Sequence_Opos__map(_1580998, _1581000, _1581002, _1581004) = c_New__Random__Sequence_Opos__bind(_1580998, _1581000, _1581004, hAPP(c_Fun_Ocomp(_1581000, 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(_1581000))))), _1580998, c_New__Random__Sequence_Opos__single(_1581000)), _1581002)))], (51489 ^ _774244) ^ [_1802088, _1802090] : [hBOOL(_1802088), -(hBOOL(hAPP(hAPP(c_fdisj, _1802090), _1802088)))], (45867 ^ _774244) ^ [_1676333, _1676335] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1676333, _1676335) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1676333), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1676335), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (51031 ^ _774244) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (48598 ^ _774244) ^ [_1745316, _1745318, _1745320] : [-(hAPP(c_List_Orotate(_1745316, _1745318), _1745320) = hAPP(c_List_Orotate(_1745316, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1745318, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745316)), _1745320))), _1745320))], (17091 ^ _774244) ^ [_1066458, _1066460] : [-(_1066458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1066460), _1066458) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066460), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1066460), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1066458), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (38730 ^ _774244) ^ [_1497783, _1497785, _1497787, _1497789, _1497791] : [c_Fun_Oinj__on(_1497783, _1497785, _1497787, _1497789), hBOOL(hAPP(hAPP(c_member(_1497785), _1497791), hAPP(c_Set_Oimage(_1497783, _1497785, _1497787), _1497789))), -(hAPP(_1497787, hAPP(c_Fun_Othe__inv__into(_1497783, _1497785, _1497789, _1497787), _1497791)) = _1497791)], (17909 ^ _774244) ^ [_1080706, _1080708] : [class_Int_Onumber__ring(_1080706), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080706), _1080708), hAPP(c_Int_Onumber__class_Onumber__of(_1080706), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1080706), _1080708))], (44582 ^ _774244) ^ [_1645614, _1645616] : [class_Complete__Lattice_Ocomplete__lattice(_1645614), -(c_Complete__Lattice_OInf__class_OInf(_1645614, _1645616) = c_Complete__Lattice_OSup__class_OSup(_1645614, hAPP(c_Set_OCollect(_1645614), hAPP(hAPP(c_COMBB(tc_fun(_1645614, tc_HOL_Obool), tc_HOL_Obool, _1645614), c_HOL_OAll(_1645614)), hAPP(hAPP(c_COMBB(tc_fun(_1645614, tc_HOL_Obool), tc_fun(_1645614, tc_HOL_Obool), _1645614), hAPP(c_COMBS(_1645614, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1645614), c_fimplies), hAPP(hAPP(c_COMBC(_1645614, tc_fun(_1645614, tc_HOL_Obool), tc_HOL_Obool), c_member(_1645614)), _1645616)))), c_Orderings_Oord__class_Oless__eq(_1645614))))))], (16663 ^ _774244) ^ [_1058321, _1058323, _1058325] : [class_Int_Onumber__ring(_1058321), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058321), hAPP(c_Int_Onumber__class_Onumber__of(_1058321), _1058323)), hAPP(c_Int_Onumber__class_Onumber__of(_1058321), _1058325)) = hAPP(c_Int_Onumber__class_Onumber__of(_1058321), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1058323), _1058325)))], (45571 ^ _774244) ^ [_1669229, _1669231, _1669233, _1669235, _1669237, _1669239] : [c_Map_Omap__comp(_1669229, _1669231, _1669233, _1669235, _1669237, _1669239) = c_Option_Ooption_ONone(_1669231), -(hAPP(_1669237, _1669239) = c_Option_Ooption_ONone(_1669229)), 45579 ^ _774244 : [(45582 ^ _774244) ^ [] : [-(hAPP(_1669235, 45578 ^ [_1669229, _1669231, _1669233, _1669235, _1669237, _1669239]) = c_Option_Ooption_ONone(_1669231))], (45580 ^ _774244) ^ [] : [-(hAPP(_1669237, _1669239) = hAPP(c_Option_Ooption_OSome(_1669229), 45578 ^ [_1669229, _1669231, _1669233, _1669235, _1669237, _1669239]))]]], (12746 ^ _774244) ^ [_986014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _986014), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _986014) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31455 ^ _774244) ^ [_1339224, _1339226] : [c_Nat__Transfer_Onat__set(_1339224), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1339226), _1339224)), -(c_Nat__Transfer_Ois__nat(_1339226))], (5426 ^ _774244) ^ [_858049, _858051] : [_858051 = _858049, -(c_List_Olist_OCons(_858051) = c_List_Olist_OCons(_858049))], (6822 ^ _774244) ^ [_884755, _884757] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_884755, _884757)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _884757)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29552 ^ _774244) ^ [_1300529, _1300531, _1300533] : [class_Orderings_Olinorder(_1300529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300529), _1300531), _1300533)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1300529, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1300529), _1300531), c_Orderings_Obot__class_Obot(tc_fun(_1300529, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1300529, _1300531, _1300533)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1300529, _1300531), _1300533))], (42638 ^ _774244) ^ [_1597646, _1597648, _1597650] : [class_Lattices_Olattice(_1597646), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597646), _1597648)), -(c_Big__Operators_Olattice__class_OInf__fin(_1597646, hAPP(hAPP(c_Set_Oinsert(_1597646), _1597650), _1597648)) = hAPP(hAPP(c_Finite__Set_Ofold(_1597646, _1597646, c_Lattices_Osemilattice__inf__class_Oinf(_1597646)), _1597650), _1597648))], (26584 ^ _774244) ^ [_1240475, _1240477] : [class_Rings_Ocomm__semiring__1(_1240475), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240475), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1240475), c_Groups_Oone__class_Oone(_1240475)), c_Groups_Oone__class_Oone(_1240475))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1240475), c_Nat_Osemiring__1__class_Oof__nat(_1240475)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1240477))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240475), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1240475), _1240477)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1240475), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1240475), _1240477)), c_Groups_Oone__class_Oone(_1240475))))], (14316 ^ _774244) ^ [_1014084, _1014086, _1014088, _1014090] : [class_Divides_Osemiring__div(_1014084), 14319 ^ _774244 : [(14326 ^ _774244) ^ [] : [-(_1014086 = c_Groups_Ozero__class_Ozero(_1014084)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1014084), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014084), _1014086), _1014088)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014084), _1014086), _1014090)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1014084), _1014088), _1014090))], (14320 ^ _774244) ^ [] : [_1014086 = c_Groups_Ozero__class_Ozero(_1014084), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1014084), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014084), _1014086), _1014088)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014084), _1014086), _1014090)) = c_Groups_Ozero__class_Ozero(_1014084))]]], (20421 ^ _774244) ^ [_1123486, _1123488, _1123490, _1123492] : [class_Fields_Ofield(_1123486), -(_1123488 = c_Groups_Ozero__class_Ozero(_1123486)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1123486), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123486), _1123490), _1123488)), _1123492) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123486), hAPP(hAPP(c_Power_Opower__class_Opower(_1123486), _1123490), _1123492)), hAPP(hAPP(c_Power_Opower__class_Opower(_1123486), _1123488), _1123492)))], (29514 ^ _774244) ^ [_1299789, _1299791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1299789), _1299791)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1299789), hAPP(c_Nat_OSuc, _1299791)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1299791), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1299789), _1299791)))], (51299 ^ _774244) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (43085 ^ _774244) ^ [_1607306, _1607308] : [-(c_Transitive__Closure_Ortrancl(_1607306, c_Transitive__Closure_Ortrancl(_1607306, _1607308)) = c_Transitive__Closure_Ortrancl(_1607306, _1607308))], (1684 ^ _774244) ^ [_798018, _798020] : [-(class_Rings_Osemiring(_798018)), _798020 = _798018, class_Rings_Osemiring(_798020)], (50753 ^ _774244) ^ [_1792221, _1792223, _1792225] : [-(hBOOL(hAPP(hAPP(c_member(_1792221), _1792223), hAPP(c_List_Oset(_1792221), _1792225)))), -(c_List_Oremdups(_1792221, hAPP(hAPP(c_List_Olist_OCons(_1792221), _1792223), _1792225)) = hAPP(hAPP(c_List_Olist_OCons(_1792221), _1792223), c_List_Oremdups(_1792221, _1792225)))], (51259 ^ _774244) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (47664 ^ _774244) ^ [_1721946, _1721948, _1721950] : [_1721948 = c_List_Olist_ONil(_1721946), -(hAPP(hAPP(c_List_Oappend(_1721946), _1721948), _1721950) = _1721950)], (5540 ^ _774244) ^ [_859746, _859748, _859750, _859752, _859754, _859756] : [-(c_COMBB(_859756, _859752, _859748) = c_COMBB(_859754, _859750, _859746)), _859756 = _859754, _859752 = _859750, _859748 = _859746], (45676 ^ _774244) ^ [_1671870, _1671872, _1671874] : [-(hAPP(hAPP(c_Option_Omap(_1671870, _1671872), _1671874), c_Option_Ooption_ONone(_1671870)) = c_Option_Ooption_ONone(_1671872))], (43674 ^ _774244) ^ [_1622755, _1622757, _1622759, _1622761, _1622763] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622755, tc_fun(_1622757, tc_HOL_Obool)), _1622759), hAPP(hAPP(c_COMBB(tc_fun(_1622757, tc_HOL_Obool), tc_fun(_1622757, tc_HOL_Obool), _1622755), hAPP(c_Set_Oinsert(_1622757), _1622761)), _1622763)) = hAPP(hAPP(c_Set_Oinsert(_1622757), _1622761), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622755, tc_fun(_1622757, tc_HOL_Obool)), _1622759), _1622763)))], (38339 ^ _774244) ^ [_1489141, _1489143, _1489145, _1489147, _1489149, _1489151] : [c_Fun_Oinj__on(_1489141, _1489143, _1489145, _1489147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489141, tc_HOL_Obool)), _1489149), _1489147)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489141, tc_HOL_Obool)), _1489151), _1489147)), -(hAPP(c_Set_Oimage(_1489141, _1489143, _1489145), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1489141, tc_HOL_Obool)), _1489149), _1489151)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1489143, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1489141, _1489143, _1489145), _1489149)), hAPP(c_Set_Oimage(_1489141, _1489143, _1489145), _1489151)))], (28978 ^ _774244) ^ [_1289891, _1289893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1289891, tc_HOL_Obool)), _1289893), c_Orderings_Obot__class_Obot(tc_fun(_1289891, tc_HOL_Obool))))], (36709 ^ _774244) ^ [_1453738, _1453740, _1453742, _1453744] : [class_Orderings_Olinorder(_1453738), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453738, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1453738), _1453740)), c_SetInterval_Oord__class_OatLeastAtMost(_1453738, _1453742, _1453744)) = c_SetInterval_Oord__class_OatLeastAtMost(_1453738, _1453742, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1453738), _1453740), _1453744)))], (51221 ^ _774244) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (44190 ^ _774244) ^ [_1636515, _1636517, _1636519] : [c_Relation_Ototal__on(_1636515, _1636517, _1636519), -(c_Relation_Ototal__on(_1636515, _1636517, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1636515, _1636515), tc_HOL_Obool)), _1636519), c_Relation_OId(_1636515))))], (45385 ^ _774244) ^ [_1664662, _1664664, _1664666, _1664668] : [-(c_Map_Omap__add(_1664662, _1664664, _1664666, c_Map_Omap__of(_1664662, _1664664, _1664668)) = c_List_Ofoldr(tc_prod(_1664662, _1664664), tc_fun(_1664662, tc_Option_Ooption(_1664664)), hAPP(c_Product__Type_Oprod_Oprod__case(_1664662, _1664664, tc_fun(tc_fun(_1664662, tc_Option_Ooption(_1664664)), tc_fun(_1664662, tc_Option_Ooption(_1664664)))), hAPP(hAPP(c_COMBC(_1664662, tc_fun(_1664664, tc_Option_Ooption(_1664664)), tc_fun(_1664664, tc_fun(tc_fun(_1664662, tc_Option_Ooption(_1664664)), tc_fun(_1664662, tc_Option_Ooption(_1664664))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1664664), tc_fun(tc_fun(_1664662, tc_Option_Ooption(_1664664)), tc_fun(_1664662, tc_Option_Ooption(_1664664)))), tc_fun(tc_fun(_1664664, tc_Option_Ooption(_1664664)), tc_fun(_1664664, tc_fun(tc_fun(_1664662, tc_Option_Ooption(_1664664)), tc_fun(_1664662, tc_Option_Ooption(_1664664))))), _1664662), c_COMBB(tc_Option_Ooption(_1664664), tc_fun(tc_fun(_1664662, tc_Option_Ooption(_1664664)), tc_fun(_1664662, tc_Option_Ooption(_1664664))), _1664664)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1664662, tc_Option_Ooption(_1664664)), tc_fun(tc_Option_Ooption(_1664664), tc_fun(_1664662, tc_Option_Ooption(_1664664)))), tc_fun(tc_Option_Ooption(_1664664), tc_fun(tc_fun(_1664662, tc_Option_Ooption(_1664664)), tc_fun(_1664662, tc_Option_Ooption(_1664664)))), _1664662), c_COMBC(tc_fun(_1664662, tc_Option_Ooption(_1664664)), tc_Option_Ooption(_1664664), tc_fun(_1664662, tc_Option_Ooption(_1664664)))), hAPP(c_COMBC(tc_fun(_1664662, tc_Option_Ooption(_1664664)), _1664662, tc_fun(tc_Option_Ooption(_1664664), tc_fun(_1664662, tc_Option_Ooption(_1664664)))), c_Fun_Ofun__upd(_1664662, tc_Option_Ooption(_1664664)))))), c_Option_Ooption_OSome(_1664664))), _1664668, _1664666))], (43763 ^ _774244) ^ [_1625335, _1625337] : [c_Wellfounded_Oacyclic(_1625335, hAPP(c_Relation_Oconverse(_1625335, _1625335), _1625337)), -(c_Wellfounded_Oacyclic(_1625335, _1625337))], (28507 ^ _774244) ^ [_1278682, _1278684, _1278686, _1278688] : [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), _1278682, _1278684)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1278686, _1278688))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1278682), _1278684)), 28514 ^ _774244 : [(28517 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1278684), _1278688)))], (28515 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1278686), _1278682)))]]], (17449 ^ _774244) ^ [_1072992, _1072994, _1072996, _1072998] : [class_Rings_Olinordered__semidom(_1072992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1072994), _1072996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072992), c_Groups_Oone__class_Oone(_1072992)), _1072998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072992), hAPP(hAPP(c_Power_Opower__class_Opower(_1072992), _1072998), _1072994)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072992), _1072998), _1072996))))], (46122 ^ _774244) ^ [_1682614, _1682616] : [hAPP(c_Finite__Set_Ocard(_1682614), hAPP(c_List_Oset(_1682614), _1682616)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682614)), _1682616), -(hBOOL(hAPP(c_List_Odistinct(_1682614), _1682616)))], (48628 ^ _774244) ^ [_1745971, _1745973, _1745975] : [hAPP(c_List_Orotate(_1745971, _1745973), _1745975) = c_List_Olist_ONil(_1745971), -(_1745975 = c_List_Olist_ONil(_1745971))], (13224 ^ _774244) ^ [_994057, _994059] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994057), _994059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994059), _994057)))], (10147 ^ _774244) ^ [_941533, _941535] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _941533), _941535))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _941535), _941533)))], (35008 ^ _774244) ^ [_1414973, _1414975, _1414977, _1414979, _1414981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1414973, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1414975, _1414973, _1414977), _1414979)), _1414981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1414973, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1414975, tc_HOL_Obool), tc_fun(_1414973, tc_HOL_Obool), c_Set_Oimage(_1414975, _1414973, _1414977)), hAPP(c_Set_OPow(_1414975), _1414979))), hAPP(c_Set_OPow(_1414973), _1414981))))], (11080 ^ _774244) ^ [_956507, _956509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _956507)), hAPP(c_Nat_OSuc, _956509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956507), _956509)))], (5466 ^ _774244) ^ [_858661, _858663, _858665, _858667] : [-(c_Enum_Osublists(_858667, _858663) = c_Enum_Osublists(_858665, _858661)), _858667 = _858665, _858663 = _858661], (18961 ^ _774244) ^ [_1097792] : [c_Int_OPls = _1097792, -(c_Int_OPls = c_Int_OBit0(_1097792))], (18985 ^ _774244) ^ [_1098166] : [-(c_Int_OBit0(_1098166) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1098166), _1098166))], (5886 ^ _774244) ^ [_868366, _868368, _868370, _868372, _868374] : [hAPP(_868366, 5887 ^ [_868366, _868368, _868370, _868372, _868374]) = hAPP(c_Nat_Onat_Onat__rec(_868368, _868370, _868372), 5887 ^ [_868366, _868368, _868370, _868372, _868374]), -(hAPP(_868366, hAPP(c_Nat_OSuc, _868374)) = hAPP(hAPP(_868372, _868374), hAPP(_868366, _868374)))], (17469 ^ _774244) ^ [_1073378, _1073380, _1073382, _1073384] : [class_Rings_Olinordered__semidom(_1073378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1073380), _1073382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073378), c_Groups_Oone__class_Oone(_1073378)), _1073384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073378), hAPP(hAPP(c_Power_Opower__class_Opower(_1073378), _1073384), _1073380)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073378), _1073384), _1073382))))], (9796 ^ _774244) ^ [_935633, _935635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _935633)), hAPP(c_Int_Onat, _935635))), 9799 ^ _774244 : [(9802 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _935633), _935635)))], (9800 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935635)))]]], (15512 ^ _774244) ^ [_1035866, _1035868, _1035870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035866), _1035870)), _1035868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035866), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035868), _1035870))))], (41798 ^ _774244) ^ [_1578061, _1578063, _1578065] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1578061, _1578063)), _1578065)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1578061), hAPP(c_Relation_ODomain(_1578061, _1578063), _1578065))))], (40945 ^ _774244) ^ [_1551910, _1551912, _1551914, _1551916] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1551910), hAPP(c_Set_OCollect(_1551910), _1551912))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1551914), hAPP(c_Set_OCollect(_1551914), hAPP(hAPP(c_COMBB(tc_fun(_1551910, tc_HOL_Obool), tc_HOL_Obool, _1551914), c_HOL_OEx(_1551910)), hAPP(hAPP(c_COMBC(_1551914, tc_fun(_1551910, tc_HOL_Obool), tc_fun(_1551910, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1551910, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1551910, tc_HOL_Obool), tc_fun(_1551910, tc_HOL_Obool)), _1551914), c_COMBS(_1551910, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1551910, tc_HOL_Obool), tc_fun(_1551910, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1551914), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1551910), c_fconj)), hAPP(hAPP(c_COMBC(_1551914, tc_fun(_1551910, _1551914), tc_fun(_1551910, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1551914, tc_HOL_Obool), tc_fun(tc_fun(_1551910, _1551914), tc_fun(_1551910, tc_HOL_Obool)), _1551914), c_COMBB(_1551914, tc_HOL_Obool, _1551910)), c_fequal)), _1551916)))), _1551912))))))], (43799 ^ _774244) ^ [_1626185, _1626187, _1626189, _1626191, _1626193] : [-(_1626185 = c_Orderings_Obot__class_Obot(tc_fun(_1626187, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626187, tc_fun(_1626189, tc_HOL_Obool)), _1626185), hAPP(hAPP(c_COMBB(tc_fun(_1626189, tc_HOL_Obool), tc_fun(_1626189, tc_HOL_Obool), _1626187), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1626189, tc_HOL_Obool)), _1626191)), _1626193)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1626189, tc_HOL_Obool)), _1626191), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626187, tc_fun(_1626189, tc_HOL_Obool)), _1626185), _1626193)))], (23323 ^ _774244) ^ [_1177744, _1177746, _1177748, _1177750] : [hAPP(c_Product__Type_Ofst(_1177744, _1177746), _1177748) = hAPP(c_Product__Type_Ofst(_1177744, _1177746), _1177750), hAPP(c_Product__Type_Osnd(_1177744, _1177746), _1177748) = hAPP(c_Product__Type_Osnd(_1177744, _1177746), _1177750), -(_1177748 = _1177750)], (10988 ^ _774244) ^ [_954908] : [_954908 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954908), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (17915 ^ _774244) ^ [_1080817] : [class_Int_Onumber__ring(_1080817), -(hAPP(c_Int_Onumber__class_Onumber__of(_1080817), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1080817), c_Groups_Oone__class_Oone(_1080817)))], (25101 ^ _774244) ^ [_1212297, _1212299, _1212301] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212297), _1212299)), _1212299 = _1212301, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212297), _1212301)))], (36303 ^ _774244) ^ [_1444277, _1444279, _1444281, _1444283, _1444285] : [class_Lattices_Olattice(_1444277), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444279, _1444277)), _1444281), _1444283), _1444285) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444277), hAPP(_1444281, _1444285)), hAPP(_1444283, _1444285)))], (16705 ^ _774244) ^ [_1059228, _1059230, _1059232] : [class_Int_Onumber__ring(_1059228), -(hAPP(c_Int_Onumber__class_Onumber__of(_1059228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1059230), _1059232)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1059228), hAPP(c_Int_Onumber__class_Onumber__of(_1059228), _1059230)), hAPP(c_Int_Onumber__class_Onumber__of(_1059228), _1059232)))], (22260 ^ _774244) ^ [_1157539, _1157541] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1157539)), hAPP(c_Code__Numeral_Oof__nat, _1157541)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1157539), _1157541)))], (48412 ^ _774244) ^ [_1741269, _1741271, _1741273, _1741275] : [-(hAPP(hAPP(c_List_Odrop(_1741269), _1741271), hAPP(hAPP(c_List_Olist_OCons(_1741269), _1741273), _1741275)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1741269), hAPP(hAPP(c_List_Olist_OCons(_1741269), _1741273), _1741275), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1741269), tc_List_Olist(_1741269)), c_List_Odrop(_1741269)), _1741275), _1741271))], (31391 ^ _774244) ^ [_1338169, _1338171, _1338173] : [class_Orderings_Oord(_1338169), 31394 ^ _774244 : [(31401 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338169), _1338173), _1338171)), -(hBOOL(hAPP(hAPP(c_member(_1338169), _1338171), hAPP(c_SetInterval_Oord__class_OatLeast(_1338169), _1338173))))], (31395 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1338169), _1338171), hAPP(c_SetInterval_Oord__class_OatLeast(_1338169), _1338173))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338169), _1338173), _1338171)))]]], (51377 ^ _774244) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (35207 ^ _774244) ^ [_1419329, _1419331, _1419333, _1419335, _1419337, _1419339] : [-(hAPP(hAPP(c_Fun_Ocomp(_1419329, _1419331, _1419333, _1419335), _1419337), _1419339) = hAPP(_1419335, hAPP(_1419337, _1419339)))], (27786 ^ _774244) ^ [_1264609, _1264611] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264609, tc_HOL_Obool)), _1264611), _1264611) = _1264611)], (45738 ^ _774244) ^ [_1673368, _1673370, _1673372] : [-(c_Map_Odom(_1673368, _1673370, c_Map_Omap__of(_1673368, _1673370, _1673372)) = hAPP(c_Set_Oimage(tc_prod(_1673368, _1673370), _1673368, c_Product__Type_Ofst(_1673368, _1673370)), hAPP(c_List_Oset(tc_prod(_1673368, _1673370)), _1673372)))], (12594 ^ _774244) ^ [_983361, _983363, _983365, _983367] : [class_Rings_Olinordered__semiring__strict(_983361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983361), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983361), _983363), _983365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983361), _983363), _983367))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983361), c_Groups_Ozero__class_Ozero(_983361)), _983363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983361), _983365), _983367)))], (10896 ^ _774244) ^ [_953419, _953421, _953423, _953425] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_953419), 10899 ^ _774244 : [(10906 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953419), _953421), _953425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953419), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953419), _953421), _953423)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953419), _953425), _953423))))], (10900 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953419), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953419), _953421), _953423)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953419), _953425), _953423))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953419), _953421), _953425)))]]], (43595 ^ _774244) ^ [_1620668, _1620670, _1620672, _1620674] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1620668, tc_fun(_1620670, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1620668, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1620670, tc_HOL_Obool), tc_fun(_1620670, tc_HOL_Obool), _1620668), hAPP(c_COMBC(_1620670, tc_fun(_1620670, tc_HOL_Obool), tc_HOL_Obool), c_member(_1620670))), _1620672)), _1620674)), -(hBOOL(hAPP(hAPP(c_member(_1620670), _1620674), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1620668, tc_fun(_1620670, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1620668, tc_HOL_Obool))), _1620672))))], (44052 ^ _774244) ^ [_1633172, _1633174] : [-(c_Relation_Orefl__on(_1633172, c_Orderings_Otop__class_Otop(tc_fun(_1633172, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1633172, _1633172), tc_HOL_Obool)), _1633174), c_Relation_OId(_1633172))))], (27824 ^ _774244) ^ [_1265497, _1265499, _1265501, _1265503] : [class_Lattices_Osemilattice__sup(_1265497), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265497), _1265499), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265497), _1265501), _1265503)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265497), _1265501), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265497), _1265499), _1265503)))], (3244 ^ _774244) ^ [_824066, _824068, _824070, _824072, _824074, _824076] : [-(c_SetInterval_Oord_OatLeast(_824076, _824072, _824068) = c_SetInterval_Oord_OatLeast(_824074, _824070, _824066)), _824076 = _824074, _824072 = _824070, _824068 = _824066], (41671 ^ _774244) ^ [_1575019, _1575021, _1575023, _1575025] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575019, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1575019, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1575021, _1575019), _1575023)), hAPP(c_Relation_ORange(_1575021, _1575019), _1575025))), hAPP(c_Relation_ORange(_1575021, _1575019), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1575021, _1575019), tc_HOL_Obool)), _1575023), _1575025)))))], (21099 ^ _774244) ^ [_1135641, _1135643] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135641), _1135643), hAPP(c_Int_Onumber__class_Onumber__of(_1135641), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1135641)), class_Fields_Ofield__inverse__zero(_1135641), class_Int_Onumber__ring(_1135641)], (48777 ^ _774244) ^ [_1749091, _1749093] : [class_Complete__Lattice_Ocomplete__lattice(_1749091), -(c_Complete__Lattice_OSup__class_OSup(_1749091, hAPP(c_List_Oset(_1749091), _1749093)) = hAPP(c_List_Ofoldl(_1749091, _1749091, c_Lattices_Osemilattice__sup__class_Osup(_1749091), c_Orderings_Obot__class_Obot(_1749091)), _1749093))], (24317 ^ _774244) ^ [_1196641, _1196643, _1196645, _1196647] : [class_Orderings_Olinorder(_1196641), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196641), _1196643), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196641), _1196645), _1196647)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196641), _1196645), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196641), _1196643), _1196647)))], (18735 ^ _774244) ^ [] : [-(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))))))], (32286 ^ _774244) ^ [_1358877, _1358879] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358877), _1358879)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1358877), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358879))))], (41418 ^ _774244) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (16447 ^ _774244) ^ [_1054104, _1054106, _1054108] : [class_Groups_Oordered__ab__group__add__abs(_1054104), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054104), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054104), hAPP(c_Groups_Oabs__class_Oabs(_1054104), _1054106)), hAPP(c_Groups_Oabs__class_Oabs(_1054104), _1054108))), hAPP(c_Groups_Oabs__class_Oabs(_1054104), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054104), _1054108), _1054106)))))], (13573 ^ _774244) ^ [_1000534] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1000534) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48370 ^ _774244) ^ [_1740258, _1740260, _1740262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740258)), _1740262)), _1740260)), -(hAPP(hAPP(c_List_Odrop(_1740258), _1740260), _1740262) = c_List_Olist_ONil(_1740258))], (7231 ^ _774244) ^ [_891513, _891515, _891517, _891519, _891521, _891523] : [c_Nitpick_Opair__box_OPairBox(_891513, _891515, _891517, _891519) = c_Nitpick_Opair__box_OPairBox(_891513, _891515, _891521, _891523), 7234 ^ _774244 : [(7237 ^ _774244) ^ [] : [-(_891519 = _891523)], (7235 ^ _774244) ^ [] : [-(_891517 = _891521)]]], (35723 ^ _774244) ^ [_1431914, _1431916, _1431918, _1431920, _1431922] : [hAPP(c_Relation_OImage(_1431914, _1431914, _1431916), hAPP(hAPP(c_Set_Oinsert(_1431914), _1431918), c_Orderings_Obot__class_Obot(tc_fun(_1431914, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1431914, _1431914, _1431916), hAPP(hAPP(c_Set_Oinsert(_1431914), _1431920), c_Orderings_Obot__class_Obot(tc_fun(_1431914, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1431914, _1431922, _1431916), hBOOL(hAPP(hAPP(c_member(_1431914), _1431920), _1431922)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1431914, _1431914)), hAPP(hAPP(c_Product__Type_OPair(_1431914, _1431914), _1431918), _1431920)), _1431916)))], (47644 ^ _774244) ^ [_1721440, _1721442, _1721444, _1721446, _1721448, _1721450] : [-(c_List_Ofoldr(_1721440, _1721442, _1721444, hAPP(hAPP(c_List_Oappend(_1721440), _1721446), _1721448), _1721450) = c_List_Ofoldr(_1721440, _1721442, _1721444, _1721446, c_List_Ofoldr(_1721440, _1721442, _1721444, _1721448, _1721450)))], (6303 ^ _774244) ^ [_875449, _875451, _875453, _875455, _875457, _875459] : [-(c_Com_Ocom_OCall(_875449, _875451, _875453) = c_Com_Ocom_OCall(_875455, _875457, _875459)), _875449 = _875455, _875451 = _875457, _875453 = _875459], (1484 ^ _774244) ^ [_795518, _795520] : [-(class_Groups_Oab__semigroup__mult(_795518)), _795520 = _795518, class_Groups_Oab__semigroup__mult(_795520)], (23579 ^ _774244) ^ [_1183035, _1183037, _1183039] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1183035, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1183035, tc_HOL_Obool)), _1183037), _1183039)), _1183039) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1183035, tc_HOL_Obool)), _1183037), _1183039))], (21974 ^ _774244) ^ [_1151841] : [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), _1151841))), 21977 ^ _774244 : [(21984 ^ _774244) ^ [] : [-(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), _1151841))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1151841)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1151841)), 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), _1151841)))))], (21978 ^ _774244) ^ [] : [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), _1151841)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1151841)) = 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), _1151841))))]]], (22770 ^ _774244) ^ [_1167459, _1167461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1167459)), 22773 ^ _774244 : [(22780 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1167461))), 22783 ^ _774244 : [(22790 ^ _774244) ^ [] : [-(_1167459 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1167459, _1167461) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1167459), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1167461))))], (22784 ^ _774244) ^ [] : [_1167459 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1167459, _1167461) = 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)))]]], (22774 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1167461)), -(c_Divides_Odivmod__int(_1167459, _1167461) = c_Divides_OposDivAlg(_1167459, _1167461))]]], (13505 ^ _774244) ^ [_999082, _999084, _999086, _999088, _999090, _999092] : [class_Divides_Osemiring__div(_999082), c_Divides_Odiv__class_Omod(_999082, _999084, _999086) = c_Divides_Odiv__class_Omod(_999082, _999088, _999086), c_Divides_Odiv__class_Omod(_999082, _999090, _999086) = c_Divides_Odiv__class_Omod(_999082, _999092, _999086), -(c_Divides_Odiv__class_Omod(_999082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999082), _999084), _999090), _999086) = c_Divides_Odiv__class_Omod(_999082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999082), _999088), _999092), _999086))], (30793 ^ _774244) ^ [_1326304, _1326306, _1326308, _1326310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1326304, _1326306)), hAPP(hAPP(c_Product__Type_OPair(_1326304, _1326306), _1326308), _1326310)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1326304, _1326306), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1326304, tc_fun(_1326306, tc_HOL_Obool))), _1326308), _1326310)))], (43951 ^ _774244) ^ [_1630110, _1630112, _1630114, _1630116, _1630118] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630110, _1630110)), hAPP(hAPP(c_Product__Type_OPair(_1630110, _1630110), hAPP(_1630112, hAPP(c_Nat_OSuc, 43952 ^ [_1630110, _1630112, _1630114, _1630116, _1630118]))), hAPP(_1630112, 43952 ^ [_1630110, _1630112, _1630114, _1630116, _1630118]))), c_Transitive__Closure_Ortrancl(_1630110, _1630114))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630110, _1630110)), hAPP(hAPP(c_Product__Type_OPair(_1630110, _1630110), hAPP(_1630112, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1630116), _1630118))), hAPP(_1630112, _1630116))), c_Transitive__Closure_Ortrancl(_1630110, _1630114))))], (10365 ^ _774244) ^ [_944848, _944850, _944852, _944854] : [class_Orderings_Oord(_944848), 10368 ^ _774244 : [(10375 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944848), hAPP(_944852, 10376 ^ [_944848, _944850, _944852, _944854])), hAPP(_944854, 10376 ^ [_944848, _944850, _944852, _944854]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944850, _944848)), _944852), _944854)))], (10369 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944850, _944848)), _944852), _944854)), 10372 ^ _774244 : [(10373 ^ _774244) ^ [_945005] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944848), hAPP(_944852, _945005)), hAPP(_944854, _945005))))]]]]], (17553 ^ _774244) ^ [_1074922, _1074924] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074922)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1074922)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1074924)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074922)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1074924))))], (39336 ^ _774244) ^ [_1512015, _1512017, _1512019, _1512021, _1512023, _1512025] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1512015, _1512017, _1512019, _1512021, _1512023), _1512025)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1512015), _1512023)))], (28821 ^ _774244) ^ [_1286240, _1286242] : [class_Lattices_Oboolean__algebra(_1286240), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286240), hAPP(c_Groups_Ouminus__class_Ouminus(_1286240), _1286242)), _1286242) = c_Orderings_Otop__class_Otop(_1286240))], (38802 ^ _774244) ^ [_1499495, _1499497, _1499499, _1499501, _1499503, _1499505] : [-(hAPP(c_Set_Ovimage(_1499495, _1499497, _1499499), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1499501, tc_fun(_1499497, tc_HOL_Obool)), _1499503), _1499505)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1499501, tc_fun(_1499495, tc_HOL_Obool)), _1499503), hAPP(hAPP(c_COMBB(tc_fun(_1499497, tc_HOL_Obool), tc_fun(_1499495, tc_HOL_Obool), _1499501), c_Set_Ovimage(_1499495, _1499497, _1499499)), _1499505)))], (51283 ^ _774244) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (31477 ^ _774244) ^ [_1340358, _1340360, _1340362, _1340364, _1340366, _1340368, _1340370, _1340372] : [c_Finite__Set_Ofolding__image__simple(_1340358, _1340360, _1340362, _1340364, _1340366, _1340368), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340360), _1340370)), hBOOL(hAPP(hAPP(c_member(_1340360), _1340372), _1340370)), -(hAPP(_1340368, _1340370) = hAPP(hAPP(_1340362, hAPP(_1340366, _1340372)), hAPP(_1340368, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340360, tc_HOL_Obool)), _1340370), hAPP(hAPP(c_Set_Oinsert(_1340360), _1340372), c_Orderings_Obot__class_Obot(tc_fun(_1340360, tc_HOL_Obool)))))))], (40735 ^ _774244) ^ [_1544739, _1544741, _1544743, _1544745] : [-(hAPP(c_Set_Ovimage(_1544739, _1544741, _1544743), _1544745) = hAPP(c_Set_OCollect(_1544739), hAPP(hAPP(c_COMBC(_1544739, tc_fun(_1544741, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1544741, tc_fun(tc_fun(_1544741, tc_HOL_Obool), tc_HOL_Obool), _1544739), c_member(_1544741)), _1544743)), _1544745)))], (28689 ^ _774244) ^ [_1283453, _1283455, _1283457] : [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), _1283453), _1283455))), -(hBOOL(hAPP(hAPP(_1283457, _1283453), _1283455))), 28696 ^ _774244 : [(28699 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 28694 ^ [_1283453, _1283455, _1283457]), 28695 ^ [_1283453, _1283455, _1283457])), -(hBOOL(hAPP(hAPP(_1283457, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28694 ^ [_1283453, _1283455, _1283457]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 28695 ^ [_1283453, _1283455, _1283457])))], (28705 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1283457, 28694 ^ [_1283453, _1283455, _1283457]), 28695 ^ [_1283453, _1283455, _1283457]))], (28697 ^ _774244) ^ [] : [-(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), 28694 ^ [_1283453, _1283455, _1283457]), 28695 ^ [_1283453, _1283455, _1283457]))))]]], (40500 ^ _774244) ^ [_1539482, _1539484] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1539482), c_Int_OInteg)), hBOOL(hAPP(_1539484, hAPP(c_Int_ORep__Integ, 40505 ^ [_1539482, _1539484]))), -(hBOOL(hAPP(_1539484, _1539482)))], (14302 ^ _774244) ^ [_1013782, _1013784] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1013782, _1013784)), _1013784) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50850 ^ _774244) ^ [_1794260, _1794262, _1794264, _1794266, _1794268] : [hBOOL(hAPP(hAPP(c_member(_1794260), _1794262), hAPP(c_List_Oset(_1794260), _1794264))), -(hBOOL(hAPP(_1794266, _1794262))), -(c_List_OdropWhile(_1794260, _1794266, hAPP(hAPP(c_List_Oappend(_1794260), _1794264), _1794268)) = hAPP(hAPP(c_List_Oappend(_1794260), c_List_OdropWhile(_1794260, _1794266, _1794264)), _1794268))], (49442 ^ _774244) ^ [_1764132, _1764134] : [-(c_List_Ofoldr(tc_List_Olist(_1764132), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1764132)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1764132))), c_List_Otranspose(_1764132, _1764134), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1764132))), hAPP(c_List_Ofilter(tc_List_Olist(_1764132), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1764132)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1764132), tc_List_Olist(_1764132), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1764132)))), _1764134)))], (35102 ^ _774244) ^ [_1416993, _1416995, _1416997, _1416999, _1417001] : [c_Finite__Set_Ofolding__one__idem(_1416993, _1416995, _1416997), hBOOL(hAPP(c_Finite__Set_Ofinite(_1416993), _1416999)), -(_1416999 = c_Orderings_Obot__class_Obot(tc_fun(_1416993, tc_HOL_Obool))), -(hAPP(_1416997, hAPP(hAPP(c_Set_Oinsert(_1416993), _1417001), _1416999)) = hAPP(hAPP(_1416995, _1417001), hAPP(_1416997, _1416999)))], (38369 ^ _774244) ^ [_1489842, _1489844, _1489846, _1489848] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1489842), _1489844)), 38372 ^ _774244 : [(38379 ^ _774244) ^ [] : [hAPP(c_Finite__Set_Ocard(_1489846), hAPP(c_Set_Oimage(_1489842, _1489846, _1489848), _1489844)) = hAPP(c_Finite__Set_Ocard(_1489842), _1489844), -(c_Fun_Oinj__on(_1489842, _1489846, _1489848, _1489844))], (38373 ^ _774244) ^ [] : [c_Fun_Oinj__on(_1489842, _1489846, _1489848, _1489844), -(hAPP(c_Finite__Set_Ocard(_1489846), hAPP(c_Set_Oimage(_1489842, _1489846, _1489848), _1489844)) = hAPP(c_Finite__Set_Ocard(_1489842), _1489844))]]], (11289 ^ _774244) ^ [_960061, _960063] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _960061), _960063))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _960061), _960063)), -(_960061 = _960063)], (51057 ^ _774244) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (4514 ^ _774244) ^ [_844061, _844063] : [_844063 = _844061, -(c_Orderings_Oord__class_Omin(_844063) = c_Orderings_Oord__class_Omin(_844061))], (10970 ^ _774244) ^ [_954587, _954589, _954591] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954587)), _954589) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954587)), _954591), -(_954589 = _954591)], (30188 ^ _774244) ^ [_1312012, _1312014, _1312016] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312012), _1312014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1312012), _1312014)), hAPP(c_Finite__Set_Ocard(_1312012), hAPP(hAPP(c_Set_Oinsert(_1312012), _1312016), _1312014)))))], (15930 ^ _774244) ^ [_1044850, _1044852] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1044850), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1044852), _1044850)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044852), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044852, _1044850)))], (24981 ^ _774244) ^ [_1210370, _1210372] : [_1210370 = _1210372, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210370), _1210372)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210372), _1210370)))], (51495 ^ _774244) ^ [_1802175, _1802177] : [hBOOL(hAPP(hAPP(c_fdisj, _1802175), _1802177)), -(hBOOL(_1802175)), -(hBOOL(_1802177))], (40623 ^ _774244) ^ [_1541927, _1541929, _1541931] : [-(hAPP(c_Set_OCollect(_1541927), hAPP(hAPP(c_COMBS(_1541927, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541927), c_fdisj), _1541929)), _1541931)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1541927, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1541927), _1541929)), hAPP(c_Set_OCollect(_1541927), _1541931)))], (9454 ^ _774244) ^ [_929689, _929691, _929693] : [class_Rings_Olinordered__semiring__strict(_929689), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929689), c_Groups_Ozero__class_Ozero(_929689)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929689), _929691), _929693))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929689), c_Groups_Ozero__class_Ozero(_929689)), _929693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929689), c_Groups_Ozero__class_Ozero(_929689)), _929691)))], (15456 ^ _774244) ^ [_1034916, _1034918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1034916)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1034918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034918), _1034916)), _1034918)))], (43431 ^ _774244) ^ [_1615395, _1615397, _1615399, _1615401, _1615403, _1615405] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615395, tc_fun(_1615397, tc_HOL_Obool)), _1615399), hAPP(hAPP(c_COMBC(_1615395, tc_fun(_1615401, tc_fun(_1615397, tc_HOL_Obool)), tc_fun(_1615397, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615401, tc_HOL_Obool), tc_fun(tc_fun(_1615401, tc_fun(_1615397, tc_HOL_Obool)), tc_fun(_1615397, tc_HOL_Obool)), _1615395), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615401, tc_fun(_1615397, tc_HOL_Obool))), _1615403)), _1615405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615401, tc_fun(_1615397, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615395, tc_fun(_1615401, tc_HOL_Obool)), _1615399), _1615403)), _1615405))], (48512 ^ _774244) ^ [_1743890, _1743892, _1743894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1743890), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743892)), _1743894))), -(_1743894 = hAPP(hAPP(c_List_Oappend(_1743892), hAPP(hAPP(c_List_Otake(_1743892), _1743890), _1743894)), hAPP(hAPP(c_List_Olist_OCons(_1743892), hAPP(hAPP(c_List_Onth(_1743892), _1743894), _1743890)), hAPP(hAPP(c_List_Odrop(_1743892), hAPP(c_Nat_OSuc, _1743890)), _1743894))))], (50767 ^ _774244) ^ [_1792491, _1792493] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1792491), _1792493) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1792491)), c_List_Oembed__list(_1792493))))], (42167 ^ _774244) ^ [_1587628, _1587630, _1587632] : [hBOOL(hAPP(_1587628, _1587630)), -(hBOOL(hAPP(_1587628, c_Hilbert__Choice_OEps(_1587632, _1587628))))], (44518 ^ _774244) ^ [_1644305, _1644307] : [class_Complete__Lattice_Ocomplete__lattice(_1644305), -(c_Complete__Lattice_OInf__class_OInf(_1644305, hAPP(hAPP(c_Set_Oinsert(_1644305), _1644307), c_Orderings_Obot__class_Obot(tc_fun(_1644305, tc_HOL_Obool)))) = _1644307)], (22812 ^ _774244) ^ [_1168057, _1168059, _1168061] : [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), _1168057), _1168059))), -(hBOOL(hAPP(hAPP(_1168061, _1168057), _1168059))), 22819 ^ _774244 : [(22822 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1168061, 22817 ^ [_1168057, _1168059, _1168061]), 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)))), 22818 ^ [_1168057, _1168059, _1168061])))), -(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), 22817 ^ [_1168057, _1168059, _1168061]), 22818 ^ [_1168057, _1168059, _1168061])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 22818 ^ [_1168057, _1168059, _1168061]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22832 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(_1168061, 22817 ^ [_1168057, _1168059, _1168061]), 22818 ^ [_1168057, _1168059, _1168061]))], (22820 ^ _774244) ^ [] : [-(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), 22817 ^ [_1168057, _1168059, _1168061]), 22818 ^ [_1168057, _1168059, _1168061]))))]]], (35789 ^ _774244) ^ [_1433395, _1433397, _1433399, _1433401, _1433403] : [c_Equiv__Relations_Oequiv(_1433395, _1433397, _1433399), hBOOL(hAPP(hAPP(c_member(tc_prod(_1433395, _1433395)), hAPP(hAPP(c_Product__Type_OPair(_1433395, _1433395), _1433401), _1433403)), _1433399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1433395, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1433395, _1433395, _1433399), hAPP(hAPP(c_Set_Oinsert(_1433395), _1433401), c_Orderings_Obot__class_Obot(tc_fun(_1433395, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1433395, _1433395, _1433399), hAPP(hAPP(c_Set_Oinsert(_1433395), _1433403), c_Orderings_Obot__class_Obot(tc_fun(_1433395, tc_HOL_Obool)))))))], (8762 ^ _774244) ^ [_917300] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _917300) = _917300)], (37031 ^ _774244) ^ [_1461067, _1461069, _1461071, _1461073, _1461075] : [class_Groups_Ocomm__monoid__mult(_1461067), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461069), _1461071)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461069), _1461073)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461069, tc_HOL_Obool)), _1461071), _1461073) = c_Orderings_Obot__class_Obot(tc_fun(_1461069, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1461069, _1461067), _1461075), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461069, tc_HOL_Obool)), _1461071), _1461073)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1461067), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1461069, _1461067), _1461075), _1461071)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1461069, _1461067), _1461075), _1461073)))], (22426 ^ _774244) ^ [_1160668, _1160670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1160668)), 22429 ^ _774244 : [(22436 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160670), _1160668))), -(c_Divides_OposDivAlg(_1160670, _1160668) = hAPP(c_Divides_Oadjust(_1160668), c_Divides_OposDivAlg(_1160670, 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)))), _1160668))))], (22430 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160670), _1160668)), -(c_Divides_OposDivAlg(_1160670, _1160668) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1160670))]]], (46158 ^ _774244) ^ [_1683382, _1683384, _1683386, _1683388] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683382)), _1683384) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683386)), _1683388), -(hAPP(hAPP(c_List_Omap(tc_prod(_1683382, _1683386), _1683386), c_Product__Type_Osnd(_1683382, _1683386)), hAPP(hAPP(c_List_Ozip(_1683382, _1683386), _1683384), _1683388)) = _1683388)], (40037 ^ _774244) ^ [_1530846, _1530848, _1530850, _1530852, _1530854] : [c_Relation_Orefl__on(_1530846, _1530848, _1530850), c_Relation_Orefl__on(_1530846, _1530852, _1530854), -(c_Relation_Orefl__on(_1530846, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530846, tc_HOL_Obool)), _1530848), _1530852), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530846, _1530846), tc_HOL_Obool)), _1530850), _1530854)))], (5296 ^ _774244) ^ [_856140, _856142] : [_856142 = _856140, -(c_List_Ohd(_856142) = c_List_Ohd(_856140))], (43735 ^ _774244) ^ [_1624800, _1624802, _1624804, _1624806, _1624808] : [-(_1624800 = c_Orderings_Obot__class_Obot(tc_fun(_1624802, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624804, tc_HOL_Obool)), _1624806), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1624802, tc_fun(_1624804, tc_HOL_Obool)), _1624800), _1624808)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1624802, tc_fun(_1624804, tc_HOL_Obool)), _1624800), hAPP(hAPP(c_COMBB(tc_fun(_1624804, tc_HOL_Obool), tc_fun(_1624804, tc_HOL_Obool), _1624802), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624804, tc_HOL_Obool)), _1624806)), _1624808)))], (13208 ^ _774244) ^ [_993811, _993813, _993815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993811), _993813)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993813), _993815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993811), _993815)))], (4316 ^ _774244) ^ [_841038, _841040] : [_841040 = _841038, -(c_HOL_OEx(_841040) = c_HOL_OEx(_841038))], (30049 ^ _774244) ^ [_1309439, _1309441, _1309443, _1309445] : [class_Groups_Ocomm__monoid__add(_1309439), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1309441), _1309443))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1309441, _1309439), _1309445), _1309443) = c_Groups_Ozero__class_Ozero(_1309439))], (17565 ^ _774244) ^ [_1075103, _1075105] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075103)))), 17568 ^ _774244 : [(17575 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075105)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075103), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075105)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075103), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075105))))], (17569 ^ _774244) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075105))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075103), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075105)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075103))]]], (2488 ^ _774244) ^ [_811830, _811832, _811834, _811836] : [-(c_Divides_Odivmod__int__rel(_811836, _811832) = c_Divides_Odivmod__int__rel(_811834, _811830)), _811836 = _811834, _811832 = _811830], (19371 ^ _774244) ^ [] : [-(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)))))], (1894 ^ _774244) ^ [_801761, _801763, _801765, _801767, _801769, _801771, _801773, _801775, _801777, _801779] : [-(c_Sum__Type_Osum_Osum__size(_801779, _801775, _801771, _801767, _801763) = c_Sum__Type_Osum_Osum__size(_801777, _801773, _801769, _801765, _801761)), _801779 = _801777, _801775 = _801773, _801771 = _801769, _801767 = _801765, _801763 = _801761], (19057 ^ _774244) ^ [_1099440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1099440))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1099440)))], (18871 ^ _774244) ^ [_1096143, _1096145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096143), 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)))), _1096145))), 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)))), _1096143)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1096145), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1096143))], (41144 ^ _774244) ^ [_1561305, _1561307, _1561309] : [-(hAPP(c_Fun_Ocomp(_1561305, _1561307, _1561305, _1561309), c_Fun_Oid(_1561305)) = _1561309)], (39102 ^ _774244) ^ [_1506638, _1506640] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506638), _1506640)), -(hAPP(c_Finite__Set_Ocard(_1506638), _1506640) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1506638, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1506638), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1506640))], (46401 ^ _774244) ^ [_1691408, _1691410, _1691412, _1691414, _1691416, _1691418] : [-(hAPP(hAPP(c_List_Ozip(_1691408, _1691410), hAPP(hAPP(c_List_Olist_OCons(_1691408), _1691412), _1691414)), hAPP(hAPP(c_List_Olist_OCons(_1691410), _1691416), _1691418)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1691408, _1691410)), hAPP(hAPP(c_Product__Type_OPair(_1691408, _1691410), _1691412), _1691416)), hAPP(hAPP(c_List_Ozip(_1691408, _1691410), _1691414), _1691418)))], (4440 ^ _774244) ^ [_842946, _842948, _842950, _842952] : [-(c_Complete__Lattice_OSup__class_OSup(_842952, _842948) = c_Complete__Lattice_OSup__class_OSup(_842950, _842946)), _842952 = _842950, _842948 = _842946], (47973 ^ _774244) ^ [_1729298, _1729300, _1729302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729298)), _1729300)), _1729302)), -(hAPP(hAPP(c_List_Otake(_1729298), _1729302), _1729300) = _1729300)], (50747 ^ _774244) ^ [_1792096, _1792098, _1792100] : [hBOOL(hAPP(hAPP(c_member(_1792096), _1792098), hAPP(c_List_Oset(_1792096), _1792100))), -(c_List_Oremdups(_1792096, hAPP(hAPP(c_List_Olist_OCons(_1792096), _1792098), _1792100)) = c_List_Oremdups(_1792096, _1792100))], (3564 ^ _774244) ^ [_829134, _829136, _829138, _829140] : [-(c_Wellfounded_Omin__ext(_829140, _829136) = c_Wellfounded_Omin__ext(_829138, _829134)), _829140 = _829138, _829136 = _829134], (24231 ^ _774244) ^ [_1195073, _1195075, _1195077, _1195079] : [class_Orderings_Olinorder(_1195073), 24234 ^ _774244 : [(24243 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195073), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195073), _1195075), _1195077)), _1195079))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195073), _1195075), _1195079)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195073), _1195077), _1195079))], (24235 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195073), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195073), _1195075), _1195077)), _1195079)), 24238 ^ _774244 : [(24241 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195073), _1195077), _1195079)))], (24239 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195073), _1195075), _1195079)))]]]]], (31575 ^ _774244) ^ [_1343811, _1343813, _1343815] : [-(hBOOL(hAPP(hAPP(c_member(_1343811), _1343813), _1343815))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1343811, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1343811), _1343813), _1343815)), hAPP(hAPP(c_Set_Oinsert(_1343811), _1343813), c_Orderings_Obot__class_Obot(tc_fun(_1343811, tc_HOL_Obool)))) = _1343815)], (43711 ^ _774244) ^ [_1624234, _1624236, _1624238, _1624240, _1624242] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1624234, tc_fun(_1624236, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1624234), _1624238), _1624240)), _1624242) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624236, tc_HOL_Obool)), hAPP(_1624242, _1624238)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1624234, tc_fun(_1624236, tc_HOL_Obool)), _1624240), _1624242)))], (7325 ^ _774244) ^ [_893277, _893279, _893281, _893283] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_893277), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893277), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893277), _893279), _893281)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893277), _893279), _893283))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893277), _893281), _893283)))], (28880 ^ _774244) ^ [_1287892] : [c_Orderings_Otop__class_Otop(tc_fun(_1287892, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1287892, tc_HOL_Obool))], (48382 ^ _774244) ^ [_1740506, _1740508, _1740510, _1740512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1740506), _1740508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1740510, tc_HOL_Obool)), hAPP(c_List_Oset(_1740510), hAPP(hAPP(c_List_Odrop(_1740510), _1740508), _1740512))), hAPP(c_List_Oset(_1740510), hAPP(hAPP(c_List_Odrop(_1740510), _1740506), _1740512)))))], (39475 ^ _774244) ^ [_1514978, _1514980, _1514982, _1514984] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514978), _1514980)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514978), _1514982)), -(_1514982 = c_Orderings_Obot__class_Obot(tc_fun(_1514978, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1514978, tc_HOL_Obool), tc_fun(_1514978, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1514978, tc_HOL_Obool), tc_fun(_1514978, tc_HOL_Obool)), _1514980), _1514982)), c_Wellfounded_Omax__ext(_1514978, _1514984)))), 39489 ^ _774244 : [(39492 ^ _774244) ^ [_1515383] : [hBOOL(hAPP(hAPP(c_member(_1514978), _1515383), _1514982)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1514978, _1514978)), hAPP(hAPP(c_Product__Type_OPair(_1514978, _1514978), 39488 ^ [_1514978, _1514980, _1514982, _1514984]), _1515383)), _1514984))], (39490 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514978), 39488 ^ [_1514978, _1514980, _1514982, _1514984]), _1514980)))]]], (22999 ^ _774244) ^ [_1172152, _1172154, _1172156, _1172158, _1172160, _1172162] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1172152, _1172154), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1172156), _1172158))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1172152, _1172154), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1172160), _1172162))), -(_1172154 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1172158 = _1172162)], (19393 ^ _774244) ^ [_1105312] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1105312), _1105312)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1105312)], (370 ^ _774244) ^ [_779837, _779839, _779841, _779843] : [-(c_Equiv__Relations_Oequivp(_779841, _779837)), c_Equiv__Relations_Oequivp(_779843, _779839), _779843 = _779841, _779839 = _779837], (35983 ^ _774244) ^ [_1437388, _1437390, _1437392, _1437394] : [class_Lattices_Osemilattice__inf(_1437388), 35986 ^ _774244 : [(35995 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437388), _1437390), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1437388), _1437392), _1437394)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437388), _1437390), _1437392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437388), _1437390), _1437394))], (35987 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437388), _1437390), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1437388), _1437392), _1437394))), 35990 ^ _774244 : [(35993 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437388), _1437390), _1437394)))], (35991 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437388), _1437390), _1437392)))]]]]], (3386 ^ _774244) ^ [_826291, _826293] : [_826293 = _826291, -(c_Random__Sequence_Osingle(_826293) = c_Random__Sequence_Osingle(_826291))], (51447 ^ _774244) ^ [] : [-(hBOOL(c_fTrue))], (32359 ^ _774244) ^ [_1360434, _1360436, _1360438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1360434, tc_HOL_Obool)), _1360436), hAPP(hAPP(c_Set_Oinsert(_1360434), _1360438), c_Orderings_Obot__class_Obot(tc_fun(_1360434, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1360434, _1360438, _1360436) = _1360438)], (45787 ^ _774244) ^ [_1674555, _1674557, _1674559, _1674561] : [hBOOL(hAPP(c_List_Odistinct(_1674555), hAPP(hAPP(c_List_Omap(_1674557, _1674555), _1674559), _1674561))), 45790 ^ _774244 : [(45793 ^ _774244) ^ [] : [-(c_Fun_Oinj__on(_1674557, _1674555, _1674559, hAPP(c_List_Oset(_1674557), _1674561)))], (45791 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1674557), _1674561)))]]], (5260 ^ _774244) ^ [_855584, _855586] : [_855586 = _855584, -(c_List_Otl(_855586) = c_List_Otl(_855584))], (35326 ^ _774244) ^ [_1422479] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1422479) = 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), _1422479), 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))))))], (44099 ^ _774244) ^ [_1634434, _1634436, _1634438, _1634440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1634434, _1634436), tc_HOL_Obool)), _1634438), _1634440)), c_Relation_Osingle__valued(_1634434, _1634436, _1634440), -(c_Relation_Osingle__valued(_1634434, _1634436, _1634438))], (17559 ^ _774244) ^ [_1075001, _1075003] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1075001))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075001), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075003)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47030 ^ _774244) ^ [_1706615, _1706617, _1706619, _1706621, _1706623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706615), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706617)), _1706619))), -(hAPP(hAPP(c_List_Onth(_1706621), hAPP(hAPP(c_List_Omap(_1706617, _1706621), _1706623), _1706619)), _1706615) = hAPP(_1706623, hAPP(hAPP(c_List_Onth(_1706617), _1706619), _1706615)))], (34281 ^ _774244) ^ [_1397999, _1398001, _1398003, _1398005] : [-(hAPP(c_Map_Orestrict__map(_1397999, _1398001, _1398003, c_Orderings_Obot__class_Obot(tc_fun(_1397999, tc_HOL_Obool))), _1398005) = c_Option_Ooption_ONone(_1398001))], (8459 ^ _774244) ^ [_912080, _912082, _912084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _912080), _912082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _912084)), -(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), _912084)), _912080)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _912084)), _912082))))], (50571 ^ _774244) ^ [_1788882, _1788884, _1788886] : [-(c_List_OtakeWhile(_1788882, _1788884, _1788886) = hAPP(hAPP(c_List_Otake(_1788882), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788882)), c_List_OtakeWhile(_1788882, _1788884, _1788886))), _1788886))], (10089 ^ _774244) ^ [_940523, _940525, _940527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940523), _940525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940527), _940523)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940527), _940525))))], (6323 ^ _774244) ^ [_875810, _875812, _875814, _875816] : [c_Com_Ocom_OCall(_875810, _875812, _875814) = c_Com_Ocom_OBODY(_875816)], (37089 ^ _774244) ^ [_1462238, _1462240, _1462242] : [class_Lattices_Olattice(_1462238), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462238), _1462240)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462238), _1462242)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462238, tc_HOL_Obool)), _1462240), _1462242) = c_Orderings_Obot__class_Obot(tc_fun(_1462238, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1462238), c_Big__Operators_Olattice__class_OSup__fin(_1462238, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1462238, tc_HOL_Obool)), _1462240), _1462242))), c_Big__Operators_Olattice__class_OSup__fin(_1462238, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462238, tc_HOL_Obool)), _1462240), _1462242))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1462238), c_Big__Operators_Olattice__class_OSup__fin(_1462238, _1462240)), c_Big__Operators_Olattice__class_OSup__fin(_1462238, _1462242)))], (5514 ^ _774244) ^ [_859363, _859365, _859367, _859369] : [-(tc_prod(_859369, _859365) = tc_prod(_859367, _859363)), _859369 = _859367, _859365 = _859363], (11677 ^ _774244) ^ [_966813, _966815, _966817, _966819] : [class_Rings_Oordered__semiring(_966813), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966813), _966815), _966817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966813), c_Groups_Ozero__class_Ozero(_966813)), _966819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966813), _966815), _966819)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966813), _966817), _966819))))], (18197 ^ _774244) ^ [_1084957] : [-(c_Int_Opred(_1084957) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1084957), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5360 ^ _774244) ^ [_857092, _857094] : [_857094 = _857092, -(c_Groups_Ozero__class_Ozero(_857094) = c_Groups_Ozero__class_Ozero(_857092))], (33872 ^ _774244) ^ [_1389326, _1389328, _1389330, _1389332, _1389334] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1389326)), hAPP(c_Set_Oimage(_1389328, tc_Option_Ooption(_1389326), _1389330), c_Orderings_Otop__class_Otop(tc_fun(_1389328, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1389326)), hAPP(c_Set_Oimage(_1389328, tc_Option_Ooption(_1389326), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1389328, tc_Option_Ooption(_1389326)), _1389330), _1389332), hAPP(c_Option_Ooption_OSome(_1389326), _1389334))), c_Orderings_Otop__class_Otop(tc_fun(_1389328, tc_HOL_Obool))))))], (48216 ^ _774244) ^ [_1736216, _1736218, _1736220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1736216, _1736216), tc_HOL_Obool)), _1736218), _1736220)), c_Relation_Orefl__on(_1736216, c_Orderings_Otop__class_Otop(tc_fun(_1736216, tc_HOL_Obool)), _1736220), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1736216), tc_List_Olist(_1736216)), tc_HOL_Obool)), c_List_Olistrel1(_1736216, _1736218)), c_List_Olistrel(_1736216, _1736220))))], (7806 ^ _774244) ^ [_901730, _901732, _901734, _901736] : [hAPP(c_Sum__Type_OInl(_901730, _901732), _901734) = hAPP(c_Sum__Type_OInl(_901730, _901732), _901736), -(_901734 = _901736)], (21972 ^ _774244) ^ [_1151810] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1151810)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1151810)], (11573 ^ _774244) ^ [_964948, _964950, _964952] : [class_Rings_Olinordered__ring__strict(_964948), 11576 ^ _774244 : [(11591 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964948), _964950), _964952)), c_Groups_Ozero__class_Ozero(_964948)))), 11592 ^ _774244 : [(11599 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964948), _964950), c_Groups_Ozero__class_Ozero(_964948))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964948), c_Groups_Ozero__class_Ozero(_964948)), _964952))], (11593 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964948), c_Groups_Ozero__class_Ozero(_964948)), _964950)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964948), _964952), c_Groups_Ozero__class_Ozero(_964948)))]]], (11577 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964948), _964950), _964952)), c_Groups_Ozero__class_Ozero(_964948))), 11582 ^ _774244 : [(11585 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964948), _964952), c_Groups_Ozero__class_Ozero(_964948))))], (11583 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964948), c_Groups_Ozero__class_Ozero(_964948)), _964950)))]], 11586 ^ _774244 : [(11589 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964948), c_Groups_Ozero__class_Ozero(_964948)), _964952)))], (11587 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964948), _964950), c_Groups_Ozero__class_Ozero(_964948))))]]]]], (41963 ^ _774244) ^ [_1582057, _1582059, _1582061, _1582063] : [-(c_New__Random__Sequence_Oneg__map(_1582057, _1582059, _1582061, _1582063) = c_New__Random__Sequence_Oneg__bind(_1582057, _1582059, _1582063, hAPP(c_Fun_Ocomp(_1582059, 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(_1582059)))))), _1582057, c_New__Random__Sequence_Oneg__single(_1582059)), _1582061)))], (49487 ^ _774244) ^ [_1765359, _1765361] : [-(c_Random_Opick(_1765359, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1765359), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1765359, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1765359, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1765359)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1765361)) = c_Random_Opick(_1765359, _1765361))], (26516 ^ _774244) ^ [_1238693, _1238695, _1238697, _1238699, _1238701] : [class_Fields_Ofield(_1238693), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1238693), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238695, _1238693), _1238697), _1238699)), _1238701) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238695, _1238693), hAPP(hAPP(c_COMBC(_1238695, _1238693, _1238693), hAPP(hAPP(c_COMBB(_1238693, tc_fun(_1238693, _1238693), _1238695), c_Rings_Oinverse__class_Odivide(_1238693)), _1238697)), _1238701)), _1238699))], (7421 ^ _774244) ^ [_894679, _894681] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894679), _894681))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894679), hAPP(c_Nat_OSuc, _894681))), -(_894681 = _894679)], (18853 ^ _774244) ^ [_1095787, _1095789] : [-(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), _1095787)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1095789)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1095787))) = 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), _1095789)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1095787)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23075 ^ _774244) ^ [_1173110, _1173112, _1173114, _1173116] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1173110, _1173112), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1173114), _1173116))), -(_1173112 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1173110), _1173112) = _1173114)], (23727 ^ _774244) ^ [_1185929, _1185931, _1185933] : [class_Orderings_Olinorder(_1185929), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185929), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1185929), _1185931), _1185933)), _1185931)))], (48720 ^ _774244) ^ [_1747932, _1747934, _1747936, _1747938, _1747940] : [-(c_List_Olist_Olist__size(_1747932, _1747934, hAPP(hAPP(c_List_Omap(_1747936, _1747932), _1747938), _1747940)) = c_List_Olist_Olist__size(_1747936, hAPP(c_Fun_Ocomp(_1747932, tc_Nat_Onat, _1747936, _1747934), _1747938), _1747940))], (33522 ^ _774244) ^ [_1382806, _1382808, _1382810] : [class_Orderings_Olinorder(_1382806), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382806), _1382808)), hBOOL(hAPP(hAPP(c_member(_1382806), _1382810), _1382808)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1382806), _1382810), c_Big__Operators_Olattice_OSup__fin(_1382806, c_Orderings_Oord__class_Omax(_1382806), _1382808)) = c_Big__Operators_Olattice_OSup__fin(_1382806, c_Orderings_Oord__class_Omax(_1382806), _1382808))], (23603 ^ _774244) ^ [_1183552, _1183554, _1183556, _1183558] : [class_Orderings_Olinorder(_1183552), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183552), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183552), _1183554), _1183556)), _1183558) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183552), _1183554), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183552), _1183556), _1183558)))], (15178 ^ _774244) ^ [_1029531, _1029533, _1029535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029531), _1029533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029531), _1029535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029535), _1029533)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029535), _1029531))))], (18133 ^ _774244) ^ [_1084015] : [class_Int_Onumber__ring(_1084015), -(c_Groups_Ozero__class_Ozero(_1084015) = hAPP(c_Int_Onumber__class_Onumber__of(_1084015), c_Int_OPls))], (17313 ^ _774244) ^ [_1070463, _1070465, _1070467] : [class_Rings_Olinordered__idom(_1070463), -(hAPP(c_Groups_Oabs__class_Oabs(_1070463), hAPP(hAPP(c_Power_Opower__class_Opower(_1070463), hAPP(c_Groups_Ouminus__class_Ouminus(_1070463), _1070465)), _1070467)) = hAPP(c_Groups_Oabs__class_Oabs(_1070463), hAPP(hAPP(c_Power_Opower__class_Opower(_1070463), _1070465), _1070467)))], (41879 ^ _774244) ^ [_1580773, _1580775, _1580777, _1580779] : [41880 ^ _774244 : [(41881 ^ _774244) ^ [_1580827] : [hBOOL(hAPP(hAPP(_1580777, _1580779), _1580827))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1580773, _1580775, _1580777), _1580779)))], (49555 ^ _774244) ^ [_1767029, _1767031, _1767033, _1767035] : [c_List_Oupt(_1767029, _1767031) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1767033), _1767035), 49558 ^ _774244 : [(49563 ^ _774244) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1767029), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1767031) = _1767035)], (49561 ^ _774244) ^ [] : [-(_1767029 = _1767033)], (49559 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1767029), _1767031)))]]], (43211 ^ _774244) ^ [_1610308, _1610310, _1610312, _1610314, _1610316] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1610308, _1610308)), hAPP(hAPP(c_Product__Type_OPair(_1610308, _1610308), _1610310), _1610312)), c_Transitive__Closure_Ortrancl(_1610308, _1610314))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1610308, _1610308)), hAPP(hAPP(c_Product__Type_OPair(_1610308, _1610308), _1610312), _1610316)), c_Transitive__Closure_Otrancl(_1610308, _1610314))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610308, _1610308)), hAPP(hAPP(c_Product__Type_OPair(_1610308, _1610308), _1610310), _1610316)), c_Transitive__Closure_Otrancl(_1610308, _1610314))))], (9038 ^ _774244) ^ [_922241, _922243] : [class_Rings_Ocomm__semiring__1(_922241), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922241), _922243), c_Groups_Ozero__class_Ozero(_922241)) = c_Groups_Ozero__class_Ozero(_922241))], (38672 ^ _774244) ^ [] : [-(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))))], (31954 ^ _774244) ^ [_1352205, _1352207, _1352209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352205)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1352207), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1352209)), 31961 ^ _774244 : [(31962 ^ _774244) ^ [_1352413] : [31964 ^ _774244 : [(31970 ^ _774244) ^ [] : [-(_1352413 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 31966 ^ [_1352205, _1352207, _1352209, _1352413]), 31963 ^ [_1352205, _1352207, _1352209, _1352413]))], (31968 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31966 ^ [_1352205, _1352207, _1352209, _1352413]), _1352209)))], (31965 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31963 ^ [_1352205, _1352207, _1352209, _1352413]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1352205))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1352207), _1352413)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1352207), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1352413), _1352205))))]]], (1866 ^ _774244) ^ [_801287, _801289] : [_801289 = _801287, -(c_Nat_Onat_Onat__size(_801289) = c_Nat_Onat_Onat__size(_801287))], (4966 ^ _774244) ^ [_850985, _850987, _850989, _850991] : [-(c_List_Olist__update(_850991, _850987) = c_List_Olist__update(_850989, _850985)), _850991 = _850989, _850987 = _850985], (41872 ^ _774244) ^ [_1580658, _1580660, _1580662, _1580664] : [hBOOL(hAPP(c_Predicate_ODomainP(_1580658, _1580660, _1580662), _1580664)), -(hBOOL(hAPP(hAPP(_1580662, _1580664), 41875 ^ [_1580658, _1580660, _1580662, _1580664])))], (41342 ^ _774244) ^ [_1567875, _1567877] : [c_Wellfounded_Owf(_1567875, hAPP(hAPP(c_Relation_Orel__comp(_1567875, _1567875, _1567875), _1567877), _1567877)), -(c_Wellfounded_Owf(_1567875, _1567877))], (19225 ^ _774244) ^ [_1102384, _1102386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1102384)), c_Int_OBit1(_1102386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102384), _1102386)))], (17015 ^ _774244) ^ [_1065256] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065256)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1065256)))], (32298 ^ _774244) ^ [_1359100, _1359102] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359102), _1359100)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1359100), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359102))))], (36637 ^ _774244) ^ [_1452040, _1452042, _1452044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452040, tc_HOL_Obool)), _1452042), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1452040, tc_HOL_Obool)), _1452044))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452040, tc_HOL_Obool)), _1452042), _1452044) = c_Orderings_Obot__class_Obot(tc_fun(_1452040, tc_HOL_Obool)))], (11218 ^ _774244) ^ [_958702, _958704, _958706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958702), _958704)), _958706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _958704), _958706)))], (25713 ^ _774244) ^ [_1223034] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223034), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1223034 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (47626 ^ _774244) ^ [_1721059, _1721061, _1721063, _1721065] : [_1721061 = _1721065, -(hAPP(hAPP(c_List_Oappend(_1721059), _1721061), _1721063) = hAPP(hAPP(c_List_Oappend(_1721059), _1721065), _1721063))], (20849 ^ _774244) ^ [_1131417, _1131419, _1131421, _1131423] : [class_Fields_Ofield(_1131417), -(_1131419 = c_Groups_Ozero__class_Ozero(_1131417)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131417), _1131421), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131417), _1131423), _1131419)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131417), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131417), _1131419), _1131421)), _1131423)), _1131419))], (34954 ^ _774244) ^ [_1413691, _1413693] : [hAPP(c_Set_OPow(_1413691), _1413693) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1413691, tc_HOL_Obool), tc_HOL_Obool))], (2626 ^ _774244) ^ [_813991, _813993, _813995, _813997, _813999, _814001, _814003, _814005] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_814005, _814001, _813997, _813993) = c_New__Random__Sequence_Opos__not__random__dseq(_814003, _813999, _813995, _813991)), _814005 = _814003, _814001 = _813999, _813997 = _813995, _813993 = _813991], (35191 ^ _774244) ^ [_1418916, _1418918, _1418920, _1418922, _1418924, _1418926] : [-(hAPP(c_Set_Oimage(_1418916, _1418918, hAPP(c_Fun_Ocomp(_1418920, _1418918, _1418916, _1418922), _1418924)), _1418926) = hAPP(c_Set_Oimage(_1418920, _1418918, _1418922), hAPP(c_Set_Oimage(_1418916, _1418920, _1418924), _1418926)))], (38033 ^ _774244) ^ [_1483406, _1483408, _1483410, _1483412, _1483414] : [c_Fun_Oinj__on(_1483406, _1483408, _1483410, _1483412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483406, tc_HOL_Obool)), _1483414), _1483412)), -(c_Fun_Oinj__on(_1483406, _1483408, _1483410, _1483414))], (33814 ^ _774244) ^ [_1388338, _1388340, _1388342, _1388344, _1388346] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388338, _1388340), _1388342), _1388344), _1388346) = _1388342, -(hAPP(_1388342, _1388344) = _1388346)], (44056 ^ _774244) ^ [_1633348, _1633350] : [-(c_Relation_Oirrefl(_1633348, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1633348, _1633348), tc_HOL_Obool)), _1633350), c_Relation_OId(_1633348))))], (1584 ^ _774244) ^ [_796768, _796770] : [-(class_Nat_Osemiring__char__0(_796768)), _796770 = _796768, class_Nat_Osemiring__char__0(_796770)], (7141 ^ _774244) ^ [_890218] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _890218), hAPP(c_Nat_OSuc, _890218))))], (2284 ^ _774244) ^ [_808668, _808670, _808672, _808674] : [-(c_Nitpick_Onat__lcm(_808674, _808670) = c_Nitpick_Onat__lcm(_808672, _808668)), _808674 = _808672, _808670 = _808668], (39989 ^ _774244) ^ [_1529943, _1529945, _1529947] : [class_Groups_Oab__semigroup__mult(_1529943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1529943), _1529945)), -(_1529945 = c_Orderings_Obot__class_Obot(tc_fun(_1529943, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1529943), _1529947)), -(_1529947 = c_Orderings_Obot__class_Obot(tc_fun(_1529943, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529943, tc_HOL_Obool)), _1529945), _1529947) = c_Orderings_Obot__class_Obot(tc_fun(_1529943, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1529943, c_Groups_Otimes__class_Otimes(_1529943)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1529943, tc_HOL_Obool)), _1529945), _1529947)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1529943), hAPP(c_Finite__Set_Ofold1(_1529943, c_Groups_Otimes__class_Otimes(_1529943)), _1529945)), hAPP(c_Finite__Set_Ofold1(_1529943, c_Groups_Otimes__class_Otimes(_1529943)), _1529947)))], (39774 ^ _774244) ^ [_1523335, _1523337, _1523339, _1523341] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523335), _1523337)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1523335, _1523335), tc_HOL_Obool)), _1523339), hAPP(hAPP(c_Product__Type_OSigma(_1523335, _1523335), _1523337), hAPP(c_COMBK(tc_fun(_1523335, tc_HOL_Obool), _1523335), _1523337)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1523335, tc_HOL_Obool)), _1523341), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1523335), _1523337), _1523339))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523335), _1523341)))], (23355 ^ _774244) ^ [_1178520, _1178522, _1178524, _1178526, _1178528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1178520, tc_HOL_Obool)), _1178522), _1178524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1178520, tc_HOL_Obool)), _1178526), _1178528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1178520, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1178520, tc_HOL_Obool)), _1178522), _1178528)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1178520, tc_HOL_Obool)), _1178524), _1178526))))], (13383 ^ _774244) ^ [_996737, _996739, _996741, _996743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996737)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _996739), _996741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _996741), 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), _996739), c_Divides_Odiv__class_Omod(tc_Int_Oint, _996743, _996737))), _996741)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51421 ^ _774244) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (22088 ^ _774244) ^ [_1153739] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1153739)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1153739)), 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))))], (22496 ^ _774244) ^ [_1162340, _1162342, _1162344, _1162346, _1162348] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1162340, _1162342), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1162344), _1162346))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162342)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162348), _1162340), _1162342), 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), _1162348), _1162344)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162348), _1162346)), _1162342))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162348), _1162346), _1162342)))))], (36293 ^ _774244) ^ [_1443986, _1443988, _1443990, _1443992] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443986, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443986, tc_HOL_Obool)), _1443988), _1443990)), _1443992) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443986, tc_HOL_Obool)), _1443988), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443986, tc_HOL_Obool)), _1443990), _1443992)))], (6077 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (51055 ^ _774244) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (48490 ^ _774244) ^ [_1743275, _1743277, _1743279, _1743281] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1743275) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1743277), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1743275)), hAPP(hAPP(c_List_Olist_OCons(_1743277), _1743279), _1743281)) = hAPP(hAPP(c_List_Odrop(_1743277), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1743275)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1743281))], (44014 ^ _774244) ^ [_1632392, _1632394, _1632396] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1632392, _1632394, _1632394), _1632396), c_Relation_OId(_1632394)) = _1632396)], (12247 ^ _774244) ^ [_976967, _976969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _976967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _976969)), 12254 ^ _774244 : [(12261 ^ _774244) ^ [] : [_976967 = _976969, -(hAPP(c_Int_Onat, _976967) = hAPP(c_Int_Onat, _976969))], (12255 ^ _774244) ^ [] : [hAPP(c_Int_Onat, _976967) = hAPP(c_Int_Onat, _976969), -(_976967 = _976969)]]], (17307 ^ _774244) ^ [_1070308, _1070310, _1070312, _1070314] : [class_Groups_Omonoid__mult(_1070308), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1070308), _1070310), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070312), _1070314)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070308), hAPP(hAPP(c_Power_Opower__class_Opower(_1070308), _1070310), _1070312)), hAPP(hAPP(c_Power_Opower__class_Opower(_1070308), _1070310), _1070314)))], (13443 ^ _774244) ^ [_997807, _997809] : [class_Divides_Osemiring__div(_997807), -(c_Divides_Odiv__class_Omod(_997807, c_Groups_Ozero__class_Ozero(_997807), _997809) = c_Groups_Ozero__class_Ozero(_997807))], (30164 ^ _774244) ^ [_1311614, _1311616] : [hAPP(c_Finite__Set_Ocard(_1311614), _1311616) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1311616 = c_Orderings_Obot__class_Obot(tc_fun(_1311614, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311614), _1311616))], (51093 ^ _774244) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (22973 ^ _774244) ^ [_1171521, _1171523, _1171525, _1171527, _1171529] : [hAPP(c_Product__Type_Osnd(_1171521, _1171523), hAPP(hAPP(c_Product__Type_OPair(_1171521, _1171523), _1171525), _1171527)) = _1171529, -(_1171527 = _1171529)], (32476 ^ _774244) ^ [_1362934] : [class_Rings_Oring__1(_1362934), -(hBOOL(hAPP(hAPP(c_member(_1362934), c_Groups_Ozero__class_Ozero(_1362934)), c_Int_Oring__1__class_OInts(_1362934))))], (7489 ^ _774244) ^ [_895786, _895788, _895790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _895788), _895790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _895786), _895788)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _895786), _895790))))], (43637 ^ _774244) ^ [_1621820, _1621822, _1621824, _1621826, _1621828] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1621820, tc_fun(_1621822, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1621820, tc_HOL_Obool)), _1621824), _1621826)), _1621828) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1621822, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1621820, tc_fun(_1621822, tc_HOL_Obool)), _1621824), _1621828)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1621820, tc_fun(_1621822, tc_HOL_Obool)), _1621826), _1621828)))], (34327 ^ _774244) ^ [_1398863, _1398865, _1398867, _1398869, _1398871] : [class_Groups_Ocomm__monoid__mult(_1398863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398865), _1398867)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398865, _1398863), _1398869), hAPP(hAPP(c_Set_Oinsert(_1398865), _1398871), _1398867)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398863), hAPP(_1398869, _1398871)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398865, _1398863), _1398869), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398865, tc_HOL_Obool)), _1398867), hAPP(hAPP(c_Set_Oinsert(_1398865), _1398871), c_Orderings_Obot__class_Obot(tc_fun(_1398865, tc_HOL_Obool)))))))], (33374 ^ _774244) ^ [_1379843, _1379845, _1379847, _1379849] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1379843, _1379845)), c_Sum__Type_OPlus(_1379843, _1379845, _1379847, _1379849))), 33377 ^ _774244 : [(33380 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1379845), _1379849)))], (33378 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1379843), _1379847)))]]], (18763 ^ _774244) ^ [_1094186, _1094188] : [class_Int_Onumber__ring(_1094186), class_Rings_Olinordered__idom(_1094186), 18770 ^ _774244 : [(18777 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094188), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094186), hAPP(c_Int_Onumber__class_Onumber__of(_1094186), _1094188)), c_Groups_Oone__class_Oone(_1094186))))], (18771 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094186), hAPP(c_Int_Onumber__class_Onumber__of(_1094186), _1094188)), c_Groups_Oone__class_Oone(_1094186))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094188), c_Int_OBit1(c_Int_OPls))))]]], (46834 ^ _774244) ^ [_1702342, _1702344] : [-(c_List_Olistrelp(_1702342, _1702344, c_List_Olist_ONil(_1702342), c_List_Olist_ONil(_1702342)))], (42886 ^ _774244) ^ [_1602639, _1602641, _1602643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602639, _1602639), tc_HOL_Obool)), _1602641), hAPP(hAPP(c_Product__Type_OSigma(_1602639, _1602639), _1602643), hAPP(c_COMBK(tc_fun(_1602639, tc_HOL_Obool), _1602639), _1602643)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602639, _1602639), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1602639, _1602641)), hAPP(hAPP(c_Product__Type_OSigma(_1602639, _1602639), _1602643), hAPP(c_COMBK(tc_fun(_1602639, tc_HOL_Obool), _1602639), _1602643)))))], (40894 ^ _774244) ^ [_1550266, _1550268, _1550270] : [class_Orderings_Olinorder(_1550266), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550266), _1550268)), -(_1550268 = c_Orderings_Obot__class_Obot(tc_fun(_1550266, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1550266), _1550270), c_Big__Operators_Olattice_OInf__fin(_1550266, c_Orderings_Oord__class_Omin(_1550266), _1550268)) = c_Big__Operators_Olattice_OInf__fin(_1550266, c_Orderings_Oord__class_Omin(_1550266), hAPP(c_Set_OCollect(_1550266), hAPP(hAPP(c_COMBB(tc_fun(_1550266, tc_HOL_Obool), tc_HOL_Obool, _1550266), c_HOL_OEx(_1550266)), hAPP(hAPP(c_COMBC(_1550266, tc_fun(_1550266, tc_HOL_Obool), tc_fun(_1550266, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550266, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1550266, tc_HOL_Obool), tc_fun(_1550266, tc_HOL_Obool)), _1550266), c_COMBS(_1550266, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550266, tc_HOL_Obool), tc_fun(_1550266, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1550266), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550266), c_fconj)), hAPP(hAPP(c_COMBC(_1550266, tc_fun(_1550266, _1550266), tc_fun(_1550266, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550266, tc_HOL_Obool), tc_fun(tc_fun(_1550266, _1550266), tc_fun(_1550266, tc_HOL_Obool)), _1550266), c_COMBB(_1550266, tc_HOL_Obool, _1550266)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1550266), _1550270))))), hAPP(hAPP(c_COMBC(_1550266, tc_fun(_1550266, tc_HOL_Obool), tc_HOL_Obool), c_member(_1550266)), _1550268))))))], (50761 ^ _774244) ^ [_1792340, _1792342, _1792344, _1792346, _1792348] : [c_Finite__Set_Ofun__left__comm(_1792340, _1792342, _1792344), -(hAPP(hAPP(c_Finite__Set_Ofold(_1792340, _1792342, _1792344), _1792346), hAPP(c_List_Oset(_1792340), _1792348)) = hAPP(c_List_Ofoldl(_1792342, _1792340, hAPP(c_COMBC(_1792340, _1792342, _1792342), _1792344), _1792346), c_List_Oremdups(_1792340, _1792348)))], (51249 ^ _774244) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (48937 ^ _774244) ^ [_1752993, _1752995, _1752997] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1752993)), _1752995), c_List_Olists(_1752993, _1752997))), 48940 ^ _774244 : [(48941 ^ _774244) ^ [_1753101] : [hBOOL(hAPP(hAPP(c_member(_1752993), _1753101), hAPP(c_List_Oset(_1752993), _1752995))), -(hBOOL(hAPP(hAPP(c_member(_1752993), _1753101), _1752997)))]]], (27432 ^ _774244) ^ [_1257995] : [-(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)), _1257995)) = hAPP(c_Int_Onat, _1257995))], (954 ^ _774244) ^ [_788893, _788895] : [-(class_Lattices_Obounded__lattice(_788893)), _788895 = _788893, class_Lattices_Obounded__lattice(_788895)], (30657 ^ _774244) ^ [_1321533, _1321535, _1321537, _1321539, _1321541, _1321543] : [hBOOL(hAPP(hAPP(c_member(_1321533), _1321535), _1321537)), hBOOL(hAPP(hAPP(c_member(_1321539), _1321541), hAPP(_1321543, _1321535))), -(hBOOL(hAPP(hAPP(c_member(_1321539), _1321541), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1321533, tc_fun(_1321539, tc_HOL_Obool)), _1321537), _1321543))))], (51061 ^ _774244) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (43958 ^ _774244) ^ [_1630424, _1630426, _1630428, _1630430] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1630424, tc_fun(_1630424, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1630424, tc_fun(tc_prod(_1630424, _1630424), tc_HOL_Obool), tc_fun(_1630424, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1630424, tc_fun(tc_fun(tc_prod(_1630424, _1630424), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1630424, _1630424), tc_HOL_Obool), tc_fun(_1630424, tc_HOL_Obool)), _1630424), c_COMBC(_1630424, tc_fun(tc_prod(_1630424, _1630424), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1630424, tc_prod(_1630424, _1630424)), tc_fun(_1630424, tc_fun(tc_fun(tc_prod(_1630424, _1630424), tc_HOL_Obool), tc_HOL_Obool)), _1630424), hAPP(c_COMBB(tc_prod(_1630424, _1630424), tc_fun(tc_fun(tc_prod(_1630424, _1630424), tc_HOL_Obool), tc_HOL_Obool), _1630424), c_member(tc_prod(_1630424, _1630424)))), c_Product__Type_OPair(_1630424, _1630424)))), _1630426)), c_fequal), _1630428), _1630430)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630424, _1630424)), hAPP(hAPP(c_Product__Type_OPair(_1630424, _1630424), _1630428), _1630430)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1630424, _1630424), tc_HOL_Obool)), _1630426), c_Relation_OId(_1630424)))))], (50965 ^ _774244) ^ [_1796606, _1796608] : [class_Lattices_Oboolean__algebra(_1796606), -(class_Lattices_Oboolean__algebra(tc_fun(_1796608, _1796606)))], (2908 ^ _774244) ^ [_818640, _818642, _818644, _818646, _818648, _818650, _818652, _818654] : [-(c_Lazy__Sequence_Ohb__bind(_818654, _818650, _818646, _818642) = c_Lazy__Sequence_Ohb__bind(_818652, _818648, _818644, _818640)), _818654 = _818652, _818650 = _818648, _818646 = _818644, _818642 = _818640], (37335 ^ _774244) ^ [_1467172, _1467174, _1467176, _1467178, _1467180, _1467182, _1467184, _1467186, _1467188] : [c_Equiv__Relations_Oequiv(_1467172, _1467174, _1467176), c_Equiv__Relations_Oequiv(_1467178, _1467180, _1467182), c_Equiv__Relations_Ocongruent2(_1467172, _1467178, tc_fun(_1467184, tc_HOL_Obool), _1467176, _1467182, _1467186), hBOOL(hAPP(hAPP(c_member(_1467178), _1467188), _1467180)), -(c_Equiv__Relations_Ocongruent(_1467172, tc_fun(_1467184, tc_HOL_Obool), _1467176, hAPP(hAPP(c_COMBB(tc_fun(_1467178, tc_fun(_1467184, tc_HOL_Obool)), tc_fun(_1467184, tc_HOL_Obool), _1467172), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1467178, tc_fun(_1467184, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1467178, _1467178, _1467182), hAPP(hAPP(c_Set_Oinsert(_1467178), _1467188), c_Orderings_Obot__class_Obot(tc_fun(_1467178, tc_HOL_Obool)))))), _1467186)))], (17167 ^ _774244) ^ [_1067889] : [-(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), _1067889)) = 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), _1067889))))], (7335 ^ _774244) ^ [_893481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893481), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44640 ^ _774244) ^ [_1647398, _1647400, _1647402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1647398, tc_HOL_Obool), tc_HOL_Obool)), _1647400), _1647402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1647398, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1647398, tc_HOL_Obool), _1647400)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1647398, tc_HOL_Obool), _1647402))))], (44097 ^ _774244) ^ [_1634405, _1634407] : [-(c_Relation_Osingle__valued(_1634405, _1634405, c_Relation_OId__on(_1634405, _1634407)))], (51395 ^ _774244) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (6768 ^ _774244) ^ [_883535, _883537, _883539, _883541, _883543, _883545, _883547, _883549, _883551, _883553, _883555, _883557] : [-(c_Com_Ocom_Ocom__rec(_883535, _883537, _883539, _883541, _883543, _883545, _883547, _883549, _883551, c_Com_Ocom_OLocal(_883553, _883555, _883557)) = hAPP(hAPP(hAPP(hAPP(_883541, _883553), _883555), _883557), c_Com_Ocom_Ocom__rec(_883535, _883537, _883539, _883541, _883543, _883545, _883547, _883549, _883551, _883557)))], (49687 ^ _774244) ^ [_1769349, _1769351, _1769353, _1769355] : [class_Orderings_Olinorder(_1769349), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1769349), _1769351), _1769353)), c_List_Olinorder__class_Osorted(_1769349, hAPP(hAPP(c_List_Olist_OCons(_1769349), _1769353), _1769355)), -(c_List_Olinorder__class_Osorted(_1769349, hAPP(hAPP(c_List_Olist_OCons(_1769349), _1769351), hAPP(hAPP(c_List_Olist_OCons(_1769349), _1769353), _1769355))))], (37107 ^ _774244) ^ [_1462586, _1462588, _1462590] : [class_Orderings_Olinorder(_1462586), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462586), _1462588)), -(_1462588 = c_Orderings_Obot__class_Obot(tc_fun(_1462586, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462586), _1462590)), -(_1462590 = c_Orderings_Obot__class_Obot(tc_fun(_1462586, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462586, tc_HOL_Obool)), _1462588), _1462590) = c_Orderings_Obot__class_Obot(tc_fun(_1462586, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1462586, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1462586, tc_HOL_Obool)), _1462588), _1462590)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1462586), c_Big__Operators_Olinorder__class_OMin(_1462586, _1462588)), c_Big__Operators_Olinorder__class_OMin(_1462586, _1462590)))], (14530 ^ _774244) ^ [_1017624, _1017626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017624)), 14533 ^ _774244 : [(14542 ^ _774244) ^ [] : [-(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), _1017624), _1017626)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1017626), _1017624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017626))], (14534 ^ _774244) ^ [] : [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), _1017624), _1017626))), 14537 ^ _774244 : [(14540 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017626)))], (14538 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1017626), _1017624)))]]]]], (44847 ^ _774244) ^ [_1651700, _1651702] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1651700, tc_HOL_Obool)), _1651702)), 44853 ^ _774244 : [(44856 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1651700), 44852 ^ [_1651700, _1651702]))], (44854 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1651700, tc_HOL_Obool)), 44852 ^ [_1651700, _1651702]), _1651702)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1651700), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1651700, tc_HOL_Obool), _1651702))))], (38529 ^ _774244) ^ [_1493230, _1493232, _1493234, _1493236, _1493238] : [-(c_Fun_Oinj__on(_1493230, _1493232, _1493234, hAPP(hAPP(c_Set_Oinsert(_1493230), _1493236), _1493238))), c_Fun_Oinj__on(_1493230, _1493232, _1493234, _1493238), -(hBOOL(hAPP(hAPP(c_member(_1493232), hAPP(_1493234, _1493236)), hAPP(c_Set_Oimage(_1493230, _1493232, _1493234), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493230, tc_HOL_Obool)), _1493238), hAPP(hAPP(c_Set_Oinsert(_1493230), _1493236), c_Orderings_Obot__class_Obot(tc_fun(_1493230, tc_HOL_Obool))))))))], (15272 ^ _774244) ^ [_1031179, _1031181, _1031183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031179), _1031181)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031179), _1031183)), 15279 ^ _774244 : [(15286 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031181), _1031183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031181), _1031179)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031183), _1031179))))], (15280 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031181), _1031179)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031183), _1031179))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031181), _1031183)))]]], (34578 ^ _774244) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (36131 ^ _774244) ^ [_1440278, _1440280, _1440282, _1440284] : [hBOOL(hAPP(hAPP(c_member(_1440278), _1440280), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440278, tc_HOL_Obool)), _1440282), _1440284))), -(hBOOL(hAPP(hAPP(c_member(_1440278), _1440280), _1440284)))], (19361 ^ _774244) ^ [_1104725] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1104725), 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), _1104725), _1104725))], (2762 ^ _774244) ^ [_816107, _816109, _816111, _816113] : [-(c_Nitpick_Oinverse__frac(_816113, _816109) = c_Nitpick_Oinverse__frac(_816111, _816107)), _816113 = _816111, _816109 = _816107], (16415 ^ _774244) ^ [_1053324, _1053326, _1053328] : [class_Groups_Oordered__ab__group__add__abs(_1053324), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053324), hAPP(c_Groups_Oabs__class_Oabs(_1053324), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053324), _1053326), _1053328))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053324), hAPP(c_Groups_Oabs__class_Oabs(_1053324), _1053326)), hAPP(c_Groups_Oabs__class_Oabs(_1053324), _1053328)))))], (31733 ^ _774244) ^ [_1347204, _1347206, _1347208] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1347204), _1347206)), -(hBOOL(hAPP(hAPP(c_member(_1347204), _1347208), _1347206))), -(hAPP(c_Finite__Set_Ocard(_1347204), hAPP(hAPP(c_Set_Oinsert(_1347204), _1347208), _1347206)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1347204), _1347206)))], (8524 ^ _774244) ^ [_913237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _913237), 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)), _913237)), _913237)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14836 ^ _774244) ^ [_1023305, _1023307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023305)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023307)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1023305, _1023307)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1023305), hAPP(c_Int_Onat, _1023307)))], (7070 ^ _774244) ^ [_889032, _889034] : [c_Com_Ocom_OWhile(_889032, _889034) = c_Com_Ocom_OSKIP], (6380 ^ _774244) ^ [_876823, _876825] : [_876823 = c_Option_Ooption_ONone(_876825), 6383 ^ _774244 : [(6384 ^ _774244) ^ [_876895] : [_876823 = hAPP(c_Option_Ooption_OSome(_876825), _876895)]]], (18449 ^ _774244) ^ [_1089117, _1089119] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1089117)))), _1089119) = 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)))), _1089117)), _1089119))], (17161 ^ _774244) ^ [_1067750, _1067752, _1067754, _1067756] : [class_Groups_Omonoid__mult(_1067750), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1067750), _1067752), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1067754), _1067756)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1067750), hAPP(hAPP(c_Power_Opower__class_Opower(_1067750), _1067752), _1067754)), _1067756))], (43970 ^ _774244) ^ [_1631272, _1631274] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631272, _1631272)), hAPP(hAPP(c_Product__Type_OPair(_1631272, _1631272), _1631274), _1631274)), c_Relation_OId(_1631272))))], (1946 ^ _774244) ^ [_802605, _802607, _802609, _802611, _802613, _802615] : [-(c_Com_Ocom_OLocal(_802615, _802611, _802607) = c_Com_Ocom_OLocal(_802613, _802609, _802605)), _802615 = _802613, _802611 = _802609, _802607 = _802605], (50294 ^ _774244) ^ [_1781541, _1781543] : [-(hAPP(c_List_Orev(_1781541), _1781543) = hAPP(c_List_Ofoldl(tc_List_Olist(_1781541), _1781541, hAPP(c_COMBC(_1781541, tc_List_Olist(_1781541), tc_List_Olist(_1781541)), c_List_Olist_OCons(_1781541)), c_List_Olist_ONil(_1781541)), _1781543))], (18171 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (18507 ^ _774244) ^ [_1090183, _1090185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090183), _1090185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1090183)), c_Int_OBit1(_1090185))))], (51083 ^ _774244) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (6760 ^ _774244) ^ [_883346, _883348, _883350, _883352, _883354] : [c_Com_Ocom_OSemi(_883346, _883348) = c_Com_Ocom_OLocal(_883350, _883352, _883354)], (7897 ^ _774244) ^ [_903276, _903278, _903280, _903282, _903284] : [c_Sum__Type_OSumr(_903276, _903278, _903280, _903282) = c_Sum__Type_OSumr(_903276, _903278, _903280, _903284), -(_903282 = _903284)], (32292 ^ _774244) ^ [_1358999, _1359001] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1358999), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359001))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359001), _1358999)))], (7265 ^ _774244) ^ [_892114, _892116, _892118, _892120] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_892114), 7268 ^ _774244 : [(7275 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892114), _892118), _892120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892114), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892114), _892116), _892118)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892114), _892116), _892120))))], (7269 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892114), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892114), _892116), _892118)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892114), _892116), _892120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892114), _892118), _892120)))]]], (45876 ^ _774244) ^ [_1676559, _1676561] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1676559, _1676561)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1676559, _1676561))], (46457 ^ _774244) ^ [_1692639, _1692641, _1692643] : [_1692639 = hAPP(hAPP(c_List_Olist_OCons(_1692641), _1692643), _1692639)], (30085 ^ _774244) ^ [_1310052, _1310054, _1310056, _1310058] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310052), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310052, tc_HOL_Obool)), _1310054), _1310058))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1310052), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310052, tc_HOL_Obool)), _1310054), hAPP(hAPP(c_Set_Oinsert(_1310052), _1310056), _1310058)))))], (17619 ^ _774244) ^ [_1075902] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1075902))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1075902)) = _1075902)], (23733 ^ _774244) ^ [_1186036, _1186038, _1186040] : [class_Orderings_Olinorder(_1186036), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186036), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186036), _1186038), _1186040)), _1186040)))], (24509 ^ _774244) ^ [_1200647] : [class_Orderings_Olinorder(_1200647), -(c_Orderings_Oord_Omax(_1200647, hAPP(c_COMBC(_1200647, _1200647, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1200647))) = c_Orderings_Oord__class_Omin(_1200647))], (18283 ^ _774244) ^ [_1086341, _1086343] : [class_Int_Onumber__ring(_1086341), class_Rings_Olinordered__idom(_1086341), 18290 ^ _774244 : [(18297 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086343), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086341), hAPP(c_Int_Onumber__class_Onumber__of(_1086341), _1086343)), c_Groups_Ozero__class_Ozero(_1086341))))], (18291 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086341), hAPP(c_Int_Onumber__class_Onumber__of(_1086341), _1086343)), c_Groups_Ozero__class_Ozero(_1086341))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086343), c_Int_OPls)))]]], (19251 ^ _774244) ^ [_1102859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1102859))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1102859)))], (23337 ^ _774244) ^ [_1178026, _1178028, _1178030] : [-(hAPP(hAPP(c_Product__Type_OPair(_1178026, _1178028), hAPP(c_Product__Type_Ofst(_1178026, _1178028), _1178030)), hAPP(c_Product__Type_Osnd(_1178026, _1178028), _1178030)) = _1178030)], (12121 ^ _774244) ^ [_974903, _974905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974903)), _974905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974903), _974905)))], (28928 ^ _774244) ^ [_1288900, _1288902, _1288904, _1288906] : [_1288906 = c_Orderings_Obot__class_Obot(tc_fun(_1288902, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_1288900, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1288902, _1288900, _1288904), _1288906))], (48312 ^ _774244) ^ [_1739022, _1739024, _1739026, _1739028] : [-(hAPP(hAPP(c_List_Odrop(_1739022), hAPP(c_Nat_OSuc, _1739024)), hAPP(hAPP(c_List_Olist_OCons(_1739022), _1739026), _1739028)) = hAPP(hAPP(c_List_Odrop(_1739022), _1739024), _1739028))], (12752 ^ _774244) ^ [_986117] : [hAPP(c_Int_Onat, _986117) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _986117), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11349 ^ _774244) ^ [_961100, _961102] : [class_Rings_Olinordered__idom(_961100), 11352 ^ _774244 : [(11359 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _961102), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961100), hAPP(c_Int_Oring__1__class_Oof__int(_961100), _961102)), c_Groups_Ozero__class_Ozero(_961100))))], (11353 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961100), hAPP(c_Int_Oring__1__class_Oof__int(_961100), _961102)), c_Groups_Ozero__class_Ozero(_961100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _961102), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (51123 ^ _774244) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (29798 ^ _774244) ^ [_1305029, _1305031, _1305033] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1305029), _1305033)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305029), hAPP(hAPP(c_Set_Oinsert(_1305029), _1305031), _1305033))))], (24655 ^ _774244) ^ [_1203638, _1203640, _1203642] : [-(c_Nitpick_Otimes__frac(_1203638, _1203640, _1203642) = hAPP(hAPP(c_Nitpick_Ofrac(_1203638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1203638), _1203640)), hAPP(c_Nitpick_Onum(_1203638), _1203642))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1203638), _1203640)), hAPP(c_Nitpick_Odenom(_1203638), _1203642))))], (47734 ^ _774244) ^ [_1723181, _1723183, _1723185] : [-(c_List_Olist_ONil(_1723181) = hAPP(hAPP(c_List_Oappend(_1723181), _1723183), _1723185)), _1723183 = c_List_Olist_ONil(_1723181), _1723185 = c_List_Olist_ONil(_1723181)], (22923 ^ _774244) ^ [_1170378, _1170380, _1170382, _1170384] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1170378, _1170380, _1170382), hAPP(hAPP(c_COMBB(tc_fun(_1170380, tc_prod(_1170378, _1170380)), tc_fun(_1170380, _1170382), _1170378), hAPP(c_COMBB(tc_prod(_1170378, _1170380), _1170382, _1170380), _1170384)), c_Product__Type_OPair(_1170378, _1170380))) = _1170384)], (41593 ^ _774244) ^ [_1573269, _1573271] : [c_Wellfounded_Owf(_1573269, _1573271), -(c_Wellfounded_Owf(tc_List_Olist(_1573269), c_List_Olex(_1573269, _1573271)))], (27175 ^ _774244) ^ [_1252537, _1252539, _1252541, _1252543] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252537), _1252539)), 27178 ^ _774244 : [(27179 ^ _774244) ^ [_1252695] : [27181 ^ _774244 : [(27187 ^ _774244) ^ [] : [-(_1252695 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27183 ^ [_1252537, _1252539, _1252541, _1252543, _1252695]), 27180 ^ [_1252537, _1252539, _1252541, _1252543, _1252695]))], (27185 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27183 ^ [_1252537, _1252539, _1252541, _1252543, _1252695]), _1252541)))], (27182 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27180 ^ [_1252537, _1252539, _1252541, _1252543, _1252695]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1252539))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1252695), _1252543)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1252695), _1252539)), _1252543)))]]], (17895 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (5786 ^ _774244) ^ [_866470, _866472, _866474, _866476, _866478, _866480, _866482, _866484, _866486, _866488] : [-(c_Com_Ocom_Ocom__rec(_866470, _866472, _866474, _866476, _866478, _866480, _866482, _866484, _866486, c_Com_Ocom_OBODY(_866488)) = hAPP(_866484, _866488))], (28168 ^ _774244) ^ [_1271902, _1271904, _1271906, _1271908] : [class_Orderings_Olinorder(_1271902), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271902), _1271904), _1271906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271902), _1271906), _1271908)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271902, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1271902, _1271904), _1271906)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1271902, _1271906), _1271908)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1271902, _1271904), _1271908))], (32280 ^ _774244) ^ [_1358776, _1358778] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1358776), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358778))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358776), _1358778)))], (16669 ^ _774244) ^ [_1058456, _1058458, _1058460] : [class_Int_Onumber__ring(_1058456), -(hAPP(c_Int_Onumber__class_Onumber__of(_1058456), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1058458), _1058460)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058456), hAPP(c_Int_Onumber__class_Onumber__of(_1058456), _1058458)), hAPP(c_Int_Onumber__class_Onumber__of(_1058456), _1058460)))], (11305 ^ _774244) ^ [_960338, _960340, _960342, _960344, _960346] : [c_Natural_Oevaln(_960338, _960340, _960342, _960344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960342), _960346)), -(c_Natural_Oevaln(_960338, _960340, _960346, _960344))], (16505 ^ _774244) ^ [_1055170, _1055172, _1055174] : [class_Rings_Olinordered__idom(_1055170), 16508 ^ _774244 : [(16517 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055170), hAPP(c_Groups_Oabs__class_Oabs(_1055170), _1055172)), _1055174))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055170), _1055172), _1055174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055170), hAPP(c_Groups_Ouminus__class_Ouminus(_1055170), _1055172)), _1055174))], (16509 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055170), hAPP(c_Groups_Oabs__class_Oabs(_1055170), _1055172)), _1055174)), 16512 ^ _774244 : [(16515 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055170), hAPP(c_Groups_Ouminus__class_Ouminus(_1055170), _1055172)), _1055174)))], (16513 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055170), _1055172), _1055174)))]]]]], (51097 ^ _774244) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (17249 ^ _774244) ^ [_1069274, _1069276, _1069278] : [class_Rings_Olinordered__semidom(_1069274), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069274), c_Groups_Oone__class_Oone(_1069274)), _1069276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069274), c_Groups_Oone__class_Oone(_1069274)), hAPP(hAPP(c_Power_Opower__class_Opower(_1069274), _1069276), _1069278))))], (41434 ^ _774244) ^ [_1569472, _1569474, _1569476] : [c_Wellfounded_Owf(_1569472, _1569474), -(c_Wellfounded_Owf(_1569472, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1569472, _1569472), tc_HOL_Obool)), _1569476), _1569474)))], (50625 ^ _774244) ^ [_1789782, _1789784, _1789786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789782)), c_List_OtakeWhile(_1789782, _1789784, _1789786))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789782)), _1789786))), hBOOL(hAPP(_1789784, hAPP(hAPP(c_List_Onth(_1789782), _1789786), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789782)), c_List_OtakeWhile(_1789782, _1789784, _1789786)))))], (44552 ^ _774244) ^ [_1645116, _1645118, _1645120] : [class_Complete__Lattice_Ocomplete__lattice(_1645116), -(c_Complete__Lattice_OInf__class_OInf(_1645116, hAPP(hAPP(c_Set_Oinsert(_1645116), _1645118), hAPP(hAPP(c_Set_Oinsert(_1645116), _1645120), c_Orderings_Obot__class_Obot(tc_fun(_1645116, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1645116), _1645118), _1645120))], (8870 ^ _774244) ^ [_919518] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _919518))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28483 ^ _774244) ^ [_1278158, _1278160] : [class_Orderings_Olinorder(_1278158), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1278158, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1278158), _1278160)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1278158), _1278160))], (27878 ^ _774244) ^ [_1266524, _1266526, _1266528, _1266530, _1266532] : [class_Lattices_Olattice(_1266524), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266526, _1266524)), _1266528), _1266530), _1266532) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266524), hAPP(_1266528, _1266532)), hAPP(_1266530, _1266532)))], (42173 ^ _774244) ^ [_1587721, _1587723] : [-(c_Hilbert__Choice_OEps(_1587721, hAPP(c_fequal, _1587723)) = _1587723)], (47313 ^ _774244) ^ [_1713631, _1713633, _1713635, _1713637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713631)), _1713633)), _1713635)), -(hAPP(hAPP(c_List_Olist__update(_1713631, _1713633), _1713635), _1713637) = _1713633)], (40386 ^ _774244) ^ [_1537071, _1537073, _1537075] : [class_Orderings_Olinorder(_1537071), -(_1537073 = c_Orderings_Obot__class_Obot(tc_fun(_1537071, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1537071, tc_HOL_Obool)), _1537073), _1537075)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537071), _1537075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1537071), hAPP(c_Finite__Set_Ofold1(_1537071, c_Orderings_Oord__class_Omin(_1537071)), _1537075)), hAPP(c_Finite__Set_Ofold1(_1537071, c_Orderings_Oord__class_Omin(_1537071)), _1537073))))], (19413 ^ _774244) ^ [_1105654, _1105656, _1105658] : [class_Rings_Olinordered__semidom(_1105654), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105654), hAPP(hAPP(c_Power_Opower__class_Opower(_1105654), _1105656), 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(_1105654), _1105658), 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(_1105654), c_Groups_Ozero__class_Ozero(_1105654)), _1105658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105654), _1105656), _1105658)))], (17483 ^ _774244) ^ [_1073643, _1073645, _1073647] : [class_Rings_Oring__1(_1073643), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1073643), hAPP(c_Groups_Ouminus__class_Ouminus(_1073643), _1073645)), _1073647) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073643), hAPP(hAPP(c_Power_Opower__class_Opower(_1073643), hAPP(c_Groups_Ouminus__class_Ouminus(_1073643), c_Groups_Oone__class_Oone(_1073643))), _1073647)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073643), _1073645), _1073647)))], (24731 ^ _774244) ^ [_1205902, _1205904, _1205906, _1205908] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1205902), _1205904), _1205906), _1205908) = 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(_1205902)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1205902), _1205904)))], (18691 ^ _774244) ^ [_1093147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1093147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1093147))))], (45391 ^ _774244) ^ [_1665024, _1665026, _1665028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1665024), _1665026)), -(c_Smallcheck_Osmall_H(_1665028, _1665024, _1665026) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (23639 ^ _774244) ^ [_1184374, _1184376, _1184378] : [class_Orderings_Olinorder(_1184374), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184374), _1184376), _1184378) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184374), _1184378), _1184376))], (16837 ^ _774244) ^ [_1061876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1061876), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1061876) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1061876))], (96 ^ _774244) ^ [_775534, _775536, _775538, _775540, _775542, _775544, _775546, _775548] : [-(c_Nat__Transfer_Otransfer__morphism(_775546, _775542, _775538, _775534)), c_Nat__Transfer_Otransfer__morphism(_775548, _775544, _775540, _775536), _775548 = _775546, _775544 = _775542, _775540 = _775538, _775536 = _775534], (8206 ^ _774244) ^ [_908330, _908332, _908334] : [class_Orderings_Olinorder(_908330), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908330), _908332), _908334))), -(_908332 = _908334), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908330), _908334), _908332)))], (38710 ^ _774244) ^ [_1497320, _1497322, _1497324, _1497326] : [c_Fun_Oinj__on(_1497320, _1497322, _1497324, c_Orderings_Otop__class_Otop(tc_fun(_1497320, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1497320, _1497322, c_Orderings_Otop__class_Otop(tc_fun(_1497320, tc_HOL_Obool)), _1497324), hAPP(_1497324, _1497326)) = _1497326)], (3812 ^ _774244) ^ [_833004, _833006, _833008, _833010, _833012, _833014] : [-(c_Finite__Set_Ofold__image(_833014, _833010, _833006) = c_Finite__Set_Ofold__image(_833012, _833008, _833004)), _833014 = _833012, _833010 = _833008, _833006 = _833004], (32028 ^ _774244) ^ [_1353707, _1353709, _1353711, _1353713, _1353715, _1353717] : [hBOOL(hAPP(hAPP(_1353707, _1353709), _1353711)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353713, tc_fun(_1353715, tc_HOL_Obool))), _1353717), _1353707), _1353709), _1353711)))], (19003 ^ _774244) ^ [_1098489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098489), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1098489)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (46028 ^ _774244) ^ [_1680382, _1680384, _1680386] : [class_Orderings_Olinorder(_1680382), hBOOL(hAPP(c_Finite__Set_Ofinite(_1680382), _1680384)), -(c_List_Olinorder__class_Osorted__list__of__set(_1680382, hAPP(hAPP(c_Set_Oinsert(_1680382), _1680386), _1680384)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680382, _1680382, c_COMBI(_1680382)), _1680386), c_List_Olinorder__class_Osorted__list__of__set(_1680382, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1680382, tc_HOL_Obool)), _1680384), hAPP(hAPP(c_Set_Oinsert(_1680382), _1680386), c_Orderings_Obot__class_Obot(tc_fun(_1680382, tc_HOL_Obool)))))))], (22554 ^ _774244) ^ [_1163429, _1163431, _1163433] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1163429, _1163431), _1163433)), 22557 ^ _774244 : [(22558 ^ _774244) ^ [_1163514] : [hBOOL(hAPP(hAPP(_1163431, _1163514), _1163433)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1163429, _1163431), _1163514)))]]], (4676 ^ _774244) ^ [_846490, _846492] : [_846492 = _846490, -(c_Set_OCollect(_846492) = c_Set_OCollect(_846490))], (47712 ^ _774244) ^ [_1722803, _1722805, _1722807] : [_1722803 = hAPP(hAPP(c_List_Oappend(_1722805), _1722803), _1722807), -(_1722807 = c_List_Olist_ONil(_1722805))], (32608 ^ _774244) ^ [_1365254, _1365256] : [class_Rings_Osemiring__1(_1365254), -(hBOOL(hAPP(hAPP(c_member(_1365254), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1365254), _1365256)), c_Nat_Osemiring__1__class_ONats(_1365254))))], (50150 ^ _774244) ^ [_1778141, _1778143] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1778141)), c_List_Otranspose__rel(_1778141)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1778141)), c_List_Olist_ONil(_1778141)), _1778143))), -(c_List_Otranspose(_1778141, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1778141)), c_List_Olist_ONil(_1778141)), _1778143)) = c_List_Otranspose(_1778141, _1778143))], (51053 ^ _774244) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (9316 ^ _774244) ^ [_927151, _927153] : [class_Groups_Oab__group__add(_927151), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927151), hAPP(c_Groups_Ouminus__class_Ouminus(_927151), _927153)), _927153) = c_Groups_Ozero__class_Ozero(_927151))], (46657 ^ _774244) ^ [_1698323, _1698325, _1698327, _1698329, _1698331] : [class_Groups_Ocomm__monoid__add(_1698323), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1698323), hAPP(hAPP(c_List_Omap(_1698325, _1698323), hAPP(hAPP(c_COMBS(_1698325, _1698323, _1698323), hAPP(hAPP(c_COMBB(_1698323, tc_fun(_1698323, _1698323), _1698325), c_Groups_Oplus__class_Oplus(_1698323)), _1698327)), _1698329)), _1698331)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1698323), hAPP(c_List_Omonoid__add__class_Olistsum(_1698323), hAPP(hAPP(c_List_Omap(_1698325, _1698323), _1698327), _1698331))), hAPP(c_List_Omonoid__add__class_Olistsum(_1698323), hAPP(hAPP(c_List_Omap(_1698325, _1698323), _1698329), _1698331))))], (51175 ^ _774244) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11811 ^ _774244) ^ [_969380, _969382, _969384] : [class_Rings_Oordered__cancel__semiring(_969380), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969380), _969382), _969384)), c_Groups_Ozero__class_Ozero(_969380)))), 11816 ^ _774244 : [(11823 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969380), _969382), c_Groups_Ozero__class_Ozero(_969380))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969380), c_Groups_Ozero__class_Ozero(_969380)), _969384))], (11817 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969380), c_Groups_Ozero__class_Ozero(_969380)), _969382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969380), _969384), c_Groups_Ozero__class_Ozero(_969380)))]]], (50292 ^ _774244) ^ [_1781497, _1781499] : [-(c_List_Oconcat(_1781497, _1781499) = hAPP(c_List_Ofoldl(tc_List_Olist(_1781497), tc_List_Olist(_1781497), c_List_Oappend(_1781497), c_List_Olist_ONil(_1781497)), _1781499))], (51349 ^ _774244) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (9014 ^ _774244) ^ [_921725, _921727, _921729] : [class_Groups_Oab__group__add(_921725), -(hAPP(c_Groups_Ouminus__class_Ouminus(_921725), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921725), _921727), _921729)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921725), hAPP(c_Groups_Ouminus__class_Ouminus(_921725), _921727)), hAPP(c_Groups_Ouminus__class_Ouminus(_921725), _921729)))], (47184 ^ _774244) ^ [_1710388, _1710390, _1710392, _1710394] : [_1710388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1710390), hAPP(hAPP(c_List_Olist_OCons(_1710390), _1710392), _1710394)), _1710388) = _1710392)], (17873 ^ _774244) ^ [_1080223, _1080225] : [class_Rings_Osemiring__1(_1080223), 17876 ^ _774244 : [(17883 ^ _774244) ^ [] : [_1080225 = c_Groups_Ozero__class_Ozero(_1080223), -(c_Int_Oiszero(_1080223, _1080225))], (17877 ^ _774244) ^ [] : [c_Int_Oiszero(_1080223, _1080225), -(_1080225 = c_Groups_Ozero__class_Ozero(_1080223))]]], (19615 ^ _774244) ^ [_1109276, _1109278, _1109280] : [class_Groups_Omonoid__mult(_1109276), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1109276), _1109278), 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)))), _1109280))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109276), _1109278), hAPP(hAPP(c_Power_Opower__class_Opower(_1109276), hAPP(hAPP(c_Power_Opower__class_Opower(_1109276), _1109278), _1109280)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (41813 ^ _774244) ^ [_1578398, _1578400, _1578402, _1578404] : [41814 ^ _774244 : [(41815 ^ _774244) ^ [_1578473] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578398, _1578402)), hAPP(hAPP(c_Product__Type_OPair(_1578398, _1578402), _1578400), _1578473)), _1578404))]], -(hBOOL(hAPP(hAPP(c_member(_1578398), _1578400), hAPP(c_Relation_ODomain(_1578398, _1578402), _1578404))))], (854 ^ _774244) ^ [_787415, _787417, _787419, _787421, _787423, _787425] : [-(c_Relation_Orefl__on(_787423, _787419, _787415)), c_Relation_Orefl__on(_787425, _787421, _787417), _787425 = _787423, _787421 = _787419, _787417 = _787415], (37448 ^ _774244) ^ [_1470784, _1470786, _1470788, _1470790, _1470792, _1470794] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1470784, _1470786)), hAPP(hAPP(c_Product__Type_OPair(_1470784, _1470786), _1470792), _1470794)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool)), _1470788), _1470790))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470784, tc_fun(_1470786, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1470784, tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_fun(_1470786, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470786, tc_fun(tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_fun(_1470786, tc_HOL_Obool)), _1470784), c_COMBC(_1470786, tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470786, tc_prod(_1470784, _1470786)), tc_fun(_1470786, tc_fun(tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_HOL_Obool)), _1470784), hAPP(c_COMBB(tc_prod(_1470784, _1470786), tc_fun(tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_HOL_Obool), _1470786), c_member(tc_prod(_1470784, _1470786)))), c_Product__Type_OPair(_1470784, _1470786)))), _1470788)), hAPP(hAPP(c_COMBC(_1470784, tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_fun(_1470786, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470786, tc_fun(tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_fun(_1470786, tc_HOL_Obool)), _1470784), c_COMBC(_1470786, tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470786, tc_prod(_1470784, _1470786)), tc_fun(_1470786, tc_fun(tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_HOL_Obool)), _1470784), hAPP(c_COMBB(tc_prod(_1470784, _1470786), tc_fun(tc_fun(tc_prod(_1470784, _1470786), tc_HOL_Obool), tc_HOL_Obool), _1470786), c_member(tc_prod(_1470784, _1470786)))), c_Product__Type_OPair(_1470784, _1470786)))), _1470790)), _1470792), _1470794)))], (7881 ^ _774244) ^ [_903035, _903037, _903039] : [class_Nat_Osemiring__char__0(_903035), 7884 ^ _774244 : [(7891 ^ _774244) ^ [] : [_903037 = _903039, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_903035), _903037) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_903035), _903039))], (7885 ^ _774244) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_903035), _903037) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_903035), _903039), -(_903037 = _903039)]]], (31693 ^ _774244) ^ [_1346291, _1346293, _1346295, _1346297] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1346291, tc_HOL_Obool)), _1346293), hAPP(hAPP(c_Set_Oinsert(_1346291), _1346295), _1346297)))), 31696 ^ _774244 : [(31699 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1346291, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346291, tc_HOL_Obool)), _1346293), hAPP(hAPP(c_Set_Oinsert(_1346291), _1346295), c_Orderings_Obot__class_Obot(tc_fun(_1346291, tc_HOL_Obool))))), _1346297))], (31697 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1346291), _1346295), _1346293)))]], 31700 ^ _774244 : [(31703 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1346291, tc_HOL_Obool)), _1346293), _1346297))], (31701 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1346291), _1346295), _1346293))]]], (46186 ^ _774244) ^ [_1683941, _1683943, _1683945] : [hBOOL(hAPP(hAPP(c_member(_1683941), _1683943), hAPP(c_List_Oset(_1683941), _1683945))), -(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(_1683941)), _1683945))))], (26982 ^ _774244) ^ [_1248504, _1248506] : [26984 ^ _774244 : [(26987 ^ _774244) ^ [] : [hBOOL(hAPP(_1248506, 26983 ^ [_1248504, _1248506]))], (26985 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26983 ^ [_1248504, _1248506]), _1248504)))]], 26988 ^ _774244 : [(26989 ^ _774244) ^ [_1248654] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1248654), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248504))), -(hBOOL(hAPP(_1248506, _1248654)))]]], (34970 ^ _774244) ^ [_1414081, _1414083, _1414085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1414081, tc_HOL_Obool)), _1414083), _1414085)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1414081, tc_HOL_Obool)), _1414083), hAPP(c_Set_OPow(_1414081), _1414085))))], (7513 ^ _774244) ^ [_896256, _896258, _896260, _896262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _896256), _896258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _896260), _896262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _896256), _896260)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _896258), _896262))))], (40807 ^ _774244) ^ [_1547744, _1547746, _1547748, _1547750, _1547752, _1547754] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1547744), _1547746)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547748), _1547750)), 40817 ^ _774244 : [(40820 ^ _774244) ^ [] : [hAPP(c_Finite__Set_Ocard(_1547744), hAPP(c_Set_OCollect(_1547744), hAPP(hAPP(c_COMBS(_1547744, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547744), c_fconj), hAPP(hAPP(c_COMBC(_1547744, tc_fun(_1547744, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547744)), _1547746))), hAPP(hAPP(c_COMBC(_1547744, _1547748, tc_HOL_Obool), _1547752), 40816 ^ [_1547744, _1547746, _1547748, _1547750, _1547752, _1547754])))) = _1547754], (40818 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547748), 40816 ^ [_1547744, _1547746, _1547748, _1547750, _1547752, _1547754]), _1547750)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1547744, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1547748, tc_HOL_Obool), tc_Nat_Onat, _1547744), c_Finite__Set_Ocard(_1547748)), hAPP(hAPP(c_COMBB(tc_fun(_1547748, tc_HOL_Obool), tc_fun(_1547748, tc_HOL_Obool), _1547744), c_Set_OCollect(_1547748)), hAPP(hAPP(c_COMBB(tc_fun(_1547748, tc_HOL_Obool), tc_fun(_1547748, tc_HOL_Obool), _1547744), hAPP(c_COMBS(_1547748, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547748), c_fconj), hAPP(hAPP(c_COMBC(_1547748, tc_fun(_1547748, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547748)), _1547750)))), _1547752)))), _1547746) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1547754), hAPP(c_Finite__Set_Ocard(_1547748), _1547750)))], (34668 ^ _774244) ^ [_1407371, _1407373, _1407375, _1407377, _1407379, _1407381] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1407377, _1407377)), hAPP(hAPP(c_Product__Type_OPair(_1407377, _1407377), hAPP(_1407381, _1407373)), hAPP(_1407381, _1407375))), _1407379)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1407371, _1407371)), hAPP(hAPP(c_Product__Type_OPair(_1407371, _1407371), _1407373), _1407375)), hAPP(hAPP(c_Relation_Oinv__image(_1407377, _1407371), _1407379), _1407381))))], (29712 ^ _774244) ^ [_1303304, _1303306] : [29713 ^ _774244 : [(29716 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1303306), _1303304))], (29714 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1303304), _1303306)))]], -(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)))), _1303304, _1303306) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (36559 ^ _774244) ^ [_1450266, _1450268, _1450270, _1450272] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1450266, tc_HOL_Obool)), _1450268), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450266, tc_HOL_Obool)), _1450270), _1450272)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1450266, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1450266, tc_HOL_Obool)), _1450268), _1450270)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1450266, tc_HOL_Obool)), _1450268), _1450272)))], (19257 ^ _774244) ^ [_1102942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1102942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1102942))))], (44524 ^ _774244) ^ [_1644412] : [class_Complete__Lattice_Ocomplete__lattice(_1644412), -(c_Complete__Lattice_OInf__class_OInf(_1644412, c_Orderings_Obot__class_Obot(tc_fun(_1644412, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1644412))], (48907 ^ _774244) ^ [_1752322, _1752324, _1752326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1752322, tc_HOL_Obool)), _1752324), _1752326)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1752322), tc_HOL_Obool)), c_List_Olists(_1752322, _1752324)), c_List_Olists(_1752322, _1752326))))], (42788 ^ _774244) ^ [_1600367, _1600369, _1600371] : [class_Orderings_Olinorder(_1600367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600367), _1600369)), -(hBOOL(hAPP(hAPP(c_member(_1600367), _1600371), _1600369))), -(c_Big__Operators_Olattice_OInf__fin(_1600367, c_Orderings_Oord__class_Omin(_1600367), hAPP(hAPP(c_Set_Oinsert(_1600367), _1600371), _1600369)) = hAPP(hAPP(c_Finite__Set_Ofold(_1600367, _1600367, c_Orderings_Oord__class_Omin(_1600367)), _1600371), _1600369))], (7351 ^ _774244) ^ [_893666, _893668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893666), _893668)), _893668 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26590 ^ _774244) ^ [_1240676, _1240678, _1240680] : [class_Fields_Ofield(_1240676), -(_1240678 = c_Groups_Oone__class_Oone(_1240676)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1240676), hAPP(c_Power_Opower__class_Opower(_1240676), _1240678)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1240680)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240676), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1240676), hAPP(hAPP(c_Power_Opower__class_Opower(_1240676), _1240678), _1240680)), c_Groups_Oone__class_Oone(_1240676))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1240676), _1240678), c_Groups_Oone__class_Oone(_1240676))))], (41282 ^ _774244) ^ [_1565780, _1565782, _1565784, _1565786, _1565788, _1565790, _1565792] : [c_Predicate_Opred__comp(_1565780, _1565782, _1565784, hAPP(hAPP(c_COMBC(_1565780, tc_fun(tc_prod(_1565780, _1565782), tc_HOL_Obool), tc_fun(_1565782, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565782, tc_fun(tc_fun(tc_prod(_1565780, _1565782), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1565780, _1565782), tc_HOL_Obool), tc_fun(_1565782, tc_HOL_Obool)), _1565780), c_COMBC(_1565782, tc_fun(tc_prod(_1565780, _1565782), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565782, tc_prod(_1565780, _1565782)), tc_fun(_1565782, tc_fun(tc_fun(tc_prod(_1565780, _1565782), tc_HOL_Obool), tc_HOL_Obool)), _1565780), hAPP(c_COMBB(tc_prod(_1565780, _1565782), tc_fun(tc_fun(tc_prod(_1565780, _1565782), tc_HOL_Obool), tc_HOL_Obool), _1565782), c_member(tc_prod(_1565780, _1565782)))), c_Product__Type_OPair(_1565780, _1565782)))), _1565786), hAPP(hAPP(c_COMBC(_1565782, tc_fun(tc_prod(_1565782, _1565784), tc_HOL_Obool), tc_fun(_1565784, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565784, tc_fun(tc_fun(tc_prod(_1565782, _1565784), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1565782, _1565784), tc_HOL_Obool), tc_fun(_1565784, tc_HOL_Obool)), _1565782), c_COMBC(_1565784, tc_fun(tc_prod(_1565782, _1565784), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565784, tc_prod(_1565782, _1565784)), tc_fun(_1565784, tc_fun(tc_fun(tc_prod(_1565782, _1565784), tc_HOL_Obool), tc_HOL_Obool)), _1565782), hAPP(c_COMBB(tc_prod(_1565782, _1565784), tc_fun(tc_fun(tc_prod(_1565782, _1565784), tc_HOL_Obool), tc_HOL_Obool), _1565784), c_member(tc_prod(_1565782, _1565784)))), c_Product__Type_OPair(_1565782, _1565784)))), _1565788), _1565790, _1565792), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565780, _1565784)), hAPP(hAPP(c_Product__Type_OPair(_1565780, _1565784), _1565790), _1565792)), hAPP(hAPP(c_Relation_Orel__comp(_1565780, _1565782, _1565784), _1565786), _1565788))))], (4812 ^ _774244) ^ [_848638, _848640] : [_848640 = _848638, -(c_Int_Onumber__class_Onumber__of(_848640) = c_Int_Onumber__class_Onumber__of(_848638))], (24585 ^ _774244) ^ [] : [-(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)))], (18737 ^ _774244) ^ [_1093810] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1093810))) = 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)))), _1093810))], (50200 ^ _774244) ^ [_1779506, _1779508, _1779510] : [_1779508 = hAPP(hAPP(c_List_Olist_OCons(_1779506), _1779510), c_List_Olist_ONil(_1779506)), -(hAPP(c_List_Orev(_1779506), _1779508) = hAPP(hAPP(c_List_Olist_OCons(_1779506), _1779510), c_List_Olist_ONil(_1779506)))], (23343 ^ _774244) ^ [_1178181, _1178183] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1178181), _1178183) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1178181, _1178183)))], (24137 ^ _774244) ^ [_1193401, _1193403, _1193405, _1193407] : [class_Orderings_Olinorder(_1193401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193401), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1193401), _1193403), _1193405)), _1193407)), 24144 ^ _774244 : [(24147 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193401), _1193405), _1193407)))], (24145 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193401), _1193403), _1193407)))]]], (49802 ^ _774244) ^ [_1771338, _1771340] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1771338), _1771340) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1771338, _1771340)))], (24531 ^ _774244) ^ [_1201081, _1201083, _1201085, _1201087] : [-(c_Sum__Type_Osum_Osum__case(_1201081, _1201083, _1201085, hAPP(hAPP(c_COMBB(tc_sum(_1201081, _1201085), _1201083, _1201081), _1201087), c_Sum__Type_OInl(_1201081, _1201085)), hAPP(hAPP(c_COMBB(tc_sum(_1201081, _1201085), _1201083, _1201085), _1201087), c_Sum__Type_OInr(_1201085, _1201081))) = _1201087)], (36895 ^ _774244) ^ [_1458209, _1458211, _1458213, _1458215, _1458217] : [c_Equiv__Relations_Oequiv(_1458209, _1458211, _1458213), hBOOL(hAPP(hAPP(c_member(tc_fun(_1458209, tc_HOL_Obool)), _1458215), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1458209), _1458211), _1458213))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1458209, tc_HOL_Obool)), _1458217), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1458209), _1458211), _1458213))), -(_1458215 = _1458217), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458209, tc_HOL_Obool)), _1458215), _1458217) = c_Orderings_Obot__class_Obot(tc_fun(_1458209, tc_HOL_Obool)))], (48801 ^ _774244) ^ [_1749579, _1749581, _1749583] : [class_Orderings_Olinorder(_1749579), -(c_Big__Operators_Olinorder__class_OMin(_1749579, hAPP(c_List_Oset(_1749579), hAPP(hAPP(c_List_Olist_OCons(_1749579), _1749581), _1749583))) = hAPP(c_List_Ofoldl(_1749579, _1749579, c_Orderings_Oord__class_Omin(_1749579), _1749581), _1749583))], (39928 ^ _774244) ^ [_1527980, _1527982, _1527984, _1527986, _1527988, _1527990, _1527992] : [-(hAPP(c_Product__Type_Ofst(_1527980, _1527982), hAPP(c_Product__Type_Omap__pair(_1527984, _1527980, _1527986, _1527982, _1527988, _1527990), _1527992)) = hAPP(_1527988, hAPP(c_Product__Type_Ofst(_1527984, _1527986), _1527992)))], (47592 ^ _774244) ^ [_1720296, _1720298, _1720300, _1720302, _1720304] : [-(hAPP(hAPP(c_List_Oappend(_1720296), _1720298), _1720300) = hAPP(hAPP(c_List_Oappend(_1720296), _1720302), _1720304)), 47593 ^ _774244 : [(47600 ^ _774244) ^ [_1720520] : [hAPP(hAPP(c_List_Oappend(_1720296), _1720298), _1720520) = _1720302, _1720300 = hAPP(hAPP(c_List_Oappend(_1720296), _1720520), _1720304)], (47594 ^ _774244) ^ [_1720408] : [_1720298 = hAPP(hAPP(c_List_Oappend(_1720296), _1720302), _1720408), hAPP(hAPP(c_List_Oappend(_1720296), _1720408), _1720300) = _1720304]]], (15302 ^ _774244) ^ [_1031761, _1031763, _1031765] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031763), _1031765)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031761), _1031763)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031761), _1031765)))], (668 ^ _774244) ^ [_784612, _784614, _784616, _784618, _784620, _784622] : [-(c_Finite__Set_Ofolding__one(_784620, _784616, _784612)), c_Finite__Set_Ofolding__one(_784622, _784618, _784614), _784622 = _784620, _784618 = _784616, _784614 = _784612], (17385 ^ _774244) ^ [_1071889, _1071891] : [class_Power_Opower(_1071889), class_Rings_Osemiring__0(_1071889), 17392 ^ _774244 : [(17399 ^ _774244) ^ [] : [-(_1071891 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1071889), c_Groups_Ozero__class_Ozero(_1071889)), _1071891) = c_Groups_Ozero__class_Ozero(_1071889))], (17393 ^ _774244) ^ [] : [_1071891 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1071889), c_Groups_Ozero__class_Ozero(_1071889)), _1071891) = c_Groups_Oone__class_Oone(_1071889))]]], (19231 ^ _774244) ^ [_1102485, _1102487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102485), _1102487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1102485)), c_Int_OBit1(_1102487))))], (4596 ^ _774244) ^ [_845282, _845284, _845286, _845288] : [-(c_List_Olistrel1(_845288, _845284) = c_List_Olistrel1(_845286, _845282)), _845288 = _845286, _845284 = _845282], (51023 ^ _774244) ^ [_1797367, _1797369] : [class_Groups_Ominus(_1797367), -(class_Groups_Ominus(tc_fun(_1797369, _1797367)))], (44985 ^ _774244) ^ [_1655445, _1655447, _1655449, _1655451, _1655453] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1655445, _1655445)), hAPP(hAPP(c_Product__Type_OPair(_1655445, _1655445), _1655447), _1655449)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1655445, _1655445), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1655451)), _1655453))), 44989 ^ _774244 : [(44992 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655445, _1655445)), hAPP(hAPP(c_Product__Type_OPair(_1655445, _1655445), 44988 ^ [_1655445, _1655447, _1655449, _1655451, _1655453]), _1655449)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1655445, _1655445), tc_HOL_Obool), _1655451), _1655453))))], (44990 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655445, _1655445)), hAPP(hAPP(c_Product__Type_OPair(_1655445, _1655445), _1655447), 44988 ^ [_1655445, _1655447, _1655449, _1655451, _1655453])), _1655453)))]]], (24753 ^ _774244) ^ [_1206546, _1206548, _1206550, _1206552, _1206554, _1206556] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1206546, _1206548, _1206550, _1206552), _1206554), _1206556) = hAPP(_1206552, hAPP(hAPP(c_Product__Type_OPair(_1206546, _1206548), _1206554), _1206556)))], (41782 ^ _774244) ^ [_1577675, _1577677, _1577679] : [_1577679 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1577675, _1577677), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1577675, _1577677), _1577679) = c_Orderings_Obot__class_Obot(tc_fun(_1577675, tc_HOL_Obool)))], (49701 ^ _774244) ^ [_1769602, _1769604, _1769606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1769602), _1769604)), -(c_List_Oupt(_1769602, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1769604), _1769606)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1769602, _1769604)), c_List_Oupt(_1769604, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1769604), _1769606))))], (50296 ^ _774244) ^ [_1781596, _1781598, _1781600] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1781596), tc_List_Olist(_1781596), c_List_Oappend(_1781596), _1781598), _1781600) = hAPP(hAPP(c_List_Oappend(_1781596), _1781598), c_List_Oconcat(_1781596, _1781600)))], (41232 ^ _774244) ^ [_1563757, _1563759, _1563761, _1563763] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1563757, _1563759, _1563761), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1563757, _1563759), tc_HOL_Obool))), _1563763) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1563757, _1563761), tc_HOL_Obool)))], (43889 ^ _774244) ^ [_1628726, _1628728, _1628730, _1628732, _1628734] : [class_Complete__Lattice_Ocomplete__lattice(_1628726), hBOOL(hAPP(hAPP(c_member(_1628728), _1628730), _1628732)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1628726), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628728, _1628726), _1628732), _1628734)), hAPP(_1628734, _1628730))))], (11635 ^ _774244) ^ [_966048, _966050, _966052] : [class_Rings_Oordered__cancel__semiring(_966048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966048), c_Groups_Ozero__class_Ozero(_966048)), _966050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966048), _966052), c_Groups_Ozero__class_Ozero(_966048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966048), _966052), _966050)), c_Groups_Ozero__class_Ozero(_966048))))], (1604 ^ _774244) ^ [_797018, _797020] : [-(class_Orderings_Opreorder(_797018)), _797020 = _797018, class_Orderings_Opreorder(_797020)], (22626 ^ _774244) ^ [_1164780, _1164782, _1164784, _1164786] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1164780, _1164782), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1164784), _1164786))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1164780, _1164782) = _1164786)], (8742 ^ _774244) ^ [_916930] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _916930)) = _916930)], (47658 ^ _774244) ^ [_1721851, _1721853, _1721855] : [hAPP(hAPP(c_List_Oappend(_1721851), _1721853), _1721855) = _1721855, -(_1721853 = c_List_Olist_ONil(_1721851))], (51063 ^ _774244) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (41725 ^ _774244) ^ [_1576640, _1576642] : [c_Wellfounded_OwfP(_1576640, _1576642), -(c_Wellfounded_Owf(_1576640, hAPP(c_Set_OCollect(tc_prod(_1576640, _1576640)), hAPP(c_Product__Type_Oprod_Oprod__case(_1576640, _1576640, tc_HOL_Obool), _1576642))))], (30869 ^ _774244) ^ [_1327897, _1327899] : [hBOOL(hAPP(hAPP(c_member(_1327897), _1327899), c_Orderings_Obot__class_Obot(tc_fun(_1327897, tc_HOL_Obool))))], (34716 ^ _774244) ^ [_1408428, _1408430] : [c_Relation_Oirrefl(_1408428, _1408430), 34719 ^ _774244 : [(34720 ^ _774244) ^ [_1408510] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1408428, _1408428)), hAPP(hAPP(c_Product__Type_OPair(_1408428, _1408428), _1408510), _1408510)), _1408430))]]], (22909 ^ _774244) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (20751 ^ _774244) ^ [_1129595, _1129597, _1129599, _1129601] : [class_Fields_Olinordered__field(_1129595), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129595), _1129597), c_Groups_Ozero__class_Ozero(_1129595))), 20758 ^ _774244 : [(20765 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129595), _1129601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129595), _1129599), _1129597))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129595), _1129599), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129595), _1129601), _1129597))))], (20759 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129595), _1129599), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129595), _1129601), _1129597))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129595), _1129601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129595), _1129599), _1129597))))]]], (37879 ^ _774244) ^ [_1480463, _1480465, _1480467] : [-(c_Fun_Oinj__on(_1480463, _1480465, _1480467, c_Orderings_Obot__class_Obot(tc_fun(_1480463, tc_HOL_Obool))))], (15170 ^ _774244) ^ [_1029376] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029376), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1029376)], (29028 ^ _774244) ^ [_1290848, _1290850, _1290852, _1290854] : [29030 ^ _774244 : [(29033 ^ _774244) ^ [] : [hAPP(_1290854, 29029 ^ [_1290848, _1290850, _1290852, _1290854]) = c_Orderings_Obot__class_Obot(tc_fun(_1290850, tc_HOL_Obool))], (29031 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290848), 29029 ^ [_1290848, _1290850, _1290852, _1290854]), _1290852)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1290848, tc_fun(_1290850, tc_HOL_Obool)), _1290852), _1290854) = c_Orderings_Obot__class_Obot(tc_fun(_1290850, tc_HOL_Obool)))], (48061 ^ _774244) ^ [_1731467, _1731469, _1731471, _1731473, _1731475, _1731477] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731467), tc_List_Olist(_1731467))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731467), tc_List_Olist(_1731467)), hAPP(hAPP(c_List_Oappend(_1731467), _1731469), hAPP(hAPP(c_List_Olist_OCons(_1731467), _1731471), c_List_Olist_ONil(_1731467)))), hAPP(hAPP(c_List_Oappend(_1731467), _1731473), hAPP(hAPP(c_List_Olist_OCons(_1731467), _1731475), c_List_Olist_ONil(_1731467))))), c_List_Olistrel1(_1731467, _1731477)))), 48062 ^ _774244 : [(48069 ^ _774244) ^ [] : [_1731469 = _1731473, hBOOL(hAPP(hAPP(c_member(tc_prod(_1731467, _1731467)), hAPP(hAPP(c_Product__Type_OPair(_1731467, _1731467), _1731471), _1731475)), _1731477))], (48063 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731467), tc_List_Olist(_1731467))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731467), tc_List_Olist(_1731467)), _1731469), _1731473)), c_List_Olistrel1(_1731467, _1731477))), _1731471 = _1731475]]], (1234 ^ _774244) ^ [_792393, _792395] : [-(class_Lattices_Obounded__lattice__top(_792393)), _792395 = _792393, class_Lattices_Obounded__lattice__top(_792395)], (7726 ^ _774244) ^ [_900218, _900220] : [7727 ^ _774244 : [(7728 ^ _774244) ^ [_900271] : [_900220 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900218), _900271))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _900218), _900220)))], (17205 ^ _774244) ^ [_1068599, _1068601, _1068603] : [class_Rings_Olinordered__semidom(_1068599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068599), c_Groups_Ozero__class_Ozero(_1068599)), _1068601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068599), c_Groups_Ozero__class_Ozero(_1068599)), hAPP(hAPP(c_Power_Opower__class_Opower(_1068599), _1068601), _1068603))))], (49430 ^ _774244) ^ [_1763376, _1763378, _1763380] : [hBOOL(hAPP(c_List_Odistinct(_1763376), _1763378)), -(hAPP(c_List_Ofilter(_1763376, hAPP(hAPP(c_COMBC(_1763376, tc_fun(_1763376, tc_HOL_Obool), tc_HOL_Obool), c_member(_1763376)), hAPP(c_List_Oset(_1763376), c_List_Osublist(_1763376, _1763378, _1763380)))), _1763378) = c_List_Osublist(_1763376, _1763378, _1763380))], (19373 ^ _774244) ^ [_1104927, _1104929] : [class_Rings_Olinordered__idom(_1104927), -(hAPP(c_Groups_Oabs__class_Oabs(_1104927), hAPP(hAPP(c_Power_Opower__class_Opower(_1104927), _1104929), 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(_1104927), _1104929), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (40253 ^ _774244) ^ [_1534715, _1534717, _1534719] : [class_Orderings_Olinorder(_1534715), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534715), _1534717)), -(_1534717 = c_Orderings_Obot__class_Obot(tc_fun(_1534715, tc_HOL_Obool))), 40264 ^ _774244 : [(40274 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1534715), hAPP(c_Finite__Set_Ofold1(_1534715, c_Orderings_Oord__class_Omin(_1534715)), _1534717)), _1534719))), 40275 ^ _774244 : [(40276 ^ _774244) ^ [_1535104] : [hBOOL(hAPP(hAPP(c_member(_1534715), _1535104), _1534717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1534715), _1535104), _1534719))]]], (40265 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1534715), hAPP(c_Finite__Set_Ofold1(_1534715, c_Orderings_Oord__class_Omin(_1534715)), _1534717)), _1534719)), 40269 ^ _774244 : [(40272 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1534715), 40268 ^ [_1534715, _1534717, _1534719]), _1534719)))], (40270 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1534715), 40268 ^ [_1534715, _1534717, _1534719]), _1534717)))]]]]], (45482 ^ _774244) ^ [_1667161, _1667163, _1667165, _1667167, _1667169, _1667171, _1667173] : [hAPP(_1667161, _1667163) = hAPP(c_Option_Ooption_OSome(_1667165), _1667167), -(c_Map_Omap__comp(_1667165, _1667169, _1667171, _1667173, _1667161, _1667163) = hAPP(_1667173, _1667167))], (47565 ^ _774244) ^ [_1719606, _1719608, _1719610] : [class_Groups_Omonoid__add(_1719606), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1719606), hAPP(hAPP(c_List_Oappend(_1719606), _1719608), _1719610)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1719606), hAPP(c_List_Omonoid__add__class_Olistsum(_1719606), _1719608)), hAPP(c_List_Omonoid__add__class_Olistsum(_1719606), _1719610)))], (35550 ^ _774244) ^ [_1428058, _1428060] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1428058), c_Orderings_Obot__class_Obot(tc_fun(_1428058, tc_HOL_Obool))), _1428060) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1428058, tc_HOL_Obool), tc_HOL_Obool)))], (36745 ^ _774244) ^ [_1454568, _1454570, _1454572] : [class_Orderings_Oorder(_1454568), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454568, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1454568), _1454570)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1454568, _1454570, _1454572)) = c_Orderings_Obot__class_Obot(tc_fun(_1454568, tc_HOL_Obool)))], (32716 ^ _774244) ^ [_1367372, _1367374] : [class_Groups_Olinordered__ab__group__add(_1367372), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367372), _1367374)), -(_1367374 = c_Orderings_Obot__class_Obot(tc_fun(_1367372, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1367372), c_Big__Operators_Olinorder__class_OMin(_1367372, _1367374)) = c_Big__Operators_Olinorder__class_OMax(_1367372, hAPP(c_Set_Oimage(_1367372, _1367372, c_Groups_Ouminus__class_Ouminus(_1367372)), _1367374)))], (24765 ^ _774244) ^ [_1206783, _1206785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206783)), 24768 ^ _774244 : [(24775 ^ _774244) ^ [] : [_1206785 = 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), _1206783), _1206785)), _1206783)))], (24769 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206783), _1206785)), _1206783)), -(_1206785 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (51051 ^ _774244) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (42419 ^ _774244) ^ [_1593312, _1593314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1593312), _1593314)), -(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), _1593312), _1593314)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (31231 ^ _774244) ^ [_1335047, _1335049, _1335051, _1335053, _1335055, _1335057] : [c_Finite__Set_Ofolding__image__simple(_1335047, _1335049, _1335051, _1335053, _1335055, _1335057), -(hAPP(_1335057, c_Orderings_Obot__class_Obot(tc_fun(_1335049, tc_HOL_Obool))) = _1335053)], (6564 ^ _774244) ^ [_880004, _880006] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _880004)), _880006) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _880004), hAPP(c_Nat_OSuc, _880006)))], (33354 ^ _774244) ^ [_1379414, _1379416, _1379418, _1379420] : [c_Sum__Type_OPlus(_1379414, _1379416, _1379418, _1379420) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1379414, _1379416), tc_HOL_Obool)), 33357 ^ _774244 : [(33360 ^ _774244) ^ [] : [-(_1379420 = c_Orderings_Obot__class_Obot(tc_fun(_1379416, tc_HOL_Obool)))], (33358 ^ _774244) ^ [] : [-(_1379418 = c_Orderings_Obot__class_Obot(tc_fun(_1379414, tc_HOL_Obool)))]]], (16499 ^ _774244) ^ [_1055061, _1055063] : [class_Groups_Oordered__ab__group__add__abs(_1055061), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055061), hAPP(c_Groups_Ouminus__class_Ouminus(_1055061), _1055063)), hAPP(c_Groups_Oabs__class_Oabs(_1055061), _1055063))))], (31315 ^ _774244) ^ [_1336815, _1336817, _1336819, _1336821] : [hBOOL(hAPP(hAPP(c_member(_1336815), _1336817), _1336819)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336815, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1336815), _1336817), _1336821)), _1336819) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336815, tc_HOL_Obool)), _1336821), _1336819))], (37811 ^ _774244) ^ [_1478530, _1478532, _1478534] : [class_Lattices_Olattice(_1478530), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478530), _1478532)), -(_1478532 = c_Orderings_Obot__class_Obot(tc_fun(_1478530, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478530), _1478534)), -(_1478534 = c_Orderings_Obot__class_Obot(tc_fun(_1478530, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478530, tc_HOL_Obool)), _1478532), _1478534) = c_Orderings_Obot__class_Obot(tc_fun(_1478530, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1478530, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478530, tc_HOL_Obool)), _1478532), _1478534)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1478530), c_Big__Operators_Olattice__class_OInf__fin(_1478530, _1478532)), c_Big__Operators_Olattice__class_OInf__fin(_1478530, _1478534)))], (5893 ^ _774244) ^ [_868558, _868560, _868562] : [class_Rings_Osemiring__1(_868558), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_868558, _868560, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _868562) = _868562)], (33930 ^ _774244) ^ [_1390677, _1390679, _1390681, _1390683, _1390685] : [hAPP(_1390677, _1390679) = c_Option_Ooption_ONone(_1390681), -(c_Map_Oran(_1390683, _1390681, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1390683, tc_Option_Ooption(_1390681)), _1390677), _1390679), hAPP(c_Option_Ooption_OSome(_1390681), _1390685))) = hAPP(hAPP(c_Set_Oinsert(_1390681), _1390685), c_Map_Oran(_1390683, _1390681, _1390677)))], (45513 ^ _774244) ^ [_1667864, _1667866, _1667868, _1667870, _1667872] : [hAPP(hAPP(c_List_Omap(_1667864, _1667866), _1667868), _1667870) = hAPP(hAPP(c_List_Omap(_1667864, _1667866), _1667868), _1667872), c_Fun_Oinj__on(_1667864, _1667866, _1667868, c_Orderings_Otop__class_Otop(tc_fun(_1667864, tc_HOL_Obool))), -(_1667870 = _1667872)], (42926 ^ _774244) ^ [_1603719, _1603721, _1603723, _1603725, _1603727] : [c_Finite__Set_Ofun__left__comm(_1603719, _1603721, _1603723), -(c_Finite__Set_Ofun__left__comm(_1603725, _1603721, hAPP(hAPP(c_COMBB(_1603719, tc_fun(_1603721, _1603721), _1603725), _1603723), _1603727)))], (51197 ^ _774244) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (10660 ^ _774244) ^ [_949602, _949604, _949606] : [class_Orderings_Oorder(_949602), -(_949604 = _949606), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949602), _949604), _949606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949602), _949604), _949606)))], (34956 ^ _774244) ^ [_1413729, _1413731, _1413733] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1413729, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1413729, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1413729), _1413731)), hAPP(c_Set_OPow(_1413729), _1413733))), hAPP(c_Set_OPow(_1413729), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413729, tc_HOL_Obool)), _1413731), _1413733)))))], (42732 ^ _774244) ^ [_1599511, _1599513, _1599515] : [class_Lattices_Olattice(_1599511), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599511), _1599513)), -(hBOOL(hAPP(hAPP(c_member(_1599511), _1599515), _1599513))), -(c_Big__Operators_Olattice__class_OSup__fin(_1599511, hAPP(hAPP(c_Set_Oinsert(_1599511), _1599515), _1599513)) = hAPP(hAPP(c_Finite__Set_Ofold(_1599511, _1599511, c_Lattices_Osemilattice__sup__class_Osup(_1599511)), _1599515), _1599513))], (48524 ^ _774244) ^ [_1744281, _1744283, _1744285] : [-(_1744281 = c_List_Olist_ONil(_1744283)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744285), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744283)), _1744281))), -(hAPP(c_List_Ohd(_1744283), hAPP(hAPP(c_List_Odrop(_1744283), _1744285), _1744281)) = hAPP(hAPP(c_List_Onth(_1744283), _1744281), _1744285))], (17889 ^ _774244) ^ [_1080434] : [class_Rings_Osemiring__1(_1080434), c_Int_Oiszero(_1080434, c_Groups_Oone__class_Oone(_1080434))], (9050 ^ _774244) ^ [_922439, _922441, _922443] : [class_Rings_Ono__zero__divisors(_922439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922439), _922441), _922443) = c_Groups_Ozero__class_Ozero(_922439), -(_922441 = c_Groups_Ozero__class_Ozero(_922439)), -(_922443 = c_Groups_Ozero__class_Ozero(_922439))], (19803 ^ _774244) ^ [_1112921, _1112923] : [class_Rings_Odivision__ring(_1112921), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112921), c_Groups_Ozero__class_Ozero(_1112921)), _1112923) = c_Groups_Ozero__class_Ozero(_1112921))], (43841 ^ _774244) ^ [_1627325, _1627327, _1627329, _1627331, _1627333] : [_1627325 = c_Orderings_Obot__class_Obot(tc_fun(_1627327, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1627329, tc_HOL_Obool)), _1627331), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1627327, tc_fun(_1627329, tc_HOL_Obool)), _1627325), _1627333)) = _1627331)], (46445 ^ _774244) ^ [_1692399, _1692401, _1692403, _1692405, _1692407] : [-(hAPP(hAPP(c_List_Olist_OCons(_1692399), _1692401), _1692403) = hAPP(hAPP(c_List_Olist_OCons(_1692399), _1692405), _1692407)), _1692401 = _1692405, _1692403 = _1692407], (44624 ^ _774244) ^ [_1646998, _1647000, _1647002, _1647004] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646998, tc_fun(_1647000, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646998, tc_HOL_Obool), _1647002)), _1647004) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1646998, tc_HOL_Obool), tc_fun(_1647000, tc_HOL_Obool)), _1647002), hAPP(hAPP(c_COMBC(tc_fun(_1646998, tc_HOL_Obool), tc_fun(_1646998, tc_fun(_1647000, tc_HOL_Obool)), tc_fun(_1647000, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646998, tc_fun(_1647000, tc_HOL_Obool))), _1647004)))], (50041 ^ _774244) ^ [_1775551, _1775553, _1775555] : [class_Orderings_Olinorder(_1775551), hBOOL(hAPP(hAPP(c_member(_1775551), _1775553), hAPP(c_List_Oset(_1775551), _1775555))), c_List_Olinorder__class_Osorted(_1775551, _1775555), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1775551, _1775551, c_COMBI(_1775551)), _1775553), c_List_Oremove1(_1775551, _1775553, _1775555)) = _1775555)], (22170 ^ _774244) ^ [_1155455, _1155457] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155455) = hAPP(c_Nat_OSuc, _1155457), -(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(_1155455))), 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)), _1155457))))))], (33720 ^ _774244) ^ [_1386085, _1386087, _1386089] : [class_Orderings_Olinorder(_1386085), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386085), _1386087)), 33727 ^ _774244 : [(33734 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386085, tc_HOL_Obool)), _1386087), hAPP(hAPP(c_Set_Oinsert(_1386085), _1386089), c_Orderings_Obot__class_Obot(tc_fun(_1386085, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1386085, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1386085, c_Orderings_Oord__class_Omin(_1386085), hAPP(hAPP(c_Set_Oinsert(_1386085), _1386089), _1386087)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1386085), _1386089), c_Big__Operators_Olattice_OInf__fin(_1386085, c_Orderings_Oord__class_Omin(_1386085), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386085, tc_HOL_Obool)), _1386087), hAPP(hAPP(c_Set_Oinsert(_1386085), _1386089), c_Orderings_Obot__class_Obot(tc_fun(_1386085, tc_HOL_Obool)))))))], (33728 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386085, tc_HOL_Obool)), _1386087), hAPP(hAPP(c_Set_Oinsert(_1386085), _1386089), c_Orderings_Obot__class_Obot(tc_fun(_1386085, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1386085, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1386085, c_Orderings_Oord__class_Omin(_1386085), hAPP(hAPP(c_Set_Oinsert(_1386085), _1386089), _1386087)) = _1386089)]]], (9967 ^ _774244) ^ [_938446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _938446)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _938446)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _938446)))], (8314 ^ _774244) ^ [_909773, _909775, _909777] : [class_Orderings_Oorder(_909773), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909773), _909775), _909777)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909773), _909777), _909775))], (18555 ^ _774244) ^ [_1090932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1090932))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1090932)))], (2078 ^ _774244) ^ [_805243, _805245, _805247, _805249, _805251, _805253, _805255, _805257, _805259, _805261] : [-(c_Nitpick_Opair__box_Opair__box__case(_805261, _805257, _805253, _805249, _805245) = c_Nitpick_Opair__box_Opair__box__case(_805259, _805255, _805251, _805247, _805243)), _805261 = _805259, _805257 = _805255, _805253 = _805251, _805249 = _805247, _805245 = _805243], (32744 ^ _774244) ^ [_1367772, _1367774] : [class_Orderings_Olinorder(_1367772), -(c_Big__Operators_Olinorder__class_OMax(_1367772, hAPP(hAPP(c_Set_Oinsert(_1367772), _1367774), c_Orderings_Obot__class_Obot(tc_fun(_1367772, tc_HOL_Obool)))) = _1367774)], (16187 ^ _774244) ^ [_1049383, _1049385] : [class_Groups_Oordered__ab__group__add__abs(_1049383), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049383), _1049385), hAPP(c_Groups_Oabs__class_Oabs(_1049383), _1049385))))], (15946 ^ _774244) ^ [_1045098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1045098)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045098), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1045098)], (47881 ^ _774244) ^ [_1727199, _1727201, _1727203, _1727205, _1727207, _1727209] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727199)), _1727201) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727203)), _1727205), -(c_Map_Omap__upds(_1727199, _1727203, _1727207, _1727201, hAPP(hAPP(c_List_Oappend(_1727203), _1727205), _1727209)) = c_Map_Omap__upds(_1727199, _1727203, _1727207, _1727201, _1727205))], (48332 ^ _774244) ^ [_1739509, _1739511] : [hBOOL(hAPP(c_List_Odistinct(_1739509), hAPP(c_List_Orotate1(_1739509), _1739511))), -(hBOOL(hAPP(c_List_Odistinct(_1739509), _1739511)))], (44010 ^ _774244) ^ [_1632320] : [-(hAPP(c_Relation_Oconverse(_1632320, _1632320), c_Relation_OId(_1632320)) = c_Relation_OId(_1632320))], (40545 ^ _774244) ^ [_1540349, _1540351] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1540349)), 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)), _1540349))), 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, _1540351))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4450 ^ _774244) ^ [_843095, _843097, _843099, _843101] : [-(c_Complete__Lattice_OInf__class_OInf(_843101, _843097) = c_Complete__Lattice_OInf__class_OInf(_843099, _843095)), _843101 = _843099, _843097 = _843095], (42198 ^ _774244) ^ [_1588192, _1588194, _1588196, _1588198] : [-(c_Hilbert__Choice_OEps(tc_prod(_1588192, _1588194), hAPP(c_Product__Type_Oprod_Oprod__case(_1588192, _1588194, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1588192, tc_fun(_1588194, tc_HOL_Obool), tc_fun(_1588194, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1588194, tc_HOL_Obool), tc_fun(_1588194, tc_HOL_Obool)), _1588192), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1588194)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1588192), c_fconj), hAPP(c_fequal, _1588196)))), hAPP(c_fequal, _1588198)))) = hAPP(hAPP(c_Product__Type_OPair(_1588192, _1588194), _1588196), _1588198))], (45139 ^ _774244) ^ [_1659413, _1659415, _1659417, _1659419, _1659421, _1659423, _1659425, _1659427] : [c_Finite__Set_Ofolding__image__simple__idem(_1659413, _1659415, _1659417, _1659419, _1659421, _1659423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1659415), _1659425)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1659415), _1659427)), -(hAPP(_1659423, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659415, tc_HOL_Obool)), _1659425), _1659427)) = hAPP(hAPP(_1659417, hAPP(_1659423, _1659425)), hAPP(_1659423, _1659427)))], (41925 ^ _774244) ^ [_1581518, _1581520] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1581518, _1581518)), _1581520)), c_Wellfounded_Oacyclic(_1581518, _1581520), -(c_Wellfounded_Owf(_1581518, _1581520))], (6570 ^ _774244) ^ [_880148, _880150] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _880148), _880150), 6575 ^ _774244 : [(6578 ^ _774244) ^ [] : [-(_880150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6576 ^ _774244) ^ [] : [-(_880148 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6579 ^ _774244 : [(6582 ^ _774244) ^ [] : [-(_880150 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6580 ^ _774244) ^ [] : [-(_880148 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (50225 ^ _774244) ^ [_1780064, _1780066] : [c_List_Oconcat(_1780064, _1780066) = c_List_Olist_ONil(_1780064), 50228 ^ _774244 : [(50229 ^ _774244) ^ [_1780155] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1780064)), _1780155), hAPP(c_List_Oset(tc_List_Olist(_1780064)), _1780066))), -(_1780155 = c_List_Olist_ONil(_1780064))]]], (19285 ^ _774244) ^ [_1103465, _1103467] : [class_Int_Onumber__ring(_1103465), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103465), _1103467), hAPP(c_Int_Onumber__class_Onumber__of(_1103465), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103465), _1103467), _1103467))], (47676 ^ _774244) ^ [_1722160, _1722162, _1722164] : [_1722164 = c_List_Olist_ONil(_1722160), -(hAPP(hAPP(c_List_Oappend(_1722160), _1722162), _1722164) = _1722162)], (51169 ^ _774244) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (15684 ^ _774244) ^ [_1039380, _1039382, _1039384, _1039386, _1039388, _1039390] : [class_Rings_Oordered__ring(_1039380), 15687 ^ _774244 : [(15694 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039380), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039380), _1039382), _1039388)), _1039384)), _1039386)), _1039390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039380), _1039382), _1039384)), _1039386)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039380), _1039388), _1039384)), _1039390))))], (15688 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039380), _1039382), _1039384)), _1039386)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039380), _1039388), _1039384)), _1039390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039380), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039380), _1039382), _1039388)), _1039384)), _1039386)), _1039390)))]]], (41204 ^ _774244) ^ [_1562498, _1562500, _1562502, _1562504, _1562506] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1562498, _1562500, _1562502), _1562504), _1562506) = hAPP(c_Set_OCollect(tc_prod(_1562498, _1562502)), hAPP(c_Product__Type_Oprod_Oprod__case(_1562498, _1562502, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1562502, tc_fun(_1562500, tc_HOL_Obool)), tc_fun(_1562502, tc_HOL_Obool), _1562498), hAPP(c_COMBB(tc_fun(_1562500, tc_HOL_Obool), tc_HOL_Obool, _1562502), c_HOL_OEx(_1562500))), hAPP(hAPP(c_COMBC(_1562498, tc_fun(_1562502, tc_fun(_1562500, tc_HOL_Obool)), tc_fun(_1562502, tc_fun(_1562500, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1562500, tc_HOL_Obool), tc_fun(_1562500, tc_HOL_Obool)), tc_fun(tc_fun(_1562502, tc_fun(_1562500, tc_HOL_Obool)), tc_fun(_1562502, tc_fun(_1562500, tc_HOL_Obool))), _1562498), c_COMBB(tc_fun(_1562500, tc_HOL_Obool), tc_fun(_1562500, tc_HOL_Obool), _1562502)), hAPP(hAPP(c_COMBB(tc_fun(_1562500, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1562500, tc_HOL_Obool), tc_fun(_1562500, tc_HOL_Obool)), _1562498), c_COMBS(_1562500, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562500, tc_HOL_Obool), tc_fun(_1562500, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1562498), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1562500), c_fconj)), hAPP(hAPP(c_COMBC(_1562498, tc_fun(tc_prod(_1562498, _1562500), tc_HOL_Obool), tc_fun(_1562500, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562500, tc_fun(tc_fun(tc_prod(_1562498, _1562500), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1562498, _1562500), tc_HOL_Obool), tc_fun(_1562500, tc_HOL_Obool)), _1562498), c_COMBC(_1562500, tc_fun(tc_prod(_1562498, _1562500), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562500, tc_prod(_1562498, _1562500)), tc_fun(_1562500, tc_fun(tc_fun(tc_prod(_1562498, _1562500), tc_HOL_Obool), tc_HOL_Obool)), _1562498), hAPP(c_COMBB(tc_prod(_1562498, _1562500), tc_fun(tc_fun(tc_prod(_1562498, _1562500), tc_HOL_Obool), tc_HOL_Obool), _1562500), c_member(tc_prod(_1562498, _1562500)))), c_Product__Type_OPair(_1562498, _1562500)))), _1562504))))), hAPP(hAPP(c_COMBC(_1562502, tc_fun(tc_prod(_1562500, _1562502), tc_HOL_Obool), tc_fun(_1562500, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562500, tc_fun(tc_fun(tc_prod(_1562500, _1562502), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1562500, _1562502), tc_HOL_Obool), tc_fun(_1562500, tc_HOL_Obool)), _1562502), c_COMBC(_1562500, tc_fun(tc_prod(_1562500, _1562502), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562500, tc_prod(_1562500, _1562502)), tc_fun(_1562500, tc_fun(tc_fun(tc_prod(_1562500, _1562502), tc_HOL_Obool), tc_HOL_Obool)), _1562502), hAPP(c_COMBB(tc_prod(_1562500, _1562502), tc_fun(tc_fun(tc_prod(_1562500, _1562502), tc_HOL_Obool), tc_HOL_Obool), _1562500), c_member(tc_prod(_1562500, _1562502)))), hAPP(c_COMBC(_1562500, _1562502, tc_prod(_1562500, _1562502)), c_Product__Type_OPair(_1562500, _1562502))))), _1562506))))))], (29792 ^ _774244) ^ [_1304922, _1304924, _1304926] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1304922), hAPP(hAPP(c_Set_Oinsert(_1304922), _1304924), _1304926))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1304922), _1304926)))], (36593 ^ _774244) ^ [_1451232, _1451234] : [c_Nat__Transfer_Onat__set(_1451232), c_Nat__Transfer_Onat__set(_1451234), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1451232), _1451234) = 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), _1451232)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1451234))))], (47273 ^ _774244) ^ [_1712801, _1712803, _1712805, _1712807] : [hAPP(hAPP(c_List_Olist__update(_1712801, _1712803), _1712805), _1712807) = c_List_Olist_ONil(_1712801), -(_1712803 = c_List_Olist_ONil(_1712801))], (49665 ^ _774244) ^ [_1768963, _1768965, _1768967, _1768969] : [class_Orderings_Olinorder(_1768963), 49668 ^ _774244 : [(49677 ^ _774244) ^ [] : [-(c_List_Olinorder__class_Osorted(_1768963, hAPP(hAPP(c_List_Olist_OCons(_1768963), _1768965), hAPP(hAPP(c_List_Olist_OCons(_1768963), _1768967), _1768969)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1768963), _1768965), _1768967)), c_List_Olinorder__class_Osorted(_1768963, hAPP(hAPP(c_List_Olist_OCons(_1768963), _1768967), _1768969))], (49669 ^ _774244) ^ [] : [c_List_Olinorder__class_Osorted(_1768963, hAPP(hAPP(c_List_Olist_OCons(_1768963), _1768965), hAPP(hAPP(c_List_Olist_OCons(_1768963), _1768967), _1768969))), 49672 ^ _774244 : [(49675 ^ _774244) ^ [] : [-(c_List_Olinorder__class_Osorted(_1768963, hAPP(hAPP(c_List_Olist_OCons(_1768963), _1768967), _1768969)))], (49673 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1768963), _1768965), _1768967)))]]]]], (43133 ^ _774244) ^ [_1608466, _1608468] : [-(hAPP(c_Relation_ORange(_1608466, _1608466), c_Transitive__Closure_Ortrancl(_1608466, _1608468)) = c_Orderings_Otop__class_Otop(tc_fun(_1608466, tc_HOL_Obool)))], (436 ^ _774244) ^ [_780920, _780922, _780924, _780926, _780928, _780930, _780932, _780934] : [-(c_Wellfounded_Omax__extp(_780932, _780928, _780924, _780920)), c_Wellfounded_Omax__extp(_780934, _780930, _780926, _780922), _780934 = _780932, _780930 = _780928, _780926 = _780924, _780922 = _780920], (47836 ^ _774244) ^ [_1725644, _1725646, _1725648, _1725650, _1725652, _1725654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725644)), _1725646)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725648)), _1725650))), -(c_Map_Omap__upds(_1725644, _1725648, _1725652, hAPP(hAPP(c_List_Oappend(_1725644), _1725646), hAPP(hAPP(c_List_Olist_OCons(_1725644), _1725654), c_List_Olist_ONil(_1725644))), _1725650) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1725644, tc_Option_Ooption(_1725648)), c_Map_Omap__upds(_1725644, _1725648, _1725652, _1725646, _1725650)), _1725654), hAPP(c_Option_Ooption_OSome(_1725648), hAPP(hAPP(c_List_Onth(_1725648), _1725650), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725644)), _1725646)))))], (42628 ^ _774244) ^ [_1597461, _1597463, _1597465] : [class_Lattices_Olattice(_1597461), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597461), _1597463)), -(c_Big__Operators_Olattice__class_OSup__fin(_1597461, hAPP(hAPP(c_Set_Oinsert(_1597461), _1597465), _1597463)) = hAPP(hAPP(c_Finite__Set_Ofold(_1597461, _1597461, c_Lattices_Osemilattice__sup__class_Osup(_1597461)), _1597465), _1597463))], (41530 ^ _774244) ^ [_1571569, _1571571] : [c_FunDef_Oreduction__pair(_1571569, _1571571), 41533 ^ _774244 : [(41536 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571569, _1571569), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1571569, _1571569, _1571569), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1571569, _1571569), tc_HOL_Obool), tc_fun(tc_prod(_1571569, _1571569), tc_HOL_Obool)), _1571571)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1571569, _1571569), tc_HOL_Obool), tc_fun(tc_prod(_1571569, _1571569), tc_HOL_Obool)), _1571571))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1571569, _1571569), tc_HOL_Obool), tc_fun(tc_prod(_1571569, _1571569), tc_HOL_Obool)), _1571571))))], (41534 ^ _774244) ^ [] : [-(c_Wellfounded_Owf(_1571569, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1571569, _1571569), tc_HOL_Obool), tc_fun(tc_prod(_1571569, _1571569), tc_HOL_Obool)), _1571571)))]]], (46800 ^ _774244) ^ [_1701714] : [class_Groups_Omonoid__add(_1701714), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1701714), c_List_Olist_ONil(_1701714)) = c_Groups_Ozero__class_Ozero(_1701714))], (8736 ^ _774244) ^ [_916815, _916817] : [class_Rings_Ocomm__ring__1(_916815), -(hAPP(c_Groups_Ouminus__class_Ouminus(_916815), _916817) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916815), hAPP(c_Groups_Ouminus__class_Ouminus(_916815), c_Groups_Oone__class_Oone(_916815))), _916817))], (19267 ^ _774244) ^ [_1103097, _1103099] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1103097)), c_Int_OBit1(_1103099)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1103097)), _1103099)))], (13968 ^ _774244) ^ [_1007706, _1007708, _1007710] : [hBOOL(hAPP(_1007706, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1007708), _1007710))), 13971 ^ _774244 : [(13996 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007710), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13999 ^ _774244 : [(14000 ^ _774244) ^ [_1008370] : [-(hBOOL(hAPP(_1007706, _1008370))), 14001 ^ _774244 : [(14002 ^ _774244) ^ [_1008444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007710), _1008444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1008444), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1007708 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1007710), _1008370)), _1008444)]]]]], (13978 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007710)), 13981 ^ _774244 : [(13982 ^ _774244) ^ [_1008040] : [-(hBOOL(hAPP(_1007706, _1008040))), 13983 ^ _774244 : [(13984 ^ _774244) ^ [_1008111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1008111)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1008111), _1007710)), _1007708 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1007710), _1008040)), _1008111)]]]]], (13972 ^ _774244) ^ [] : [_1007710 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1007706, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (27848 ^ _774244) ^ [_1266015, _1266017, _1266019] : [class_Lattices_Osemilattice__sup(_1266015), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266015), _1266017), _1266019) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266015), _1266019), _1266017))], (46753 ^ _774244) ^ [_1700830, _1700832] : [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), _1700830), _1700832))), 46756 ^ _774244 : [(46763 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1700830), _1700832))), -(c_List_Oupto(_1700830, _1700832) = c_List_Olist_ONil(tc_Int_Oint))], (46757 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1700830), _1700832)), -(c_List_Oupto(_1700830, _1700832) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1700830), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1700830), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1700832)))]]], (7742 ^ _774244) ^ [_900558, _900560, _900562, _900564] : [class_Rings_Olinordered__semidom(_900558), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900558), c_Groups_Ozero__class_Ozero(_900558)), _900560)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900558), _900562), _900564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900558), _900562), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900558), _900560), _900564))))], (13353 ^ _774244) ^ [_996272, _996274, _996276, _996278] : [_996272 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _996274), _996276)), _996278), -(_996274 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _996272, _996274) = _996278), 13360 ^ _774244 : [(13363 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996278)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _996278), _996274))], (13361 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996274)))]], 13368 ^ _774244 : [(13371 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _996274), _996278)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _996278), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (13369 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996274))]]], (46663 ^ _774244) ^ [_1698554, _1698556, _1698558, _1698560, _1698562] : [class_Groups_Oab__group__add(_1698554), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1698554), hAPP(hAPP(c_List_Omap(_1698556, _1698554), hAPP(hAPP(c_COMBS(_1698556, _1698554, _1698554), hAPP(hAPP(c_COMBB(_1698554, tc_fun(_1698554, _1698554), _1698556), c_Groups_Ominus__class_Ominus(_1698554)), _1698558)), _1698560)), _1698562)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1698554), hAPP(c_List_Omonoid__add__class_Olistsum(_1698554), hAPP(hAPP(c_List_Omap(_1698556, _1698554), _1698558), _1698562))), hAPP(c_List_Omonoid__add__class_Olistsum(_1698554), hAPP(hAPP(c_List_Omap(_1698556, _1698554), _1698560), _1698562))))], (6223 ^ _774244) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5160 ^ _774244) ^ [_854054, _854056, _854058, _854060] : [-(c_List_Obutlast(_854060, _854056) = c_List_Obutlast(_854058, _854054)), _854060 = _854058, _854056 = _854054], (49049 ^ _774244) ^ [_1755440, _1755442, _1755444] : [-(_1755440 = c_List_Olist_ONil(_1755442)), -(c_List_Olast(_1755442, hAPP(hAPP(c_List_Olist_OCons(_1755442), _1755444), _1755440)) = c_List_Olast(_1755442, _1755440))], (18953 ^ _774244) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (50312 ^ _774244) ^ [_1781921, _1781923, _1781925] : [-(hAPP(c_List_Orev(_1781921), hAPP(hAPP(c_List_Oappend(_1781921), _1781923), _1781925)) = hAPP(hAPP(c_List_Oappend(_1781921), hAPP(c_List_Orev(_1781921), _1781925)), hAPP(c_List_Orev(_1781921), _1781923)))], (28236 ^ _774244) ^ [_1273355, _1273357, _1273359] : [class_Orderings_Oorder(_1273355), 28239 ^ _774244 : [(28246 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273355), _1273357), _1273359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273355, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1273355), _1273357)), hAPP(c_SetInterval_Oord__class_OatMost(_1273355), _1273359))))], (28240 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273355, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1273355), _1273357)), hAPP(c_SetInterval_Oord__class_OatMost(_1273355), _1273359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273355), _1273357), _1273359)))]]], (42746 ^ _774244) ^ [_1599725, _1599727, _1599729] : [class_Lattices_Olattice(_1599725), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599725), _1599727)), -(hBOOL(hAPP(hAPP(c_member(_1599725), _1599729), _1599727))), -(c_Big__Operators_Olattice__class_OInf__fin(_1599725, hAPP(hAPP(c_Set_Oinsert(_1599725), _1599729), _1599727)) = hAPP(hAPP(c_Finite__Set_Ofold(_1599725, _1599725, c_Lattices_Osemilattice__inf__class_Oinf(_1599725)), _1599729), _1599727))], (33316 ^ _774244) ^ [_1378573, _1378575, _1378577, _1378579] : [33317 ^ _774244 : [(33320 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1378577), _1378579)))], (33318 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1378573), _1378575)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1378573, _1378577)), c_Sum__Type_OPlus(_1378573, _1378577, _1378575, _1378579)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41566 ^ _774244) ^ [_1572580, _1572582, _1572584, _1572586] : [c_Wellfounded_Owf(_1572580, _1572582), c_Fun_Oinj__on(_1572580, _1572584, _1572586, c_Orderings_Otop__class_Otop(tc_fun(_1572580, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1572584, hAPP(c_Set_Oimage(tc_prod(_1572580, _1572580), tc_prod(_1572584, _1572584), c_Product__Type_Omap__pair(_1572580, _1572584, _1572580, _1572584, _1572586, _1572586)), _1572582)))], (7405 ^ _774244) ^ [_894446, _894448] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894446), _894448))), 7408 ^ _774244 : [(7415 ^ _774244) ^ [] : [_894446 = _894448, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894446), hAPP(c_Nat_OSuc, _894448))))], (7409 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _894446), hAPP(c_Nat_OSuc, _894448))), -(_894446 = _894448)]]], (3424 ^ _774244) ^ [_826844, _826846, _826848, _826850, _826852, _826854, _826856, _826858] : [-(c_Fun_Othe__inv__into(_826858, _826854, _826850, _826846) = c_Fun_Othe__inv__into(_826856, _826852, _826848, _826844)), _826858 = _826856, _826854 = _826852, _826850 = _826848, _826846 = _826844], (1154 ^ _774244) ^ [_791393, _791395] : [-(class_Groups_Osgn__if(_791393)), _791395 = _791393, class_Groups_Osgn__if(_791395)], (39297 ^ _774244) ^ [_1510763, _1510765, _1510767, _1510769, _1510771] : [class_Groups_Oab__semigroup__mult(_1510763), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1510763, _1510763, c_Groups_Otimes__class_Otimes(_1510763), _1510765, _1510767), _1510769)), hBOOL(hAPP(hAPP(c_member(_1510763), _1510771), _1510767)), -(hBOOL(hAPP(hAPP(c_member(_1510763), _1510765), _1510767))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1510763, _1510763, c_Groups_Otimes__class_Otimes(_1510763), _1510771, hAPP(hAPP(c_Set_Oinsert(_1510763), _1510765), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1510763, tc_HOL_Obool)), _1510767), hAPP(hAPP(c_Set_Oinsert(_1510763), _1510771), c_Orderings_Obot__class_Obot(tc_fun(_1510763, tc_HOL_Obool)))))), _1510769)))], (6319 ^ _774244) ^ [_875706, _875708, _875710] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(_875706, _875708, _875710)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12842 ^ _774244) ^ [_987562, _987564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _987562)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _987564)))), 12845 ^ _774244 : [(12848 ^ _774244) ^ [] : [-(_987564 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12846 ^ _774244) ^ [] : [-(_987562 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (46347 ^ _774244) ^ [_1689323, _1689325, _1689327] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1689323), tc_List_Olist(_1689323))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689323), tc_List_Olist(_1689323)), _1689325), _1689325)), c_List_Olistrel(_1689323, c_Transitive__Closure_Ortrancl(_1689323, _1689327)))))], (4384 ^ _774244) ^ [_842092, _842094, _842096, _842098, _842100, _842102, _842104, _842106] : [-(c_Nat_Onat_Onat__case(_842106, _842102, _842098, _842094) = c_Nat_Onat_Onat__case(_842104, _842100, _842096, _842092)), _842106 = _842104, _842102 = _842100, _842098 = _842096, _842094 = _842092], (45176 ^ _774244) ^ [_1660134, _1660136, _1660138, _1660140, _1660142, _1660144, _1660146, _1660148] : [c_Finite__Set_Ofolding__image__simple__idem(_1660134, _1660136, _1660138, _1660140, _1660142, _1660144), hBOOL(hAPP(c_Finite__Set_Ofinite(_1660136), _1660146)), hBOOL(hAPP(hAPP(c_member(_1660136), _1660148), _1660146)), -(hAPP(hAPP(_1660138, hAPP(_1660142, _1660148)), hAPP(_1660144, _1660146)) = hAPP(_1660144, _1660146))], (20859 ^ _774244) ^ [_1131595, _1131597, _1131599, _1131601] : [class_Fields_Ofield__inverse__zero(_1131595), -(_1131597 = c_Groups_Ozero__class_Ozero(_1131595)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131595), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131595), _1131599), _1131597)), _1131601) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131595), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131595), _1131599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131595), _1131601), _1131597))), _1131597))], (47766 ^ _774244) ^ [_1723891, _1723893, _1723895] : [hBOOL(hAPP(c_List_Odistinct(_1723891), hAPP(hAPP(c_List_Oappend(_1723891), _1723893), _1723895))), 47769 ^ _774244 : [(47774 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1723891, tc_HOL_Obool)), hAPP(c_List_Oset(_1723891), _1723893)), hAPP(c_List_Oset(_1723891), _1723895)) = c_Orderings_Obot__class_Obot(tc_fun(_1723891, tc_HOL_Obool)))], (47772 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1723891), _1723895)))], (47770 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1723891), _1723893)))]]], (26852 ^ _774244) ^ [_1245817, _1245819, _1245821, _1245823] : [class_Groups_Ocomm__monoid__add(_1245817), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1245819), _1245821)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245817), _1245823), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1245819, _1245821)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245817), hAPP(_1245823, _1245819)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245817), _1245823), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1245819), _1245821))))], (43435 ^ _774244) ^ [_1615606, _1615608, _1615610, _1615612, _1615614] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615606, tc_HOL_Obool)), _1615608), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615610, tc_fun(_1615606, tc_HOL_Obool)), _1615612), _1615614)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615610, tc_fun(_1615606, tc_HOL_Obool)), _1615612), hAPP(hAPP(c_COMBB(tc_fun(_1615606, tc_HOL_Obool), tc_fun(_1615606, tc_HOL_Obool), _1615610), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615606, tc_HOL_Obool)), _1615608)), _1615614)))], (51411 ^ _774244) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (44628 ^ _774244) ^ [_1647178, _1647180] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1647178), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1647178, tc_HOL_Obool), _1647180))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1647178, tc_HOL_Obool)), _1647180)))], (35318 ^ _774244) ^ [] : [-(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))], (19433 ^ _774244) ^ [_1106026, _1106028] : [class_Rings_Olinordered__idom(_1106026), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106026), hAPP(hAPP(c_Power_Opower__class_Opower(_1106026), _1106028), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1106026)))], (45662 ^ _774244) ^ [_1671586, _1671588, _1671590, _1671592] : [-(hAPP(hAPP(c_Option_Omap(_1671586, _1671588), _1671590), hAPP(c_Option_Ooption_OSome(_1671586), _1671592)) = hAPP(c_Option_Ooption_OSome(_1671588), hAPP(_1671590, _1671592)))], (42958 ^ _774244) ^ [_1604291, _1604293, _1604295, _1604297, _1604299] : [c_Finite__Set_Ofun__left__comm(_1604291, _1604293, _1604295), -(hAPP(c_Fun_Ocomp(_1604293, _1604293, _1604293, hAPP(_1604295, _1604297)), hAPP(_1604295, _1604299)) = hAPP(c_Fun_Ocomp(_1604293, _1604293, _1604293, hAPP(_1604295, _1604299)), hAPP(_1604295, _1604297)))], (40079 ^ _774244) ^ [_1531594, _1531596] : [class_Orderings_Olinorder(_1531594), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531594), _1531596)), -(c_Big__Operators_Olinorder__class_OMin(_1531594, _1531596) = hAPP(c_Finite__Set_Ofold1(_1531594, c_Orderings_Oord__class_Omin(_1531594)), _1531596))], (28312 ^ _774244) ^ [_1274847, _1274849] : [class_Orderings_Olinorder(_1274847), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1274847, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1274847), _1274849)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1274847), _1274849))], (29061 ^ _774244) ^ [_1291606, _1291608, _1291610, _1291612] : [29063 ^ _774244 : [(29066 ^ _774244) ^ [] : [hAPP(_1291612, 29062 ^ [_1291606, _1291608, _1291610, _1291612]) = c_Orderings_Obot__class_Obot(tc_fun(_1291606, tc_HOL_Obool))], (29064 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1291608), 29062 ^ [_1291606, _1291608, _1291610, _1291612]), _1291610)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1291606, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291608, tc_fun(_1291606, tc_HOL_Obool)), _1291610), _1291612))], (46856 ^ _774244) ^ [_1702714, _1702716, _1702718] : [-(hAPP(hAPP(c_List_Ozip(_1702714, _1702716), c_List_Olist_ONil(_1702714)), _1702718) = c_List_Olist_ONil(tc_prod(_1702714, _1702716)))], (15366 ^ _774244) ^ [_1033027, _1033029, _1033031] : [class_Groups_Oordered__ab__group__add(_1033027), 15369 ^ _774244 : [(15376 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033027), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033027), _1033029), _1033031)), c_Groups_Ozero__class_Ozero(_1033027))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033027), _1033029), _1033031)))], (15370 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033027), _1033029), _1033031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033027), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033027), _1033029), _1033031)), c_Groups_Ozero__class_Ozero(_1033027))))]]], (28126 ^ _774244) ^ [_1271016, _1271018, _1271020, _1271022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271016, tc_HOL_Obool)), _1271018), _1271020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271016, tc_HOL_Obool)), _1271022), _1271020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271016, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271016, tc_HOL_Obool)), _1271018), _1271022)), _1271020)))], (5086 ^ _774244) ^ [_852845, _852847, _852849, _852851, _852853, _852855, _852857, _852859, _852861, _852863] : [-(c_Map_Omap__upds(_852863, _852859, _852855, _852851, _852847) = c_Map_Omap__upds(_852861, _852857, _852853, _852849, _852845)), _852863 = _852861, _852859 = _852857, _852855 = _852853, _852851 = _852849, _852847 = _852845], (2572 ^ _774244) ^ [_813204, _813206] : [_813206 = _813204, -(c_Lazy__Sequence_Ohb__not__seq(_813206) = c_Lazy__Sequence_Ohb__not__seq(_813204))], (29128 ^ _774244) ^ [_1292804, _1292806, _1292808] : [class_Orderings_Oorder(_1292804), 29131 ^ _774244 : [(29138 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292804), _1292806), _1292808))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1292804, _1292806, _1292808) = c_Orderings_Obot__class_Obot(tc_fun(_1292804, tc_HOL_Obool)))], (29132 ^ _774244) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1292804, _1292806, _1292808) = c_Orderings_Obot__class_Obot(tc_fun(_1292804, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292804), _1292806), _1292808))]]], (28954 ^ _774244) ^ [_1289438, _1289440, _1289442] : [class_Orderings_Obot(_1289438), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1289440, _1289438)), _1289442) = c_Orderings_Obot__class_Obot(_1289438))], (17289 ^ _774244) ^ [_1069951, _1069953, _1069955] : [class_Power_Opower(_1069951), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1069951), _1069953), hAPP(c_Nat_OSuc, _1069955)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069951), _1069953), hAPP(hAPP(c_Power_Opower__class_Opower(_1069951), _1069953), _1069955)))], (26544 ^ _774244) ^ [_1239341, _1239343, _1239345] : [class_Orderings_Olinorder(_1239341), 26547 ^ _774244 : [(26554 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239341), _1239343), _1239345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1239341, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239341), _1239343)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239341), _1239345))))], (26548 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1239341, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239341), _1239343)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239341), _1239345))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239341), _1239343), _1239345)))]]], (7122 ^ _774244) ^ [_889942, _889944, _889946, _889948, _889950] : [-(c_Sum__Type_Osum_Osum__size(_889942, _889944, _889946, _889948, hAPP(c_Sum__Type_OInl(_889942, _889944), _889950)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_889946, _889950)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31090 ^ _774244) ^ [_1331943, _1331945, _1331947, _1331949, _1331951] : [-(hBOOL(hAPP(hAPP(c_member(_1331943), _1331945), hAPP(c_Set_Oimage(_1331947, _1331943, _1331949), _1331951)))), 31091 ^ _774244 : [(31092 ^ _774244) ^ [_1332013] : [hBOOL(hAPP(hAPP(c_member(_1331947), _1332013), _1331951)), _1331945 = hAPP(_1331949, _1332013)]]], (8108 ^ _774244) ^ [_907005, _907007] : [_907005 = _907007, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _907005) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _907007))], (18587 ^ _774244) ^ [_1091453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1091453), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1091453)), c_Int_OMin)))], (44610 ^ _774244) ^ [_1646456, _1646458, _1646460, _1646462] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1646456, _1646458), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646456, tc_HOL_Obool), _1646460)), _1646462) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1646456, tc_HOL_Obool), tc_fun(tc_prod(_1646456, _1646458), tc_HOL_Obool)), _1646460), hAPP(hAPP(c_COMBC(tc_fun(_1646456, tc_HOL_Obool), tc_fun(_1646456, tc_fun(_1646458, tc_HOL_Obool)), tc_fun(tc_prod(_1646456, _1646458), tc_HOL_Obool)), c_Product__Type_OSigma(_1646456, _1646458)), _1646462)))], (6095 ^ _774244) ^ [_871853, _871855, _871857, _871859, _871861, _871863] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_871853, _871855, _871857), _871859, _871861, _871863)), 6096 ^ _774244 : [(6103 ^ _774244) ^ [] : [-(hBOOL(hAPP(_871853, _871859))), c_Natural_Oevaln(_871857, _871859, _871861, _871863)], (6097 ^ _774244) ^ [] : [hBOOL(hAPP(_871853, _871859)), c_Natural_Oevaln(_871855, _871859, _871861, _871863)]]], (7664 ^ _774244) ^ [_899219, _899221] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _899219), hAPP(c_Nat_OSuc, _899221)))), 7665 ^ _774244 : [(7668 ^ _774244) ^ [_899307] : [_899219 = hAPP(c_Nat_OSuc, _899307), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _899307), _899221))], (7666 ^ _774244) ^ [] : [_899219 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (28681 ^ _774244) ^ [_1283148, _1283150, _1283152, _1283154, _1283156, _1283158] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1283148, tc_fun(_1283150, tc_HOL_Obool)), _1283152), hAPP(hAPP(c_COMBB(_1283154, tc_fun(_1283150, tc_HOL_Obool), _1283148), _1283156), _1283158)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1283154, tc_fun(_1283150, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1283148, _1283154, _1283158), _1283152)), _1283156))], (6983 ^ _774244) ^ [_887347, _887349, _887351] : [-(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887347, _887349), _887351, _887351)), 6984 ^ _774244 : [(6987 ^ _774244) ^ [_887429] : [c_Natural_Oevalc(_887349, _887351, _887429), c_Natural_Oevalc(c_Com_Ocom_OWhile(_887347, _887349), _887429, _887351)], (6985 ^ _774244) ^ [] : [-(hBOOL(hAPP(_887347, _887351)))]]], (44761 ^ _774244) ^ [_1649963, _1649965, _1649967] : [class_Complete__Lattice_Ocomplete__lattice(_1649963), -(c_Complete__Lattice_OSup__class_OSup(_1649963, hAPP(hAPP(c_Set_Oinsert(_1649963), _1649965), _1649967)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1649963), _1649965), c_Complete__Lattice_OSup__class_OSup(_1649963, _1649967)))], (31643 ^ _774244) ^ [_1345323, _1345325, _1345327, _1345329] : [c_Finite__Set_Ofolding__one(_1345323, _1345325, _1345327), -(hAPP(_1345327, hAPP(hAPP(c_Set_Oinsert(_1345323), _1345329), c_Orderings_Obot__class_Obot(tc_fun(_1345323, tc_HOL_Obool)))) = _1345329)], (1614 ^ _774244) ^ [_797143, _797145] : [-(class_Orderings_Olinorder(_797143)), _797145 = _797143, class_Orderings_Olinorder(_797145)], (51361 ^ _774244) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (12187 ^ _774244) ^ [_975985, _975987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975985)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975987)), 12194 ^ _774244 : [(12201 ^ _774244) ^ [] : [_975985 = _975987, -(hAPP(c_Int_Onat, _975985) = hAPP(c_Int_Onat, _975987))], (12195 ^ _774244) ^ [] : [hAPP(c_Int_Onat, _975985) = hAPP(c_Int_Onat, _975987), -(_975985 = _975987)]]], (19527 ^ _774244) ^ [_1107492, _1107494, _1107496] : [class_Rings_Oring__1(_1107492), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1107492), hAPP(c_Groups_Ouminus__class_Ouminus(_1107492), _1107494)), 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)))), _1107496)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1107492), _1107494), 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)))), _1107496)))], (45313 ^ _774244) ^ [_1662974, _1662976, _1662978] : [-(c_Map_Omap__add(_1662974, _1662976, hAPP(c_COMBK(tc_Option_Ooption(_1662976), _1662974), c_Option_Ooption_ONone(_1662976)), _1662978) = _1662978)], (1984 ^ _774244) ^ [_803196, _803198, _803200, _803202, _803204, _803206, _803208, _803210, _803212, _803214, _803216, _803218, _803220, _803222, _803224, _803226, _803228, _803230, _803232, _803234] : [-(c_Com_Ocom_Ocom__rec(_803234, _803230, _803226, _803222, _803218, _803214, _803210, _803206, _803202, _803198) = c_Com_Ocom_Ocom__rec(_803232, _803228, _803224, _803220, _803216, _803212, _803208, _803204, _803200, _803196)), _803234 = _803232, _803230 = _803228, _803226 = _803224, _803222 = _803220, _803218 = _803216, _803214 = _803212, _803210 = _803208, _803206 = _803204, _803202 = _803200, _803198 = _803196], (12063 ^ _774244) ^ [_973913, _973915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _973913)), _973915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _973913), _973915)))], (21455 ^ _774244) ^ [_1142278, _1142280, _1142282, _1142284] : [class_Fields_Olinordered__field__inverse__zero(_1142278), class_Int_Onumber(_1142278), 21462 ^ _774244 : [(21463 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142278), _1142280), _1142282)), hAPP(c_Int_Onumber__class_Onumber__of(_1142278), _1142284))), 21466 ^ _774244 : [(21473 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), c_Groups_Ozero__class_Ozero(_1142278)), _1142282))), 21476 ^ _774244 : [(21483 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), _1142282), c_Groups_Ozero__class_Ozero(_1142278)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), c_Groups_Ozero__class_Ozero(_1142278)), hAPP(c_Int_Onumber__class_Onumber__of(_1142278), _1142284))))], (21477 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), _1142282), c_Groups_Ozero__class_Ozero(_1142278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142278), hAPP(c_Int_Onumber__class_Onumber__of(_1142278), _1142284)), _1142282)), _1142280)))]]], (21467 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), c_Groups_Ozero__class_Ozero(_1142278)), _1142282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), _1142280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142278), hAPP(c_Int_Onumber__class_Onumber__of(_1142278), _1142284)), _1142282))))]]], (21489 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142278), _1142280), _1142282)), hAPP(c_Int_Onumber__class_Onumber__of(_1142278), _1142284)))), 21492 ^ _774244 : [(21495 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), _1142280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142278), hAPP(c_Int_Onumber__class_Onumber__of(_1142278), _1142284)), _1142282)))], (21493 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), c_Groups_Ozero__class_Ozero(_1142278)), _1142282)))]], 21496 ^ _774244 : [(21499 ^ _774244) ^ [] : [21500 ^ _774244 : [(21503 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142278), hAPP(c_Int_Onumber__class_Onumber__of(_1142278), _1142284)), _1142282)), _1142280))], (21501 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), _1142282), c_Groups_Ozero__class_Ozero(_1142278))))]], 21504 ^ _774244 : [(21507 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), c_Groups_Ozero__class_Ozero(_1142278)), hAPP(c_Int_Onumber__class_Onumber__of(_1142278), _1142284)))], (21505 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), _1142282), c_Groups_Ozero__class_Ozero(_1142278)))]]], (21497 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142278), c_Groups_Ozero__class_Ozero(_1142278)), _1142282))]]]]], (40838 ^ _774244) ^ [_1548769, _1548771, _1548773, _1548775, _1548777, _1548779] : [-(hBOOL(hAPP(hAPP(c_member(_1548769), _1548771), _1548773))), -(hAPP(c_Fun_Ooverride__on(_1548769, _1548775, _1548777, _1548779, _1548773), _1548771) = hAPP(_1548777, _1548771))], (30553 ^ _774244) ^ [_1319604, _1319606, _1319608, _1319610, _1319612, _1319614, _1319616, _1319618] : [hBOOL(hAPP(hAPP(c_member(_1319604), _1319606), _1319608)), hBOOL(hAPP(hAPP(hAPP(_1319610, _1319606), _1319612), _1319614)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1319604, tc_fun(_1319616, tc_fun(_1319618, tc_HOL_Obool))), _1319608), _1319610), _1319612), _1319614)))], (18941 ^ _774244) ^ [_1097479, _1097481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1097479)), c_Int_OBit0(_1097481))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097479), _1097481)))], (50923 ^ _774244) ^ [_1796053, _1796055] : [class_Lattices_Obounded__lattice(_1796053), -(class_Lattices_Obounded__lattice(tc_fun(_1796055, _1796053)))], (25767 ^ _774244) ^ [_1223908, _1223910, _1223912] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223908), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223910), _1223912))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223908), _1223910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223912), _1223910)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223908), _1223912)))], (29484 ^ _774244) ^ [_1299238, _1299240, _1299242] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1299238, _1299240) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1299242), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1299238 = _1299240, _1299240 = _1299242], (45345 ^ _774244) ^ [_1663669, _1663671, _1663673, _1663675] : [-(c_Map_Odom(_1663669, _1663671, c_Map_Omap__add(_1663669, _1663671, _1663673, _1663675)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1663669, tc_HOL_Obool)), c_Map_Odom(_1663669, _1663671, _1663675)), c_Map_Odom(_1663669, _1663671, _1663673)))], (7824 ^ _774244) ^ [_902043, _902045, _902047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902043), _902045)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902043), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _902045), _902047))))], (25871 ^ _774244) ^ [_1226181, _1226183, _1226185] : [class_Divides_Osemiring__div(_1226181), class_Int_Onumber(_1226181), 25878 ^ _774244 : [(25885 ^ _774244) ^ [] : [c_Divides_Odiv__class_Omod(_1226181, hAPP(c_Int_Onumber__class_Onumber__of(_1226181), _1226185), hAPP(c_Int_Onumber__class_Onumber__of(_1226181), _1226183)) = c_Groups_Ozero__class_Ozero(_1226181), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1226181), hAPP(c_Int_Onumber__class_Onumber__of(_1226181), _1226183)), hAPP(c_Int_Onumber__class_Onumber__of(_1226181), _1226185))))], (25879 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1226181), hAPP(c_Int_Onumber__class_Onumber__of(_1226181), _1226183)), hAPP(c_Int_Onumber__class_Onumber__of(_1226181), _1226185))), -(c_Divides_Odiv__class_Omod(_1226181, hAPP(c_Int_Onumber__class_Onumber__of(_1226181), _1226185), hAPP(c_Int_Onumber__class_Onumber__of(_1226181), _1226183)) = c_Groups_Ozero__class_Ozero(_1226181))]]], (8294 ^ _774244) ^ [_909467, _909469, _909471] : [class_Orderings_Oorder(_909467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909467), _909469), _909471)), _909471 = _909469], (22876 ^ _774244) ^ [_1169359, _1169361, _1169363, _1169365, _1169367, _1169369] : [-(hAPP(hAPP(c_Product__Type_OPair(_1169359, _1169361), _1169363), _1169365) = hAPP(hAPP(c_Product__Type_OPair(_1169359, _1169361), _1169367), _1169369)), _1169363 = _1169367, _1169365 = _1169369], (36191 ^ _774244) ^ [_1441626, _1441628, _1441630, _1441632] : [class_Lattices_Odistrib__lattice(_1441626), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441626), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441626), _1441628), _1441630)), _1441632) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441626), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441626), _1441628), _1441632)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441626), _1441630), _1441632)))], (18191 ^ _774244) ^ [_1084854, _1084856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1084854)), _1084856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084854), _1084856)))], (19771 ^ _774244) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (26129 ^ _774244) ^ [_1230714, _1230716, _1230718] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230714), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230716, _1230718))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230714), _1230718)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1230714), _1230716)))], (5476 ^ _774244) ^ [_858810, _858812] : [_858812 = _858810, -(c_Set_OPow(_858812) = c_Set_OPow(_858810))], (30266 ^ _774244) ^ [_1313548, _1313550, _1313552] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1313548), _1313550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1313548, tc_HOL_Obool)), _1313552), _1313550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1313548), _1313552)), hAPP(c_Finite__Set_Ocard(_1313548), _1313550))))], (5266 ^ _774244) ^ [_855669, _855671] : [_855671 = _855669, -(c_List_Orev(_855671) = c_List_Orev(_855669))], (51217 ^ _774244) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (41420 ^ _774244) ^ [_1569248, _1569250] : [c_Wellfounded_Owf(_1569248, _1569250), -(c_Wellfounded_Owf(tc_fun(_1569248, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1569248, _1569250)))], (41218 ^ _774244) ^ [_1563308, _1563310, _1563312, _1563314, _1563316, _1563318, _1563320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1563308, _1563310), tc_HOL_Obool)), _1563312), _1563314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1563310, _1563316), tc_HOL_Obool)), _1563318), _1563320)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1563308, _1563316), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1563308, _1563310, _1563316), _1563312), _1563318)), hAPP(hAPP(c_Relation_Orel__comp(_1563308, _1563310, _1563316), _1563314), _1563320))))], (10576 ^ _774244) ^ [_948404, _948406, _948408] : [class_Orderings_Opreorder(_948404), 10579 ^ _774244 : [(10588 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948404), _948406), _948408))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948404), _948406), _948408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948404), _948408), _948406)))], (10580 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948404), _948406), _948408)), 10583 ^ _774244 : [(10586 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948404), _948408), _948406))], (10584 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948404), _948406), _948408)))]]]]], (6329 ^ _774244) ^ [_875996, _875998, _876000, _876002, _876004] : [c_Com_Ocom_OSemi(_875996, _875998) = c_Com_Ocom_OCall(_876000, _876002, _876004)], (2068 ^ _774244) ^ [_805094, _805096, _805098, _805100] : [-(tc_Nitpick_Opair__box(_805100, _805096) = tc_Nitpick_Opair__box(_805098, _805094)), _805100 = _805098, _805096 = _805094], (36235 ^ _774244) ^ [_1442799, _1442801] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442799, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1442799, tc_HOL_Obool))), _1442801) = c_Orderings_Obot__class_Obot(tc_fun(_1442799, tc_HOL_Obool)))], (22014 ^ _774244) ^ [_1152588] : [-(_1152588 = 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)), _1152588)))], (36881 ^ _774244) ^ [_1457884, _1457886, _1457888, _1457890, _1457892, _1457894] : [c_Finite__Set_Ofolding(_1457884, _1457886, _1457888, _1457890), hBOOL(hAPP(c_Finite__Set_Ofinite(_1457884), _1457892)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1457884), _1457894)), -(hAPP(c_Fun_Ocomp(_1457886, _1457886, _1457886, hAPP(_1457890, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1457884, tc_HOL_Obool)), _1457892), _1457894))), hAPP(_1457890, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457884, tc_HOL_Obool)), _1457892), _1457894))) = hAPP(c_Fun_Ocomp(_1457886, _1457886, _1457886, hAPP(_1457890, _1457892)), hAPP(_1457890, _1457894)))], (8836 ^ _774244) ^ [_918857, _918859, _918861, _918863, _918865] : [class_Rings_Ocomm__semiring__1(_918857), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918857), _918859), _918861)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918857), _918863), _918865)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918857), _918859), _918863)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918857), _918861), _918865)))], (6690 ^ _774244) ^ [_881955, _881957, _881959] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_881955, _881957, _881959)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _881959)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7479 ^ _774244) ^ [_895565, _895567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _895565), _895567)), _895565))], (6239 ^ _774244) ^ [_874374] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OBODY(_874374))), -(hAPP(c_Com_Obody, _874374) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 6242 ^ [_874374]))], (3056 ^ _774244) ^ [_821004, _821006] : [_821006 = _821004, -(c_DSequence_Osingle(_821006) = c_DSequence_Osingle(_821004))], (46715 ^ _774244) ^ [_1699837, _1699839, _1699841, _1699843] : [class_Rings_Osemiring__1(_1699837), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1699837), hAPP(hAPP(c_List_Omap(_1699839, _1699837), hAPP(c_COMBK(_1699837, _1699839), _1699841)), _1699843)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1699837), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1699837), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699839)), _1699843))), _1699841))], (46086 ^ _774244) ^ [_1681869, _1681871, _1681873] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681869)), _1681871) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681869)), _1681873)), _1681871 = _1681873], (48980 ^ _774244) ^ [_1754108, _1754110, _1754112] : [48981 ^ _774244 : [(48982 ^ _774244) ^ [_1754197, _1754199] : [_1754110 = hAPP(hAPP(c_List_Olist_OCons(_1754108), _1754199), _1754197)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754108), tc_List_Olist(_1754108))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754108), tc_List_Olist(_1754108)), c_List_Olist_ONil(_1754108)), _1754110)), c_List_Olexord(_1754108, _1754112))))], (15918 ^ _774244) ^ [_1044698, _1044700] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044698, _1044700) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044698, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1044700)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29594 ^ _774244) ^ [_1301291, _1301293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301291), _1301293)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1301293, _1301291) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (45631 ^ _774244) ^ [_1670800, _1670802, _1670804, _1670806, _1670808] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1670800), tc_Option_Ooption(_1670802), tc_Option_Ooption(_1670804), hAPP(c_Option_Omap(_1670800, _1670802), _1670806)), hAPP(c_Option_Omap(_1670804, _1670800), _1670808)) = hAPP(c_Option_Omap(_1670804, _1670802), hAPP(c_Fun_Ocomp(_1670800, _1670802, _1670804, _1670806), _1670808)))], (18085 ^ _774244) ^ [_1083374, _1083376] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083374), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083374)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083376)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1083374), _1083376)))], (22981 ^ _774244) ^ [_1171705, _1171707, _1171709, _1171711, _1171713, _1171715] : [hAPP(c_Product__Type_Oapsnd(_1171705, _1171707, _1171709, _1171711), _1171713) = hAPP(c_Product__Type_Oapsnd(_1171705, _1171707, _1171709, _1171715), _1171713), -(hAPP(_1171711, hAPP(c_Product__Type_Osnd(_1171709, _1171705), _1171713)) = hAPP(_1171715, hAPP(c_Product__Type_Osnd(_1171709, _1171705), _1171713)))], (46709 ^ _774244) ^ [_1699694, _1699696, _1699698, _1699700] : [class_Groups_Ocomm__monoid__add(_1699694), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1699694), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1699694), _1699696), c_List_Oupto(_1699698, _1699700))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1699694), _1699696), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1699698, _1699700))))], (10410 ^ _774244) ^ [_945717, _945719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _945717)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _945719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945717), _945719)))], (41138 ^ _774244) ^ [_1561213, _1561215] : [-(c_Product__Type_Oapsnd(_1561213, _1561213, _1561215, c_Fun_Oid(_1561213)) = c_Fun_Oid(tc_prod(_1561215, _1561213)))], (31663 ^ _774244) ^ [_1345688, _1345690, _1345692, _1345694, _1345696] : [class_Groups_Ocomm__monoid__add(_1345688), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345690), _1345692)), -(hBOOL(hAPP(hAPP(c_member(_1345690), _1345694), _1345692))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345690, _1345688), _1345696), hAPP(hAPP(c_Set_Oinsert(_1345690), _1345694), _1345692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1345688), hAPP(_1345696, _1345694)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345690, _1345688), _1345696), _1345692)))], (4550 ^ _774244) ^ [_844601, _844603, _844605, _844607] : [-(c_Fun_Ofun__upd(_844607, _844603) = c_Fun_Ofun__upd(_844605, _844601)), _844607 = _844605, _844603 = _844601], (38323 ^ _774244) ^ [_1488800, _1488802, _1488804, _1488806, _1488808] : [c_Fun_Oinj__on(_1488800, _1488802, _1488804, c_Orderings_Otop__class_Otop(tc_fun(_1488800, tc_HOL_Obool))), 38326 ^ _774244 : [(38333 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488800, tc_HOL_Obool)), _1488806), _1488808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488802, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1488800, _1488802, _1488804), _1488806)), hAPP(c_Set_Oimage(_1488800, _1488802, _1488804), _1488808))))], (38327 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488802, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1488800, _1488802, _1488804), _1488806)), hAPP(c_Set_Oimage(_1488800, _1488802, _1488804), _1488808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488800, tc_HOL_Obool)), _1488806), _1488808)))]]], (44438 ^ _774244) ^ [_1642684, _1642686, _1642688] : [class_Complete__Lattice_Ocomplete__lattice(_1642684), 44441 ^ _774244 : [(44442 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1642684), _1642686), c_Complete__Lattice_OInf__class_OInf(_1642684, _1642688))), 44445 ^ _774244 : [(44446 ^ _774244) ^ [_1642842] : [hBOOL(hAPP(hAPP(c_member(_1642684), _1642842), _1642688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1642684), _1642686), _1642842)))]]], (44452 ^ _774244) ^ [] : [44454 ^ _774244 : [(44457 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1642684), _1642686), 44453 ^ [_1642684, _1642686, _1642688]))], (44455 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1642684), 44453 ^ [_1642684, _1642686, _1642688]), _1642688)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1642684), _1642686), c_Complete__Lattice_OInf__class_OInf(_1642684, _1642688))))]]], (49396 ^ _774244) ^ [_1762528, _1762530, _1762532, _1762534, _1762536] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762528)), hAPP(c_List_Ofilter(_1762528, _1762530), hAPP(hAPP(c_List_Omap(_1762532, _1762528), _1762534), _1762536))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762532)), hAPP(c_List_Ofilter(_1762532, hAPP(c_Fun_Ocomp(_1762528, tc_HOL_Obool, _1762532, _1762530), _1762534)), _1762536)))], (1824 ^ _774244) ^ [_800592, _800594, _800596, _800598, _800600, _800602, _800604, _800606, _800608, _800610] : [-(c_Option_Ooption_Ooption__rec(_800610, _800606, _800602, _800598, _800594) = c_Option_Ooption_Ooption__rec(_800608, _800604, _800600, _800596, _800592)), _800610 = _800608, _800606 = _800604, _800602 = _800600, _800598 = _800596, _800594 = _800592], (34612 ^ _774244) ^ [_1405598, _1405600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1405598), _1405600)), -(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), _1405598), _1405600)), c_Wellfounded_Oless__than)))], (44241 ^ _774244) ^ [_1637768, _1637770] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1637768, _1637768), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1637770) = _1637770)], (17629 ^ _774244) ^ [_1076043] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076043))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076043) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32496 ^ _774244) ^ [_1363284, _1363286, _1363288] : [class_Rings_Oring__1(_1363284), hBOOL(hAPP(hAPP(c_member(_1363284), _1363286), c_Int_Oring__1__class_OInts(_1363284))), hBOOL(hAPP(hAPP(c_member(_1363284), _1363288), c_Int_Oring__1__class_OInts(_1363284))), -(hBOOL(hAPP(hAPP(c_member(_1363284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363284), _1363286), _1363288)), c_Int_Oring__1__class_OInts(_1363284))))], (6536 ^ _774244) ^ [_879591, _879593] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _879591), _879593) = _879591, -(_879593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47682 ^ _774244) ^ [_1722279, _1722281, _1722283] : [hAPP(hAPP(c_List_Oappend(_1722279), _1722281), _1722283) = c_List_Olist_ONil(_1722279), 47685 ^ _774244 : [(47688 ^ _774244) ^ [] : [-(_1722283 = c_List_Olist_ONil(_1722279))], (47686 ^ _774244) ^ [] : [-(_1722281 = c_List_Olist_ONil(_1722279))]]], (25471 ^ _774244) ^ [_1218547, _1218549, _1218551, _1218553] : [class_Rings_Ocomm__ring__1(_1218547), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1218547), _1218549), _1218551)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1218547), _1218549), _1218553)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1218547), _1218549), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1218547), _1218551), _1218553))))], (46775 ^ _774244) ^ [_1701231, _1701233, _1701235] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1701231), tc_List_Olist(_1701231))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1701231), tc_List_Olist(_1701231)), c_List_Olist_ONil(_1701231)), _1701233)), c_List_Olistrel(_1701231, _1701235))), -(_1701233 = c_List_Olist_ONil(_1701231))], (44044 ^ _774244) ^ [] : [-(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))))], (35352 ^ _774244) ^ [_1423341, _1423343, _1423345, _1423347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1423341), _1423347)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1423345), _1423343))), -(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), _1423341), _1423343)), 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), _1423345), _1423347)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (12566 ^ _774244) ^ [_982823, _982825, _982827, _982829] : [class_Rings_Olinordered__semiring__strict(_982823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982823), _982825), _982827)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982823), _982825), _982829))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982823), c_Groups_Ozero__class_Ozero(_982823)), _982825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982823), _982827), _982829)))], (5818 ^ _774244) ^ [_867172, _867174, _867176, _867178, _867180] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_867172, _867174), _867176, _867178, _867180), 5822 ^ _774244 : [(5825 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_867174, 5821 ^ [_867172, _867174, _867176, _867178, _867180], _867178, _867180))], (5823 ^ _774244) ^ [] : [-(c_Natural_Oevaln(_867172, _867176, _867178, 5821 ^ [_867172, _867174, _867176, _867178, _867180]))]]], (24467 ^ _774244) ^ [_1199920, _1199922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1199920), _1199922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1199920)), hAPP(c_Code__Numeral_Onat__of, _1199922))))], (13431 ^ _774244) ^ [_997633, _997635] : [class_Divides_Osemiring__div(_997633), -(c_Divides_Odiv__class_Omod(_997633, _997635, _997635) = c_Groups_Ozero__class_Ozero(_997633))], (20913 ^ _774244) ^ [_1132554, _1132556, _1132558, _1132560, _1132562] : [class_Fields_Ofield(_1132554), -(_1132556 = c_Groups_Ozero__class_Ozero(_1132554)), -(_1132558 = c_Groups_Ozero__class_Ozero(_1132554)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132554), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132554), _1132560), _1132556)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132554), _1132562), _1132558)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132554), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132554), _1132560), _1132558)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132554), _1132562), _1132556))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132554), _1132556), _1132558)))], (12310 ^ _774244) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (24445 ^ _774244) ^ [_1199311] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1199311)) = _1199311)], (40711 ^ _774244) ^ [_1544157, _1544159] : [-(hAPP(c_Set_OCollect(_1544157), hAPP(c_fequal, _1544159)) = hAPP(hAPP(c_Set_Oinsert(_1544157), _1544159), c_Orderings_Obot__class_Obot(tc_fun(_1544157, tc_HOL_Obool))))], (41336 ^ _774244) ^ [_1567782, _1567784] : [c_Wellfounded_Owf(_1567782, _1567784), -(c_Wellfounded_Owf(_1567782, hAPP(hAPP(c_Relation_Orel__comp(_1567782, _1567782, _1567782), _1567784), _1567784)))], (46880 ^ _774244) ^ [_1703135, _1703137] : [c_Orderings_Obot__class_Obot(tc_fun(_1703135, tc_HOL_Obool)) = hAPP(c_List_Oset(_1703135), _1703137), -(_1703137 = c_List_Olist_ONil(_1703135))], (46064 ^ _774244) ^ [_1681370, _1681372, _1681374, _1681376] : [class_Orderings_Olinorder(_1681370), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681370, _1681370, c_COMBI(_1681370)), _1681372), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681370, _1681370, c_COMBI(_1681370)), _1681374), _1681376)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681370, _1681370, c_COMBI(_1681370)), _1681374), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681370, _1681370, c_COMBI(_1681370)), _1681372), _1681376)))], (49782 ^ _774244) ^ [_1771027, _1771029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1771027), _1771029)), -(c_List_Oupt(_1771027, _1771029) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1771027), c_List_Oupt(hAPP(c_Nat_OSuc, _1771027), _1771029)))], (7788 ^ _774244) ^ [_901396, _901398, _901400, _901402] : [hAPP(c_Sum__Type_OInr(_901396, _901398), _901400) = hAPP(c_Sum__Type_OInr(_901396, _901398), _901402), -(_901400 = _901402)], (35362 ^ _774244) ^ [_1423610, _1423612, _1423614, _1423616, _1423618, _1423620] : [c_Finite__Set_Ofolding(_1423610, _1423612, _1423614, _1423616), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423610), _1423618)), hBOOL(hAPP(hAPP(c_member(_1423610), _1423620), _1423618)), -(hAPP(_1423616, _1423618) = hAPP(c_Fun_Ocomp(_1423612, _1423612, _1423612, hAPP(_1423616, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1423610, tc_HOL_Obool)), _1423618), hAPP(hAPP(c_Set_Oinsert(_1423610), _1423620), c_Orderings_Obot__class_Obot(tc_fun(_1423610, tc_HOL_Obool)))))), hAPP(_1423614, _1423620)))], (15350 ^ _774244) ^ [_1032744, _1032746, _1032748] : [class_Groups_Oordered__ab__group__add(_1032744), 15353 ^ _774244 : [(15360 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032744), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032744), _1032746), _1032748)), c_Groups_Ozero__class_Ozero(_1032744))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032744), _1032746), _1032748)))], (15354 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032744), _1032746), _1032748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032744), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032744), _1032746), _1032748)), c_Groups_Ozero__class_Ozero(_1032744))))]]], (29248 ^ _774244) ^ [_1294754, _1294756, _1294758] : [class_Orderings_Oorder(_1294754), _1294756 = _1294758, -(c_SetInterval_Oord__class_OatLeastAtMost(_1294754, _1294756, _1294758) = hAPP(hAPP(c_Set_Oinsert(_1294754), _1294756), c_Orderings_Obot__class_Obot(tc_fun(_1294754, tc_HOL_Obool))))], (49460 ^ _774244) ^ [_1764654, _1764656, _1764658] : [-(c_List_Omap__filter(_1764654, _1764656, _1764658, c_List_Olist_ONil(_1764654)) = c_List_Olist_ONil(_1764656))], (23425 ^ _774244) ^ [_1180022, _1180024, _1180026, _1180028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1180022, tc_HOL_Obool)), _1180024), _1180026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1180022, tc_HOL_Obool)), _1180026), _1180028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1180022, tc_HOL_Obool)), _1180024), _1180028)))], (29610 ^ _774244) ^ [_1301542, _1301544] : [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)))), _1301542, _1301544), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1301542), _1301544)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1301544), _1301542)))], (20827 ^ _774244) ^ [_1131087] : [c_Nat__Transfer_Ois__nat(_1131087), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131087)))], (18011 ^ _774244) ^ [_1082241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1082241), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082241)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (41821 ^ _774244) ^ [_1578629, _1578631, _1578633, _1578635] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578629, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1578629, _1578631), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1578629, _1578631), tc_HOL_Obool)), _1578633), _1578635))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1578629, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1578629, _1578631), _1578633)), hAPP(c_Relation_ODomain(_1578629, _1578631), _1578635)))))], (17601 ^ _774244) ^ [_1075645] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1075645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075645), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (5756 ^ _774244) ^ [_865992, _865994, _865996] : [c_Natural_Oevaln(c_Com_Ocom_OSKIP, _865992, _865994, _865996), -(_865996 = _865992)], (8487 ^ _774244) ^ [_912588, _912590] : [-(hBOOL(hAPP(_912588, hAPP(c_Int_Onat, _912590)))), 8491 ^ _774244 : [(8494 ^ _774244) ^ [] : [hBOOL(hAPP(_912588, 8490 ^ [_912588, _912590]))], (8492 ^ _774244) ^ [] : [-(_912590 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8490 ^ [_912588, _912590]))]], 8495 ^ _774244 : [(8498 ^ _774244) ^ [] : [hBOOL(hAPP(_912588, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8496 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _912590), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (12770 ^ _774244) ^ [_986388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _986388)))], (18667 ^ _774244) ^ [_1092777, _1092779] : [class_Int_Onumber__ring(_1092777), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092777), _1092779), hAPP(c_Int_Onumber__class_Onumber__of(_1092777), c_Int_OBit1(c_Int_OPls))) = _1092779)], (50538 ^ _774244) ^ [_1788115, _1788117, _1788119, _1788121, _1788123] : [-(hAPP(hAPP(c_List_Ozip(_1788115, _1788117), _1788119), c_List_OtakeWhile(_1788117, _1788121, _1788123)) = c_List_OtakeWhile(tc_prod(_1788115, _1788117), hAPP(c_Fun_Ocomp(_1788117, tc_HOL_Obool, tc_prod(_1788115, _1788117), _1788121), c_Product__Type_Osnd(_1788115, _1788117)), hAPP(hAPP(c_List_Ozip(_1788115, _1788117), _1788119), _1788123)))], (22921 ^ _774244) ^ [_1170316, _1170318, _1170320, _1170322, _1170324, _1170326] : [-(hAPP(c_Product__Type_Oapsnd(_1170316, _1170318, _1170320, _1170322), hAPP(hAPP(c_Product__Type_OPair(_1170320, _1170316), _1170324), _1170326)) = hAPP(hAPP(c_Product__Type_OPair(_1170320, _1170318), _1170324), hAPP(_1170322, _1170326)))], (18899 ^ _774244) ^ [_1096708, _1096710] : [_1096708 = _1096710, -(c_Int_OBit0(_1096708) = c_Int_OBit0(_1096710))], (46627 ^ _774244) ^ [_1697492, _1697494, _1697496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1697492), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1697494), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1697494)), _1697496)))), -(hBOOL(hAPP(hAPP(c_member(_1697494), hAPP(c_Random_Opick(_1697494, _1697496), _1697492)), hAPP(c_List_Oset(_1697494), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1697494), _1697494), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1697494)), _1697496)))))], (37863 ^ _774244) ^ [_1479787, _1479789] : [c_Equiv__Relations_Oequivp(_1479787, hAPP(hAPP(c_COMBC(_1479787, tc_fun(tc_prod(_1479787, _1479787), tc_HOL_Obool), tc_fun(_1479787, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479787, tc_fun(tc_fun(tc_prod(_1479787, _1479787), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1479787, _1479787), tc_HOL_Obool), tc_fun(_1479787, tc_HOL_Obool)), _1479787), c_COMBC(_1479787, tc_fun(tc_prod(_1479787, _1479787), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479787, tc_prod(_1479787, _1479787)), tc_fun(_1479787, tc_fun(tc_fun(tc_prod(_1479787, _1479787), tc_HOL_Obool), tc_HOL_Obool)), _1479787), hAPP(c_COMBB(tc_prod(_1479787, _1479787), tc_fun(tc_fun(tc_prod(_1479787, _1479787), tc_HOL_Obool), tc_HOL_Obool), _1479787), c_member(tc_prod(_1479787, _1479787)))), c_Product__Type_OPair(_1479787, _1479787)))), _1479789)), -(c_Equiv__Relations_Oequiv(_1479787, c_Orderings_Otop__class_Otop(tc_fun(_1479787, tc_HOL_Obool)), _1479789))], (48110 ^ _774244) ^ [_1732788, _1732790] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1732788), tc_List_Olist(_1732788)), tc_HOL_Obool)), c_List_Olistrel(_1732788, _1732790)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1732788), c_List_Olistrel1(_1732788, _1732790)))))], (22090 ^ _774244) ^ [_1153776, _1153778] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1153776)), hAPP(c_Code__Numeral_Oof__nat, _1153778)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1153776), _1153778)))], (26676 ^ _774244) ^ [_1242163, _1242165, _1242167, _1242169, _1242171] : [class_Orderings_Oorder(_1242163), 26679 ^ _774244 : [(26692 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1242163, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1242163, _1242165, _1242167)), c_SetInterval_Oord__class_OatLeastAtMost(_1242163, _1242169, _1242171)))), 26693 ^ _774244 : [(26696 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242163), _1242169), _1242165)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242163), _1242167), _1242171))], (26694 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242163), _1242165), _1242167)))]]], (26680 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1242163, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1242163, _1242165, _1242167)), c_SetInterval_Oord__class_OatLeastAtMost(_1242163, _1242169, _1242171))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242163), _1242165), _1242167)), 26687 ^ _774244 : [(26690 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242163), _1242167), _1242171)))], (26688 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242163), _1242169), _1242165)))]]]]], (22736 ^ _774244) ^ [_1166802, _1166804] : [_1166802 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1166802, _1166804) = 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)))], (48344 ^ _774244) ^ [_1739713, _1739715, _1739717, _1739719] : [-(hAPP(hAPP(c_List_Odrop(_1739713), _1739715), hAPP(hAPP(c_List_Odrop(_1739713), _1739717), _1739719)) = hAPP(hAPP(c_List_Odrop(_1739713), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1739715), _1739717)), _1739719))], (16719 ^ _774244) ^ [_1059531, _1059533] : [class_Int_Onumber__ring(_1059531), -(hAPP(c_Int_Onumber__class_Onumber__of(_1059531), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1059533)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1059531), hAPP(c_Int_Onumber__class_Onumber__of(_1059531), _1059533)))], (42477 ^ _774244) ^ [_1594424, _1594426, _1594428, _1594430] : [class_Lattices_Osemilattice__inf(_1594424), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594424), _1594426)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1594424, _1594424, c_Lattices_Osemilattice__inf__class_Oinf(_1594424)), _1594428), hAPP(hAPP(c_Set_Oinsert(_1594424), _1594430), _1594426)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1594424), _1594430), hAPP(hAPP(c_Finite__Set_Ofold(_1594424, _1594424, c_Lattices_Osemilattice__inf__class_Oinf(_1594424)), _1594428), _1594426)))], (1960 ^ _774244) ^ [_802826, _802828, _802830, _802832, _802834, _802836] : [-(c_Com_Ocom_OCall(_802836, _802832, _802828) = c_Com_Ocom_OCall(_802834, _802830, _802826)), _802836 = _802834, _802832 = _802830, _802828 = _802826], (5340 ^ _774244) ^ [_856786, _856788, _856790, _856792, _856794, _856796] : [-(c_List_OtakeWhile(_856796, _856792, _856788) = c_List_OtakeWhile(_856794, _856790, _856786)), _856796 = _856794, _856792 = _856790, _856788 = _856786], (27251 ^ _774244) ^ [_1254218, _1254220] : [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)), _1254218)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254220))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1254218), _1254220)))], (37221 ^ _774244) ^ [_1464731, _1464733, _1464735] : [class_Orderings_Olinorder(_1464731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464731), _1464733)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464731), _1464735)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464731, tc_HOL_Obool)), _1464733), _1464735) = c_Orderings_Obot__class_Obot(tc_fun(_1464731, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1464731), c_Big__Operators_Olattice_OInf__fin(_1464731, c_Orderings_Oord__class_Omin(_1464731), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464731, tc_HOL_Obool)), _1464733), _1464735))), c_Big__Operators_Olattice_OInf__fin(_1464731, c_Orderings_Oord__class_Omin(_1464731), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464731, tc_HOL_Obool)), _1464733), _1464735))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1464731), c_Big__Operators_Olattice_OInf__fin(_1464731, c_Orderings_Oord__class_Omin(_1464731), _1464733)), c_Big__Operators_Olattice_OInf__fin(_1464731, c_Orderings_Oord__class_Omin(_1464731), _1464735)))], (17747 ^ _774244) ^ [_1078018, _1078020] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1078018))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078018)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078020)) = 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), _1078020)))], (41796 ^ _774244) ^ [_1577989, _1577991, _1577993, _1577995] : [-(hAPP(c_Relation_ODomain(_1577989, _1577991), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1577989, _1577991), tc_HOL_Obool)), _1577993), _1577995)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1577989, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1577989, _1577991), _1577993)), hAPP(c_Relation_ODomain(_1577989, _1577991), _1577995)))], (10598 ^ _774244) ^ [_948761, _948763, _948765] : [class_Orderings_Oorder(_948761), 10601 ^ _774244 : [(10602 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948761), _948763), _948765)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948761), _948763), _948765))), -(_948763 = _948765)], (10612 ^ _774244) ^ [] : [10613 ^ _774244 : [(10616 ^ _774244) ^ [] : [_948763 = _948765], (10614 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948761), _948763), _948765))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948761), _948763), _948765)))]]], (18017 ^ _774244) ^ [_1082338] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1082338), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082338)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1082338)))], (39690 ^ _774244) ^ [_1521312, _1521314, _1521316, _1521318, _1521320, _1521322] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1521312, _1521314)), hAPP(hAPP(c_Product__Type_OPair(_1521312, _1521314), _1521316), _1521318)), hAPP(hAPP(c_Product__Type_OSigma(_1521312, _1521314), _1521320), _1521322))), -(hBOOL(hAPP(hAPP(c_member(_1521314), _1521318), hAPP(_1521322, _1521316))))], (26085 ^ _774244) ^ [_1229930, _1229932, _1229934] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1229930), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1229932), _1229934))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1229930), _1229934)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1229930), _1229932)))], (11126 ^ _774244) ^ [_957223, _957225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957223), _957225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957223), _957225)))], (45708 ^ _774244) ^ [_1672630, _1672632, _1672634, _1672636, _1672638, _1672640] : [-(hBOOL(hAPP(hAPP(c_member(_1672630), _1672632), hAPP(c_List_Oset(_1672630), _1672634)))), -(hAPP(hAPP(c_List_Omap(_1672630, _1672636), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1672630, _1672636), _1672638), _1672632), _1672640)), _1672634) = hAPP(hAPP(c_List_Omap(_1672630, _1672636), _1672638), _1672634))], (41156 ^ _774244) ^ [_1561562, _1561564] : [-(hAPP(c_Set_Oimage(_1561562, _1561562, c_Fun_Oid(_1561562)), _1561564) = _1561564)], (42364 ^ _774244) ^ [_1592127, _1592129, _1592131] : [class_Orderings_Olinorder(_1592127), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592127), _1592129)), 42374 ^ _774244 : [(42377 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1592127), _1592131), 42373 ^ [_1592127, _1592129, _1592131]))], (42375 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1592127), 42373 ^ [_1592127, _1592129, _1592131]), _1592129)))]], hBOOL(hAPP(hAPP(c_member(_1592127), _1592131), _1592129)), -(c_Big__Operators_Olinorder__class_OMin(_1592127, _1592129) = _1592131)], (27648 ^ _774244) ^ [_1261713, _1261715, _1261717, _1261719] : [27649 ^ _774244 : [(27652 ^ _774244) ^ [] : [hBOOL(hAPP(_1261717, _1261715))], (27650 ^ _774244) ^ [] : [hBOOL(hAPP(_1261713, _1261715))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261719, tc_HOL_Obool)), _1261717), _1261713), _1261715)))], (20327 ^ _774244) ^ [_1122092, _1122094, _1122096, _1122098] : [class_Rings_Odivision__ring(_1122092), -(_1122094 = c_Groups_Ozero__class_Ozero(_1122092)), _1122096 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122092), _1122098), _1122094), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122092), _1122096), _1122094) = _1122098)], (45365 ^ _774244) ^ [_1664140, _1664142, _1664144, _1664146] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1664140)), hAPP(c_Set_Oimage(_1664142, tc_Option_Ooption(_1664140), _1664144), c_Orderings_Otop__class_Otop(tc_fun(_1664142, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1664140)), hAPP(c_Set_Oimage(_1664142, tc_Option_Ooption(_1664140), c_Map_Omap__add(_1664142, _1664140, _1664144, c_Map_Omap__of(_1664142, _1664140, _1664146))), c_Orderings_Otop__class_Otop(tc_fun(_1664142, tc_HOL_Obool))))))], (27842 ^ _774244) ^ [_1265890, _1265892, _1265894] : [class_Lattices_Osemilattice__sup(_1265890), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265890), _1265892), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265890), _1265892), _1265894)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265890), _1265892), _1265894))], (43633 ^ _774244) ^ [_1621649, _1621651, _1621653, _1621655, _1621657, _1621659] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1621649, tc_fun(_1621651, tc_HOL_Obool)), _1621653), hAPP(hAPP(c_COMBB(_1621655, tc_fun(_1621651, tc_HOL_Obool), _1621649), _1621657), _1621659)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1621655, tc_fun(_1621651, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1621649, _1621655, _1621659), _1621653)), _1621657))], (30787 ^ _774244) ^ [_1326147, _1326149, _1326151, _1326153] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1326147, tc_fun(_1326149, tc_HOL_Obool))), _1326151), _1326153)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1326147, _1326149)), hAPP(hAPP(c_Product__Type_OPair(_1326147, _1326149), _1326151), _1326153)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1326147, _1326149), tc_HOL_Obool)))))], (19877 ^ _774244) ^ [_1114555, _1114557] : [c_Nat__Transfer_Ois__nat(_1114555), c_Nat__Transfer_Ois__nat(_1114557), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1114555), _1114557)))], (34307 ^ _774244) ^ [_1398492, _1398494, _1398496, _1398498, _1398500] : [class_Groups_Ocomm__monoid__mult(_1398492), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398494), _1398496)), -(hBOOL(hAPP(hAPP(c_member(_1398494), _1398498), _1398496))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398494, _1398492), _1398500), hAPP(hAPP(c_Set_Oinsert(_1398494), _1398498), _1398496)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398492), hAPP(_1398500, _1398498)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398494, _1398492), _1398500), _1398496)))], (39108 ^ _774244) ^ [_1506765, _1506767] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506765), _1506767))), -(hAPP(c_Finite__Set_Ocard(_1506765), _1506767) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13397 ^ _774244) ^ [_996996, _996998, _997000, _997002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _996998), _997000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _997000), 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), _996998), _996996)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _996998), c_Divides_Odiv__class_Omod(tc_Int_Oint, _997002, _996996))), _997000))))], (44249 ^ _774244) ^ [_1638021, _1638023] : [-(c_Relation_Ototal__on(_1638021, c_Orderings_Obot__class_Obot(tc_fun(_1638021, tc_HOL_Obool)), _1638023))], (36937 ^ _774244) ^ [_1459059, _1459061, _1459063, _1459065, _1459067] : [c_Finite__Set_Ofolding__one(_1459059, _1459061, _1459063), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459059), _1459065)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459059), _1459067)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459059, tc_HOL_Obool)), _1459065), _1459067) = c_Orderings_Obot__class_Obot(tc_fun(_1459059, tc_HOL_Obool))), -(hAPP(hAPP(_1459061, hAPP(_1459063, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459059, tc_HOL_Obool)), _1459065), _1459067))), hAPP(_1459063, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459059, tc_HOL_Obool)), _1459065), _1459067))) = hAPP(hAPP(_1459061, hAPP(_1459063, _1459065)), hAPP(_1459063, _1459067)))], (34491 ^ _774244) ^ [_1402690, _1402692, _1402694, _1402696] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1402690), _1402692)), 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)), _1402694), _1402690)), 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)), _1402696), _1402692)), 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)), _1402694), _1402696)), _1402692)), c_FunDef_Omax__strict)))], (43729 ^ _774244) ^ [_1624667, _1624669, _1624671, _1624673, _1624675] : [_1624667 = c_Orderings_Obot__class_Obot(tc_fun(_1624669, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624671, tc_HOL_Obool)), _1624673), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1624669, tc_fun(_1624671, tc_HOL_Obool)), _1624667), _1624675)) = _1624673)], (9364 ^ _774244) ^ [_927991, _927993, _927995, _927997] : [class_Rings_Olinordered__comm__semiring__strict(_927991), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927991), _927993), _927995)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927991), c_Groups_Ozero__class_Ozero(_927991)), _927997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927991), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927991), _927997), _927993)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927991), _927997), _927995))))], (5860 ^ _774244) ^ [_867935, _867937] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _867935, _867937, _867935))], (19329 ^ _774244) ^ [_1104180, _1104182] : [class_Groups_Omonoid__mult(_1104180), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1104180), _1104182), 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(_1104180), _1104182), _1104182))], (33984 ^ _774244) ^ [_1392048, _1392050, _1392052] : [class_Groups_Ocomm__monoid__mult(_1392048), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392050, _1392048), hAPP(c_COMBK(_1392048, _1392050), c_Groups_Oone__class_Oone(_1392048))), _1392052) = c_Groups_Oone__class_Oone(_1392048))], (8338 ^ _774244) ^ [_910152, _910154, _910156, _910158] : [class_Orderings_Oorder(_910152), _910154 = _910156, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910152), _910158), _910156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910152), _910158), _910154)))], (11074 ^ _774244) ^ [_956389, _956391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956389), _956391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956389), hAPP(c_Nat_OSuc, _956391))))], (31471 ^ _774244) ^ [_1339869, _1339871, _1339873, _1339875, _1339877, _1339879] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1339871, _1339873)), hAPP(hAPP(c_Product__Type_OPair(_1339871, _1339873), _1339877), _1339879)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339869, tc_fun(tc_prod(_1339871, _1339873), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1339869, tc_HOL_Obool))), _1339875))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339869, tc_fun(_1339871, tc_fun(_1339873, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1339869, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1339871, _1339873), tc_HOL_Obool), tc_fun(_1339871, tc_fun(_1339873, tc_HOL_Obool)), _1339869), hAPP(c_COMBC(_1339871, tc_fun(tc_prod(_1339871, _1339873), tc_HOL_Obool), tc_fun(_1339873, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339873, tc_fun(tc_fun(tc_prod(_1339871, _1339873), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1339871, _1339873), tc_HOL_Obool), tc_fun(_1339873, tc_HOL_Obool)), _1339871), c_COMBC(_1339873, tc_fun(tc_prod(_1339871, _1339873), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339873, tc_prod(_1339871, _1339873)), tc_fun(_1339873, tc_fun(tc_fun(tc_prod(_1339871, _1339873), tc_HOL_Obool), tc_HOL_Obool)), _1339871), hAPP(c_COMBB(tc_prod(_1339871, _1339873), tc_fun(tc_fun(tc_prod(_1339871, _1339873), tc_HOL_Obool), tc_HOL_Obool), _1339873), c_member(tc_prod(_1339871, _1339873)))), c_Product__Type_OPair(_1339871, _1339873))))), _1339875)), _1339877), _1339879)))], (15640 ^ _774244) ^ [_1038357, _1038359, _1038361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1038357), _1038359)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038359), _1038361)), _1038357) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1038359), _1038357)), _1038361))], (26203 ^ _774244) ^ [_1231893, _1231895, _1231897] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231893), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1231895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231893), _1231897)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1231893), _1231895)))], (44251 ^ _774244) ^ [_1638070, _1638072, _1638074] : [c_Relation_Ototal__on(_1638070, _1638072, hAPP(c_Relation_Oconverse(_1638070, _1638070), _1638074)), -(c_Relation_Ototal__on(_1638070, _1638072, _1638074))], (17005 ^ _774244) ^ [_1065053, _1065055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1065053), _1065055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065053)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065055))))], (5080 ^ _774244) ^ [_852760, _852762] : [_852762 = _852760, -(c_List_Otake(_852762) = c_List_Otake(_852760))], (20551 ^ _774244) ^ [_1125879, _1125881, _1125883] : [class_Fields_Olinordered__field(_1125879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125879), _1125881), c_Groups_Ozero__class_Ozero(_1125879))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125879), c_Groups_Ozero__class_Ozero(_1125879)), _1125883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125879), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125879), _1125881), _1125883)), c_Groups_Ozero__class_Ozero(_1125879))))], (9882 ^ _774244) ^ [] : [-(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))], (37353 ^ _774244) ^ [_1467599, _1467601, _1467603, _1467605, _1467607, _1467609, _1467611] : [c_Equiv__Relations_Oequiv(_1467599, _1467601, _1467603), c_Equiv__Relations_Ocongruent(_1467599, tc_fun(_1467605, tc_HOL_Obool), _1467603, _1467607), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1467599, tc_fun(_1467605, tc_HOL_Obool)), _1467609), _1467607) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1467599, tc_fun(_1467605, tc_HOL_Obool)), _1467611), _1467607), hBOOL(hAPP(hAPP(c_member(tc_fun(_1467599, tc_HOL_Obool)), _1467609), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1467599), _1467601), _1467603))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1467599, tc_HOL_Obool)), _1467611), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1467599), _1467601), _1467603))), 37375 ^ _774244 : [(37379 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1467599), 37377 ^ [_1467599, _1467601, _1467603, _1467605, _1467607, _1467609, _1467611]), _1467601)))], (37381 ^ _774244) ^ [] : [-(hAPP(_1467607, 37374 ^ [_1467599, _1467601, _1467603, _1467605, _1467607, _1467609, _1467611]) = hAPP(_1467607, 37377 ^ [_1467599, _1467601, _1467603, _1467605, _1467607, _1467609, _1467611]))], (37383 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1467599, _1467599)), hAPP(hAPP(c_Product__Type_OPair(_1467599, _1467599), 37374 ^ [_1467599, _1467601, _1467603, _1467605, _1467607, _1467609, _1467611]), 37377 ^ [_1467599, _1467601, _1467603, _1467605, _1467607, _1467609, _1467611])), _1467603))], (37376 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1467599), 37374 ^ [_1467599, _1467601, _1467603, _1467605, _1467607, _1467609, _1467611]), _1467601)))]], -(_1467609 = _1467611)], (48162 ^ _774244) ^ [_1734525, _1734527, _1734529, _1734531] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1734525), tc_List_Olist(_1734525))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1734525), tc_List_Olist(_1734525)), _1734527), _1734529)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1734525), tc_List_Olist(_1734525)), c_List_Olistrel1(_1734525, _1734531)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1734525), tc_List_Olist(_1734525))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1734525), tc_List_Olist(_1734525)), _1734527), _1734529)), c_List_Olistrel1(_1734525, hAPP(c_Relation_Oconverse(_1734525, _1734525), _1734531)))))], (10966 ^ _774244) ^ [_954514] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954514), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42413 ^ _774244) ^ [_1593207, _1593209] : [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), _1593207), _1593209)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1593207), _1593209)))], (18343 ^ _774244) ^ [_1087265, _1087267] : [class_Int_Onumber__ring(_1087265), class_Rings_Olinordered__idom(_1087265), 18350 ^ _774244 : [(18357 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087267), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087265), hAPP(c_Int_Onumber__class_Onumber__of(_1087265), _1087267)), c_Groups_Ozero__class_Ozero(_1087265))))], (18351 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087265), hAPP(c_Int_Onumber__class_Onumber__of(_1087265), _1087267)), c_Groups_Ozero__class_Ozero(_1087265))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087267), c_Int_OPls)))]]], (9202 ^ _774244) ^ [_925197, _925199] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _925197), _925199)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _925197)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _925199)))], (51185 ^ _774244) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (49093 ^ _774244) ^ [_1756003, _1756005, _1756007, _1756009] : [49096 ^ _774244 : [(49101 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1756003, _1756003)), hAPP(hAPP(c_Product__Type_OPair(_1756003, _1756003), 49095 ^ [_1756003, _1756005, _1756007, _1756009]), 49094 ^ [_1756003, _1756005, _1756007, _1756009])), _1756005))], (49099 ^ _774244) ^ [] : [49094 ^ [_1756003, _1756005, _1756007, _1756009] = 49095 ^ [_1756003, _1756005, _1756007, _1756009]], (49097 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1756003, _1756003)), hAPP(hAPP(c_Product__Type_OPair(_1756003, _1756003), 49094 ^ [_1756003, _1756005, _1756007, _1756009]), 49095 ^ [_1756003, _1756005, _1756007, _1756009])), _1756005))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756003), tc_List_Olist(_1756003))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756003), tc_List_Olist(_1756003)), _1756007), _1756009)), c_List_Olexord(_1756003, _1756005)))), -(_1756007 = _1756009), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756003), tc_List_Olist(_1756003))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756003), tc_List_Olist(_1756003)), _1756009), _1756007)), c_List_Olexord(_1756003, _1756005))))], (19547 ^ _774244) ^ [_1107886, _1107888, _1107890] : [class_Rings_Olinordered__idom(_1107886), 19550 ^ _774244 : [(19559 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107886), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107886), hAPP(hAPP(c_Power_Opower__class_Opower(_1107886), _1107888), 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(_1107886), _1107890), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1107886)))), _1107888 = c_Groups_Ozero__class_Ozero(_1107886), _1107890 = c_Groups_Ozero__class_Ozero(_1107886)], (19551 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107886), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107886), hAPP(hAPP(c_Power_Opower__class_Opower(_1107886), _1107888), 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(_1107886), _1107890), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1107886))), 19554 ^ _774244 : [(19557 ^ _774244) ^ [] : [-(_1107890 = c_Groups_Ozero__class_Ozero(_1107886))], (19555 ^ _774244) ^ [] : [-(_1107888 = c_Groups_Ozero__class_Ozero(_1107886))]]]]], (34747 ^ _774244) ^ [_1409222, _1409224] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1409222, _1409222)), _1409224)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1409222), hAPP(c_Relation_OField(_1409222), _1409224))))], (16313 ^ _774244) ^ [_1051687, _1051689] : [class_Int_Onumber__ring(_1051687), class_Rings_Olinordered__idom(_1051687), 16320 ^ _774244 : [(16327 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051687), hAPP(c_Int_Onumber__class_Onumber__of(_1051687), _1051689)), c_Groups_Ozero__class_Ozero(_1051687)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1051687), hAPP(c_Int_Onumber__class_Onumber__of(_1051687), _1051689)) = hAPP(c_Int_Onumber__class_Onumber__of(_1051687), _1051689))], (16321 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051687), hAPP(c_Int_Onumber__class_Onumber__of(_1051687), _1051689)), c_Groups_Ozero__class_Ozero(_1051687))), -(hAPP(c_Groups_Oabs__class_Oabs(_1051687), hAPP(c_Int_Onumber__class_Onumber__of(_1051687), _1051689)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1051687), hAPP(c_Int_Onumber__class_Onumber__of(_1051687), _1051689)))]]], (29070 ^ _774244) ^ [_1291836, _1291838, _1291840] : [class_Lattices_Obounded__lattice__bot(_1291836), 29073 ^ _774244 : [(29082 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291836), _1291838), _1291840) = c_Orderings_Obot__class_Obot(_1291836)), _1291838 = c_Orderings_Obot__class_Obot(_1291836), _1291840 = c_Orderings_Obot__class_Obot(_1291836)], (29074 ^ _774244) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291836), _1291838), _1291840) = c_Orderings_Obot__class_Obot(_1291836), 29077 ^ _774244 : [(29080 ^ _774244) ^ [] : [-(_1291840 = c_Orderings_Obot__class_Obot(_1291836))], (29078 ^ _774244) ^ [] : [-(_1291838 = c_Orderings_Obot__class_Obot(_1291836))]]]]], (8818 ^ _774244) ^ [_918360, _918362, _918364, _918366] : [class_Rings_Ocomm__semiring__1(_918360), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918360), _918362), _918364)), _918366) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918360), _918362), _918366)), _918364))], (44504 ^ _774244) ^ [_1644028] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1644028, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1644028, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1644028, tc_HOL_Obool)))], (27561 ^ _774244) ^ [_1260141] : [-(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)), _1260141)))], (16077 ^ _774244) ^ [_1047525, _1047527, _1047529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1047525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1047527), 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), _1047527), _1047529))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1047525))), _1047529)))], (48077 ^ _774244) ^ [_1731935, _1731937, _1731939, _1731941, _1731943] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731935), tc_List_Olist(_1731935))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731935), tc_List_Olist(_1731935)), hAPP(hAPP(c_List_Oappend(_1731935), _1731937), _1731939)), hAPP(hAPP(c_List_Oappend(_1731935), _1731937), _1731941))), c_List_Olexord(_1731935, _1731943))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1731935, _1731935)), hAPP(hAPP(c_Product__Type_OPair(_1731935, _1731935), 48082 ^ [_1731935, _1731937, _1731939, _1731941, _1731943]), 48082 ^ [_1731935, _1731937, _1731939, _1731941, _1731943])), _1731943))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731935), tc_List_Olist(_1731935))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731935), tc_List_Olist(_1731935)), _1731939), _1731941)), c_List_Olexord(_1731935, _1731943))))], (282 ^ _774244) ^ [_778369, _778371, _778373, _778375, _778377, _778379, _778381, _778383] : [-(c_Finite__Set_Ofolding__idem(_778381, _778377, _778373, _778369)), c_Finite__Set_Ofolding__idem(_778383, _778379, _778375, _778371), _778383 = _778381, _778379 = _778377, _778375 = _778373, _778371 = _778369], (24739 ^ _774244) ^ [_1206149, _1206151, _1206153, _1206155, _1206157, _1206159, _1206161] : [hBOOL(hAPP(hAPP(_1206149, hAPP(c_Product__Type_Osnd(_1206151, _1206153), _1206155)), hAPP(c_Product__Type_Ofst(_1206151, _1206153), _1206155))), 24746 ^ _774244 : [(24749 ^ _774244) ^ [] : [hBOOL(hAPP(_1206157, hAPP(hAPP(_1206159, 24744 ^ [_1206149, _1206151, _1206153, _1206155, _1206157, _1206159, _1206161]), 24745 ^ [_1206149, _1206151, _1206153, _1206155, _1206157, _1206159, _1206161])))], (24747 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1206149, 24745 ^ [_1206149, _1206151, _1206153, _1206155, _1206157, _1206159, _1206161]), 24744 ^ [_1206149, _1206151, _1206153, _1206155, _1206157, _1206159, _1206161])))]], -(hBOOL(hAPP(_1206157, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1206151, _1206153, _1206161), _1206159), _1206155))))], (19115 ^ _774244) ^ [_1100483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1100483)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100483), c_Int_OMin)))], (6209 ^ _774244) ^ [_873874, _873876, _873878, _873880, _873882] : [c_Com_Ocom_OSemi(_873874, _873876) = c_Com_Ocom_OCond(_873878, _873880, _873882)], (2240 ^ _774244) ^ [_808000, _808002, _808004, _808006, _808008, _808010] : [-(c_Natural_Oupdate(_808010, _808006, _808002) = c_Natural_Oupdate(_808008, _808004, _808000)), _808010 = _808008, _808006 = _808004, _808002 = _808000], (39934 ^ _774244) ^ [_1528170, _1528172, _1528174, _1528176, _1528178, _1528180, _1528182, _1528184, _1528186, _1528188] : [-(c_Product__Type_Omap__pair(_1528170, _1528172, _1528174, _1528176, hAPP(c_Fun_Ocomp(_1528178, _1528172, _1528170, _1528180), _1528182), hAPP(c_Fun_Ocomp(_1528184, _1528176, _1528174, _1528186), _1528188)) = hAPP(c_Fun_Ocomp(tc_prod(_1528178, _1528184), tc_prod(_1528172, _1528176), tc_prod(_1528170, _1528174), c_Product__Type_Omap__pair(_1528178, _1528172, _1528184, _1528176, _1528180, _1528186)), c_Product__Type_Omap__pair(_1528170, _1528178, _1528174, _1528184, _1528182, _1528188)))], (7736 ^ _774244) ^ [_900416, _900418, _900420, _900422] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_900416, _900418)), c_Nitpick_Opair__box_OPairBox(_900416, _900418, _900420, _900422)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50532 ^ _774244) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (43686 ^ _774244) ^ [_1623302, _1623304, _1623306, _1623308, _1623310] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623302, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623304, tc_fun(_1623302, tc_HOL_Obool)), _1623306), _1623308)), _1623310) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1623304, tc_fun(_1623302, tc_HOL_Obool)), _1623306), hAPP(hAPP(c_COMBC(_1623304, tc_fun(_1623302, tc_HOL_Obool), tc_fun(_1623302, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1623302, tc_HOL_Obool), tc_fun(tc_fun(_1623302, tc_HOL_Obool), tc_fun(_1623302, tc_HOL_Obool)), _1623304), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623302, tc_HOL_Obool))), _1623308)), _1623310)))], (23651 ^ _774244) ^ [_1184592, _1184594] : [class_Orderings_Olinorder(_1184592), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1184592), _1184594), _1184594) = _1184594)], (33826 ^ _774244) ^ [_1388562, _1388564, _1388566, _1388568, _1388570, _1388572] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388562, _1388564), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388562, _1388564), _1388566), _1388568), _1388570)), _1388568), _1388572) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1388562, _1388564), _1388566), _1388568), _1388572))], (15658 ^ _774244) ^ [_1038746, _1038748] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1038746), _1038748)), _1038748) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1038746), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1038746, _1038748)))], (34379 ^ _774244) ^ [_1400137, _1400139, _1400141, _1400143, _1400145, _1400147] : [hBOOL(hAPP(hAPP(c_member(_1400137), _1400139), _1400141)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1400137, tc_Option_Ooption(_1400143)), c_Map_Orestrict__map(_1400137, _1400143, _1400145, _1400141)), _1400139), _1400147) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1400137, tc_Option_Ooption(_1400143)), c_Map_Orestrict__map(_1400137, _1400143, _1400145, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400137, tc_HOL_Obool)), _1400141), hAPP(hAPP(c_Set_Oinsert(_1400137), _1400139), c_Orderings_Obot__class_Obot(tc_fun(_1400137, tc_HOL_Obool)))))), _1400139), _1400147))], (22066 ^ _774244) ^ [_1153317, _1153319] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1153317), _1153319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1153317)), _1153319)))], (14191 ^ _774244) ^ [_1012075] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1012075), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1012075)], (28683 ^ _774244) ^ [_1283225, _1283227, _1283229, _1283231, _1283233] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1283225, tc_fun(_1283227, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283225, tc_HOL_Obool)), _1283229), _1283231)), _1283233) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283227, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1283225, tc_fun(_1283227, tc_HOL_Obool)), _1283229), _1283233)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1283225, tc_fun(_1283227, tc_HOL_Obool)), _1283231), _1283233)))], (44739 ^ _774244) ^ [_1649598, _1649600, _1649602] : [class_Complete__Lattice_Ocomplete__lattice(_1649598), hBOOL(hAPP(hAPP(c_member(_1649598), _1649600), _1649602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1649598), _1649600), c_Complete__Lattice_OSup__class_OSup(_1649598, _1649602))))], (27563 ^ _774244) ^ [_1260166, _1260168] : [c_Nat__Transfer_Ois__nat(_1260166), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1260166, _1260168)))], (22620 ^ _774244) ^ [_1164685, _1164687, _1164689] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1164685, _1164687), _1164689)), -(c_Divides_Odivmod__nat(_1164685, _1164687) = _1164689)], (24411 ^ _774244) ^ [_1198820] : [-(_1198820 = 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, _1198820)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1198820))))], (4374 ^ _774244) ^ [_841943, _841945, _841947, _841949] : [-(c_Transitive__Closure_Ortrancl(_841949, _841945) = c_Transitive__Closure_Ortrancl(_841947, _841943)), _841949 = _841947, _841945 = _841943], (27050 ^ _774244) ^ [_1249866, _1249868, _1249870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1249866, 27051 ^ [_1249866, _1249868, _1249870])), hAPP(_1249868, 27051 ^ [_1249866, _1249868, _1249870]))), -(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), _1249868), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1249870))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1249866), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1249870))) = 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)), _1249868)), _1249866)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1249870)))], (4322 ^ _774244) ^ [_841123, _841125, _841127, _841129] : [-(c_List_Olex(_841129, _841125) = c_List_Olex(_841127, _841123)), _841129 = _841127, _841125 = _841123], (42094 ^ _774244) ^ [_1585900, _1585902, _1585904] : [c_Wellfounded_OwfP(_1585900, hAPP(_1585902, 42095 ^ [_1585900, _1585902, _1585904])), 42102 ^ _774244 : [(42105 ^ _774244) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1585900, tc_HOL_Obool)), c_Predicate_ODomainP(_1585900, _1585900, hAPP(_1585902, 42100 ^ [_1585900, _1585902, _1585904]))), c_Predicate_ORangeP(_1585900, _1585900, hAPP(_1585902, 42101 ^ [_1585900, _1585902, _1585904]))) = c_Orderings_Obot__class_Obot(tc_fun(_1585900, tc_HOL_Obool))], (42103 ^ _774244) ^ [] : [hAPP(_1585902, 42100 ^ [_1585900, _1585902, _1585904]) = hAPP(_1585902, 42101 ^ [_1585900, _1585902, _1585904])]], -(c_Wellfounded_OwfP(_1585900, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1585904, tc_fun(_1585900, tc_fun(_1585900, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1585904, tc_HOL_Obool))), _1585902)))], (1074 ^ _774244) ^ [_790393, _790395] : [-(class_Groups_Oab__group__add(_790393)), _790395 = _790393, class_Groups_Oab__group__add(_790395)], (48047 ^ _774244) ^ [_1731057, _1731059, _1731061, _1731063, _1731065, _1731067] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731057), tc_List_Olist(_1731057))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731057), tc_List_Olist(_1731057)), hAPP(hAPP(c_List_Oappend(_1731057), _1731059), hAPP(hAPP(c_List_Olist_OCons(_1731057), _1731061), c_List_Olist_ONil(_1731057)))), hAPP(hAPP(c_List_Oappend(_1731057), _1731063), hAPP(hAPP(c_List_Olist_OCons(_1731057), _1731065), c_List_Olist_ONil(_1731057))))), c_List_Olistrel1(_1731057, _1731067))), 48052 ^ _774244 : [(48055 ^ _774244) ^ [] : [-(_1731061 = _1731065)], (48053 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731057), tc_List_Olist(_1731057))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731057), tc_List_Olist(_1731057)), _1731059), _1731063)), c_List_Olistrel1(_1731057, _1731067))))]], 48056 ^ _774244 : [(48059 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1731057, _1731057)), hAPP(hAPP(c_Product__Type_OPair(_1731057, _1731057), _1731061), _1731065)), _1731067)))], (48057 ^ _774244) ^ [] : [-(_1731059 = _1731063)]]], (27233 ^ _774244) ^ [_1253882, _1253884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1253882), _1253884)), -(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)), _1253882)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1253884))))], (23185 ^ _774244) ^ [_1174965, _1174967, _1174969, _1174971] : [_1174965 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1174967), _1174969)), _1174971), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1174965, _1174967), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1174969), _1174971)))), 23192 ^ _774244 : [(23195 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1174971), _1174967))], (23193 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174967)))]], 23200 ^ _774244 : [(23203 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1174967), _1174971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1174971), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23201 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174967))]]], (29726 ^ _774244) ^ [] : [-(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))))], (7137 ^ _774244) ^ [_890153] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _890153))))], (29702 ^ _774244) ^ [_1303143, _1303145] : [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)))), _1303143, _1303145) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1303143), _1303145)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1303145), _1303143)))], (44293 ^ _774244) ^ [_1639141, _1639143, _1639145, _1639147] : [-(hAPP(hAPP(c_Nat_Ocompow(_1639141, _1639141), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1639143), _1639145)), _1639147) = hAPP(c_Fun_Ocomp(_1639141, _1639141, _1639141, hAPP(hAPP(c_Nat_Ocompow(_1639141, _1639141), _1639143), _1639147)), hAPP(hAPP(c_Nat_Ocompow(_1639141, _1639141), _1639145), _1639147)))], (44133 ^ _774244) ^ [_1635069, _1635071, _1635073] : [c_Relation_Osingle__valued(_1635069, _1635071, _1635073), 44136 ^ _774244 : [(44137 ^ _774244) ^ [_1635190, _1635192] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635069, _1635071)), hAPP(hAPP(c_Product__Type_OPair(_1635069, _1635071), _1635192), _1635190)), _1635073)), 44140 ^ _774244 : [(44141 ^ _774244) ^ [_1635316] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635069, _1635071)), hAPP(hAPP(c_Product__Type_OPair(_1635069, _1635071), _1635192), _1635316)), _1635073)), -(_1635190 = _1635316)]]]]], (50376 ^ _774244) ^ [_1783125, _1783127] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1783125), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1783125))), c_List_Otranspose(_1783125, _1783127)))))], (2674 ^ _774244) ^ [_814763, _814765, _814767, _814769] : [-(c_Nitpick_Onumber__of__frac(_814769, _814765) = c_Nitpick_Onumber__of__frac(_814767, _814763)), _814769 = _814767, _814765 = _814763], (35552 ^ _774244) ^ [_1428104, _1428106, _1428108, _1428110, _1428112, _1428114, _1428116] : [c_Finite__Set_Ofolding__idem(_1428104, _1428106, _1428108, _1428110), -(hAPP(c_Fun_Ocomp(_1428106, _1428106, _1428112, hAPP(_1428108, _1428114)), hAPP(c_Fun_Ocomp(_1428106, _1428106, _1428112, hAPP(_1428108, _1428114)), _1428116)) = hAPP(c_Fun_Ocomp(_1428106, _1428106, _1428112, hAPP(_1428108, _1428114)), _1428116))], (44845 ^ _774244) ^ [_1651649, _1651651] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1651649, tc_HOL_Obool), _1651651) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1651649, tc_HOL_Obool), tc_fun(_1651649, tc_HOL_Obool)), _1651651), c_COMBI(tc_fun(_1651649, tc_HOL_Obool))))], (31939 ^ _774244) ^ [_1351834, _1351836, _1351838, _1351840, _1351842] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1351834, _1351836)), hAPP(hAPP(c_Product__Type_OPair(_1351834, _1351836), _1351840), _1351842)), _1351838)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1351834, _1351836, _1351838), _1351840), _1351842)))], (24341 ^ _774244) ^ [_1197213, _1197215] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1197213)), hAPP(c_Nat_OSuc, _1197215)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1197213), _1197215)))], (32020 ^ _774244) ^ [_1353532, _1353534, _1353536, _1353538] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1353532, tc_fun(_1353534, tc_HOL_Obool))), _1353536), _1353538))], (46249 ^ _774244) ^ [_1686120, _1686122, _1686124, _1686126, _1686128] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686120)), _1686122) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686124)), _1686126), 46252 ^ _774244 : [(46259 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1686120), _1686128), hAPP(c_List_Oset(_1686120), _1686122)))), -(hAPP(c_Map_Omap__of(_1686120, _1686124, hAPP(hAPP(c_List_Ozip(_1686120, _1686124), _1686122), _1686126)), _1686128) = c_Option_Ooption_ONone(_1686124))], (46253 ^ _774244) ^ [] : [hAPP(c_Map_Omap__of(_1686120, _1686124, hAPP(hAPP(c_List_Ozip(_1686120, _1686124), _1686122), _1686126)), _1686128) = c_Option_Ooption_ONone(_1686124), hBOOL(hAPP(hAPP(c_member(_1686120), _1686128), hAPP(c_List_Oset(_1686120), _1686122)))]]], (41646 ^ _774244) ^ [_1574369, _1574371, _1574373] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1574369, _1574371)), _1574373)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1574371), hAPP(c_Relation_ORange(_1574369, _1574371), _1574373))))], (5126 ^ _774244) ^ [_853535, _853537, _853539, _853541, _853543, _853545] : [-(c_Map_Omap__of(_853545, _853541, _853537) = c_Map_Omap__of(_853543, _853539, _853535)), _853545 = _853543, _853541 = _853539, _853537 = _853535], (3890 ^ _774244) ^ [_834161, _834163, _834165, _834167, _834169, _834171] : [-(c_Set_Ovimage(_834171, _834167, _834163) = c_Set_Ovimage(_834169, _834165, _834161)), _834171 = _834169, _834167 = _834165, _834163 = _834161], (48210 ^ _774244) ^ [_1736003, _1736005, _1736007, _1736009, _1736011] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1736003, _1736003)), hAPP(hAPP(c_Product__Type_OPair(_1736003, _1736003), _1736005), _1736007)), _1736009)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1736003), tc_List_Olist(_1736003))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1736003), tc_List_Olist(_1736003)), hAPP(hAPP(c_List_Olist_OCons(_1736003), _1736005), _1736011)), hAPP(hAPP(c_List_Olist_OCons(_1736003), _1736007), _1736011))), c_List_Olistrel1(_1736003, _1736009))))], (14050 ^ _774244) ^ [_1009380, _1009382, _1009384, _1009386] : [_1009380 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1009382), _1009384)), _1009386), -(_1009382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1009380), _1009382) = _1009384), 14057 ^ _774244 : [(14060 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009386)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1009386), _1009382))], (14058 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009382)))]], 14065 ^ _774244 : [(14068 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1009382), _1009386)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1009386), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14066 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009382))]]], (32375 ^ _774244) ^ [_1360746, _1360748, _1360750, _1360752, _1360754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1360746, _1360748)), hAPP(_1360746, _1360750))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1360752, _1360752)), hAPP(hAPP(c_Product__Type_OPair(_1360752, _1360752), _1360748), _1360750)), _1360754)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1360752, _1360752)), hAPP(hAPP(c_Product__Type_OPair(_1360752, _1360752), _1360748), _1360750)), c_Wellfounded_Omlex__prod(_1360752, _1360746, _1360754))))], (14014 ^ _774244) ^ [_1008666, _1008668, _1008670] : [-(hBOOL(hAPP(_1008666, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1008668), _1008670)))), 14017 ^ _774244 : [(14020 ^ _774244) ^ [] : [hBOOL(hAPP(_1008666, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14018 ^ _774244) ^ [] : [-(_1008670 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 14023 ^ _774244 : [(14024 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1008670)))], (14030 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14026 ^ [_1008666, _1008668, _1008670]), _1008670)))], (14034 ^ _774244) ^ [] : [hBOOL(hAPP(_1008666, 14025 ^ [_1008666, _1008668, _1008670]))], (14032 ^ _774244) ^ [] : [-(_1008668 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1008670), 14025 ^ [_1008666, _1008668, _1008670])), 14026 ^ [_1008666, _1008668, _1008670]))], (14028 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14026 ^ [_1008666, _1008668, _1008670])))]], 14035 ^ _774244 : [(14036 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1008670), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14042 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14038 ^ [_1008666, _1008668, _1008670]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14046 ^ _774244) ^ [] : [hBOOL(hAPP(_1008666, 14037 ^ [_1008666, _1008668, _1008670]))], (14044 ^ _774244) ^ [] : [-(_1008668 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1008670), 14037 ^ [_1008666, _1008668, _1008670])), 14038 ^ [_1008666, _1008668, _1008670]))], (14040 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1008670), 14038 ^ [_1008666, _1008668, _1008670])))]]], (27593 ^ _774244) ^ [_1260680] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1260680) = 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), _1260680))))], (14456 ^ _774244) ^ [_1016399, _1016401, _1016403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1016399), 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)), _1016401)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1016401), _1016403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016399), _1016401)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016399), _1016403))))], (30823 ^ _774244) ^ [_1327038, _1327040, _1327042, _1327044] : [30824 ^ _774244 : [(30827 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1327038), _1327040), _1327044))], (30825 ^ _774244) ^ [] : [_1327040 = _1327042]], -(hBOOL(hAPP(hAPP(c_member(_1327038), _1327040), hAPP(hAPP(c_Set_Oinsert(_1327038), _1327042), _1327044))))], (22886 ^ _774244) ^ [_1169560, _1169562, _1169564] : [hBOOL(hAPP(_1169560, 22887 ^ [_1169560, _1169562, _1169564])), 22890 ^ _774244 : [(22891 ^ _774244) ^ [_1169671, _1169673] : [-(hBOOL(hAPP(_1169560, hAPP(hAPP(c_Product__Type_OPair(_1169562, _1169564), _1169673), _1169671))))]]], (34186 ^ _774244) ^ [_1395924, _1395926, _1395928] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1395924), _1395926)), 34189 ^ _774244 : [(34190 ^ _774244) ^ [] : [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(_1395924, tc_Nat_Onat), _1395928), _1395926))), 34193 ^ _774244 : [(34194 ^ _774244) ^ [_1396092] : [hBOOL(hAPP(hAPP(c_member(_1395924), _1396092), _1395926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1395928, _1396092))))]]], (34200 ^ _774244) ^ [] : [34202 ^ _774244 : [(34205 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1395928, 34201 ^ [_1395924, _1395926, _1395928])))], (34203 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1395924), 34201 ^ [_1395924, _1395926, _1395928]), _1395926)))]], -(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(_1395924, tc_Nat_Onat), _1395928), _1395926))))]]], (5302 ^ _774244) ^ [_856225, _856227] : [_856227 = _856225, -(c_List_Olist_ONil(_856227) = c_List_Olist_ONil(_856225))], (51043 ^ _774244) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (10025 ^ _774244) ^ [_939492, _939494] : [class_Orderings_Opreorder(_939492), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939492), _939494), _939494)))], (47652 ^ _774244) ^ [_1721734, _1721736, _1721738] : [_1721734 = _1721736, -(_1721734 = hAPP(hAPP(c_List_Oappend(_1721738), c_List_Olist_ONil(_1721738)), _1721736))], (41705 ^ _774244) ^ [_1576236, _1576238, _1576240, _1576242] : [41706 ^ _774244 : [(41707 ^ _774244) ^ [_1576290] : [hBOOL(hAPP(hAPP(_1576240, _1576290), _1576242))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1576236, _1576238, _1576240), _1576242)))], (50478 ^ _774244) ^ [_1786084, _1786086, _1786088, _1786090] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1786084)), c_List_Otranspose__rel(_1786084)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1786084)), hAPP(hAPP(c_List_Olist_OCons(_1786084), _1786086), _1786088)), _1786090))), -(c_List_Otranspose(_1786084, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1786084)), hAPP(hAPP(c_List_Olist_OCons(_1786084), _1786086), _1786088)), _1786090)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1786084)), hAPP(hAPP(c_List_Olist_OCons(_1786084), _1786086), c_List_Oconcat(_1786084, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1786084), tc_List_Olist(_1786084)), c_List_Olist_Olist__case(tc_List_Olist(_1786084), _1786084, c_List_Olist_ONil(_1786084), hAPP(hAPP(c_COMBB(tc_List_Olist(_1786084), tc_fun(tc_List_Olist(_1786084), tc_List_Olist(_1786084)), _1786084), c_COMBK(tc_List_Olist(_1786084), tc_List_Olist(_1786084))), hAPP(hAPP(c_COMBC(_1786084, tc_List_Olist(_1786084), tc_List_Olist(_1786084)), c_List_Olist_OCons(_1786084)), c_List_Olist_ONil(_1786084))))), _1786090)))), c_List_Otranspose(_1786084, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1786084)), _1786088), c_List_Oconcat(tc_List_Olist(_1786084), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1786084), tc_List_Olist(tc_List_Olist(_1786084))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1786084)), _1786084, c_List_Olist_ONil(tc_List_Olist(_1786084)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1786084), tc_List_Olist(tc_List_Olist(_1786084))), _1786084), hAPP(hAPP(c_COMBC(tc_List_Olist(_1786084), tc_List_Olist(tc_List_Olist(_1786084)), tc_List_Olist(tc_List_Olist(_1786084))), c_List_Olist_OCons(tc_List_Olist(_1786084))), c_List_Olist_ONil(tc_List_Olist(_1786084)))))), _1786090))))))], (36333 ^ _774244) ^ [_1444986, _1444988, _1444990, _1444992] : [class_Lattices_Olattice(_1444986), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444986), _1444988), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444986), _1444990), _1444992)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444986), _1444990), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1444986), _1444988), _1444992)))], (15506 ^ _774244) ^ [_1035747, _1035749, _1035751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035747), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035749), _1035751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035747), _1035751)), _1035749)))], (7909 ^ _774244) ^ [] : [-(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))], (33990 ^ _774244) ^ [_1392163, _1392165, _1392167, _1392169] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1392163), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392165, tc_Int_Oint), _1392167), _1392169)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392165, _1392163), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1392163, _1392165), c_Int_Oring__1__class_Oof__int(_1392163)), _1392167)), _1392169)), class_Groups_Ocomm__monoid__mult(_1392163), class_Rings_Oring__1(_1392163)], (5776 ^ _774244) ^ [_866307, _866309, _866311, _866313, _866315, _866317] : [c_Natural_Oevaln(_866307, _866309, _866311, _866313), c_Natural_Oevaln(_866315, _866313, _866311, _866317), -(c_Natural_Oevaln(c_Com_Ocom_OSemi(_866307, _866315), _866309, _866311, _866317))], (28398 ^ _774244) ^ [_1276596, _1276598, _1276600, _1276602] : [-(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), _1276596, _1276598)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276600, _1276602)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276600), _1276602)), 28401 ^ _774244 : [(28404 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276600), _1276596)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276598), _1276602)), 28411 ^ _774244 : [(28418 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276598), _1276602)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276602), _1276598)))], (28412 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276600), _1276596)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276596), _1276600)))]]], (28402 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1276596), _1276598)))]]], (20175 ^ _774244) ^ [_1119675, _1119677, _1119679, _1119681, _1119683] : [class_Fields_Ofield(_1119675), -(_1119677 = c_Groups_Ozero__class_Ozero(_1119675)), -(_1119679 = c_Groups_Ozero__class_Ozero(_1119675)), 20186 ^ _774244 : [(20193 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119675), _1119681), _1119679) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119675), _1119683), _1119677), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119675), _1119681), _1119677) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119675), _1119683), _1119679))], (20187 ^ _774244) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119675), _1119681), _1119677) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119675), _1119683), _1119679), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119675), _1119681), _1119679) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119675), _1119683), _1119677))]]], (4332 ^ _774244) ^ [_841272, _841274, _841276, _841278, _841280, _841282] : [-(c_Map_Odom(_841282, _841278, _841274) = c_Map_Odom(_841280, _841276, _841272)), _841282 = _841280, _841278 = _841276, _841274 = _841272], (1084 ^ _774244) ^ [_790518, _790520] : [-(class_Rings_Oordered__ring(_790518)), _790520 = _790518, class_Rings_Oordered__ring(_790520)], (32832 ^ _774244) ^ [_1369142, _1369144, _1369146] : [class_Orderings_Olinorder(_1369142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369142), _1369144)), hBOOL(hAPP(hAPP(c_member(_1369142), _1369146), _1369144)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1369142), _1369146), c_Big__Operators_Olinorder__class_OMin(_1369142, _1369144)) = c_Big__Operators_Olinorder__class_OMin(_1369142, _1369144))], (25645 ^ _774244) ^ [_1221674, _1221676, _1221678] : [class_Divides_Oring__div(_1221674), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221674), _1221676), _1221678)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1221674), hAPP(c_Groups_Ouminus__class_Ouminus(_1221674), _1221678)), _1221676) = hAPP(c_Groups_Ouminus__class_Ouminus(_1221674), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1221674), _1221678), _1221676)))], (3864 ^ _774244) ^ [_833778, _833780] : [_833780 = _833778, -(c_HOL_OAll(_833780) = c_HOL_OAll(_833778))], (14426 ^ _774244) ^ [_1015870, _1015872, _1015874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1015870), _1015872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1015874), 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), _1015872), _1015874)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1015870), _1015874))))], (2974 ^ _774244) ^ [_819713, _819715, _819717, _819719, _819721, _819723, _819725, _819727] : [-(c_Lazy__Sequence_Obind(_819727, _819723, _819719, _819715) = c_Lazy__Sequence_Obind(_819725, _819721, _819717, _819713)), _819727 = _819725, _819723 = _819721, _819719 = _819717, _819715 = _819713], (19633 ^ _774244) ^ [_1109722, _1109724] : [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), _1109722))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1109724))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1109722))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1109724)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1109722)))], (48789 ^ _774244) ^ [_1749321, _1749323, _1749325] : [class_Lattices_Olattice(_1749321), -(c_Big__Operators_Olattice__class_OSup__fin(_1749321, hAPP(c_List_Oset(_1749321), hAPP(hAPP(c_List_Olist_OCons(_1749321), _1749323), _1749325))) = hAPP(c_List_Ofoldl(_1749321, _1749321, c_Lattices_Osemilattice__sup__class_Osup(_1749321), _1749323), _1749325))], (47465 ^ _774244) ^ [_1717281, _1717283, _1717285] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717281)), hAPP(hAPP(c_List_Oappend(_1717281), _1717283), _1717285)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717281)), _1717283)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717281)), _1717285)))], (51041 ^ _774244) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (10880 ^ _774244) ^ [_953112, _953114, _953116, _953118] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_953112), 10883 ^ _774244 : [(10890 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953112), _953116), _953118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953112), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953112), _953114), _953116)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953112), _953114), _953118))))], (10884 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953112), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953112), _953114), _953116)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953112), _953114), _953118))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953112), _953116), _953118)))]]], (31177 ^ _774244) ^ [_1334083, _1334085, _1334087, _1334089, _1334091, _1334093] : [hBOOL(hAPP(hAPP(c_member(_1334083), _1334085), c_SetInterval_Oord_OatLeastLessThan(_1334083, _1334087, _1334089, _1334091, _1334093))), 31180 ^ _774244 : [(31183 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1334089, _1334085), _1334093)))], (31181 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(_1334087, _1334091), _1334085)))]]], (29967 ^ _774244) ^ [_1308101, _1308103, _1308105] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1308101), _1308103)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308101), _1308105)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308101), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308101, tc_HOL_Obool)), _1308103), _1308105))))], (12218 ^ _774244) ^ [_976467] : [12220 ^ _774244 : [(12223 ^ _774244) ^ [] : [hBOOL(hAPP(_976467, hAPP(c_Int_Onat, 12219 ^ [_976467])))], (12221 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12219 ^ [_976467])))]], 12224 ^ _774244 : [(12225 ^ _774244) ^ [_976600] : [-(hBOOL(hAPP(_976467, _976600)))]]], (30483 ^ _774244) ^ [_1317997, _1317999, _1318001] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317997), _1317999)), hBOOL(hAPP(hAPP(c_member(_1317997), _1318001), _1317999)), -(hAPP(c_Finite__Set_Ocard(_1317997), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1317997, tc_HOL_Obool)), _1317999), hAPP(hAPP(c_Set_Oinsert(_1317997), _1318001), c_Orderings_Obot__class_Obot(tc_fun(_1317997, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1317997), _1317999)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47632 ^ _774244) ^ [_1721174, _1721176, _1721178, _1721180, _1721182, _1721184] : [hAPP(hAPP(c_List_Oappend(_1721174), _1721176), _1721178) = _1721180, _1721182 = hAPP(hAPP(c_List_Oappend(_1721174), _1721178), _1721184), -(hAPP(hAPP(c_List_Oappend(_1721174), _1721176), _1721182) = hAPP(hAPP(c_List_Oappend(_1721174), _1721180), _1721184))], (38864 ^ _774244) ^ [_1500985, _1500987, _1500989, _1500991, _1500993, _1500995, _1500997] : [c_Finite__Set_Ofolding__image__simple(_1500985, _1500987, _1500989, _1500991, _1500993, _1500995), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500987), _1500997)), -(hAPP(_1500995, _1500997) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1500985, _1500987, _1500989), _1500993), _1500991), _1500997))], (11246 ^ _774244) ^ [_959238, _959240, _959242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959238), _959240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959238), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959240), _959242))))], (5050 ^ _774244) ^ [_852313, _852315, _852317, _852319] : [-(c_List_Otranspose(_852319, _852315) = c_List_Otranspose(_852317, _852313)), _852319 = _852317, _852315 = _852313], (48194 ^ _774244) ^ [_1735575, _1735577, _1735579, _1735581, _1735583, _1735585] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1735575), tc_List_Olist(_1735575))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1735575), tc_List_Olist(_1735575)), hAPP(hAPP(c_List_Olist_OCons(_1735575), _1735577), _1735579)), hAPP(hAPP(c_List_Olist_OCons(_1735575), _1735581), _1735583))), c_List_Olistrel1(_1735575, _1735585)))), 48195 ^ _774244 : [(48202 ^ _774244) ^ [] : [_1735577 = _1735581, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1735575), tc_List_Olist(_1735575))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1735575), tc_List_Olist(_1735575)), _1735579), _1735583)), c_List_Olistrel1(_1735575, _1735585)))], (48196 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1735575, _1735575)), hAPP(hAPP(c_Product__Type_OPair(_1735575, _1735575), _1735577), _1735581)), _1735585)), _1735579 = _1735583]]], (2508 ^ _774244) ^ [_812128, _812130, _812132, _812134] : [-(c_Divides_OposDivAlg(_812134, _812130) = c_Divides_OposDivAlg(_812132, _812128)), _812134 = _812132, _812130 = _812128], (47826 ^ _774244) ^ [_1725357, _1725359, _1725361, _1725363] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1725357), tc_List_Olist(_1725357))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1725357), tc_List_Olist(_1725357)), _1725359), _1725361)), c_List_Olex(_1725357, _1725363)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1725357), tc_List_Olist(_1725357))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1725357), tc_List_Olist(_1725357)), _1725359), _1725361)), c_List_Olexord(_1725357, _1725363))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725357)), _1725359) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725357)), _1725361)], (11831 ^ _774244) ^ [_969756, _969758, _969760, _969762, _969764] : [class_Groups_Oordered__cancel__ab__semigroup__add(_969756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969756), _969758), _969760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969756), _969762), _969764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969756), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969756), _969758), _969762)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969756), _969760), _969764))))], (51269 ^ _774244) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (146 ^ _774244) ^ [_776281, _776283, _776285, _776287, _776289, _776291] : [-(c_Nitpick_Oless__eq__frac(_776289, _776285, _776281)), c_Nitpick_Oless__eq__frac(_776291, _776287, _776283), _776291 = _776289, _776287 = _776285, _776283 = _776281], (5995 ^ _774244) ^ [_870256, _870258, _870260, _870262, _870264, _870266] : [c_Com_Ocom_OCond(_870256, _870258, _870260) = c_Com_Ocom_OCond(_870262, _870264, _870266), 5998 ^ _774244 : [(6003 ^ _774244) ^ [] : [-(_870260 = _870266)], (6001 ^ _774244) ^ [] : [-(_870258 = _870264)], (5999 ^ _774244) ^ [] : [-(_870256 = _870262)]]], (5868 ^ _774244) ^ [_868054, _868056, _868058, _868060] : [c_Natural_Oevalc(c_Com_Ocom_OSemi(_868054, _868056), _868058, _868060), 5872 ^ _774244 : [(5875 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_868056, 5871 ^ [_868054, _868056, _868058, _868060], _868060))], (5873 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_868054, _868058, 5871 ^ [_868054, _868056, _868058, _868060]))]]], (14289 ^ _774244) ^ [_1013565, _1013567] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1013565, _1013567) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1013565 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013567), 14292 ^ [_1013565, _1013567]))], (24925 ^ _774244) ^ [_1209445, _1209447] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209445), _1209447)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209447), _1209445))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209447), _1209445)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1209445), _1209447)))], (41827 ^ _774244) ^ [_1578846, _1578848] : [c_Wellfounded_Owf(_1578846, _1578848), -(c_Wellfounded_OwfP(_1578846, c_FunDef_Oin__rel(_1578846, _1578846, _1578848)))], (31081 ^ _774244) ^ [_1331759, _1331761, _1331763, _1331765, _1331767] : [hBOOL(hAPP(hAPP(c_member(_1331759), _1331761), hAPP(c_Set_Oimage(_1331763, _1331759, _1331765), _1331767))), 31085 ^ _774244 : [(31088 ^ _774244) ^ [] : [-(_1331761 = hAPP(_1331765, 31084 ^ [_1331759, _1331761, _1331763, _1331765, _1331767]))], (31086 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331763), 31084 ^ [_1331759, _1331761, _1331763, _1331765, _1331767]), _1331767)))]]], (27195 ^ _774244) ^ [_1253009, _1253011, _1253013, _1253015] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253009), _1253011)), 27198 ^ _774244 : [(27199 ^ _774244) ^ [_1253167] : [27201 ^ _774244 : [(27207 ^ _774244) ^ [] : [-(_1253167 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27203 ^ [_1253009, _1253011, _1253013, _1253015, _1253167]), 27200 ^ [_1253009, _1253011, _1253013, _1253015, _1253167]))], (27205 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27203 ^ [_1253009, _1253011, _1253013, _1253015, _1253167]), _1253013)))], (27202 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27200 ^ [_1253009, _1253011, _1253013, _1253015, _1253167]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1253011))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253009), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1253167), _1253015)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253009), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1253167), _1253011)), _1253015)))]]], (46966 ^ _774244) ^ [_1704741, _1704743] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1704741)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1704743)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1704741), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1704743)) = c_List_Olist_ONil(tc_Int_Oint))], (20023 ^ _774244) ^ [_1116937, _1116939, _1116941] : [class_Fields_Olinordered__field__inverse__zero(_1116937), 20026 ^ _774244 : [(20041 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116937), c_Groups_Ozero__class_Ozero(_1116937)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116937), _1116939), _1116941)))), 20042 ^ _774244 : [(20049 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116937), _1116939), c_Groups_Ozero__class_Ozero(_1116937))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116937), _1116941), c_Groups_Ozero__class_Ozero(_1116937)))], (20043 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116937), c_Groups_Ozero__class_Ozero(_1116937)), _1116939)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116937), c_Groups_Ozero__class_Ozero(_1116937)), _1116941))]]], (20027 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116937), c_Groups_Ozero__class_Ozero(_1116937)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116937), _1116939), _1116941))), 20032 ^ _774244 : [(20035 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116937), c_Groups_Ozero__class_Ozero(_1116937)), _1116941)))], (20033 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116937), c_Groups_Ozero__class_Ozero(_1116937)), _1116939)))]], 20036 ^ _774244 : [(20039 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116937), _1116941), c_Groups_Ozero__class_Ozero(_1116937))))], (20037 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116937), _1116939), c_Groups_Ozero__class_Ozero(_1116937))))]]]]], (50017 ^ _774244) ^ [_1775094, _1775096] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1775094, _1775096) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1775094), _1775096)))], (35901 ^ _774244) ^ [_1435939, _1435941, _1435943, _1435945, _1435947] : [class_Lattices_Osemilattice__inf(_1435939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435939), _1435941), _1435943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435939), _1435945), _1435947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435939), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1435939), _1435941), _1435945)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1435939), _1435943), _1435947))))], (2772 ^ _774244) ^ [_816256, _816258] : [_816258 = _816256, -(c_Nitpick_Ofrac(_816258) = c_Nitpick_Ofrac(_816256))], (22680 ^ _774244) ^ [_1165836, _1165838] : [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), _1165836), _1165838))), 22683 ^ _774244 : [(22690 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1165838), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 22693 ^ _774244 : [(22702 ^ _774244) ^ [] : [-(c_Nitpick_Onorm__frac(_1165836, _1165838) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1165836), _1165838)), 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), _1165836))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1165838)))), -(_1165836 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1165838 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22694 ^ _774244) ^ [] : [22695 ^ _774244 : [(22698 ^ _774244) ^ [] : [_1165838 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (22696 ^ _774244) ^ [] : [_1165836 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1165836, _1165838) = 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)))]]], (22684 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1165838), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1165836, _1165838) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1165836), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1165838)))]]], (31801 ^ _774244) ^ [_1348622, _1348624, _1348626, _1348628] : [hBOOL(hAPP(hAPP(c_member(_1348622), _1348624), _1348626)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348622, tc_Nat_Onat), _1348628), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1348622, tc_HOL_Obool)), _1348626), hAPP(hAPP(c_Set_Oinsert(_1348622), _1348624), c_Orderings_Obot__class_Obot(tc_fun(_1348622, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348622, tc_Nat_Onat), _1348628), _1348626)), hAPP(_1348628, _1348624)))], (19679 ^ _774244) ^ [_1110641, _1110643, _1110645] : [class_Rings_Olinordered__idom(_1110641), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110641), _1110643), c_Groups_Ozero__class_Ozero(_1110641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110641), hAPP(hAPP(c_Power_Opower__class_Opower(_1110641), _1110643), 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)))), _1110645)))), c_Groups_Ozero__class_Ozero(_1110641))))], (22987 ^ _774244) ^ [_1171854, _1171856, _1171858, _1171860, _1171862, _1171864] : [hAPP(_1171860, hAPP(c_Product__Type_Osnd(_1171858, _1171854), _1171862)) = hAPP(_1171864, hAPP(c_Product__Type_Osnd(_1171858, _1171854), _1171862)), -(hAPP(c_Product__Type_Oapsnd(_1171854, _1171856, _1171858, _1171860), _1171862) = hAPP(c_Product__Type_Oapsnd(_1171854, _1171856, _1171858, _1171864), _1171862))], (6496 ^ _774244) ^ [_878970, _878972] : [class_Groups_Omonoid__add(_878970), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_878970), c_Groups_Ozero__class_Ozero(_878970)), _878972) = _878972)], (5635 ^ _774244) ^ [_864028, _864030, _864032, _864034] : [c_Natural_Oevaln(c_Com_Ocom_OBODY(_864028), _864030, _864032, _864034), 5639 ^ _774244 : [(5642 ^ _774244) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _864028)), _864030, 5638 ^ [_864028, _864030, _864032, _864034], _864034))], (5640 ^ _774244) ^ [] : [-(_864032 = hAPP(c_Nat_OSuc, 5638 ^ [_864028, _864030, _864032, _864034]))]]], (29620 ^ _774244) ^ [_1301703, _1301705] : [29621 ^ _774244 : [(29624 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1301705), _1301703))], (29622 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1301703), _1301705)))]], -(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)))), _1301703, _1301705))], (21954 ^ _774244) ^ [_1151535, _1151537] : [c_Code__Numeral_OSuc__code__numeral(_1151535) = c_Code__Numeral_OSuc__code__numeral(_1151537), -(_1151535 = _1151537)], (46703 ^ _774244) ^ [_1699551, _1699553, _1699555, _1699557] : [class_Groups_Ocomm__monoid__add(_1699551), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1699551), _1699553), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1699555, _1699557))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1699551), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1699551), _1699553), c_List_Oupto(_1699555, _1699557))))], (35572 ^ _774244) ^ [_1428640, _1428642, _1428644, _1428646, _1428648, _1428650] : [c_Finite__Set_Ofolding__idem(_1428640, _1428642, _1428644, _1428646), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428640), _1428648)), hBOOL(hAPP(hAPP(c_member(_1428640), _1428650), _1428648)), -(hAPP(c_Fun_Ocomp(_1428642, _1428642, _1428642, hAPP(_1428646, _1428648)), hAPP(_1428644, _1428650)) = hAPP(_1428646, _1428648))], (35871 ^ _774244) ^ [_1435352, _1435354, _1435356, _1435358] : [hBOOL(hAPP(hAPP(c_member(_1435352), _1435354), _1435356)), hBOOL(hAPP(hAPP(c_member(_1435352), _1435354), _1435358)), -(hBOOL(hAPP(hAPP(c_member(_1435352), _1435354), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435352, tc_HOL_Obool)), _1435356), _1435358))))], (49240 ^ _774244) ^ [_1759260, _1759262, _1759264] : [-(c_List_Obutlast(_1759260, hAPP(hAPP(c_List_Oappend(_1759260), _1759262), hAPP(hAPP(c_List_Olist_OCons(_1759260), _1759264), c_List_Olist_ONil(_1759260)))) = _1759262)], (18173 ^ _774244) ^ [] : [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)], (26385 ^ _774244) ^ [_1235239, _1235241] : [class_Orderings_Oorder(_1235239), 26392 ^ _774244 : [(26395 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235239), hAPP(_1235241, 26390 ^ [_1235239, _1235241])), hAPP(_1235241, 26391 ^ [_1235239, _1235241])))], (26393 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 26390 ^ [_1235239, _1235241]), 26391 ^ [_1235239, _1235241])))]], -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1235239, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235241))], (6818 ^ _774244) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3748 ^ _774244) ^ [_832030, _832032, _832034, _832036] : [-(c_Predicate_OPowp(_832036, _832032) = c_Predicate_OPowp(_832034, _832030)), _832036 = _832034, _832032 = _832030], (22038 ^ _774244) ^ [_1152859, _1152861] : [hAPP(c_Code__Numeral_Oof__nat, _1152859) = hAPP(c_Code__Numeral_Oof__nat, _1152861), -(_1152859 = _1152861)], (27836 ^ _774244) ^ [_1265765, _1265767, _1265769] : [class_Lattices_Olattice(_1265765), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265765), _1265767), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265765), _1265767), _1265769)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265765), _1265767), _1265769))], (28900 ^ _774244) ^ [_1288321, _1288323, _1288325, _1288327, _1288329] : [-(hAPP(hAPP(c_Set_Oinsert(_1288321), _1288323), hAPP(hAPP(c_Set_Oinsert(_1288321), _1288325), c_Orderings_Obot__class_Obot(tc_fun(_1288321, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1288321), _1288327), hAPP(hAPP(c_Set_Oinsert(_1288321), _1288329), c_Orderings_Obot__class_Obot(tc_fun(_1288321, tc_HOL_Obool))))), 28901 ^ _774244 : [(28908 ^ _774244) ^ [] : [_1288323 = _1288329, _1288325 = _1288327], (28902 ^ _774244) ^ [] : [_1288323 = _1288327, _1288325 = _1288329]]], (17019 ^ _774244) ^ [_1065332, _1065334] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1065332), _1065334) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1065334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1065332 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37591 ^ _774244) ^ [_1474481, _1474483, _1474485, _1474487, _1474489] : [class_Groups_Ocomm__monoid__add(_1474481), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474483), _1474485)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474483), _1474487)), 37605 ^ _774244 : [(37608 ^ _774244) ^ [] : [hAPP(_1474489, 37604 ^ [_1474481, _1474483, _1474485, _1474487, _1474489]) = c_Groups_Ozero__class_Ozero(_1474481)], (37606 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1474483), 37604 ^ [_1474481, _1474483, _1474485, _1474487, _1474489]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474483, tc_HOL_Obool)), _1474485), _1474487))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474483, _1474481), _1474489), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474483, tc_HOL_Obool)), _1474485), _1474487)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1474481), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474483, _1474481), _1474489), _1474485)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474483, _1474481), _1474489), _1474487)))], (28543 ^ _774244) ^ [_1279381, _1279383, _1279385, _1279387, _1279389] : [class_Complete__Lattice_Ocomplete__lattice(_1279381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1279383, tc_HOL_Obool)), _1279385), _1279387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279381), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279383, _1279381), _1279385), _1279389)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279383, _1279381), _1279387), _1279389))))], (43283 ^ _774244) ^ [_1611976, _1611978, _1611980, _1611982] : [-(c_Wellfounded_Oacyclic(_1611976, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1611976, _1611976)), hAPP(hAPP(c_Product__Type_OPair(_1611976, _1611976), _1611978), _1611980)), _1611982))), c_Wellfounded_Oacyclic(_1611976, _1611982), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611976, _1611976)), hAPP(hAPP(c_Product__Type_OPair(_1611976, _1611976), _1611980), _1611978)), c_Transitive__Closure_Ortrancl(_1611976, _1611982))))], (13052 ^ _774244) ^ [_990970, _990972, _990974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990970)), _990970 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _990972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _990970), _990974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _990972), _990970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _990974)))], (29414 ^ _774244) ^ [_1297664, _1297666, _1297668, _1297670, _1297672] : [_1297664 = c_Orderings_Obot__class_Obot(tc_fun(_1297666, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297668, tc_HOL_Obool)), _1297670), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297666, tc_fun(_1297668, tc_HOL_Obool)), _1297664), _1297672)) = _1297670)], (45795 ^ _774244) ^ [_1674706, _1674708, _1674710, _1674712] : [-(hBOOL(hAPP(c_List_Odistinct(_1674706), hAPP(hAPP(c_List_Omap(_1674708, _1674706), _1674710), _1674712)))), hBOOL(hAPP(c_List_Odistinct(_1674708), _1674712)), c_Fun_Oinj__on(_1674708, _1674706, _1674710, hAPP(c_List_Oset(_1674708), _1674712))], (3948 ^ _774244) ^ [_835090, _835092] : [_835092 = _835090, -(c_Relation_OId(_835092) = c_Relation_OId(_835090))], (25039 ^ _774244) ^ [_1211298, _1211300, _1211302] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211298), _1211300)), 25050 ^ _774244 : [(25053 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211302), _1211298))], (25051 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211298), _1211302)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211300), _1211302)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211302), _1211300)))], (32524 ^ _774244) ^ [_1363794, _1363796] : [class_Int_Onumber__ring(_1363794), -(hBOOL(hAPP(hAPP(c_member(_1363794), hAPP(c_Int_Onumber__class_Onumber__of(_1363794), _1363796)), c_Int_Oring__1__class_OInts(_1363794))))], (45529 ^ _774244) ^ [_1668186, _1668188, _1668190, _1668192, _1668194] : [c_Fun_Oinj__on(_1668186, _1668188, _1668190, c_Orderings_Otop__class_Otop(tc_fun(_1668186, tc_HOL_Obool))), 45532 ^ _774244 : [(45539 ^ _774244) ^ [] : [_1668192 = _1668194, -(hAPP(hAPP(c_List_Omap(_1668186, _1668188), _1668190), _1668192) = hAPP(hAPP(c_List_Omap(_1668186, _1668188), _1668190), _1668194))], (45533 ^ _774244) ^ [] : [hAPP(hAPP(c_List_Omap(_1668186, _1668188), _1668190), _1668192) = hAPP(hAPP(c_List_Omap(_1668186, _1668188), _1668190), _1668194), -(_1668192 = _1668194)]]], (24529 ^ _774244) ^ [_1201036, _1201038, _1201040, _1201042] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1201036, _1201038, _1201040, _1201042) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1201036, _1201038), _1201040), _1201042)))], (5482 ^ _774244) ^ [_858895, _858897] : [_858897 = _858895, -(c_List_Oset(_858897) = c_List_Oset(_858895))], (29756 ^ _774244) ^ [_1304213] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1304213), c_Orderings_Obot__class_Obot(tc_fun(_1304213, tc_HOL_Obool)))))], (31533 ^ _774244) ^ [_1341797, _1341799, _1341801, _1341803] : [hBOOL(hAPP(hAPP(c_member(_1341799), _1341803), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1341797, tc_fun(_1341799, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1341797, tc_HOL_Obool))), _1341801))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1341797, tc_fun(_1341799, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1341797, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1341799, tc_HOL_Obool), tc_fun(_1341799, tc_HOL_Obool), _1341797), hAPP(c_COMBC(_1341799, tc_fun(_1341799, tc_HOL_Obool), tc_HOL_Obool), c_member(_1341799))), _1341801)), _1341803)))], (20133 ^ _774244) ^ [_1118882, _1118884, _1118886] : [class_Fields_Olinordered__field(_1118882), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118882), _1118884), c_Groups_Ozero__class_Ozero(_1118882))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118882), _1118886), c_Groups_Ozero__class_Ozero(_1118882))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118882), c_Groups_Ozero__class_Ozero(_1118882)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118882), _1118884), _1118886))))], (46304 ^ _774244) ^ [_1687241, _1687243, _1687245] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1687241), _1687243)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1687241)), hAPP(c_Set_OCollect(tc_List_Olist(_1687241)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1687241), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1687241)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687241), tc_fun(_1687241, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1687241, tc_HOL_Obool), tc_fun(tc_fun(_1687241, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1687241)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1687241, tc_HOL_Obool))), c_List_Oset(_1687241))), _1687243))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687241), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1687241)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1687241)))), _1687245))))))], (15634 ^ _774244) ^ [_1038220, _1038222, _1038224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1038220), _1038222)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1038222), _1038220)), _1038224) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038222), _1038224)), _1038220))], (5837 ^ _774244) ^ [_867529, _867531, _867533, _867535] : [c_Natural_Oevalc(c_Com_Ocom_OSemi(_867529, _867531), _867533, _867535), 5841 ^ _774244 : [(5844 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_867531, 5840 ^ [_867529, _867531, _867533, _867535], _867535))], (5842 ^ _774244) ^ [] : [-(c_Natural_Oevalc(_867529, _867533, 5840 ^ [_867529, _867531, _867533, _867535]))]]], (15912 ^ _774244) ^ [_1044630, _1044632] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044630, _1044632) = 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), _1044630), _1044632) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044632), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044630, _1044632)))], (8130 ^ _774244) ^ [_907342, _907344] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907342), _907344) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _907344), _907342))], (6484 ^ _774244) ^ [_878726, _878728, _878730] : [_878728 = _878730, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878726), _878728) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _878726), _878730))], (18653 ^ _774244) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (7865 ^ _774244) ^ [_902792, _902794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _902792), _902794)), 7869 ^ _774244 : [(7872 ^ _774244) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _902792), 7868 ^ [_902792, _902794]) = _902794)], (7870 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7868 ^ [_902792, _902794])))]]], (25719 ^ _774244) ^ [_1223115] : [_1223115 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223115), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (4770 ^ _774244) ^ [_847951, _847953, _847955, _847957] : [-(c_List_Oupto(_847957, _847953) = c_List_Oupto(_847955, _847951)), _847957 = _847955, _847953 = _847951], (25999 ^ _774244) ^ [_1228442, _1228444, _1228446, _1228448] : [class_Orderings_Oorder(_1228442), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1228442, 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)))), _1228444), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228442), hAPP(_1228444, _1228446)), hAPP(_1228444, _1228448)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228446), _1228448)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228448), _1228446)))], (29947 ^ _774244) ^ [_1307763, _1307765, _1307767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307763, tc_HOL_Obool)), _1307765), _1307767)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307763), _1307767)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307763), _1307765)))], (31355 ^ _774244) ^ [_1337598, _1337600] : [c_Nat__Transfer_Ois__nat(_1337598), c_Nat__Transfer_Onat__set(_1337600), 31362 ^ _774244 : [(31369 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1337598)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1337600))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1337598), _1337600)))], (31363 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1337598), _1337600)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1337598)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1337600))))]]], (36535 ^ _774244) ^ [_1449538, _1449540, _1449542, _1449544, _1449546] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1449538, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1449540, _1449538, _1449542), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449540, tc_HOL_Obool)), _1449544), _1449546))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449538, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1449540, _1449538, _1449542), _1449544)), hAPP(c_Set_Oimage(_1449540, _1449538, _1449542), _1449546)))))], (9630 ^ _774244) ^ [_932858, _932860, _932862, _932864, _932866, _932868] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_932858), -(_932860 = c_Groups_Ozero__class_Ozero(_932858)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932858), _932862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932858), _932860), _932866)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932858), _932864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932858), _932860), _932868)), _932862 = _932864, -(_932866 = _932868)], (1394 ^ _774244) ^ [_794393, _794395] : [-(class_Rings_Olinordered__semiring__strict(_794393)), _794395 = _794393, class_Rings_Olinordered__semiring__strict(_794395)], (43191 ^ _774244) ^ [_1609768, _1609770, _1609772, _1609774, _1609776] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609768, _1609768)), hAPP(hAPP(c_Product__Type_OPair(_1609768, _1609768), _1609770), _1609772)), c_Transitive__Closure_Ortrancl(_1609768, _1609774))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1609768, _1609768)), hAPP(hAPP(c_Product__Type_OPair(_1609768, _1609768), _1609772), _1609776)), _1609774)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609768, _1609768)), hAPP(hAPP(c_Product__Type_OPair(_1609768, _1609768), _1609770), _1609776)), c_Transitive__Closure_Otrancl(_1609768, _1609774))))], (25495 ^ _774244) ^ [_1218983] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218983), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1218983 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31069 ^ _774244) ^ [_1331519, _1331521] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1331519), _1331521)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1331519)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1331521))))], (43811 ^ _774244) ^ [_1626518, _1626520, _1626522, _1626524, _1626526] : [-(_1626518 = c_Orderings_Obot__class_Obot(tc_fun(_1626520, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626520, tc_fun(_1626522, tc_HOL_Obool)), _1626518), hAPP(hAPP(c_COMBC(_1626520, tc_fun(_1626522, tc_HOL_Obool), tc_fun(_1626522, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1626522, tc_HOL_Obool), tc_fun(tc_fun(_1626522, tc_HOL_Obool), tc_fun(_1626522, tc_HOL_Obool)), _1626520), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1626522, tc_HOL_Obool))), _1626524)), _1626526)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1626522, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626520, tc_fun(_1626522, tc_HOL_Obool)), _1626518), _1626524)), _1626526))], (38660 ^ _774244) ^ [_1496385, _1496387] : [-(c_Fun_Oinj__on(_1496385, tc_Option_Ooption(_1496385), c_Option_Ooption_OSome(_1496385), _1496387))], (46565 ^ _774244) ^ [_1695400, _1695402, _1695404] : [-(c_List_Oset__Cons(_1695400, _1695402, _1695404) = hAPP(c_Set_OCollect(tc_List_Olist(_1695400)), hAPP(hAPP(c_COMBB(tc_fun(_1695400, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1695400)), c_HOL_OEx(_1695400)), hAPP(hAPP(c_COMBB(tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool)), tc_fun(_1695400, tc_HOL_Obool), tc_List_Olist(_1695400)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool), tc_HOL_Obool, _1695400), c_HOL_OEx(tc_List_Olist(_1695400)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695400), tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool)), tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1695400, tc_fun(tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool))), tc_fun(tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool)), tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool))), tc_List_Olist(_1695400)), c_COMBS(_1695400, tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1695400, tc_fun(tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool))), tc_List_Olist(_1695400)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1695400), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool)), _1695400), c_COMBS(tc_List_Olist(_1695400), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool)), tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1695400)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1695400), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1695400), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1695400)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695400), tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_List_Olist(_1695400))), tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1695400), tc_List_Olist(_1695400)), tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool)), tc_fun(tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_List_Olist(_1695400))), tc_fun(_1695400, tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool))), tc_List_Olist(_1695400)), c_COMBB(tc_fun(tc_List_Olist(_1695400), tc_List_Olist(_1695400)), tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool), _1695400)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1695400), tc_List_Olist(_1695400)), tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool)), tc_List_Olist(_1695400)), c_COMBB(tc_List_Olist(_1695400), tc_HOL_Obool, tc_List_Olist(_1695400))), c_fequal))), c_List_Olist_OCons(_1695400)))))), hAPP(hAPP(c_COMBC(_1695400, tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool)), _1695400), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1695400))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1695400), c_fconj), hAPP(hAPP(c_COMBC(_1695400, tc_fun(_1695400, tc_HOL_Obool), tc_HOL_Obool), c_member(_1695400)), _1695402)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695400), tc_fun(tc_List_Olist(_1695400), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1695400))), _1695404)))))))], (28982 ^ _774244) ^ [_1289972, _1289974] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289972, tc_HOL_Obool)), _1289974), c_Orderings_Obot__class_Obot(tc_fun(_1289972, tc_HOL_Obool))) = _1289974)], (47291 ^ _774244) ^ [_1713185, _1713187, _1713189, _1713191, _1713193, _1713195] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1713185, _1713187), hAPP(hAPP(c_List_Ozip(_1713185, _1713187), _1713189), _1713191)), _1713193), _1713195) = hAPP(hAPP(c_List_Ozip(_1713185, _1713187), hAPP(hAPP(c_List_Olist__update(_1713185, _1713189), _1713193), hAPP(c_Product__Type_Ofst(_1713185, _1713187), _1713195))), hAPP(hAPP(c_List_Olist__update(_1713187, _1713191), _1713193), hAPP(c_Product__Type_Osnd(_1713185, _1713187), _1713195))))], (6834 ^ _774244) ^ [_884967, _884969] : [_884969 = c_Option_Ooption_ONone(_884967), -(c_Option_Ois__none(_884967, _884969))], (6358 ^ _774244) ^ [_876571, _876573] : [-(hAPP(c_Option_Othe(_876571), hAPP(c_Option_Ooption_OSome(_876571), _876573)) = _876573)], (38027 ^ _774244) ^ [_1483293, _1483295, _1483297, _1483299, _1483301] : [c_Fun_Oinj__on(_1483293, _1483295, _1483297, _1483299), -(c_Fun_Oinj__on(_1483293, _1483295, _1483297, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1483293, tc_HOL_Obool)), _1483299), _1483301)))], (19869 ^ _774244) ^ [_1114398, _1114400, _1114402] : [class_Fields_Olinordered__field__inverse__zero(_1114398), -(hAPP(c_Groups_Oabs__class_Oabs(_1114398), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114398), _1114400), _1114402)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114398), hAPP(c_Groups_Oabs__class_Oabs(_1114398), _1114400)), hAPP(c_Groups_Oabs__class_Oabs(_1114398), _1114402)))], (42834 ^ _774244) ^ [_1601301, _1601303, _1601305, _1601307, _1601309] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601301, _1601301)), hAPP(hAPP(c_Product__Type_OPair(_1601301, _1601301), _1601303), _1601305)), c_Transitive__Closure_Otrancl(_1601301, _1601307))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1601301, _1601301)), hAPP(hAPP(c_Product__Type_OPair(_1601301, _1601301), _1601305), _1601309)), c_Transitive__Closure_Otrancl(_1601301, _1601307))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601301, _1601301)), hAPP(hAPP(c_Product__Type_OPair(_1601301, _1601301), _1601303), _1601309)), c_Transitive__Closure_Otrancl(_1601301, _1601307))))], (34541 ^ _774244) ^ [_1403540, _1403542, _1403544, _1403546] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1403540), _1403542)), 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)), _1403540), _1403544)), 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)), _1403542), _1403546)), 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)), _1403542), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1403544), _1403546))), c_FunDef_Omin__weak)))], (42708 ^ _774244) ^ [_1599072, _1599074, _1599076, _1599078] : [class_Complete__Lattice_Ocomplete__lattice(_1599072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599074), _1599076)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1599074, _1599072), _1599076), _1599078) = hAPP(hAPP(c_Finite__Set_Ofold(_1599074, _1599072, hAPP(hAPP(c_COMBB(_1599072, tc_fun(_1599072, _1599072), _1599074), c_Lattices_Osemilattice__sup__class_Osup(_1599072)), _1599078)), c_Orderings_Obot__class_Obot(_1599072)), _1599076))], (29286 ^ _774244) ^ [_1295452, _1295454, _1295456] : [class_Orderings_Oorder(_1295452), 29289 ^ _774244 : [(29296 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295452), _1295454), _1295456))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1295452, _1295454, _1295456) = c_Orderings_Obot__class_Obot(tc_fun(_1295452, tc_HOL_Obool)))], (29290 ^ _774244) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1295452, _1295454, _1295456) = c_Orderings_Obot__class_Obot(tc_fun(_1295452, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295452), _1295454), _1295456))]]], (48865 ^ _774244) ^ [_1751263, _1751265, _1751267] : [-(c_List_Olist_Olist__size(_1751263, _1751265, _1751267) = 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(_1751263, tc_Nat_Onat), _1751265), _1751267))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751263)), _1751267)))], (36463 ^ _774244) ^ [_1448030, _1448032] : [class_Lattices_Oboolean__algebra(_1448030), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1448030), _1448032), hAPP(c_Groups_Ouminus__class_Ouminus(_1448030), _1448032)) = c_Orderings_Obot__class_Obot(_1448030))], (14283 ^ _774244) ^ [_1013510] : [-(_1013510 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1013510), _1013510) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (2932 ^ _774244) ^ [_819026, _819028, _819030, _819032, _819034, _819036, _819038, _819040] : [-(c_New__Random__Sequence_Opos__empty(_819040, _819036, _819032, _819028) = c_New__Random__Sequence_Opos__empty(_819038, _819034, _819030, _819026)), _819040 = _819038, _819036 = _819034, _819032 = _819030, _819028 = _819026], (27676 ^ _774244) ^ [_1262193, _1262195, _1262197, _1262199, _1262201] : [-(hAPP(c_Set_Oimage(_1262193, _1262195, _1262197), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262193, tc_HOL_Obool)), _1262199), _1262201)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262195, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1262193, _1262195, _1262197), _1262199)), hAPP(c_Set_Oimage(_1262193, _1262195, _1262197), _1262201)))], (47174 ^ _774244) ^ [_1710137, _1710139, _1710141] : [-(hBOOL(hAPP(hAPP(c_member(_1710137), _1710139), hAPP(c_List_Oset(_1710137), _1710141)))), 47175 ^ _774244 : [(47176 ^ _774244) ^ [_1710211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1710211), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710137)), _1710141))), hAPP(hAPP(c_List_Onth(_1710137), _1710141), _1710211) = _1710139]]], (45629 ^ _774244) ^ [_1670732, _1670734, _1670736, _1670738, _1670740, _1670742] : [-(hAPP(hAPP(c_Option_Omap(_1670732, _1670734), _1670736), hAPP(hAPP(c_Option_Omap(_1670738, _1670732), _1670740), _1670742)) = hAPP(hAPP(c_Option_Omap(_1670738, _1670734), hAPP(c_Fun_Ocomp(_1670732, _1670734, _1670738, _1670736), _1670740)), _1670742))], (15336 ^ _774244) ^ [_1032469, _1032471, _1032473] : [-(hBOOL(hAPP(_1032469, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1032471), _1032473))))), 15339 ^ _774244 : [(15342 ^ _774244) ^ [] : [hBOOL(hAPP(_1032469, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1032471)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1032473))))], (15340 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032473), _1032471)))]], 15343 ^ _774244 : [(15346 ^ _774244) ^ [] : [hBOOL(hAPP(_1032469, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15344 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1032471), _1032473)))]]], (10181 ^ _774244) ^ [_942005, _942007, _942009, _942011] : [class_Orderings_Oorder(_942005), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942005), _942007), _942009)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942005), _942011), _942007)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942005), _942011), _942009)))], (31295 ^ _774244) ^ [_1336386, _1336388, _1336390, _1336392, _1336394] : [_1336386 = hAPP(_1336388, _1336390), -(hBOOL(hAPP(hAPP(c_member(_1336392), _1336386), hAPP(c_Set_Oimage(_1336394, _1336392, _1336388), c_Orderings_Otop__class_Otop(tc_fun(_1336394, tc_HOL_Obool))))))], (26273 ^ _774244) ^ [_1233309] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1233309), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1233309) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (44550 ^ _774244) ^ [_1645036, _1645038, _1645040] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1645036, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1645036, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1645036, tc_HOL_Obool), _1645038)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1645036, tc_HOL_Obool), _1645040))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1645036, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1645036, tc_HOL_Obool), tc_HOL_Obool)), _1645038), _1645040)))))], (9100 ^ _774244) ^ [_923129, _923131] : [class_Rings_Omult__zero(_923129), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923129), _923131), c_Groups_Ozero__class_Ozero(_923129)) = c_Groups_Ozero__class_Ozero(_923129))], (36499 ^ _774244) ^ [_1448870, _1448872, _1448874, _1448876] : [-(hBOOL(hAPP(hAPP(c_member(_1448870), _1448872), _1448874))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448870, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1448870), _1448872), _1448876)), _1448874) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448870, tc_HOL_Obool)), _1448876), _1448874))], (18517 ^ _774244) ^ [_1090370] : [c_Int_OBit1(_1090370) = c_Int_OMin, -(_1090370 = c_Int_OMin)], (37387 ^ _774244) ^ [_1468569, _1468571, _1468573, _1468575, _1468577, _1468579, _1468581, _1468583, _1468585, _1468587, _1468589] : [c_Equiv__Relations_Oequiv(_1468569, _1468571, _1468573), c_Equiv__Relations_Oequiv(_1468575, _1468577, _1468579), c_Equiv__Relations_Ocongruent2(_1468569, _1468575, tc_fun(_1468581, tc_HOL_Obool), _1468573, _1468579, _1468583), hBOOL(hAPP(hAPP(c_member(tc_fun(_1468569, tc_HOL_Obool)), _1468585), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1468569), _1468571), _1468573))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1468575, tc_HOL_Obool)), _1468587), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1468575), _1468577), _1468579))), 37409 ^ _774244 : [(37415 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1468581, tc_HOL_Obool)), hAPP(hAPP(_1468583, 37408 ^ [_1468569, _1468571, _1468573, _1468575, _1468577, _1468579, _1468581, _1468583, _1468585, _1468587, _1468589]), 37411 ^ [_1468569, _1468571, _1468573, _1468575, _1468577, _1468579, _1468581, _1468583, _1468585, _1468587, _1468589])), _1468589))], (37413 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1468575), 37411 ^ [_1468569, _1468571, _1468573, _1468575, _1468577, _1468579, _1468581, _1468583, _1468585, _1468587, _1468589]), _1468577)))], (37410 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1468569), 37408 ^ [_1468569, _1468571, _1468573, _1468575, _1468577, _1468579, _1468581, _1468583, _1468585, _1468587, _1468589]), _1468571)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1468581, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1468569, tc_fun(_1468581, tc_HOL_Obool)), _1468585), hAPP(hAPP(c_COMBB(tc_fun(_1468575, tc_fun(_1468581, tc_HOL_Obool)), tc_fun(_1468581, tc_HOL_Obool), _1468569), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1468575, tc_fun(_1468581, tc_HOL_Obool)), _1468587)), _1468583))), _1468589)))], (6246 ^ _774244) ^ [_874475] : [6247 ^ _774244 : [(6248 ^ _774244) ^ [_874522] : [hAPP(c_Com_Obody, _874475) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _874522)]], -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OBODY(_874475))))], (50667 ^ _774244) ^ [_1790738] : [-(c_List_Oembed__list(_1790738) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1790738))], (39924 ^ _774244) ^ [_1527849, _1527851, _1527853, _1527855, _1527857, _1527859, _1527861, _1527863] : [-(hAPP(c_Product__Type_Omap__pair(_1527849, _1527851, _1527853, _1527855, _1527857, _1527859), hAPP(hAPP(c_Product__Type_OPair(_1527849, _1527853), _1527861), _1527863)) = hAPP(hAPP(c_Product__Type_OPair(_1527851, _1527855), hAPP(_1527857, _1527861)), hAPP(_1527859, _1527863)))], (36505 ^ _774244) ^ [_1448943, _1448945, _1448947, _1448949] : [-(hBOOL(hAPP(hAPP(c_member(_1448943), _1448945), _1448947))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448943, tc_HOL_Obool)), _1448947), hAPP(hAPP(c_Set_Oinsert(_1448943), _1448945), _1448949)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448943, tc_HOL_Obool)), _1448947), _1448949))], (10870 ^ _774244) ^ [_952917, _952919, _952921, _952923] : [class_Groups_Oordered__ab__semigroup__add(_952917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952917), _952919), _952921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952917), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952917), _952919), _952923)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952917), _952921), _952923))))], (2264 ^ _774244) ^ [_808370, _808372, _808374, _808376] : [-(c_SMT_Oz3mod(_808376, _808372) = c_SMT_Oz3mod(_808374, _808370)), _808376 = _808374, _808372 = _808370], (11166 ^ _774244) ^ [_957785, _957787] : [11167 ^ _774244 : [(11170 ^ _774244) ^ [] : [_957785 = _957787], (11168 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957785), _957787))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957785), _957787)))], (47760 ^ _774244) ^ [_1723795, _1723797, _1723799, _1723801] : [-(hBOOL(hAPP(hAPP(c_member(_1723795), _1723797), hAPP(c_List_Oset(_1723795), _1723799)))), -(c_List_Oremove1(_1723795, _1723797, hAPP(hAPP(c_List_Oappend(_1723795), _1723799), _1723801)) = hAPP(hAPP(c_List_Oappend(_1723795), _1723799), c_List_Oremove1(_1723795, _1723797, _1723801)))], (22967 ^ _774244) ^ [_1171370, _1171372, _1171374, _1171376, _1171378, _1171380, _1171382] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1171370, _1171372, tc_fun(_1171374, tc_HOL_Obool)), _1171376), hAPP(hAPP(c_Product__Type_OPair(_1171370, _1171372), _1171378), _1171380)), _1171382)), -(hBOOL(hAPP(hAPP(hAPP(_1171376, _1171378), _1171380), _1171382)))], (1574 ^ _774244) ^ [_796643, _796645] : [-(class_Rings_Ocomm__semiring(_796643)), _796645 = _796643, class_Rings_Ocomm__semiring(_796645)], (24115 ^ _774244) ^ [_1193052, _1193054, _1193056, _1193058] : [class_Orderings_Olinorder(_1193052), 24118 ^ _774244 : [(24119 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193052), _1193054), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1193052), _1193056), _1193058))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193052), _1193054), _1193056))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193052), _1193054), _1193058)))], (24129 ^ _774244) ^ [] : [24130 ^ _774244 : [(24133 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193052), _1193054), _1193058))], (24131 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193052), _1193054), _1193056))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193052), _1193054), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1193052), _1193056), _1193058))))]]], (50941 ^ _774244) ^ [_1796290, _1796292] : [class_Lattices_Obounded__lattice(_1796290), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1796292, _1796290)))], (11943 ^ _774244) ^ [_971699, _971701] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971699), _971701) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _971699 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _971701 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38011 ^ _774244) ^ [_1482872, _1482874, _1482876, _1482878] : [38013 ^ _774244 : [(38017 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482872), 38015 ^ [_1482872, _1482874, _1482876, _1482878]), _1482878)))], (38019 ^ _774244) ^ [] : [-(hAPP(_1482876, 38012 ^ [_1482872, _1482874, _1482876, _1482878]) = hAPP(_1482876, 38015 ^ [_1482872, _1482874, _1482876, _1482878]))], (38021 ^ _774244) ^ [] : [38012 ^ [_1482872, _1482874, _1482876, _1482878] = 38015 ^ [_1482872, _1482874, _1482876, _1482878]], (38014 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482872), 38012 ^ [_1482872, _1482874, _1482876, _1482878]), _1482878)))]], -(c_Fun_Oinj__on(_1482872, _1482874, _1482876, _1482878))], (20833 ^ _774244) ^ [_1131160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131160)), -(c_Nat__Transfer_Ois__nat(_1131160))], (49565 ^ _774244) ^ [_1767202, _1767204, _1767206, _1767208] : [-(c_List_Oupt(_1767202, _1767204) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1767206), _1767208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1767202), _1767204)), _1767202 = _1767206, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1767202), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1767204) = _1767208], (29584 ^ _774244) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (14480 ^ _774244) ^ [_1016809, _1016811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1016809), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14483 ^ _774244 : [(14490 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1016811), 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), _1016811), _1016809))))], (14484 ^ _774244) ^ [] : [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), _1016811), _1016809))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1016811), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (42072 ^ _774244) ^ [_1585438, _1585440, _1585442, _1585444] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1585438), _1585440)), 42078 ^ _774244 : [(42081 ^ _774244) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1585442), hAPP(_1585444, 42077 ^ [_1585438, _1585440, _1585442, _1585444])))], (42079 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1585438), 42077 ^ [_1585438, _1585440, _1585442, _1585444]), _1585440)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1585442), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1585438, tc_fun(_1585442, tc_HOL_Obool)), _1585440), _1585444))))], (6888 ^ _774244) ^ [_885724, _885726, _885728, _885730] : [c_Com_Ocom_OWhile(_885724, _885726) = c_Com_Ocom_OWhile(_885728, _885730), 6891 ^ _774244 : [(6894 ^ _774244) ^ [] : [-(_885726 = _885730)], (6892 ^ _774244) ^ [] : [-(_885724 = _885728)]]], (10446 ^ _774244) ^ [_946348, _946350] : [-(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), _946348), _946350)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _946348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _946350))], (9544 ^ _774244) ^ [_931345, _931347, _931349, _931351] : [class_Rings_Olinordered__ring__strict(_931345), 9547 ^ _774244 : [(9562 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931345), _931347), _931349)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931345), _931347), _931351)))), 9563 ^ _774244 : [(9570 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931345), _931347), c_Groups_Ozero__class_Ozero(_931345))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931345), _931351), _931349))], (9564 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931345), c_Groups_Ozero__class_Ozero(_931345)), _931347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931345), _931349), _931351))]]], (9548 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931345), _931347), _931349)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931345), _931347), _931351))), 9553 ^ _774244 : [(9556 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931345), _931349), _931351)))], (9554 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931345), c_Groups_Ozero__class_Ozero(_931345)), _931347)))]], 9557 ^ _774244 : [(9560 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931345), _931351), _931349)))], (9558 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931345), _931347), c_Groups_Ozero__class_Ozero(_931345))))]]]]], (43135 ^ _774244) ^ [_1608505, _1608507] : [-(hAPP(c_Relation_ODomain(_1608505, _1608505), c_Transitive__Closure_Ortrancl(_1608505, _1608507)) = c_Orderings_Otop__class_Otop(tc_fun(_1608505, tc_HOL_Obool)))], (1594 ^ _774244) ^ [_796893, _796895] : [-(class_Rings_Ozero__neq__one(_796893)), _796895 = _796893, class_Rings_Ozero__neq__one(_796895)], (25567 ^ _774244) ^ [_1220117, _1220119, _1220121] : [class_Divides_Osemiring__div(_1220117), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1220117), _1220119), _1220121)), -(c_Divides_Odiv__class_Omod(_1220117, _1220121, _1220119) = c_Groups_Ozero__class_Ozero(_1220117))], (46134 ^ _774244) ^ [_1682852, _1682854, _1682856, _1682858, _1682860] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682852)), _1682854) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682856)), _1682858), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682852)), _1682860) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682856)), _1682858), hBOOL(hAPP(c_List_Odistinct(_1682856), _1682858)), c_Map_Omap__of(_1682856, _1682852, hAPP(hAPP(c_List_Ozip(_1682856, _1682852), _1682858), _1682854)) = c_Map_Omap__of(_1682856, _1682852, hAPP(hAPP(c_List_Ozip(_1682856, _1682852), _1682858), _1682860)), -(_1682854 = _1682860)], (38948 ^ _774244) ^ [_1502796, _1502798, _1502800, _1502802] : [-(hAPP(c_Set_Ovimage(_1502796, _1502798, _1502800), _1502802) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1502798, tc_fun(_1502796, tc_HOL_Obool)), _1502802), hAPP(hAPP(c_COMBB(tc_fun(_1502798, tc_HOL_Obool), tc_fun(_1502796, tc_HOL_Obool), _1502798), c_Set_Ovimage(_1502796, _1502798, _1502800)), hAPP(hAPP(c_COMBC(_1502798, tc_fun(_1502798, tc_HOL_Obool), tc_fun(_1502798, tc_HOL_Obool)), c_Set_Oinsert(_1502798)), c_Orderings_Obot__class_Obot(tc_fun(_1502798, tc_HOL_Obool))))))], (7701 ^ _774244) ^ [_899839, _899841] : [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), _899839), _899841))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _899839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _899841)))], (46214 ^ _774244) ^ [_1684510, _1684512] : [-(c_List_Olenlex(_1684510, _1684512) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1684510), tc_List_Olist(_1684510))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1684510), tc_List_Olist(_1684510), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1684510), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1684510), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool)), tc_List_Olist(_1684510)), c_COMBS(tc_List_Olist(_1684510), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool), tc_fun(tc_List_Olist(_1684510), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1684510)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1684510)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1684510), tc_fun(tc_List_Olist(_1684510), tc_Nat_Onat), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1684510), tc_Nat_Onat), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool)), tc_List_Olist(_1684510)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1684510))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1684510)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1684510))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1684510)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1684510), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1684510), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool)), tc_List_Olist(_1684510)), c_COMBS(tc_List_Olist(_1684510), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool), tc_fun(tc_List_Olist(_1684510), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1684510)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1684510)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1684510), tc_fun(tc_List_Olist(_1684510), tc_Nat_Onat), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1684510), tc_Nat_Onat), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool)), tc_List_Olist(_1684510)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1684510))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1684510)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1684510))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1684510)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1684510), tc_fun(tc_prod(tc_List_Olist(_1684510), tc_List_Olist(_1684510)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1684510), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1684510), tc_List_Olist(_1684510)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1684510), tc_List_Olist(_1684510)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1684510), tc_HOL_Obool)), tc_List_Olist(_1684510)), c_COMBC(tc_List_Olist(_1684510), tc_fun(tc_prod(tc_List_Olist(_1684510), tc_List_Olist(_1684510)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1684510), tc_prod(tc_List_Olist(_1684510), tc_List_Olist(_1684510))), tc_fun(tc_List_Olist(_1684510), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1684510), tc_List_Olist(_1684510)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1684510)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1684510), tc_List_Olist(_1684510)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1684510), tc_List_Olist(_1684510)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1684510)), c_member(tc_prod(tc_List_Olist(_1684510), tc_List_Olist(_1684510))))), c_Product__Type_OPair(tc_List_Olist(_1684510), tc_List_Olist(_1684510))))), c_List_Olex(_1684510, _1684512)))))))], (10620 ^ _774244) ^ [_949059, _949061, _949063] : [class_Orderings_Olinorder(_949059), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949059), _949061), _949063))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949059), _949063), _949061)))], (6630 ^ _774244) ^ [_881001, _881003, _881005] : [hAPP(c_Option_Ooption_OSome(_881001), _881003) = hAPP(c_Option_Ooption_OSome(_881001), _881005), -(_881003 = _881005)], (47802 ^ _774244) ^ [_1724660, _1724662, _1724664, _1724666, _1724668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724660), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724662)), _1724664))), -(hAPP(hAPP(c_List_Olist__update(_1724662, hAPP(hAPP(c_List_Oappend(_1724662), _1724664), _1724666)), _1724660), _1724668) = hAPP(hAPP(c_List_Oappend(_1724662), hAPP(hAPP(c_List_Olist__update(_1724662, _1724664), _1724660), _1724668)), _1724666))], (46932 ^ _774244) ^ [_1704073, _1704075, _1704077] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1704073), tc_List_Olist(_1704073))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1704073), tc_List_Olist(_1704073)), c_List_Olist_ONil(_1704073)), _1704075)), c_List_Olex(_1704073, _1704077)))], (40337 ^ _774244) ^ [_1536194, _1536196, _1536198] : [class_Orderings_Olinorder(_1536194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536194), _1536196)), -(_1536196 = c_Orderings_Obot__class_Obot(tc_fun(_1536194, tc_HOL_Obool))), 40348 ^ _774244 : [(40349 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1536194), _1536198), hAPP(c_Finite__Set_Ofold1(_1536194, c_Orderings_Oord__class_Omin(_1536194)), _1536196))), 40352 ^ _774244 : [(40353 ^ _774244) ^ [_1536487] : [hBOOL(hAPP(hAPP(c_member(_1536194), _1536487), _1536196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1536194), _1536198), _1536487)))]]], (40359 ^ _774244) ^ [] : [40361 ^ _774244 : [(40364 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1536194), _1536198), 40360 ^ [_1536194, _1536196, _1536198]))], (40362 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536194), 40360 ^ [_1536194, _1536196, _1536198]), _1536196)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1536194), _1536198), hAPP(c_Finite__Set_Ofold1(_1536194, c_Orderings_Oord__class_Omin(_1536194)), _1536196))))]]], (16273 ^ _774244) ^ [_1050988] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050988)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050988))], (5666 ^ _774244) ^ [_864549, _864551] : [_864549 = _864551, -(hAPP(c_Nat_OSuc, _864549) = hAPP(c_Nat_OSuc, _864551))], (22060 ^ _774244) ^ [_1153214, _1153216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1153214)), _1153216)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1153214), _1153216)))], (3738 ^ _774244) ^ [_831881, _831883, _831885, _831887] : [-(c_Lazy__Sequence_Ohb__single(_831887, _831883) = c_Lazy__Sequence_Ohb__single(_831885, _831881)), _831887 = _831885, _831883 = _831881], (2212 ^ _774244) ^ [_807550, _807552, _807554, _807556, _807558, _807560, _807562, _807564] : [-(c_Sum__Type_OSuml(_807564, _807560, _807556, _807552) = c_Sum__Type_OSuml(_807562, _807558, _807554, _807550)), _807564 = _807562, _807560 = _807558, _807556 = _807554, _807552 = _807550], (50216 ^ _774244) ^ [_1779858, _1779860] : [50218 ^ _774244 : [(50221 ^ _774244) ^ [] : [50217 ^ [_1779858, _1779860] = c_List_Olist_ONil(_1779858)], (50219 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1779858)), 50217 ^ [_1779858, _1779860]), hAPP(c_List_Oset(tc_List_Olist(_1779858)), _1779860))))]], -(c_List_Olist_ONil(_1779858) = c_List_Oconcat(_1779858, _1779860))], (18991 ^ _774244) ^ [_1098281] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1098281)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1098281)))], (9078 ^ _774244) ^ [_922831, _922833, _922835] : [class_Rings_Oring__no__zero__divisors(_922831), 9081 ^ _774244 : [(9082 ^ _774244) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922831), _922833), _922835) = c_Groups_Ozero__class_Ozero(_922831), -(_922833 = c_Groups_Ozero__class_Ozero(_922831)), -(_922835 = c_Groups_Ozero__class_Ozero(_922831))], (9092 ^ _774244) ^ [] : [9093 ^ _774244 : [(9096 ^ _774244) ^ [] : [_922835 = c_Groups_Ozero__class_Ozero(_922831)], (9094 ^ _774244) ^ [] : [_922833 = c_Groups_Ozero__class_Ozero(_922831)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922831), _922833), _922835) = c_Groups_Ozero__class_Ozero(_922831))]]], (51255 ^ _774244) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (48102 ^ _774244) ^ [_1732598, _1732600] : [-(c_List_Olistrel(_1732598, c_Transitive__Closure_Ortrancl(_1732598, _1732600)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1732598), c_List_Olistrel1(_1732598, _1732600)))], (24041 ^ _774244) ^ [_1191751, _1191753, _1191755, _1191757] : [class_Orderings_Olinorder(_1191751), 24044 ^ _774244 : [(24053 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191751), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191751), _1191753), _1191755)), _1191757))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191751), _1191753), _1191757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191751), _1191755), _1191757))], (24045 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191751), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1191751), _1191753), _1191755)), _1191757)), 24048 ^ _774244 : [(24051 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191751), _1191755), _1191757)))], (24049 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191751), _1191753), _1191757)))]]]]], (46519 ^ _774244) ^ [_1693927, _1693929, _1693931] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693927)), hAPP(hAPP(c_List_Olist_OCons(_1693927), _1693929), _1693931)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693927)), _1693931)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42938 ^ _774244) ^ [_1603967] : [class_Groups_Oab__semigroup__mult(_1603967), -(c_Finite__Set_Ofun__left__comm(_1603967, _1603967, c_Groups_Otimes__class_Otimes(_1603967)))], (24163 ^ _774244) ^ [_1193895, _1193897, _1193899, _1193901] : [class_Orderings_Olinorder(_1193895), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193895), _1193897), _1193899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193895), _1193901), _1193899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193895), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1193895), _1193897), _1193901)), _1193899)))], (51229 ^ _774244) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (47935 ^ _774244) ^ [_1728320, _1728322, _1728324, _1728326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1728320), _1728322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1728324, tc_HOL_Obool)), hAPP(c_List_Oset(_1728324), hAPP(hAPP(c_List_Otake(_1728324), _1728320), _1728326))), hAPP(c_List_Oset(_1728324), hAPP(hAPP(c_List_Otake(_1728324), _1728322), _1728326)))))], (6790 ^ _774244) ^ [_884150, _884152, _884154, _884156] : [class_Rings_Ocomm__semiring__1(_884150), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884150), _884152), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884150), _884154), _884156)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884150), _884152), _884154)), _884156))], (37442 ^ _774244) ^ [_1470127, _1470129, _1470131, _1470133, _1470135, _1470137] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470127, tc_fun(_1470129, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1470127, tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_fun(_1470129, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470129, tc_fun(tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_fun(_1470129, tc_HOL_Obool)), _1470127), c_COMBC(_1470129, tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470129, tc_prod(_1470127, _1470129)), tc_fun(_1470129, tc_fun(tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_HOL_Obool)), _1470127), hAPP(c_COMBB(tc_prod(_1470127, _1470129), tc_fun(tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_HOL_Obool), _1470129), c_member(tc_prod(_1470127, _1470129)))), c_Product__Type_OPair(_1470127, _1470129)))), _1470131)), hAPP(hAPP(c_COMBC(_1470127, tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_fun(_1470129, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470129, tc_fun(tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_fun(_1470129, tc_HOL_Obool)), _1470127), c_COMBC(_1470129, tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470129, tc_prod(_1470127, _1470129)), tc_fun(_1470129, tc_fun(tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_HOL_Obool)), _1470127), hAPP(c_COMBB(tc_prod(_1470127, _1470129), tc_fun(tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool), tc_HOL_Obool), _1470129), c_member(tc_prod(_1470127, _1470129)))), c_Product__Type_OPair(_1470127, _1470129)))), _1470133)), _1470135), _1470137)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1470127, _1470129)), hAPP(hAPP(c_Product__Type_OPair(_1470127, _1470129), _1470135), _1470137)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1470127, _1470129), tc_HOL_Obool)), _1470131), _1470133))))], (9935 ^ _774244) ^ [_938007, _938009] : [class_Rings_Olinordered__idom(_938007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938007), _938009), c_Groups_Ozero__class_Ozero(_938007))), -(c_Groups_Osgn__class_Osgn(_938007, _938009) = hAPP(c_Groups_Ouminus__class_Ouminus(_938007), c_Groups_Oone__class_Oone(_938007)))], (48394 ^ _774244) ^ [_1740875, _1740877, _1740879, _1740881] : [hAPP(hAPP(c_List_Oappend(_1740875), _1740877), _1740879) = _1740881, 48397 ^ _774244 : [(48400 ^ _774244) ^ [] : [-(_1740879 = hAPP(hAPP(c_List_Odrop(_1740875), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740875)), _1740877)), _1740881))], (48398 ^ _774244) ^ [] : [-(_1740877 = hAPP(hAPP(c_List_Otake(_1740875), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740875)), _1740877)), _1740881))]]], (48634 ^ _774244) ^ [_1746066, _1746068, _1746070] : [_1746070 = c_List_Olist_ONil(_1746066), -(hAPP(c_List_Orotate(_1746066, _1746068), _1746070) = c_List_Olist_ONil(_1746066))], (48626 ^ _774244) ^ [_1745900, _1745902, _1745904, _1745906] : [-(hAPP(c_List_Orotate(_1745900, _1745902), hAPP(c_List_Orotate(_1745900, _1745904), _1745906)) = hAPP(c_List_Orotate(_1745900, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1745902), _1745904)), _1745906))], (31289 ^ _774244) ^ [_1336239, _1336241, _1336243, _1336245, _1336247] : [hBOOL(hAPP(hAPP(c_member(_1336239), _1336241), _1336243)), -(hAPP(hAPP(c_Set_Oinsert(_1336245), hAPP(_1336247, _1336241)), hAPP(c_Set_Oimage(_1336239, _1336245, _1336247), _1336243)) = hAPP(c_Set_Oimage(_1336239, _1336245, _1336247), _1336243))], (32316 ^ _774244) ^ [_1359473, _1359475, _1359477, _1359479] : [hBOOL(hAPP(hAPP(c_member(_1359473), _1359475), c_SetInterval_Oord_OatMost(_1359473, _1359477, _1359479))), -(hBOOL(hAPP(hAPP(_1359477, _1359475), _1359479)))], (23049 ^ _774244) ^ [_1172824, _1172826] : [-(_1172824 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1172826, _1172824), c_Divides_Odivmod__int(_1172826, _1172824))))], (5658 ^ _774244) ^ [_864423] : [hAPP(c_Nat_OSuc, _864423) = _864423], (22004 ^ _774244) ^ [_1152371, _1152373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1152371), _1152373)), -(c_Divides_Odivmod__nat(_1152373, _1152371) = 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), _1152373), _1152371)), _1152371))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152373), _1152371), _1152371)))], (8872 ^ _774244) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19809 ^ _774244) ^ [_1113020, _1113022] : [class_Rings_Odivision__ring__inverse__zero(_1113020), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113020), _1113022), c_Groups_Ozero__class_Ozero(_1113020)) = c_Groups_Ozero__class_Ozero(_1113020))], (37471 ^ _774244) ^ [_1471791, _1471793, _1471795, _1471797, _1471799] : [class_Fields_Ofield(_1471791), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471793), _1471795)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471793), _1471797)), 37485 ^ _774244 : [(37488 ^ _774244) ^ [] : [-(hAPP(_1471799, 37484 ^ [_1471791, _1471793, _1471795, _1471797, _1471799]) = c_Groups_Ozero__class_Ozero(_1471791))], (37486 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471793), 37484 ^ [_1471791, _1471793, _1471795, _1471797, _1471799]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471793, tc_HOL_Obool)), _1471795), _1471797))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1471793, _1471791), _1471799), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1471793, tc_HOL_Obool)), _1471795), _1471797)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1471791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1471791), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1471793, _1471791), _1471799), _1471795)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1471793, _1471791), _1471799), _1471797))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1471793, _1471791), _1471799), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471793, tc_HOL_Obool)), _1471795), _1471797))))], (9676 ^ _774244) ^ [_933680] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _933680)), _933680) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51471 ^ _774244) ^ [_1801827, _1801829] : [hBOOL(hAPP(hAPP(c_fconj, _1801827), _1801829)), -(hBOOL(_1801827))], (7543 ^ _774244) ^ [_896814, _896816, _896818] : [c_Com_Ocom_OBODY(_896814) = c_Com_Ocom_OAss(_896816, _896818)], (32956 ^ _774244) ^ [_1371162, _1371164, _1371166] : [class_Orderings_Olinorder(_1371162), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371162), _1371164)), -(_1371166 = c_Orderings_Obot__class_Obot(tc_fun(_1371162, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1371162, tc_HOL_Obool)), _1371166), _1371164)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1371162), c_Big__Operators_Olinorder__class_OMin(_1371162, _1371166)), c_Big__Operators_Olinorder__class_OMin(_1371162, _1371164)) = c_Big__Operators_Olinorder__class_OMin(_1371162, _1371164))], (42916 ^ _774244) ^ [_1603448, _1603450, _1603452, _1603454, _1603456, _1603458] : [c_Finite__Set_Ofun__left__comm(_1603448, _1603450, _1603452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1603448), _1603454)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1603448, _1603450, _1603452), _1603456), hAPP(hAPP(c_Set_Oinsert(_1603448), _1603458), _1603454)) = hAPP(hAPP(_1603452, _1603458), hAPP(hAPP(c_Finite__Set_Ofold(_1603448, _1603450, _1603452), _1603456), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1603448, tc_HOL_Obool)), _1603454), hAPP(hAPP(c_Set_Oinsert(_1603448), _1603458), c_Orderings_Obot__class_Obot(tc_fun(_1603448, tc_HOL_Obool)))))))], (21705 ^ _774244) ^ [_1147127, _1147129, _1147131, _1147133] : [class_Fields_Olinordered__field__inverse__zero(_1147127), class_Int_Onumber(_1147127), 21712 ^ _774244 : [(21713 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147127), hAPP(c_Int_Onumber__class_Onumber__of(_1147127), _1147129)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147127), _1147131), _1147133))), 21716 ^ _774244 : [(21723 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147127), c_Groups_Ozero__class_Ozero(_1147127)), _1147133))), 21726 ^ _774244 : [(21733 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147127), _1147133), c_Groups_Ozero__class_Ozero(_1147127)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147127), hAPP(c_Int_Onumber__class_Onumber__of(_1147127), _1147129)), c_Groups_Ozero__class_Ozero(_1147127))))], (21727 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147127), _1147133), c_Groups_Ozero__class_Ozero(_1147127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147127), _1147131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147127), hAPP(c_Int_Onumber__class_Onumber__of(_1147127), _1147129)), _1147133))))]]], (21717 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147127), c_Groups_Ozero__class_Ozero(_1147127)), _1147133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147127), hAPP(c_Int_Onumber__class_Onumber__of(_1147127), _1147129)), _1147133)), _1147131)))]]], (21739 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147127), hAPP(c_Int_Onumber__class_Onumber__of(_1147127), _1147129)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147127), _1147131), _1147133)))), 21742 ^ _774244 : [(21745 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147127), hAPP(c_Int_Onumber__class_Onumber__of(_1147127), _1147129)), _1147133)), _1147131))], (21743 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147127), c_Groups_Ozero__class_Ozero(_1147127)), _1147133)))]], 21746 ^ _774244 : [(21749 ^ _774244) ^ [] : [21750 ^ _774244 : [(21753 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147127), _1147131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147127), hAPP(c_Int_Onumber__class_Onumber__of(_1147127), _1147129)), _1147133)))], (21751 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147127), _1147133), c_Groups_Ozero__class_Ozero(_1147127))))]], 21754 ^ _774244 : [(21757 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147127), hAPP(c_Int_Onumber__class_Onumber__of(_1147127), _1147129)), c_Groups_Ozero__class_Ozero(_1147127)))], (21755 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147127), _1147133), c_Groups_Ozero__class_Ozero(_1147127)))]]], (21747 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147127), c_Groups_Ozero__class_Ozero(_1147127)), _1147133))]]]]], (19219 ^ _774244) ^ [_1102262, _1102264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102262), _1102264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1102262)), c_Int_OBit1(_1102264))))], (18177 ^ _774244) ^ [_1084641] : [class_Int_Onumber__ring(_1084641), -(c_Int_Oiszero(_1084641, hAPP(c_Int_Onumber__class_Onumber__of(_1084641), c_Int_OPls)))], (12326 ^ _774244) ^ [_978291, _978293, _978295] : [class_Groups_Oordered__comm__monoid__add(_978291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978291), c_Groups_Ozero__class_Ozero(_978291)), _978293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978291), c_Groups_Ozero__class_Ozero(_978291)), _978295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978291), c_Groups_Ozero__class_Ozero(_978291)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978291), _978293), _978295))))], (30891 ^ _774244) ^ [_1328175, _1328177] : [_1328177 = c_Orderings_Obot__class_Obot(tc_fun(_1328175, tc_HOL_Obool)), 30894 ^ _774244 : [(30895 ^ _774244) ^ [_1328255] : [hBOOL(hAPP(hAPP(c_member(_1328175), _1328255), _1328177))]]], (43395 ^ _774244) ^ [_1614394, _1614396, _1614398, _1614400] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1614398), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614394, tc_fun(_1614398, tc_HOL_Obool)), _1614396), _1614400)))), 43396 ^ _774244 : [(43397 ^ _774244) ^ [_1614468] : [hBOOL(hAPP(hAPP(c_member(_1614394), _1614468), _1614396)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614398), hAPP(_1614400, _1614468)))]]], (42828 ^ _774244) ^ [_1601188, _1601190] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1601188, _1601188)), _1601190)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1601188, _1601188)), c_Transitive__Closure_Otrancl(_1601188, _1601190))))], (17921 ^ _774244) ^ [_1080914] : [class_Int_Onumber__ring(_1080914), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1080914), c_Groups_Oone__class_Oone(_1080914)) = hAPP(c_Int_Onumber__class_Onumber__of(_1080914), c_Int_OMin))], (32385 ^ _774244) ^ [_1360993, _1360995, _1360997, _1360999, _1361001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1360993, _1360995)), hAPP(_1360993, _1360997))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1360999, _1360999)), hAPP(hAPP(c_Product__Type_OPair(_1360999, _1360999), _1360995), _1360997)), c_Wellfounded_Omlex__prod(_1360999, _1360993, _1361001))))], (49966 ^ _774244) ^ [_1774078] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1774078) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1774078)))], (45561 ^ _774244) ^ [_1668899, _1668901, _1668903, _1668905, _1668907, _1668909] : [-(hAPP(hAPP(c_List_Omap(_1668899, _1668901), _1668903), hAPP(hAPP(c_List_Omap(_1668905, _1668899), _1668907), _1668909)) = hAPP(hAPP(c_List_Omap(_1668905, _1668901), hAPP(c_Fun_Ocomp(_1668899, _1668901, _1668905, _1668903), _1668907)), _1668909))], (41466 ^ _774244) ^ [_1570125, _1570127, _1570129] : [c_Wellfounded_Owf(_1570125, _1570127), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570125, _1570125)), hAPP(hAPP(c_Product__Type_OPair(_1570125, _1570125), _1570129), _1570129)), _1570127))], (9212 ^ _774244) ^ [_925425] : [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, _925425))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _925425)))], (5700 ^ _774244) ^ [_865068, _865070, _865072, _865074] : [c_Natural_Oevaln(_865068, _865070, _865072, _865074), -(c_Natural_Oevalc(_865068, _865070, _865074))], (6079 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (25145 ^ _774244) ^ [_1212993, _1212995] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212993), _1212995)), 25148 ^ _774244 : [(25155 ^ _774244) ^ [] : [_1212995 = _1212993, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212995), _1212993)))], (25149 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212995), _1212993)), -(_1212995 = _1212993)]]], (44546 ^ _774244) ^ [_1644833, _1644835, _1644837] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1644833, tc_HOL_Obool)), _1644835), _1644837) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1644833, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1644833, tc_HOL_Obool)), _1644835), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1644833, tc_HOL_Obool)), _1644837), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1644833, tc_HOL_Obool), tc_HOL_Obool))))))], (26261 ^ _774244) ^ [_1233065, _1233067, _1233069] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233065, _1233067) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233069, _1233067), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1233067), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1233065), _1233069))))], (2708 ^ _774244) ^ [_815282, _815284, _815286, _815288] : [-(c_HOL_OLet(_815288, _815284) = c_HOL_OLet(_815286, _815282)), _815288 = _815286, _815284 = _815282], (14135 ^ _774244) ^ [_1011039] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011039) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48712 ^ _774244) ^ [_1747715, _1747717, _1747719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1747715), _1747717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1747715), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1747717), _1747719))))], (1860 ^ _774244) ^ [_801202, _801204] : [_801204 = _801202, -(c_HOL_Obool_Obool__size(_801204) = c_HOL_Obool_Obool__size(_801202))], (44775 ^ _774244) ^ [_1650251, _1650253, _1650255, _1650257, _1650259] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1650251, tc_fun(_1650253, tc_HOL_Obool)), _1650255), hAPP(hAPP(c_COMBS(_1650251, tc_fun(_1650253, tc_HOL_Obool), tc_fun(_1650253, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650253, tc_HOL_Obool), tc_fun(tc_fun(_1650253, tc_HOL_Obool), tc_fun(_1650253, tc_HOL_Obool)), _1650251), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1650253, tc_HOL_Obool))), _1650257)), _1650259)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1650253, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1650253, tc_HOL_Obool), hAPP(c_Set_Oimage(_1650251, tc_fun(_1650253, tc_HOL_Obool), _1650257), _1650255))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1650253, tc_HOL_Obool), hAPP(c_Set_Oimage(_1650251, tc_fun(_1650253, tc_HOL_Obool), _1650259), _1650255))))], (51419 ^ _774244) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (17011 ^ _774244) ^ [_1065164, _1065166] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065164)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065166)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1065164), _1065166)))], (28202 ^ _774244) ^ [_1272717, _1272719, _1272721, _1272723] : [class_Orderings_Olinorder(_1272717), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272717), _1272719), _1272721)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272717), _1272721), _1272723)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272717, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1272717, _1272719, _1272721)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1272717, _1272721, _1272723)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1272717, _1272719, _1272723))], (35863 ^ _774244) ^ [_1435177, _1435179, _1435181, _1435183] : [hBOOL(hAPP(hAPP(c_member(_1435177), _1435179), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435177, tc_HOL_Obool)), _1435181), _1435183))), 35866 ^ _774244 : [(35869 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1435177), _1435179), _1435183)))], (35867 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1435177), _1435179), _1435181)))]]], (5629 ^ _774244) ^ [_863933, _863935, _863937, _863939] : [c_Natural_Oevaln(_863933, _863935, _863937, _863939), -(c_Natural_Oevaln(_863933, _863935, hAPP(c_Nat_OSuc, _863937), _863939))], (41599 ^ _774244) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (22925 ^ _774244) ^ [_1170446, _1170448, _1170450, _1170452, _1170454, _1170456, _1170458, _1170460] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1170446, _1170448, _1170450), _1170452), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1170454, _1170456, tc_prod(_1170446, _1170448)), _1170458), _1170460)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1170454, _1170456, _1170450), hAPP(hAPP(c_COMBB(tc_fun(_1170456, tc_prod(_1170446, _1170448)), tc_fun(_1170456, _1170450), _1170454), hAPP(c_COMBB(tc_prod(_1170446, _1170448), _1170450, _1170456), hAPP(c_Product__Type_Oprod_Oprod__case(_1170446, _1170448, _1170450), _1170452))), _1170458)), _1170460))], (28679 ^ _774244) ^ [_1283064, _1283066, _1283068, _1283070, _1283072, _1283074] : [-(hAPP(c_Set_Oimage(_1283064, _1283066, _1283068), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1283070, tc_fun(_1283064, tc_HOL_Obool)), _1283072), _1283074)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1283070, tc_fun(_1283066, tc_HOL_Obool)), _1283072), hAPP(hAPP(c_COMBB(tc_fun(_1283064, tc_HOL_Obool), tc_fun(_1283066, tc_HOL_Obool), _1283070), c_Set_Oimage(_1283064, _1283066, _1283068)), _1283074)))], (1474 ^ _774244) ^ [_795393, _795395] : [-(class_Rings_Olinordered__semidom(_795393)), _795395 = _795393, class_Rings_Olinordered__semidom(_795395)], (26568 ^ _774244) ^ [_1240037, _1240039, _1240041, _1240043] : [class_Groups_Oab__group__add(_1240037), 26571 ^ _774244 : [(26578 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1240039), _1240041))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1240037), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1240037, _1240037), hAPP(hAPP(c_COMBB(_1240037, tc_fun(_1240037, _1240037), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1240037)), _1240043)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1240037, tc_Nat_Onat), _1240043), 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, _1240039, _1240041)) = c_Groups_Ozero__class_Ozero(_1240037))], (26572 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1240039), _1240041)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1240037), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1240037, _1240037), hAPP(hAPP(c_COMBB(_1240037, tc_fun(_1240037, _1240037), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1240037)), _1240043)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1240037, tc_Nat_Onat), _1240043), 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, _1240039, _1240041)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1240037), hAPP(_1240043, _1240039)), hAPP(_1240043, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1240041), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (48620 ^ _774244) ^ [_1745791, _1745793, _1745795] : [hBOOL(hAPP(c_List_Odistinct(_1745791), _1745795)), -(hBOOL(hAPP(c_List_Odistinct(_1745791), hAPP(c_List_Orotate(_1745791, _1745793), _1745795))))], (20091 ^ _774244) ^ [_1118117, _1118119, _1118121] : [class_Fields_Olinordered__field(_1118117), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118117), c_Groups_Ozero__class_Ozero(_1118117)), _1118119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118117), c_Groups_Ozero__class_Ozero(_1118117)), _1118121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118117), c_Groups_Ozero__class_Ozero(_1118117)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118117), _1118119), _1118121))))], (27585 ^ _774244) ^ [_1260554] : [c_Nat__Transfer_Onat__set(_1260554), -(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), _1260554)) = _1260554)], (7375 ^ _774244) ^ [_893961, _893963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893961), hAPP(c_Nat_OSuc, _893963))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893961), _893963))), -(_893961 = _893963)], (41524 ^ _774244) ^ [_1571447] : [class_Orderings_Owellorder(_1571447), -(c_Wellfounded_Owf(_1571447, hAPP(c_Set_OCollect(tc_prod(_1571447, _1571447)), hAPP(c_Product__Type_Oprod_Oprod__case(_1571447, _1571447, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1571447)))))], (51429 ^ _774244) ^ [_1801250, _1801252, _1801254, _1801256, _1801258, _1801260] : [-(hAPP(hAPP(hAPP(c_COMBC(_1801250, _1801252, _1801254), _1801256), _1801258), _1801260) = hAPP(hAPP(_1801256, _1801260), _1801258))], (43247 ^ _774244) ^ [_1611097, _1611099, _1611101, _1611103] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611097, _1611097)), hAPP(hAPP(c_Product__Type_OPair(_1611097, _1611097), _1611099), _1611101)), c_Transitive__Closure_Ortrancl(_1611097, _1611103))), hBOOL(hAPP(hAPP(c_member(_1611097), _1611101), c_Wellfounded_Oacc(_1611097, _1611103))), -(hBOOL(hAPP(hAPP(c_member(_1611097), _1611099), c_Wellfounded_Oacc(_1611097, _1611103))))], (36415 ^ _774244) ^ [_1446563, _1446565, _1446567, _1446569] : [class_Lattices_Osemilattice__inf(_1446563), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446563), _1446565), _1446567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446563), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1446563), _1446569), _1446565)), _1446567)))], (24867 ^ _774244) ^ [_1208474, _1208476] : [class_Rings_Ocomm__semiring__1(_1208474), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208474), c_Groups_Ozero__class_Ozero(_1208474)), _1208476)), -(_1208476 = c_Groups_Ozero__class_Ozero(_1208474))], (45381 ^ _774244) ^ [_1664572, _1664574, _1664576] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1664572), c_Map_Odom(_1664572, _1664574, c_Map_Omap__of(_1664572, _1664574, _1664576)))))], (5406 ^ _774244) ^ [_857751, _857753, _857755, _857757] : [-(c_List_Oconcat(_857757, _857753) = c_List_Oconcat(_857755, _857751)), _857757 = _857755, _857753 = _857751], (50999 ^ _774244) ^ [_1797051, _1797053] : [class_Orderings_Otop(_1797051), -(class_Orderings_Otop(tc_fun(_1797053, _1797051)))], (19639 ^ _774244) ^ [_1109859, _1109861] : [-(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), _1109859)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1109861))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1109859))) = 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), _1109861)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1109859)))], (22200 ^ _774244) ^ [_1156223] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156223))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1156223)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22158 ^ _774244) ^ [_1155188, _1155190] : [hAPP(c_Nat_OSuc, _1155188) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155190), -(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(_1155190))), 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)), _1155188))))))], (5060 ^ _774244) ^ [_852462, _852464, _852466, _852468] : [-(c_Product__Type_Osnd(_852468, _852464) = c_Product__Type_Osnd(_852466, _852462)), _852468 = _852466, _852464 = _852462], (47024 ^ _774244) ^ [_1706461, _1706463, _1706465, _1706467] : [-(hAPP(hAPP(c_List_Onth(_1706461), hAPP(hAPP(c_List_Olist_OCons(_1706461), _1706463), _1706465)), _1706467) = c_Nat_Onat_Onat__case(_1706461, _1706463, hAPP(c_List_Onth(_1706461), _1706465), _1706467))], (24723 ^ _774244) ^ [_1205635, _1205637, _1205639, _1205641] : [-(c_HOL_OThe(tc_prod(_1205635, _1205637), hAPP(c_Product__Type_Oprod_Oprod__case(_1205635, _1205637, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1205635, tc_fun(_1205637, tc_HOL_Obool), tc_fun(_1205637, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1205637, tc_HOL_Obool), tc_fun(_1205637, tc_HOL_Obool)), _1205635), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1205637)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1205635), c_fconj), hAPP(c_fequal, _1205639)))), hAPP(c_fequal, _1205641)))) = hAPP(hAPP(c_Product__Type_OPair(_1205635, _1205637), _1205639), _1205641))], (3116 ^ _774244) ^ [_821946, _821948, _821950, _821952] : [-(c_Set_Othe__elem(_821952, _821948) = c_Set_Othe__elem(_821950, _821946)), _821952 = _821950, _821948 = _821946], (17999 ^ _774244) ^ [_1082031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1082031)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1082031) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (6049 ^ _774244) ^ [_871130, _871132] : [hBOOL(hAPP(c_Com_OWT, _871130)), hBOOL(hAPP(c_Com_OWT, _871132)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_871130, _871132))))], (27382 ^ _774244) ^ [_1257037, _1257039, _1257041] : [class_Orderings_Olinorder(_1257037), 27385 ^ _774244 : [(27392 ^ _774244) ^ [] : [_1257039 = _1257041, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257037), _1257039) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257037), _1257041))], (27386 ^ _774244) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257037), _1257039) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257037), _1257041), -(_1257039 = _1257041)]]], (11212 ^ _774244) ^ [_958591, _958593, _958595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958591), _958593)), _958595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _958591), _958595)))], (41737 ^ _774244) ^ [_1576852] : [-(c_Wellfounded_OwfP(_1576852, hAPP(c_COMBK(tc_fun(_1576852, tc_HOL_Obool), _1576852), hAPP(c_COMBK(tc_HOL_Obool, _1576852), c_fFalse))))], (50801 ^ _774244) ^ [_1793383, _1793385] : [-(c_List_OdropWhile(_1793383, _1793385, c_List_Olist_ONil(_1793383)) = c_List_Olist_ONil(_1793383))], (18549 ^ _774244) ^ [_1090819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090819), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1090819)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (44700 ^ _774244) ^ [_1648540, _1648542, _1648544] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1648540, tc_HOL_Obool)), _1648542), _1648544)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648540, tc_HOL_Obool)), _1648542), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1648540, tc_HOL_Obool), _1648544))))], (39604 ^ _774244) ^ [_1518729, _1518731, _1518733, _1518735] : [hAPP(hAPP(c_Product__Type_OSigma(_1518729, _1518731), _1518733), hAPP(c_COMBK(tc_fun(_1518731, tc_HOL_Obool), _1518729), _1518735)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518729, _1518731), tc_HOL_Obool)), -(_1518733 = c_Orderings_Obot__class_Obot(tc_fun(_1518729, tc_HOL_Obool))), -(_1518735 = c_Orderings_Obot__class_Obot(tc_fun(_1518731, tc_HOL_Obool)))], (35159 ^ _774244) ^ [_1418085, _1418087] : [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)), _1418085), 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)), _1418087), 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)), _1418085), _1418087)), c_Int_Ointrel)))], (2410 ^ _774244) ^ [_810627, _810629, _810631, _810633, _810635, _810637] : [-(c_Nat_Onat_Onat__rec(_810637, _810633, _810629) = c_Nat_Onat_Onat__rec(_810635, _810631, _810627)), _810637 = _810635, _810633 = _810631, _810629 = _810627], (7840 ^ _774244) ^ [_902374, _902376, _902378, _902380, _902382] : [-(hAPP(c_Sum__Type_OSumr(_902374, _902376, _902378, _902380), hAPP(c_Sum__Type_OInr(_902374, _902378), _902382)) = hAPP(_902380, _902382))], (12131 ^ _774244) ^ [_975067, _975069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975067)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975069)), -(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), _975067), _975069))))], (15420 ^ _774244) ^ [_1034209, _1034211, _1034213] : [class_Groups_Ogroup__add(_1034209), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034209), _1034211), hAPP(c_Groups_Ouminus__class_Ouminus(_1034209), _1034213)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034209), _1034211), _1034213))], (21889 ^ _774244) ^ [_1150554, _1150556, _1150558] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1150554, _1150556, _1150558, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1150556)], (48098 ^ _774244) ^ [_1732495, _1732497] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1732495), tc_List_Olist(_1732495)), tc_HOL_Obool)), c_List_Olistrel1(_1732495, c_Transitive__Closure_Ortrancl(_1732495, _1732497))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1732495), c_List_Olistrel1(_1732495, _1732497)))))], (27402 ^ _774244) ^ [_1257366, _1257368, _1257370] : [-(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)), _1257366)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1257368), _1257370)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1257368), _1257366)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1257370), _1257366)))], (9204 ^ _774244) ^ [_925243, _925245, _925247] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _925243), _925245)), _925247) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _925243), _925247)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _925245), _925247)))], (14790 ^ _774244) ^ [_1022413, _1022415, _1022417] : [-(hBOOL(hAPP(_1022413, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1022415, _1022417)))), 14793 ^ _774244 : [(14796 ^ _774244) ^ [] : [hBOOL(hAPP(_1022413, _1022415))], (14794 ^ _774244) ^ [] : [-(_1022417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14797 ^ _774244 : [(14802 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14800 ^ [_1022413, _1022415, _1022417]), _1022417)))], (14804 ^ _774244) ^ [] : [-(_1022415 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022417), 14799 ^ [_1022413, _1022415, _1022417])), 14800 ^ [_1022413, _1022415, _1022417]))], (14806 ^ _774244) ^ [] : [hBOOL(hAPP(_1022413, 14800 ^ [_1022413, _1022415, _1022417]))], (14798 ^ _774244) ^ [] : [_1022417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (31237 ^ _774244) ^ [_1335156, _1335158, _1335160] : [hBOOL(hAPP(hAPP(c_member(_1335156), _1335158), hAPP(hAPP(c_Set_Oinsert(_1335156), _1335160), c_Orderings_Obot__class_Obot(tc_fun(_1335156, tc_HOL_Obool))))), -(_1335158 = _1335160)], (51257 ^ _774244) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (4682 ^ _774244) ^ [_846575, _846577, _846579, _846581, _846583, _846585, _846587, _846589] : [-(c_Option_Ooption_Ooption__case(_846589, _846585, _846581, _846577) = c_Option_Ooption_Ooption__case(_846587, _846583, _846579, _846575)), _846589 = _846587, _846585 = _846583, _846581 = _846579, _846577 = _846575], (14672 ^ _774244) ^ [_1020024, _1020026, _1020028] : [class_Divides_Osemiring__div(_1020024), -(_1020026 = c_Groups_Ozero__class_Ozero(_1020024)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020024), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020024), _1020026), _1020028)), _1020026) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020024), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020024), _1020028), _1020026)), c_Groups_Oone__class_Oone(_1020024)))], (13583 ^ _774244) ^ [_1000747, _1000749] : [-(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, _1000747, _1000749)), _1000749) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1000747), _1000749))], (21934 ^ _774244) ^ [_1151269, _1151271] : [_1151269 = _1151271, -(c_Random_Oinc__shift(_1151269, _1151271) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (51345 ^ _774244) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (16281 ^ _774244) ^ [_1051159, _1051161, _1051163] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1051159), _1051161)), _1051163) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1051159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1051161), _1051163)))], (39596 ^ _774244) ^ [_1518405, _1518407, _1518409, _1518411, _1518413, _1518415] : [class_Groups_Ocomm__monoid__add(_1518405), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1518407, _1518405), hAPP(hAPP(c_COMBC(_1518407, tc_fun(_1518409, tc_HOL_Obool), _1518405), hAPP(hAPP(c_COMBB(tc_fun(_1518409, _1518405), tc_fun(tc_fun(_1518409, tc_HOL_Obool), _1518405), _1518407), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1518409, _1518405)), _1518411)), _1518413)), _1518415) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1518407, _1518409), _1518405), hAPP(c_Product__Type_Oprod_Oprod__case(_1518407, _1518409, _1518405), _1518411)), hAPP(hAPP(c_Product__Type_OSigma(_1518407, _1518409), _1518415), hAPP(c_COMBK(tc_fun(_1518409, tc_HOL_Obool), _1518407), _1518413))))], (10105 ^ _774244) ^ [_940837, _940839] : [_940837 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940837), _940839), -(_940839 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_940837 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6396 ^ _774244) ^ [_877164, _877166, _877168] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_877164, _877166, _877168)) = 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(_877166)), c_Com_Ocom_Ocom__size(_877168))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44263 ^ _774244) ^ [_1638258, _1638260, _1638262, _1638264] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1638258, _1638258)), hAPP(hAPP(c_Product__Type_OPair(_1638258, _1638258), _1638260), _1638262)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638258, _1638258), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1638264))), -(_1638260 = _1638262)], (28519 ^ _774244) ^ [_1278903, _1278905, _1278907, _1278909] : [-(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), _1278903, _1278905)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1278907, _1278909)))), 28520 ^ _774244 : [(28523 ^ _774244) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1278907), _1278903)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1278905), _1278909))], (28521 ^ _774244) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1278903), _1278905)))]]], (47012 ^ _774244) ^ [_1706106, _1706108, _1706110, _1706112, _1706114, _1706116] : [-(hAPP(c_List_Olist_Olist__case(_1706106, _1706108, _1706110, _1706112), hAPP(hAPP(c_List_Olist_OCons(_1706108), _1706114), _1706116)) = hAPP(hAPP(_1706112, _1706114), _1706116))], (44920 ^ _774244) ^ [_1653625, _1653627, _1653629, _1653631, _1653633, _1653635, _1653637] : [c_Finite__Set_Ofun__left__comm(_1653625, _1653627, _1653629), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1653625, _1653627, _1653629, _1653631, hAPP(hAPP(c_Set_Oinsert(_1653625), _1653633), _1653635)), _1653637)), -(hBOOL(hAPP(hAPP(c_member(_1653625), _1653633), _1653635))), 44932 ^ _774244 : [(44935 ^ _774244) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1653625, _1653627, _1653629, _1653631, _1653635), 44931 ^ [_1653625, _1653627, _1653629, _1653631, _1653633, _1653635, _1653637])))], (44933 ^ _774244) ^ [] : [-(_1653637 = hAPP(hAPP(_1653629, _1653633), 44931 ^ [_1653625, _1653627, _1653629, _1653631, _1653633, _1653635, _1653637]))]]], (7507 ^ _774244) ^ [_896133, _896135, _896137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _896133), _896135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _896133), _896137)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _896135), _896137))))], (22997 ^ _774244) ^ [_1172117, _1172119] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1172117, _1172119) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1172117, _1172119)))], (21970 ^ _774244) ^ [_1151771, _1151773, _1151775, _1151777] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1151771, _1151773, _1151775, c_Code__Numeral_OSuc__code__numeral(_1151777)) = hAPP(_1151775, _1151777))], (20401 ^ _774244) ^ [_1123190, _1123192, _1123194] : [class_Rings_Odivision__ring(_1123190), -(_1123192 = c_Groups_Ozero__class_Ozero(_1123190)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1123190), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123190), _1123194), _1123192)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123190), _1123194), hAPP(c_Groups_Ouminus__class_Ouminus(_1123190), _1123192)))], (19921 ^ _774244) ^ [_1115134, _1115136] : [c_Nat__Transfer_Ois__nat(_1115134), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1115134), _1115136)))], (6293 ^ _774244) ^ [_875302, _875304, _875306, _875308, _875310, _875312] : [c_Com_Ocom_OCall(_875302, _875304, _875306) = c_Com_Ocom_OCall(_875308, _875310, _875312), 6296 ^ _774244 : [(6301 ^ _774244) ^ [] : [-(_875306 = _875312)], (6299 ^ _774244) ^ [] : [-(_875304 = _875310)], (6297 ^ _774244) ^ [] : [-(_875302 = _875308)]]], (39664 ^ _774244) ^ [_1520635, _1520637] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1520635, _1520637), c_Orderings_Otop__class_Otop(tc_fun(_1520635, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1520637, tc_HOL_Obool), _1520635), c_Orderings_Otop__class_Otop(tc_fun(_1520637, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1520635, _1520637), tc_HOL_Obool)))], (13625 ^ _774244) ^ [_1001494, _1001496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001494)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1001494, _1001496)), _1001494)))], (11150 ^ _774244) ^ [_957567, _957569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957567), _957569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957567), _957569)))], (47159 ^ _774244) ^ [_1709788, _1709790, _1709792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709788), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709790)), _1709792))), -(hBOOL(hAPP(hAPP(c_member(_1709790), hAPP(hAPP(c_List_Onth(_1709790), _1709792), _1709788)), hAPP(c_List_Oset(_1709790), _1709792))))], (8102 ^ _774244) ^ [_906920, _906922] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _906920) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _906922), -(_906920 = _906922)], (51237 ^ _774244) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (4198 ^ _774244) ^ [_839161, _839163, _839165, _839167] : [-(c_Hilbert__Choice_OEps(_839167, _839163) = c_Hilbert__Choice_OEps(_839165, _839161)), _839167 = _839165, _839163 = _839161], (24481 ^ _774244) ^ [_1200183, _1200185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1200183), _1200185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1200183)), hAPP(c_Code__Numeral_Onat__of, _1200185))))], (28721 ^ _774244) ^ [_1284228, _1284230] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284228, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1284228, tc_HOL_Obool))), _1284230) = c_Orderings_Otop__class_Otop(tc_fun(_1284228, tc_HOL_Obool)))], (50653 ^ _774244) ^ [_1790456] : [c_List_Onat__list(_1790456), -(c_List_Oembed__list(c_List_Oreturn__list(_1790456)) = _1790456)], (29901 ^ _774244) ^ [_1306994] : [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)), _1306994))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1306994)))], (47285 ^ _774244) ^ [_1713013, _1713015, _1713017] : [-(hAPP(hAPP(c_List_Olist__update(_1713013, c_List_Olist_ONil(_1713013)), _1713015), _1713017) = c_List_Olist_ONil(_1713013))], (21879 ^ _774244) ^ [_1150465, _1150467] : [-(_1150465 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1150465, _1150467) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1150465), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1150467)))], (28016 ^ _774244) ^ [_1268998, _1269000, _1269002, _1269004] : [class_Lattices_Osemilattice__sup(_1268998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268998), _1269000), _1269002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268998), _1269000), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268998), _1269004), _1269002))))], (49363 ^ _774244) ^ [_1761802, _1761804, _1761806, _1761808] : [-(hAPP(c_List_Ofilter(_1761802, _1761804), c_List_Oremove1(_1761802, _1761806, _1761808)) = c_List_Oremove1(_1761802, _1761806, hAPP(c_List_Ofilter(_1761802, _1761804), _1761808)))], (31443 ^ _774244) ^ [_1339002, _1339004, _1339006, _1339008, _1339010] : [class_Complete__Lattice_Ocomplete__lattice(_1339002), hBOOL(hAPP(hAPP(c_member(_1339004), _1339006), _1339008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339002), hAPP(_1339010, _1339006)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339004, _1339002), _1339008), _1339010))))], (14642 ^ _774244) ^ [_1019373, _1019375, _1019377] : [-(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), _1019373), _1019375)), _1019377)), _1019375) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1019377), _1019375))], (15298 ^ _774244) ^ [_1031647, _1031649, _1031651] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1031647), _1031649)), _1031651) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1031647), _1031651)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1031649), _1031651)))], (8744 ^ _774244) ^ [_916959, _916961] : [class_Rings_Oring__1(_916959), -(hAPP(c_Int_Oring__1__class_Oof__int(_916959), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _916961)) = hAPP(c_Groups_Ouminus__class_Ouminus(_916959), hAPP(c_Int_Oring__1__class_Oof__int(_916959), _916961)))], (43607 ^ _774244) ^ [_1621130, _1621132, _1621134] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1621130, _1621132)), hAPP(c_Relation_Oconverse(_1621132, _1621130), _1621134))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1621132, _1621130)), _1621134)))], (37518 ^ _774244) ^ [_1472814, _1472816, _1472818, _1472820, _1472822, _1472824] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472814, tc_fun(_1472816, tc_HOL_Obool))), _1472818), _1472820), _1472822), _1472824)), -(hBOOL(hAPP(hAPP(_1472818, _1472822), _1472824)))]], input).
% 53.32/52.39 ncf('1',plain,[51529 : v_P(51538 ^ [], 51539 ^ []), 51533 : c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn)), 51539 ^ [], v_n, 51542 ^ []), 51533 : -(v_Q(51538 ^ [], 51542 ^ [])), 51548 : v_P(51557 ^ [], 51558 ^ []), 51552 : c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn), 51558 ^ [], hAPP(c_Nat_OSuc, v_n), 51561 ^ []), 51552 : -(v_Q(51557 ^ [], 51561 ^ []))],start(51527 ^ 0,bind([[_2049204, _2049206, _2049269, _2049455, _2049457, _2049520], [51539 ^ [], 51538 ^ [], 51542 ^ [], 51558 ^ [], 51557 ^ [], 51561 ^ []]]))).
% 53.32/52.39 ncf('1.1',plain,[-(v_P(51538 ^ [], 51539 ^ []))],extension(51541 ^ 3)).
% 53.32/52.39 ncf('1.2',plain,[-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn)), 51539 ^ [], v_n, 51542 ^ [])), c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn), 51539 ^ [], hAPP(c_Nat_OSuc, v_n), 51542 ^ [])],extension(5617 ^ 5,bind([[_863713, _863715, _863717, _863719], [v_pn, 51539 ^ [], v_n, 51542 ^ []]]))).
% 53.32/52.39 ncf('1.2.1',plain,[-(c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn), 51539 ^ [], hAPP(c_Nat_OSuc, v_n), 51542 ^ []))],extension(51544 ^ 6)).
% 53.32/52.39 ncf('1.3',plain,[v_Q(51538 ^ [], 51542 ^ [])],extension(51546 ^ 5)).
% 53.32/52.39 ncf('1.4',plain,[-(v_P(51557 ^ [], 51558 ^ []))],extension(51560 ^ 3)).
% 53.32/52.39 ncf('1.5',plain,[-(c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn), 51558 ^ [], hAPP(c_Nat_OSuc, v_n), 51561 ^ [])), c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn)), 51558 ^ [], v_n, 51561 ^ [])],extension(5611 ^ 5,bind([[_863581, _863583, _863585, _863587], [v_pn, 51558 ^ [], v_n, 51561 ^ []]]))).
% 53.32/52.39 ncf('1.5.1',plain,[-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn)), 51558 ^ [], v_n, 51561 ^ []))],extension(51563 ^ 6)).
% 53.32/52.39 ncf('1.6',plain,[v_Q(51557 ^ [], 51561 ^ [])],extension(51565 ^ 5)).
% 53.32/52.39 %-----------------------------------------------------
% 53.32/52.39 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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